Identifier
Mp00072:
Permutations
—binary search tree: left to right⟶
Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-1Cc0005;cc-rep-2
[1]=>[.,.]=>[1,0]=>[1]
[1,2]=>[.,[.,.]]=>[1,1,0,0]=>[2]
[2,1]=>[[.,.],.]=>[1,0,1,0]=>[1,1]
[1,2,3]=>[.,[.,[.,.]]]=>[1,1,1,0,0,0]=>[3]
[1,3,2]=>[.,[[.,.],.]]=>[1,1,0,1,0,0]=>[2,1]
[2,1,3]=>[[.,.],[.,.]]=>[1,0,1,1,0,0]=>[1,2]
[2,3,1]=>[[.,.],[.,.]]=>[1,0,1,1,0,0]=>[1,2]
[3,1,2]=>[[.,[.,.]],.]=>[1,1,0,0,1,0]=>[2,1]
[3,2,1]=>[[[.,.],.],.]=>[1,0,1,0,1,0]=>[1,1,1]
[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0]=>[4]
[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0]=>[3,1]
[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]=>[2,2]
[1,3,4,2]=>[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]=>[2,2]
[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0]=>[3,1]
[1,4,3,2]=>[.,[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0]=>[2,1,1]
[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>[1,3]
[2,1,4,3]=>[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>[1,2,1]
[2,3,1,4]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>[1,3]
[2,3,4,1]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>[1,3]
[2,4,1,3]=>[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>[1,2,1]
[2,4,3,1]=>[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>[1,2,1]
[3,1,2,4]=>[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>[2,2]
[3,1,4,2]=>[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>[2,2]
[3,2,1,4]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>[1,1,2]
[3,2,4,1]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>[1,1,2]
[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>[2,2]
[3,4,2,1]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>[1,1,2]
[4,1,2,3]=>[[.,[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0]=>[3,1]
[4,1,3,2]=>[[.,[[.,.],.]],.]=>[1,1,0,1,0,0,1,0]=>[2,1,1]
[4,2,1,3]=>[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]=>[1,2,1]
[4,2,3,1]=>[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]=>[1,2,1]
[4,3,1,2]=>[[[.,[.,.]],.],.]=>[1,1,0,0,1,0,1,0]=>[2,1,1]
[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1]
[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[5]
[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]
[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[3,2]
[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[3,2]
[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]
[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]
[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3]
[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]
[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3]
[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3]
[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]
[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]
[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2]
[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2]
[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]
[1,4,3,5,2]=>[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]
[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2]
[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]
[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]
[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]
[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]
[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]
[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]
[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]
[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]
[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]
[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]
[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]
[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[2,3,5,1,4]=>[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]
[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]
[2,4,1,3,5]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,4,1,5,3]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,4,5,1,3]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[2,5,1,3,4]=>[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]
[2,5,1,4,3]=>[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]
[2,5,3,1,4]=>[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]
[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]
[2,5,4,1,3]=>[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]
[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]
[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[3,1,4,5,2]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[3,1,5,2,4]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[3,1,5,4,2]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[3,2,5,1,4]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[3,2,5,4,1]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[3,4,1,5,2]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[3,5,1,2,4]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[3,5,2,1,4]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[3,5,2,4,1]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[3,5,4,1,2]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[3,5,4,2,1]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[4,1,2,5,3]=>[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]
[4,1,3,5,2]=>[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]
[4,1,5,2,3]=>[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[4,1,5,3,2]=>[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]
[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,2,1,5,3]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,2,5,3,1]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[4,3,1,5,2]=>[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]
[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]
[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]
[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]
[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]
[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]
[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]=>[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]
[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]
[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]
[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]
[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]
[5,2,4,1,3]=>[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]
[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]
[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]
[5,3,1,4,2]=>[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]
[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]
[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]
[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]
[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]
[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]
[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]
[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]
[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]
[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]
[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]
[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]
[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]
[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]
[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,2]
[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]
[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]
[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]
[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]
[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]
[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]
[1,2,4,6,3,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]
[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]
[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]
[1,2,5,3,6,4]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]
[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]
[1,2,5,4,6,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]
[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]
[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]
[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]
[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]
[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]
[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]
[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]
[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]
[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]
[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]
[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]
[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]
[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]
[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]
[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]
[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]
[1,3,4,6,2,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]
[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]
[1,3,5,2,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,5,2,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,5,4,2,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,5,4,6,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,5,6,2,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,5,6,4,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,3,6,2,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]
[1,3,6,2,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]
[1,3,6,4,2,5]=>[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]
[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]
[1,3,6,5,2,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]
[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]
[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,4,2,5,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,4,2,5,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,4,2,6,3,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,4,2,6,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,4,3,5,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,4,3,5,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,4,3,6,2,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,4,3,6,5,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,4,5,2,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,4,5,3,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,4,5,3,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,4,6,2,3,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,4,6,3,2,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,4,6,3,5,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,4,6,5,2,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,4,6,5,3,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]
[1,5,2,3,6,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]
[1,5,2,4,3,6]=>[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]
[1,5,2,4,6,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]
[1,5,2,6,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]
[1,5,2,6,4,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]
[1,5,3,2,4,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,3,2,6,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,3,4,6,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,3,6,4,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,4,2,3,6]=>[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]
[1,5,4,2,6,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]
[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]
[1,5,4,3,6,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]
[1,5,4,6,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]
[1,5,4,6,3,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]
[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]
[1,5,6,2,4,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]
[1,5,6,3,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,6,3,4,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]
[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]
[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]
[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]
[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]
[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]
[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]
[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]
[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]
[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]
[1,6,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]
[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]
[1,6,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]
[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]
[1,6,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]
[1,6,4,2,5,3]=>[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]
[1,6,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]
[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]
[1,6,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]
[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]
[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]
[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]
[1,6,5,3,2,4]=>[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]
[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]
[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]
[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]
[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,1,4,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,1,4,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,1,5,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,1,5,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,1,5,6,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,1,6,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,1,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[2,3,1,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[2,3,4,6,1,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[2,3,5,1,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,5,1,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,5,6,1,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[2,3,6,1,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[2,3,6,1,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[2,3,6,4,1,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[2,3,6,5,1,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[2,4,1,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,1,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,1,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,1,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,1,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,1,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,3,1,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,3,6,1,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,5,1,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,5,1,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,5,3,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,5,3,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,5,6,1,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[2,4,6,1,3,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,6,1,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,6,3,1,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,6,3,5,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,6,5,1,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,4,6,5,3,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[2,5,1,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,1,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,1,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,1,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,1,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,1,6,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,3,1,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,3,1,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,3,4,1,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,3,4,6,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,3,6,1,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,3,6,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,4,1,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,4,1,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,4,3,1,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,4,3,6,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,4,6,1,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,4,6,3,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,6,1,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,6,1,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,6,3,1,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,6,3,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[2,5,6,4,1,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,5,6,4,3,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[2,6,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[2,6,1,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[2,6,1,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,1,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,1,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[2,6,1,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[2,6,3,1,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[2,6,3,1,5,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[2,6,3,4,1,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[2,6,3,5,1,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[2,6,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[2,6,4,1,3,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,4,1,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,4,3,1,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,4,3,5,1]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,4,5,1,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[2,6,5,1,3,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[2,6,5,1,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[2,6,5,3,1,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[2,6,5,4,1,3]=>[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,1,2,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,1,2,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,2,5,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,1,4,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,1,4,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,1,4,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,1,4,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,1,4,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,1,4,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,1,5,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,5,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,5,4,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,5,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,5,6,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,1,6,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,1,6,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,1,6,4,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,1,6,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,1,6,5,2,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,1,6,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,1,5,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,2,4,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,2,4,6,1,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,2,5,1,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,5,1,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,5,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,5,6,1,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,5,6,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,2,6,1,4,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,2,6,1,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,2,6,4,1,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,2,6,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,2,6,5,1,4]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,2,6,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,4,1,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,4,1,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,4,1,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,4,1,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,4,2,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,4,2,6,1,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,4,2,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,4,5,1,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[3,4,6,1,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,4,6,1,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,4,6,2,1,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,4,6,2,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,4,6,5,1,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[3,4,6,5,2,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[3,5,1,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,1,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,1,4,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,1,6,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,2,1,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,2,1,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,2,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,2,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,2,6,1,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,2,6,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,4,1,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,4,1,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,4,2,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,4,2,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,4,6,1,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,4,6,2,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,6,1,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,6,1,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,6,2,1,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,6,2,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,5,6,4,1,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[3,5,6,4,2,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[3,6,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,6,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,6,1,4,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,6,1,5,2,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,6,2,1,4,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,6,2,1,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,6,2,4,1,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,6,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,6,2,5,1,4]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,6,2,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,6,4,1,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,6,4,1,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,6,4,2,1,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,6,4,2,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,6,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[3,6,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[3,6,5,1,2,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,6,5,1,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,6,5,2,1,4]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,6,5,2,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[3,6,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[3,6,5,4,2,1]=>[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,1,2,5,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,1,2,5,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,1,2,6,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,1,2,6,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,1,3,2,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,1,3,5,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,1,3,5,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,1,3,6,2,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,1,3,6,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,1,5,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,1,5,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,1,5,3,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,1,5,3,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,1,5,6,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,1,5,6,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,1,6,2,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,1,6,3,2,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,1,6,3,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,1,6,5,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,1,6,5,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,1,5,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,1,5,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,1,6,3,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,1,6,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,3,6,1,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,3,6,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,5,1,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,5,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,5,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,5,6,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,5,6,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,2,6,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,6,3,1,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,6,3,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,6,5,1,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,2,6,5,3,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,3,1,2,6,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,3,1,5,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,3,1,5,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,3,1,6,2,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,3,1,6,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,3,2,6,1,5]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,3,2,6,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,3,5,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,3,6,1,2,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,3,6,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,3,6,2,1,5]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,3,6,2,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,3,6,5,1,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,3,6,5,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,5,1,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,5,1,3,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,1,3,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,1,6,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,5,1,6,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,2,1,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,2,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,2,6,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,2,6,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,3,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[4,5,6,1,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[4,6,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,6,1,2,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,6,1,3,2,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,1,3,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,6,1,5,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,2,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,2,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,2,3,1,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,2,3,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,2,5,1,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,2,5,3,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,3,1,2,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,3,2,1,5]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,6,3,2,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,6,3,5,1,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,3,5,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[4,6,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,5,2,1,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[4,6,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[4,6,5,3,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[5,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[5,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[5,1,2,4,6,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[5,1,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[5,1,2,6,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[5,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,3,2,6,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,3,4,2,6]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,3,4,6,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,3,6,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,3,6,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,4,2,3,6]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[5,1,4,2,6,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[5,1,4,3,2,6]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[5,1,4,3,6,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[5,1,4,6,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[5,1,4,6,3,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[5,1,6,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[5,1,6,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[5,1,6,3,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,6,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,1,6,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[5,1,6,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,1,3,6,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,1,4,6,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,1,6,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,1,6,4,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,3,1,6,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,3,6,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,4,1,3,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,4,1,6,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,4,3,6,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,4,6,3,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,6,1,4,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,6,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,6,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,2,6,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,1,2,6,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,1,4,6,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,1,6,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,1,6,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,2,6,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,6,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,6,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,3,6,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,3,6,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[5,4,1,2,6,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[5,4,1,3,2,6]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,1,3,6,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[5,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,2,1,6,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,2,6,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,2,6,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[5,4,6,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[5,6,1,3,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[5,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[5,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[5,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,6,3,1,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]
[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]
[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]
[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]
[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]
[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]
[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]
[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]
[6,1,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]
[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]
[6,1,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]
[6,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]
[6,1,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]
[6,1,4,2,5,3]=>[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]
[6,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]
[6,1,4,3,5,2]=>[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]
[6,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]
[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]
[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]
[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]
[6,1,5,3,2,4]=>[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]
[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]
[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]
[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]
[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]
[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]
[6,2,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]
[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[6,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]
[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[6,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]
[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]
[6,2,4,1,3,5]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,4,1,5,3]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[6,2,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]
[6,2,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]
[6,2,5,3,1,4]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]
[6,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]
[6,2,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]
[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]
[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[6,3,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[6,3,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[6,3,1,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[6,3,1,5,2,4]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[6,3,1,5,4,2]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[6,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[6,3,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[6,3,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[6,3,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[6,3,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[6,3,5,2,1,4]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[6,3,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[6,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[6,4,1,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[6,4,1,3,2,5]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,1,3,5,2]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[6,4,1,5,3,2]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,2,1,5,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,2,5,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]
[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]
[6,5,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]
[6,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]
[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]
[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]
[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]
[6,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]
[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]
[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]
[6,5,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]
[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]
[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]
[6,5,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]
[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]
[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]
[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]
[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]
[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]
[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]
[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]
[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]
[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]
[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]
[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]
[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]
[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]
[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]
[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]
[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]
[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]
[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]
[1,2,3,5,7,4,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]
[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]
[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]
[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]
[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]
[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]
[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]
[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]
[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]
[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]
[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]
[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]
[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]
[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]
[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]
[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]
[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]
[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,2,4,5,3,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]
[1,2,4,5,3,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]
[1,2,4,5,6,3,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]
[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]
[1,2,4,5,7,3,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]
[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]
[1,2,4,6,3,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,6,3,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,6,5,3,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,6,5,7,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,6,7,3,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,6,7,5,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,2,4,7,3,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]
[1,2,4,7,3,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,2,4,7,5,3,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]
[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]
[1,2,4,7,6,3,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,2,4,7,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,2,5,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,2,5,3,4,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,2,5,3,6,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,2,5,3,6,7,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,2,5,3,7,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,2,5,3,7,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,2,5,4,7,3,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,2,5,6,4,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,2,5,6,4,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,2,5,6,7,4,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,2,5,7,4,3,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,2,5,7,4,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,2,5,7,6,3,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,2,5,7,6,4,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]
[1,2,6,3,4,7,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]
[1,2,6,3,5,4,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,3,5,7,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,3,7,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]
[1,2,6,3,7,5,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,4,3,7,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,4,7,5,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,5,3,4,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,5,3,7,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]
[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]
[1,2,6,5,7,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,5,7,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]
[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]
[1,2,6,7,3,5,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,7,4,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,7,4,5,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]
[1,2,6,7,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]
[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]
[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]
[1,2,7,3,5,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]
[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]
[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]
[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]
[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]
[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]
[1,2,7,4,5,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]
[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]
[1,2,7,4,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]
[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]
[1,2,7,5,3,4,6]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]
[1,2,7,5,3,6,4]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]
[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]
[1,2,7,5,4,6,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]
[1,2,7,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]
[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]
[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]
[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]
[1,2,7,6,4,3,5]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]
[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]
[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,2,5,7,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,2,6,4,7,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,2,6,7,5,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,2,7,6,4,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,3,4,2,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,2,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,2,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,3,4,2,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,3,4,5,2,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,3,4,5,2,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,3,4,5,6,2,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,3,4,5,7,2,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,3,4,6,2,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,6,2,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,6,5,2,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,6,5,7,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,6,7,2,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,6,7,5,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,3,4,7,2,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,3,4,7,2,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,3,4,7,5,2,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,3,4,7,6,2,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,3,4,7,6,5,2]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,3,5,2,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,2,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,2,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,2,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,2,7,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,2,7,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,4,2,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,4,2,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,4,6,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,4,6,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,4,7,2,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,4,7,6,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,6,2,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,6,2,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,6,4,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,6,4,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,6,7,2,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,6,7,4,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,3,5,7,2,4,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,7,2,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,7,4,2,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,7,4,6,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,7,6,2,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,5,7,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,3,6,2,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,2,4,7,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,2,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,2,5,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,2,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,2,7,5,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,4,2,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,4,2,7,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,4,5,2,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,4,5,7,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,4,7,2,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,4,7,5,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,5,2,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,5,2,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,5,4,2,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,5,4,7,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,5,7,2,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,5,7,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,7,2,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,7,2,5,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,7,4,2,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,7,4,5,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,3,6,7,5,2,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,6,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,3,7,2,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,3,7,2,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,2,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,2,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,2,6,4,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,2,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,3,7,4,2,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,3,7,4,2,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,4,5,2,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,3,7,4,6,2,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,4,6,5,2]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,5,2,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,5,2,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,5,4,2,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,5,4,6,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,5,6,2,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,5,6,4,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,3,7,6,2,4,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,6,2,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,3,7,6,4,2,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,6,4,5,2]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,3,7,6,5,2,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,3,7,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,2,3,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,3,6,7,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,3,7,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,2,3,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,2,5,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,2,5,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,2,5,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,2,5,6,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,2,5,7,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,2,5,7,6,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,2,6,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,6,3,7,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,6,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,6,5,7,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,6,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,6,7,5,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,2,7,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,2,7,3,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,2,7,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,2,7,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,2,7,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,2,7,6,5,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,3,5,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,3,5,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,3,5,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,3,5,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,3,5,7,2,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,3,5,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,3,6,2,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,6,2,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,6,5,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,6,5,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,6,7,2,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,6,7,5,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,3,7,2,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,3,7,2,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,3,7,5,2,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,3,7,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,3,7,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,3,7,6,5,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,5,2,7,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,5,2,7,6,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,5,3,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,5,3,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,5,3,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,5,3,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,5,3,7,2,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,5,3,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,5,6,2,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,5,6,2,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,5,6,3,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,5,6,3,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,5,6,7,2,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,4,5,6,7,3,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,4,5,7,2,3,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,5,7,2,6,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,5,7,3,2,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,5,7,3,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,5,7,6,2,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,4,5,7,6,3,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,2,3,7,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,2,5,7,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,2,7,5,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,3,2,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,3,2,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,3,5,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,3,5,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,3,7,2,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,3,7,5,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,5,2,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,5,2,7,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,5,3,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,5,3,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,5,7,2,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,5,7,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,7,2,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,7,2,5,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,7,3,2,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,7,3,5,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,6,7,5,2,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,4,6,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,7,2,3,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,7,2,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,7,2,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,7,2,6,5,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,7,3,2,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,7,3,2,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,7,3,5,2,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,7,3,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,7,3,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,7,3,6,5,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,7,5,2,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,7,5,2,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,7,5,3,2,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,7,5,3,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,7,5,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,4,7,5,6,3,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,4,7,6,2,3,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,7,6,2,5,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,7,6,3,2,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,7,6,3,5,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,4,7,6,5,2,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,4,7,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,5,2,3,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,2,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,2,3,6,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,2,3,6,7,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,2,3,7,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,2,3,7,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,2,4,3,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,2,4,3,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,2,4,6,3,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,2,4,6,7,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,2,4,7,3,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,2,4,7,6,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,2,6,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,2,6,4,3,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,2,6,4,7,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,2,6,7,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,2,6,7,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,2,7,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,2,7,3,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,2,7,4,3,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,2,7,4,6,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,2,7,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,2,7,6,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,3,2,4,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,2,4,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,2,6,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,2,6,7,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,2,7,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,2,7,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,4,7,2,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,6,2,7,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,6,4,2,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,6,4,7,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,6,7,2,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,6,7,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,3,7,2,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,7,4,2,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,7,4,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,7,6,2,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,3,7,6,4,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,4,2,3,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,4,2,3,7,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,4,2,6,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,4,2,6,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,4,2,7,3,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,4,2,7,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,4,3,7,2,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,4,6,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,4,6,2,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,4,6,3,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,4,6,3,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,4,6,7,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,4,6,7,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,4,7,2,3,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,4,7,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,4,7,3,2,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,4,7,3,6,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,4,7,6,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,4,7,6,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,6,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,6,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,6,2,4,3,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,2,4,7,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,2,7,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,6,2,7,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,3,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,3,2,7,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,3,4,2,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,3,4,7,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,3,7,2,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,3,7,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,4,3,2,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,6,4,3,7,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,6,4,7,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,4,7,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,5,6,7,2,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,7,3,2,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,7,3,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,5,6,7,4,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,5,6,7,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,5,7,2,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,7,2,3,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,7,2,4,3,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,2,4,6,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,2,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,7,2,6,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,3,2,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,3,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,3,4,2,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,3,4,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,3,6,2,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,3,6,4,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,4,2,3,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,4,3,2,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,7,4,3,6,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,7,4,6,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,4,6,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,5,7,6,2,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,5,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,6,3,2,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,6,3,4,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,5,7,6,4,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,5,7,6,4,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,6,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,6,2,3,4,7,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,6,2,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,3,5,7,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,3,7,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,6,2,3,7,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,4,3,7,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,4,5,3,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,4,5,7,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,4,7,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,4,7,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,5,3,7,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,5,4,3,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,2,5,4,7,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,2,5,7,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,5,7,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,2,7,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,6,2,7,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,7,4,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,7,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,2,7,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,2,7,5,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,3,2,4,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,2,4,7,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,2,5,4,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,2,5,7,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,2,7,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,2,7,5,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,4,2,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,4,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,4,7,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,5,2,4,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,5,2,7,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,5,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,5,4,7,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,5,7,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,5,7,4,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,7,2,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,7,2,5,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,7,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,7,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,3,7,5,4,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,4,2,3,5,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,2,3,7,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,2,5,3,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,2,5,7,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,2,7,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,2,7,5,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,3,2,7,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,3,5,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,3,5,7,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,3,7,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,3,7,5,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,5,2,3,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,5,2,7,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,5,3,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,5,3,7,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,5,7,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,5,7,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,7,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,7,2,5,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,7,3,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,7,3,5,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,4,7,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,4,7,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,5,2,3,4,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,6,5,2,3,7,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,6,5,2,4,3,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,2,4,7,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,2,7,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,6,5,2,7,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,3,2,4,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,3,2,7,4]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,3,4,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,3,4,7,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,3,7,2,4]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,3,7,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,4,2,3,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,4,2,7,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,6,5,4,7,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,4,7,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,6,5,7,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,6,5,7,2,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,7,3,2,4]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,7,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,5,7,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,5,7,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,6,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,6,7,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,7,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,7,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,7,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,6,7,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,7,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,7,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,7,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,7,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,6,7,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,7,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,7,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,7,4,2,5,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,7,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,7,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,6,7,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,6,7,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,6,7,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,7,5,3,2,4]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,7,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,6,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]
[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]
[1,7,2,3,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]
[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]
[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]
[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]
[1,7,2,4,3,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]
[1,7,2,4,3,6,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]
[1,7,2,4,5,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]
[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]
[1,7,2,4,6,3,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]
[1,7,2,4,6,5,3]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]
[1,7,2,5,3,4,6]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]
[1,7,2,5,3,6,4]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]
[1,7,2,5,4,3,6]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]
[1,7,2,5,4,6,3]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]
[1,7,2,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]
[1,7,2,5,6,4,3]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]
[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]
[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]
[1,7,2,6,4,3,5]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,2,6,4,5,3]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]
[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]
[1,7,3,2,4,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]
[1,7,3,2,4,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,2,5,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,2,5,6,4]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,2,6,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,2,6,5,4]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]
[1,7,3,4,2,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]
[1,7,3,4,2,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,4,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]
[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]
[1,7,3,4,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,5,2,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,5,2,6,4]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,5,4,2,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,5,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,7,3,6,2,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,6,2,5,4]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]
[1,7,3,6,4,2,5]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,7,3,6,5,2,4]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]
[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]
[1,7,4,2,3,5,6]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,7,4,2,3,6,5]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,4,2,5,3,6]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,7,4,2,5,6,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,7,4,2,6,3,5]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,4,2,6,5,3]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,7,4,3,2,6,5]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,7,4,3,5,2,6]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,7,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,7,4,3,6,2,5]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,7,4,3,6,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,7,4,5,2,3,6]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,7,4,5,2,6,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,7,4,5,3,2,6]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,7,4,5,3,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,7,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,7,4,5,6,3,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,7,4,6,2,3,5]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,4,6,2,5,3]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,4,6,3,2,5]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,7,4,6,3,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,7,4,6,5,2,3]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,7,4,6,5,3,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,7,5,2,3,4,6]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]
[1,7,5,2,3,6,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]
[1,7,5,2,4,3,6]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,2,4,6,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,2,6,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]
[1,7,5,2,6,4,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,3,2,4,6]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,3,2,6,4]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,3,4,2,6]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,3,4,6,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,3,6,2,4]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,3,6,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,4,2,3,6]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,4,2,6,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]
[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]
[1,7,5,4,6,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,4,6,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]
[1,7,5,6,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]
[1,7,5,6,2,4,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,6,3,2,4]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,7,5,6,4,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,7,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]
[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]
[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]
[1,7,6,2,4,3,5]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,7,6,2,4,5,3]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]
[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,7,6,3,2,4,5]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,7,6,3,2,5,4]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,7,6,3,4,2,5]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,7,6,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,7,6,3,5,2,4]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,7,6,3,5,4,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,7,6,4,2,3,5]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,7,6,4,2,5,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,7,6,4,3,5,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,7,6,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]
[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,7,6,5,3,2,4]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,7,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]
[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,1,3,5,7,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,1,3,6,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,1,3,6,7,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,1,3,7,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,1,4,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,1,4,5,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,1,4,5,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,1,4,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,6,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,1,4,7,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,1,4,7,3,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,1,4,7,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,1,4,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,1,4,7,6,3,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,1,4,7,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,1,5,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,1,5,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,1,5,3,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,1,5,3,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,1,5,3,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,1,5,3,7,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,1,5,4,7,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,1,5,6,4,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,1,5,6,4,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,1,5,6,7,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,1,5,6,7,4,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,1,5,7,4,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,1,5,7,4,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,1,5,7,6,3,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,1,5,7,6,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,1,6,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,1,6,3,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,1,6,3,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,3,5,7,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,1,6,3,7,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,4,3,7,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,4,7,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,5,3,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,5,3,7,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,1,6,5,7,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,5,7,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,1,6,7,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,1,6,7,3,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,7,4,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,7,4,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,1,6,7,5,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,1,7,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[2,1,7,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[2,1,7,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,1,7,3,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,1,7,3,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[2,1,7,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,1,7,4,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,1,7,4,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,1,7,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,1,7,5,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,1,7,5,3,6,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,1,7,5,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,1,7,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,1,7,5,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,1,7,5,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,1,7,6,3,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[2,1,7,6,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,1,7,6,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,1,7,6,4,5,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,1,7,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[2,3,1,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[2,3,1,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,1,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,1,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[2,3,1,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[2,3,1,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,1,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,1,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,1,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,1,5,7,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,1,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,1,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,1,6,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,1,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,1,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,1,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,1,6,7,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,1,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[2,3,1,7,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[2,3,1,7,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,1,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,1,7,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[2,3,1,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[2,3,4,1,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[2,3,4,1,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,1,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,1,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[2,3,4,1,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[2,3,4,5,1,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[2,3,4,5,7,1,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[2,3,4,6,1,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,6,1,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,6,5,1,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,6,5,7,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,6,7,1,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,6,7,5,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[2,3,4,7,1,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[2,3,4,7,1,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[2,3,4,7,5,1,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[2,3,4,7,6,1,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[2,3,5,1,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,1,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,1,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,1,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,1,7,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,1,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,4,1,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,4,1,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,4,6,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,4,6,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,4,7,1,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,4,7,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,6,1,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,6,1,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,6,4,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,6,4,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,6,7,1,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,6,7,4,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[2,3,5,7,1,4,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,7,1,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,7,4,1,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,7,4,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,7,6,1,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,5,7,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[2,3,6,1,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,1,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,1,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,1,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,1,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,1,7,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,4,1,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,4,1,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,4,5,1,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,4,5,7,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,4,7,1,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,4,7,5,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,5,1,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,5,1,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,5,4,1,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,5,4,7,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,5,7,1,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,5,7,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,7,1,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,7,1,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,7,4,1,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,7,4,5,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[2,3,6,7,5,1,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,6,7,5,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[2,3,7,1,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[2,3,7,1,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,1,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,1,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,1,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,1,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[2,3,7,4,1,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[2,3,7,4,1,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,4,5,1,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[2,3,7,4,6,1,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,4,6,5,1]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,5,1,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,5,1,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,5,4,1,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,5,4,6,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,5,6,1,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,5,6,4,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[2,3,7,6,1,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,6,1,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[2,3,7,6,4,1,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,6,4,5,1]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[2,3,7,6,5,1,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[2,3,7,6,5,4,1]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[2,4,1,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,1,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,1,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,1,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,1,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,1,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,1,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,1,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,1,5,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,1,5,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,1,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,6,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,1,7,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,1,7,3,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,1,7,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,1,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,1,7,6,3,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,1,7,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,3,1,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,3,1,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,1,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,1,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,3,1,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,3,5,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,3,5,7,1,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,3,5,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,3,6,1,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,6,1,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,6,7,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,6,7,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,3,7,1,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,3,7,1,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,3,7,5,1,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,3,7,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,3,7,6,1,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,3,7,6,5,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,5,1,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,1,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,1,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,1,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,1,7,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,1,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,3,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,3,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,3,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,3,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,3,7,1,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,3,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,6,1,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,6,1,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,6,3,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,6,3,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,6,7,1,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,6,7,3,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[2,4,5,7,1,3,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,7,1,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,7,3,1,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,7,3,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,7,6,1,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,5,7,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[2,4,6,1,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,1,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,1,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,1,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,1,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,1,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,3,1,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,3,1,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,3,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,3,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,3,7,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,3,7,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,5,1,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,5,1,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,5,3,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,5,3,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,5,7,1,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,5,7,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,7,1,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,7,1,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,7,3,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,7,3,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,7,5,1,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,6,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[2,4,7,1,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,1,3,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,1,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,1,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,1,6,3,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,1,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,3,1,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,3,1,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,3,5,1,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,3,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,3,6,1,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,3,6,5,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,5,1,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,5,1,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,5,3,1,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,5,3,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,5,6,1,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,5,6,3,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[2,4,7,6,1,3,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,6,1,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,6,3,1,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,6,3,5,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,6,5,1,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,4,7,6,5,3,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[2,5,1,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,1,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,1,3,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,1,3,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,1,3,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,1,3,7,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,1,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,1,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,1,4,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,1,4,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,1,4,7,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,1,4,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,1,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,1,6,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,1,6,4,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,1,6,4,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,1,6,7,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,1,6,7,4,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,1,7,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,1,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,1,7,4,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,1,7,4,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,1,7,6,3,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,1,7,6,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,3,1,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,1,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,1,6,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,1,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,1,7,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,1,7,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,4,1,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,4,1,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,4,6,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,4,6,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,4,7,1,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,4,7,6,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,6,1,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,6,1,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,6,4,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,6,4,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,6,7,1,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,6,7,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,3,7,1,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,7,1,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,7,4,1,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,7,4,6,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,7,6,1,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,3,7,6,4,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,4,1,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,1,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,1,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,1,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,1,7,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,1,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,3,1,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,3,1,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,3,6,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,3,6,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,3,7,1,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,3,7,6,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,6,1,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,6,1,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,6,3,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,6,3,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,6,7,1,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,6,7,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,4,7,1,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,7,1,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,7,3,1,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,7,3,6,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,7,6,1,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,4,7,6,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,6,1,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,1,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,1,4,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,1,4,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,1,7,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,1,7,4,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,3,1,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,3,1,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,3,4,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,3,4,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,3,7,1,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,3,7,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,4,1,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,4,1,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,4,3,1,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,4,3,7,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,4,7,1,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,4,7,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,7,1,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,7,1,4,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,7,3,1,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,7,3,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[2,5,6,7,4,1,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,6,7,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[2,5,7,1,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,1,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,1,4,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,1,4,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,1,6,3,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,1,6,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,3,1,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,3,1,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,3,4,1,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,3,4,6,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,3,6,1,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,3,6,4,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,4,1,3,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,4,1,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,4,3,1,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,4,3,6,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,4,6,1,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,4,6,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,6,1,3,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,6,1,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,6,3,1,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,6,3,4,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[2,5,7,6,4,1,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,5,7,6,4,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[2,6,1,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,1,3,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,1,3,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,3,5,7,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,1,3,7,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,4,3,7,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,4,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,4,7,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,5,3,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,5,3,7,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,1,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,1,5,7,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,5,7,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,1,7,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,1,7,3,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,7,4,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,7,4,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,1,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,1,7,5,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,3,1,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,1,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,1,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,1,5,7,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,1,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,1,7,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,4,1,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,4,1,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,4,5,1,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,4,5,7,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,4,7,1,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,4,7,5,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,5,1,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,5,1,7,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,5,4,1,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,5,4,7,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,5,7,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,5,7,4,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,7,1,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,7,1,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,7,4,1,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,7,4,5,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,3,7,5,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,3,7,5,4,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,4,1,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,1,3,7,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,1,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,1,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,1,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,1,7,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,3,1,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,3,1,7,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,3,5,1,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,3,5,7,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,3,7,1,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,3,7,5,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,5,1,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,5,1,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,5,3,1,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,5,3,7,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,5,7,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,5,7,3,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,7,1,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,7,1,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,7,3,1,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,7,3,5,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,7,5,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,4,7,5,3,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,5,1,3,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,1,3,7,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,1,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,1,4,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,1,7,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,1,7,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,3,1,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,3,1,7,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,3,4,1,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,3,4,7,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,3,7,1,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,3,7,4,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,4,1,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,4,1,7,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,4,3,1,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,4,3,7,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,4,7,1,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,4,7,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,7,1,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,7,1,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,7,3,1,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,7,3,4,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,5,7,4,1,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,5,7,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,7,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,7,1,3,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,1,4,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,1,4,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,1,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,1,5,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,7,3,1,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,7,3,1,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,3,4,1,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,7,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[2,6,7,3,5,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,4,1,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,4,1,5,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,4,3,1,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,4,3,5,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,4,5,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[2,6,7,5,1,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,5,1,4,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,7,5,3,1,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[2,6,7,5,4,1,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,6,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[2,7,1,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[2,7,1,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[2,7,1,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,1,3,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,1,3,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[2,7,1,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[2,7,1,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,1,4,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,1,4,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,1,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,1,4,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,1,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,1,5,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,1,5,3,6,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,1,5,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,1,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,1,5,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,1,5,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,1,6,3,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[2,7,1,6,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,1,6,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,1,6,4,5,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,1,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,1,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[2,7,3,1,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[2,7,3,1,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,1,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,1,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,1,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,1,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[2,7,3,4,1,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[2,7,3,4,1,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,4,5,1,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[2,7,3,4,6,1,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,4,6,5,1]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,5,1,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,5,1,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,5,4,1,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,5,4,6,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,5,6,1,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,5,6,4,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[2,7,3,6,1,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,6,1,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[2,7,3,6,4,1,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,6,4,5,1]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[2,7,3,6,5,1,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[2,7,3,6,5,4,1]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[2,7,4,1,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,1,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,1,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,1,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,1,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,1,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,3,1,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,3,1,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,3,5,1,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,3,5,6,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,3,6,1,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,3,6,5,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,5,1,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,5,1,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,5,3,1,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,5,3,6,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,5,6,1,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,5,6,3,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[2,7,4,6,1,3,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,6,1,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,6,3,1,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,6,3,5,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,6,5,1,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,4,6,5,3,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[2,7,5,1,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,1,3,6,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,1,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,1,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,1,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,1,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,3,1,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,3,1,6,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,3,4,1,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,3,4,6,1]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,3,6,1,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,3,6,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,4,1,3,6]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,4,1,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,4,3,1,6]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,4,3,6,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,4,6,1,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,4,6,3,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,6,1,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,6,1,4,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,6,3,1,4]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,6,3,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[2,7,5,6,4,1,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,5,6,4,3,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[2,7,6,1,3,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[2,7,6,1,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,1,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,1,4,5,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,1,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,1,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[2,7,6,3,1,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[2,7,6,3,1,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,3,4,1,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[2,7,6,3,4,5,1]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[2,7,6,3,5,1,4]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,3,5,4,1]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,4,1,3,5]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,4,1,5,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,4,3,1,5]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,4,3,5,1]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,4,5,1,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,4,5,3,1]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[2,7,6,5,1,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,5,1,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[2,7,6,5,3,1,4]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,5,3,4,1]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[2,7,6,5,4,1,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,1,2,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,1,2,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,2,4,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,2,4,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,1,2,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,1,2,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,2,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,2,5,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,2,5,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,2,5,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,2,5,7,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,2,6,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,2,6,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,2,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,2,6,5,7,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,2,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,2,6,7,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,2,7,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,1,2,7,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,1,2,7,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,2,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,2,7,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,1,2,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,1,4,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,1,4,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,1,4,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,2,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,1,4,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,1,4,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,1,4,5,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,1,4,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,1,4,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,1,4,5,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,1,4,5,7,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,1,4,6,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,6,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,6,5,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,6,5,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,6,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,6,7,5,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,1,4,7,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,1,4,7,2,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,1,4,7,5,2,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,1,4,7,5,6,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,1,4,7,6,2,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,1,4,7,6,5,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,1,5,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,2,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,2,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,2,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,2,7,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,4,6,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,4,6,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,4,7,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,4,7,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,6,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,6,4,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,6,4,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,6,7,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,6,7,4,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,1,5,7,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,7,4,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,7,4,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,7,6,2,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,5,7,6,4,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,1,6,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,2,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,2,5,7,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,2,7,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,4,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,4,2,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,4,5,7,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,4,7,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,5,2,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,5,4,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,5,4,7,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,5,7,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,5,7,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,7,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,7,2,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,7,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,7,4,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,1,6,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,6,7,5,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,1,7,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,1,7,2,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,1,7,2,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,2,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,2,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,1,7,2,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,1,7,4,2,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,1,7,4,2,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,1,7,4,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,1,7,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,1,7,4,6,2,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,1,7,4,6,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,1,7,5,2,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,5,2,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,5,4,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,5,4,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,5,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,5,6,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,1,7,6,2,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,1,7,6,2,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,1,7,6,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,1,7,6,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,1,7,6,5,2,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,1,7,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,1,5,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,1,6,4,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,1,6,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,1,7,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,2,4,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,2,4,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,1,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,2,4,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,2,4,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,2,4,5,7,1,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,2,4,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,2,4,6,1,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,6,1,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,6,7,1,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,6,7,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,2,4,7,1,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,2,4,7,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,2,4,7,5,1,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,2,4,7,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,2,4,7,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,2,4,7,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,2,5,1,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,1,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,1,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,1,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,1,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,1,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,4,7,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,6,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,6,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,6,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,6,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,6,7,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,6,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,2,5,7,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,7,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,7,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,7,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,7,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,5,7,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,2,6,1,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,1,4,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,1,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,1,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,4,1,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,4,1,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,4,5,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,4,7,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,4,7,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,7,1,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,7,4,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,7,4,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,2,6,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,6,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,2,7,1,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,2,7,1,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,1,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,1,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,1,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,1,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,2,7,4,1,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,2,7,4,1,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,4,5,1,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,2,7,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,2,7,4,6,1,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,4,6,5,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,5,1,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,5,1,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,5,4,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,5,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,5,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,5,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,2,7,6,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,6,1,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,2,7,6,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,6,4,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,2,7,6,5,1,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,2,7,6,5,4,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,1,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,1,5,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,1,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,1,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,1,5,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,1,5,7,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,1,6,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,6,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,6,5,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,6,5,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,6,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,6,7,5,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,1,7,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,1,7,2,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,1,7,5,2,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,1,7,5,6,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,1,7,6,2,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,1,7,6,5,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,2,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,2,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,1,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,2,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,2,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,2,5,7,1,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,2,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,2,6,1,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,6,1,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,6,7,1,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,6,7,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,2,7,1,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,2,7,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,2,7,5,1,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,2,7,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,2,7,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,2,7,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,5,1,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,5,1,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,5,1,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,5,1,7,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,5,1,7,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,5,2,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,5,2,7,1,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,5,2,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,5,6,1,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,5,6,1,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[3,4,5,7,1,2,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,5,7,1,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,5,7,2,1,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,5,7,2,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,5,7,6,1,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[3,4,5,7,6,2,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[3,4,6,1,2,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,1,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,1,5,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,1,5,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,1,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,1,7,5,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,2,1,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,2,1,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,2,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,2,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,2,7,1,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,2,7,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,5,1,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,5,1,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,5,2,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,5,2,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,5,7,1,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,5,7,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,7,1,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,7,1,5,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,7,2,1,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,7,2,5,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,6,7,5,1,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[3,4,6,7,5,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[3,4,7,1,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,7,1,2,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,7,1,5,2,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,7,1,5,6,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,7,1,6,2,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,7,1,6,5,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,7,2,1,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,7,2,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,7,2,5,1,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,7,2,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,7,2,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,7,2,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,7,5,1,2,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,7,5,1,6,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,7,5,2,1,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,7,5,2,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,7,5,6,1,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[3,4,7,5,6,2,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[3,4,7,6,1,2,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,7,6,1,5,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,7,6,2,1,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,7,6,2,5,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,4,7,6,5,1,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[3,4,7,6,5,2,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[3,5,1,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,2,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,2,6,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,2,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,2,7,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,4,6,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,4,6,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,4,7,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,4,7,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,6,4,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,6,4,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,6,7,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,6,7,4,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,7,4,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,7,4,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,7,6,2,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,1,7,6,4,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,2,1,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,1,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,1,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,1,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,1,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,1,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,4,7,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,6,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,6,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,6,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,6,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,6,7,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,6,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,2,7,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,7,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,7,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,7,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,7,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,2,7,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,4,1,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,4,1,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,4,1,6,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,4,1,6,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,4,1,7,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,4,1,7,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,4,2,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,4,2,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,4,2,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,4,2,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,4,2,7,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,4,2,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,4,6,1,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,4,6,1,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,4,6,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,4,6,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,4,6,7,1,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,4,6,7,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,4,7,1,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,4,7,1,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,4,7,2,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,4,7,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,4,7,6,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,4,7,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,6,1,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,1,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,1,4,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,1,4,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,1,7,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,1,7,4,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,2,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,2,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,2,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,2,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,2,7,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,2,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,4,1,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,4,1,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,4,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,4,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,4,7,1,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,4,7,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,7,1,2,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,7,1,4,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,7,2,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,7,2,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,6,7,4,1,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[3,5,6,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[3,5,7,1,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,1,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,1,4,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,1,4,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,1,6,2,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,1,6,4,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,2,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,2,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,2,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,2,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,2,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,2,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,4,1,2,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,4,1,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,4,2,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,4,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,4,6,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,4,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,6,1,2,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,6,1,4,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,6,2,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,6,2,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,5,7,6,4,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[3,5,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[3,6,1,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,2,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,2,5,7,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,2,7,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,4,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,4,2,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,4,5,7,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,4,7,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,5,2,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,5,4,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,5,4,7,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,5,7,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,5,7,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,7,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,7,2,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,7,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,7,4,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,1,7,5,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,2,1,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,1,4,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,1,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,1,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,4,1,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,4,1,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,4,5,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,4,7,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,4,7,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,7,1,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,7,4,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,7,4,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,2,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,2,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,4,1,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,1,2,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,1,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,1,5,7,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,1,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,1,7,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,2,1,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,2,1,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,2,5,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,2,5,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,2,7,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,2,7,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,5,1,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,5,1,7,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,5,2,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,5,2,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,5,7,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,5,7,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,7,1,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,7,1,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,7,2,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,7,2,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,4,7,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,4,7,5,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,5,1,2,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,1,2,7,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,1,4,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,1,4,7,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,1,7,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,1,7,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,2,1,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,2,1,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,2,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,2,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,2,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,2,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,4,1,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,4,1,7,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,4,2,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,4,2,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,4,7,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,4,7,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,7,1,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,7,1,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,7,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,7,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,5,7,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,5,7,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,7,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,7,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,7,1,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,7,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,7,1,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,7,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,7,2,1,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,7,2,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,7,2,4,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,7,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,7,2,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,7,2,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,7,4,1,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,7,4,1,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,7,4,2,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,7,4,2,5,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,7,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[3,6,7,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[3,6,7,5,1,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,7,5,1,4,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,7,5,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,7,5,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,6,7,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[3,6,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[3,7,1,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,1,2,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,1,2,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,2,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,2,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,1,2,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,1,4,2,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,1,4,2,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,1,4,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,1,4,6,2,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,1,4,6,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,1,5,2,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,5,2,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,5,4,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,5,4,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,5,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,5,6,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,1,6,2,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,1,6,2,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,1,6,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,1,6,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,1,6,5,2,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,2,1,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,2,1,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,1,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,1,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,1,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,1,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,2,4,1,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,2,4,1,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,4,5,1,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,2,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,2,4,6,1,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,4,6,5,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,5,1,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,5,1,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,5,4,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,5,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,5,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,5,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,2,6,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,6,1,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,2,6,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,6,4,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,2,6,5,1,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,2,6,5,4,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,4,1,2,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,4,1,2,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,4,1,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,4,1,6,2,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,4,1,6,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,4,2,1,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,4,2,1,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,4,2,5,1,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,4,2,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,4,2,6,1,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,4,2,6,5,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,4,5,1,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,4,5,1,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,4,5,2,1,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,4,5,2,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,4,5,6,1,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[3,7,4,5,6,2,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[3,7,4,6,1,2,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,4,6,1,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,4,6,2,1,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,4,6,2,5,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,4,6,5,1,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[3,7,4,6,5,2,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[3,7,5,1,2,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,1,2,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,1,4,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,1,4,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,1,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,1,6,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,2,1,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,2,1,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,2,4,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,2,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,2,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,2,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,4,1,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,4,1,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,4,2,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,4,2,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,4,6,1,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,4,6,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,6,1,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,6,1,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,6,2,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,6,2,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,5,6,4,1,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[3,7,5,6,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[3,7,6,1,2,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,6,1,2,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,6,1,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,6,1,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,6,1,5,2,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,6,1,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,6,2,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,6,2,1,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,6,2,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,6,2,4,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,6,2,5,1,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,6,2,5,4,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,6,4,1,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,6,4,1,5,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,6,4,2,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,6,4,2,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,6,4,5,1,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[3,7,6,4,5,2,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[3,7,6,5,1,2,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,6,5,1,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,6,5,2,1,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,6,5,2,4,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[3,7,6,5,4,1,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[3,7,6,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,2,3,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,2,3,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,3,6,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,3,7,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,2,3,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,2,5,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,2,5,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,2,5,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,2,5,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,2,5,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,2,5,7,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,2,6,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,6,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,6,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,6,5,7,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,6,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,6,7,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,2,7,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,2,7,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,2,7,5,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,2,7,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,2,7,6,3,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,2,7,6,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,3,2,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,3,2,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,3,2,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,2,6,7,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,2,7,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,3,2,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,3,5,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,3,5,2,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,3,5,6,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,3,5,6,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,3,5,7,2,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,3,5,7,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,3,6,2,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,6,2,7,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,6,5,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,6,5,7,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,6,7,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,6,7,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,3,7,2,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,3,7,2,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,3,7,5,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,3,7,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,3,7,6,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,3,7,6,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,5,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,5,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,5,2,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,5,2,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,5,2,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,5,2,7,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,5,3,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,5,3,2,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,5,3,6,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,5,3,6,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,5,3,7,2,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,5,3,7,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,5,6,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,5,6,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,5,6,3,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,5,6,3,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,5,6,7,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,1,5,6,7,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,1,5,7,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,5,7,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,5,7,3,2,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,5,7,3,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,5,7,6,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,1,5,7,6,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,1,6,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,2,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,2,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,2,5,7,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,2,7,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,3,2,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,3,2,7,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,3,5,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,3,5,7,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,3,7,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,3,7,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,5,2,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,5,2,7,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,5,3,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,5,3,7,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,5,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,5,7,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,7,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,7,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,7,3,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,7,3,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,6,7,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,1,6,7,5,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,1,7,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,7,2,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,7,2,5,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,7,2,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,7,2,6,3,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,7,2,6,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,7,3,2,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,7,3,2,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,7,3,5,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,7,3,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,7,3,6,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,7,3,6,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,7,5,2,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,7,5,2,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,7,5,3,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,7,5,3,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,7,5,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,1,7,5,6,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,1,7,6,2,3,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,7,6,2,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,7,6,3,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,7,6,3,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,1,7,6,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,1,7,6,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,1,3,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,3,6,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,3,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,1,3,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,1,5,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,1,5,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,1,5,6,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,1,5,6,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,1,5,7,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,1,5,7,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,1,6,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,6,3,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,6,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,6,5,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,6,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,6,7,5,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,1,7,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,1,7,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,1,7,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,1,7,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,1,7,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,1,7,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,1,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,3,5,1,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,3,5,7,1,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,3,5,7,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,3,6,1,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,6,1,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,6,5,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,6,5,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,6,7,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,6,7,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,3,7,1,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,3,7,1,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,3,7,5,1,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,3,7,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,3,7,6,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,3,7,6,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,1,6,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,1,6,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,1,7,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,1,7,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,3,1,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,3,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,3,7,1,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,3,7,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,6,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,6,1,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,6,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,6,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,6,7,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,6,7,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,2,5,7,1,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,7,1,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,7,3,1,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,7,3,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,7,6,1,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,5,7,6,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,1,3,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,1,5,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,1,7,5,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,3,1,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,3,1,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,3,5,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,3,5,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,3,7,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,3,7,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,5,1,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,5,1,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,5,3,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,5,3,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,5,7,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,5,7,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,7,1,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,7,1,5,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,7,3,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,7,3,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,7,5,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,6,7,5,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,1,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,3,1,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,3,1,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,3,5,1,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,3,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,3,6,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,3,6,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,5,1,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,5,1,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,5,3,1,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,5,3,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,5,6,1,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,5,6,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,2,7,6,1,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,6,1,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,6,3,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,6,3,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,6,5,1,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,2,7,6,5,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,1,2,5,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,1,2,6,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,2,6,7,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,2,7,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,1,2,7,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,1,5,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,1,5,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,1,5,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,1,5,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,1,5,7,2,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,1,5,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,1,6,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,6,2,7,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,6,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,6,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,6,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,6,7,5,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,1,7,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,1,7,2,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,1,7,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,1,7,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,1,7,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,1,7,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,2,5,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,2,5,7,1,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,2,5,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,2,6,1,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,6,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,6,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,6,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,6,7,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,6,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,2,7,1,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,2,7,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,2,7,5,1,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,2,7,5,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,2,7,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,2,7,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,5,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,5,1,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,5,1,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,5,1,7,2,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,5,1,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,5,2,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,5,2,7,1,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,5,2,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,5,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,5,6,1,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,5,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,3,5,7,1,2,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,5,7,1,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,5,7,2,1,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,5,7,2,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,5,7,6,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,3,5,7,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,3,6,1,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,1,2,7,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,1,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,1,7,5,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,2,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,2,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,2,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,5,1,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,5,1,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,5,7,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,7,1,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,7,1,5,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,7,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,6,7,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,3,6,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,3,7,1,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,7,1,2,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,7,1,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,7,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,7,1,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,7,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,7,2,1,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,7,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,7,2,5,1,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,7,2,5,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,7,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,7,2,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,7,5,1,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,7,5,1,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,7,5,2,1,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,7,5,2,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,7,5,6,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,3,7,5,6,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,3,7,6,1,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,7,6,1,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,7,6,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,7,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,3,7,6,5,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,3,7,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,1,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,1,2,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,1,2,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,1,2,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,1,2,7,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,1,3,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,1,3,2,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,1,3,6,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,1,3,6,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,1,3,7,2,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,1,3,7,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,1,6,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,1,6,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,1,6,3,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,1,6,3,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,1,6,7,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,1,6,7,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,1,7,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,1,7,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,1,7,3,2,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,1,7,3,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,1,7,6,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,1,7,6,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,1,6,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,1,6,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,1,7,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,1,7,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,3,1,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,3,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,3,7,1,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,3,7,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,6,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,6,1,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,6,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,6,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,6,7,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,6,7,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,2,7,1,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,7,1,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,7,3,1,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,7,3,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,7,6,1,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,2,7,6,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,3,1,7,2,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,3,1,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,3,2,1,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,3,2,7,1,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,3,2,7,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,3,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,3,6,1,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,3,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,3,7,1,2,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,3,7,1,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,3,7,2,1,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,3,7,2,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,3,7,6,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,3,7,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,6,1,3,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,1,3,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,1,7,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,6,1,7,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,2,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,2,1,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,2,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,2,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,2,7,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,2,7,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,3,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,3,1,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,6,3,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[4,5,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,7,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,7,1,3,2,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,1,3,6,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,1,6,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,7,1,6,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,2,1,3,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,2,1,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,2,3,1,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,2,3,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,2,6,1,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,2,6,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,3,1,2,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,3,1,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,3,2,1,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,7,3,2,6,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,7,3,6,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,3,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,5,7,6,1,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[4,5,7,6,1,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,6,2,1,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,6,2,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[4,5,7,6,3,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[4,5,7,6,3,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[4,6,1,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,2,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,2,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,2,5,7,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,2,7,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,3,2,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,3,2,7,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,3,5,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,3,5,7,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,3,7,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,3,7,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,5,2,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,5,2,7,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,5,3,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,5,3,7,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,5,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,5,7,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,7,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,7,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,7,3,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,7,3,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,1,7,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,1,7,5,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,2,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,1,3,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,1,5,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,1,7,5,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,3,1,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,3,1,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,3,5,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,3,5,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,3,7,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,3,7,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,5,1,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,5,1,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,5,3,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,5,3,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,5,7,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,5,7,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,7,1,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,7,1,5,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,7,3,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,7,3,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,7,5,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,2,7,5,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,3,1,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,1,2,7,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,1,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,1,7,5,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,2,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,2,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,2,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,5,1,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,5,1,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,5,7,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,7,1,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,7,1,5,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,7,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,3,7,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,3,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,5,1,2,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,5,1,2,7,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,5,1,3,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,1,3,7,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,1,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,5,1,7,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,2,1,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,2,1,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,2,3,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,2,3,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,2,7,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,2,7,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,3,1,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,3,1,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,3,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,5,3,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,5,3,7,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,3,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,5,7,1,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,5,7,1,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,7,2,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,7,2,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,5,7,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,5,7,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,7,1,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,7,1,3,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,1,3,5,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,7,1,5,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,2,1,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,2,1,5,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,2,3,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,2,3,5,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,2,5,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,2,5,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,3,1,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,3,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,7,3,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,7,3,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,3,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,6,7,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[4,6,7,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,5,2,1,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[4,6,7,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[4,6,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[4,7,1,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,1,2,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,1,2,5,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,1,2,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,1,2,6,3,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,1,2,6,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,1,3,2,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,1,3,2,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,1,3,5,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,1,3,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,1,3,6,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,1,3,6,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,1,5,2,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,1,5,2,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,1,5,3,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,1,5,3,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,1,5,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,1,5,6,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,1,6,2,3,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,1,6,2,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,1,6,3,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,1,6,3,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,1,6,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,2,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,1,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,3,1,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,3,1,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,3,5,1,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,3,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,3,6,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,3,6,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,5,1,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,5,1,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,5,3,1,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,5,3,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,5,6,1,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,5,6,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,2,6,1,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,6,1,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,6,3,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,6,3,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,6,5,1,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,2,6,5,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,3,1,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,3,1,2,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,3,1,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,3,1,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,3,2,1,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,3,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,3,2,5,1,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,3,2,5,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,3,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,3,2,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,3,5,1,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,3,5,1,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,3,5,2,1,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,3,5,2,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,3,5,6,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,3,5,6,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,3,6,1,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,3,6,1,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,3,6,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,3,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,3,6,5,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,3,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,5,1,2,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,5,1,2,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,5,1,3,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,1,3,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,1,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,5,1,6,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,2,1,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,2,1,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,2,3,1,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,2,3,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,2,6,1,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,2,6,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,3,1,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,3,1,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,3,2,1,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,5,3,2,6,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,5,3,6,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,3,6,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,5,6,1,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[4,7,5,6,1,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,6,2,1,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,6,2,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[4,7,5,6,3,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[4,7,5,6,3,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[4,7,6,1,2,3,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,6,1,2,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,6,1,3,2,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,1,3,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,1,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,2,1,3,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,2,1,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,2,3,1,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,2,3,5,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,2,5,1,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,2,5,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,3,1,2,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,3,1,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,3,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,6,3,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,6,3,5,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,3,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[4,7,6,5,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[4,7,6,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,5,2,1,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,5,2,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[4,7,6,5,3,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[4,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,2,3,4,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,2,3,6,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,2,3,6,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,2,3,7,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,2,3,7,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,2,4,3,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,2,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,2,4,6,3,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,2,4,6,7,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,2,4,7,3,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,2,4,7,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,2,6,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,2,6,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,2,6,4,3,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,2,6,4,7,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,2,6,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,2,6,7,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,2,7,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,2,7,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,2,7,4,3,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,2,7,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,2,7,6,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,2,7,6,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,3,2,4,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,2,6,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,2,6,7,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,2,7,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,2,7,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,4,2,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,4,2,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,4,6,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,4,6,7,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,4,7,2,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,4,7,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,6,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,6,2,7,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,6,4,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,6,4,7,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,6,7,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,6,7,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,3,7,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,7,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,7,4,2,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,7,4,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,7,6,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,3,7,6,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,4,2,3,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,4,2,3,7,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,4,2,6,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,4,2,6,7,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,4,2,7,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,4,2,7,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,4,3,2,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,4,3,2,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,4,3,6,2,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,4,3,6,7,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,4,3,7,2,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,4,3,7,6,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,4,6,2,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,4,6,2,7,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,4,6,3,2,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,4,6,3,7,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,4,6,7,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,4,6,7,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,4,7,2,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,4,7,2,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,4,7,3,2,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,4,7,3,6,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,4,7,6,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,4,7,6,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,6,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,6,2,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,6,2,4,3,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,2,4,7,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,2,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,6,2,7,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,3,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,3,2,7,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,3,4,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,3,4,7,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,3,7,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,3,7,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,4,2,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,4,2,7,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,4,3,2,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,6,4,3,7,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,6,4,7,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,4,7,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,6,7,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,1,6,7,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,7,3,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,7,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,1,6,7,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,1,6,7,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,1,7,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,7,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,7,2,4,3,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,2,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,7,2,6,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,3,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,3,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,3,4,2,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,3,4,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,3,6,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,3,6,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,4,2,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,4,2,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,4,3,2,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,7,4,3,6,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,7,4,6,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,4,6,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,1,7,6,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,1,7,6,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,6,3,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,6,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,1,7,6,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,1,7,6,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,1,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,1,3,6,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,1,3,6,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,1,3,7,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,1,3,7,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,1,4,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,1,4,6,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,1,4,6,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,1,4,7,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,1,4,7,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,1,6,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,1,6,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,1,6,4,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,1,6,4,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,1,6,7,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,1,6,7,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,1,7,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,1,7,3,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,1,7,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,1,7,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,1,7,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,1,7,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,1,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,1,6,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,1,6,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,1,7,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,1,7,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,4,7,1,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,6,1,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,6,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,6,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,6,7,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,6,7,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,3,7,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,7,4,1,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,7,4,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,7,6,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,3,7,6,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,4,1,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,1,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,1,6,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,1,7,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,1,7,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,3,6,1,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,3,6,7,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,3,7,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,3,7,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,6,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,6,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,6,3,1,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,6,3,7,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,6,7,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,6,7,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,4,7,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,7,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,7,3,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,7,3,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,7,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,4,7,6,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,6,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,1,4,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,1,4,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,1,7,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,1,7,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,3,1,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,3,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,3,7,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,3,7,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,4,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,4,3,1,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,4,3,7,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,4,7,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,4,7,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,7,1,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,7,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,7,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,2,6,7,4,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,6,7,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,2,7,1,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,1,3,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,1,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,1,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,3,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,3,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,3,4,1,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,3,4,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,3,6,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,3,6,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,4,3,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,4,3,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,4,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,4,6,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,6,1,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,6,3,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,6,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,2,7,6,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,2,7,6,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,2,4,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,2,6,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,2,6,7,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,2,7,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,2,7,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,4,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,4,2,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,4,6,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,4,6,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,4,7,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,4,7,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,6,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,6,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,6,4,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,6,4,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,6,7,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,6,7,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,1,7,2,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,7,2,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,7,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,7,4,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,7,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,1,7,6,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,1,4,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,1,6,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,1,6,7,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,1,7,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,1,7,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,4,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,4,7,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,4,7,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,6,1,7,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,6,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,6,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,6,7,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,6,7,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,7,4,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,7,4,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,7,6,1,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,2,7,6,4,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,4,1,2,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,4,1,6,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,4,1,6,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,4,1,7,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,4,1,7,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,4,2,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,4,2,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,4,2,7,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,4,2,7,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,4,6,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,4,6,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,4,6,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,4,6,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,4,6,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,4,7,1,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,4,7,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,4,7,2,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,4,7,2,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,4,7,6,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,4,7,6,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,1,4,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,1,4,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,1,7,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,1,7,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,2,1,7,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,2,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,2,7,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,2,7,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,4,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,4,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,7,1,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,7,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,7,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,6,7,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,3,6,7,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,3,7,1,2,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,1,2,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,1,4,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,2,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,2,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,2,4,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,2,4,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,2,6,1,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,2,6,4,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,4,1,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,4,2,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,4,2,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,4,6,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,4,6,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,6,1,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,6,2,1,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,6,2,4,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,3,7,6,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,3,7,6,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,1,2,3,7,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,1,2,6,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,1,2,6,7,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,1,2,7,3,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,1,2,7,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,1,3,2,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,1,3,2,7,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,1,3,6,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,1,3,6,7,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,1,3,7,2,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,1,3,7,6,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,1,6,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,1,6,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,1,6,3,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,1,6,3,7,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,1,6,7,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,1,6,7,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,1,7,2,3,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,1,7,2,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,1,7,3,2,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,1,7,3,6,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,1,7,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,1,7,6,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,1,3,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,1,6,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,1,6,7,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,1,7,3,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,3,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,3,6,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,3,7,1,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,3,7,6,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,6,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,6,1,7,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,6,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,6,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,6,7,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,6,7,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,2,7,1,3,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,7,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,7,3,1,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,7,3,6,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,7,6,1,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,2,7,6,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,3,1,2,7,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,3,1,6,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,3,1,6,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,3,1,7,2,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,3,6,1,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,3,6,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,3,7,1,2,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,3,7,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,3,7,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,3,7,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,3,7,6,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,3,7,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,6,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,6,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,6,1,3,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,1,3,7,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,1,7,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,6,1,7,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,2,1,7,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,2,7,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,2,7,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,3,1,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,6,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,6,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,4,6,7,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,4,6,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,4,7,1,2,3,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,7,1,2,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,7,1,3,2,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,1,3,6,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,7,1,6,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,2,1,3,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,2,3,1,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,2,3,6,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,2,6,1,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,2,6,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,3,1,2,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,7,3,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,7,3,6,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,4,7,6,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,4,7,6,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,6,2,1,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,6,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,4,7,6,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,4,7,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,6,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,6,1,2,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,6,1,2,4,3,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,2,4,7,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,2,7,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,6,1,2,7,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,3,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,3,2,7,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,3,4,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,3,4,7,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,3,7,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,3,7,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,4,2,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,4,2,7,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,4,3,2,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,1,4,3,7,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,1,4,7,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,4,7,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,1,7,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,6,1,7,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,7,3,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,7,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,1,7,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,1,7,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,2,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,1,4,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,1,4,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,1,7,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,1,7,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,3,1,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,3,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,3,7,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,3,7,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,4,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,4,3,1,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,4,3,7,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,4,7,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,4,7,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,7,1,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,7,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,7,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,2,7,4,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,2,7,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,3,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,1,4,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,1,4,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,1,7,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,1,7,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,2,1,7,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,2,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,2,7,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,2,7,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,4,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,4,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,7,1,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,7,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,7,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,3,7,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,3,7,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,4,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,4,1,3,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,1,3,7,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,1,7,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,4,1,7,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,2,1,7,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,2,7,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,2,7,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,3,1,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,4,7,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,4,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[5,6,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,7,1,3,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,7,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,7,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,7,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[5,6,7,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,7,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,7,3,1,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,7,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,7,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[5,6,7,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,7,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[5,7,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,7,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,7,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,2,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,7,1,2,6,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,3,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,3,4,2,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,3,4,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,3,6,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,3,6,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,4,2,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,4,2,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,4,3,2,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,1,4,3,6,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,1,4,6,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,4,6,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,1,6,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,7,1,6,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,6,3,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,6,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,1,6,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,1,6,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,1,3,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,1,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,1,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,3,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,3,6,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,4,3,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,4,6,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,6,1,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,6,3,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,6,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,2,6,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,1,2,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,1,4,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,2,6,4,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,6,2,1,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,6,2,4,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,3,6,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,3,6,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,4,1,2,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,4,1,3,2,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,1,3,6,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,2,6,1,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,2,6,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,7,4,3,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,7,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,7,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,4,6,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,4,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[5,7,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[5,7,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,6,1,3,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[5,7,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,6,3,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[5,7,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[5,7,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[5,7,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[5,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[6,1,2,3,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[6,1,2,3,5,4,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,3,5,7,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,3,7,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[6,1,2,3,7,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,4,3,7,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,4,5,3,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,4,5,7,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,4,7,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,4,7,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,5,3,4,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,5,3,7,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,5,4,3,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,2,5,4,7,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,2,5,7,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,5,7,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,2,7,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[6,1,2,7,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,7,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,7,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,2,7,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,2,7,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,3,2,4,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,2,4,7,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,2,5,7,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,2,7,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,2,7,5,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,4,2,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,4,2,7,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,4,5,2,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,4,5,7,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,4,7,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,4,7,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,5,2,4,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,5,2,7,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,5,4,2,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,5,4,7,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,5,7,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,5,7,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,7,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,7,2,5,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,7,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,7,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,3,7,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,3,7,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,4,2,3,5,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,2,3,7,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,2,5,3,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,2,5,7,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,2,7,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,2,7,5,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,3,2,5,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,3,2,7,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,3,5,2,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,3,5,7,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,3,7,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,3,7,5,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,5,2,3,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,5,2,7,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,5,3,2,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,5,3,7,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,5,7,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,5,7,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,7,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,7,2,5,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,7,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,7,3,5,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,4,7,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,4,7,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,5,2,3,4,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[6,1,5,2,3,7,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[6,1,5,2,4,3,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,2,4,7,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,2,7,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[6,1,5,2,7,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,3,2,4,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,3,2,7,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,3,4,2,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,3,4,7,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,3,7,2,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,3,7,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,4,2,3,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,4,2,7,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,4,3,2,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[6,1,5,4,3,7,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[6,1,5,4,7,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,4,7,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[6,1,5,7,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[6,1,5,7,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,7,3,2,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,7,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,5,7,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,5,7,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[6,1,7,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[6,1,7,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,7,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,7,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,7,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[6,1,7,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,7,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,7,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,7,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,7,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,1,7,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,7,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,7,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,7,4,2,5,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,7,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,7,4,3,5,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,7,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,1,7,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,1,7,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[6,1,7,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,7,5,3,2,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,7,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,1,7,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,1,7,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,1,3,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,1,3,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,3,5,7,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,3,7,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,1,3,7,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,4,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,4,3,7,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,4,5,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,4,5,7,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,4,7,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,4,7,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,5,3,4,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,5,3,7,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,5,4,3,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,1,5,4,7,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,1,5,7,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,5,7,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,1,7,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,1,7,3,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,7,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,7,4,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,1,7,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,1,7,5,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,1,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,1,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,1,5,7,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,1,7,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,1,7,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,4,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,4,7,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,5,1,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,5,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,5,4,7,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,5,7,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,5,7,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,7,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,7,1,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,7,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,7,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,3,7,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,4,1,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,1,3,7,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,1,5,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,1,5,7,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,1,7,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,1,7,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,3,1,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,3,1,7,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,3,5,7,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,3,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,3,7,5,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,5,1,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,5,3,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,5,3,7,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,5,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,5,7,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,7,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,7,1,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,7,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,7,3,5,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,7,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,4,7,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,5,1,3,4,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,1,3,7,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,1,4,3,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,1,4,7,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,1,7,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,1,7,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,3,1,4,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,3,1,7,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,3,4,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,3,4,7,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,3,7,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,3,7,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,4,1,3,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,4,1,7,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,4,3,7,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,4,7,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,4,7,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,7,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,7,1,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,7,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,7,3,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,5,7,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,5,7,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,7,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,7,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,7,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,7,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,7,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,2,7,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,4,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,4,1,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,2,7,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,7,5,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,2,7,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,2,4,7,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,2,5,4,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,2,5,7,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,2,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,2,7,5,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,4,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,4,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,4,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,4,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,4,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,5,2,4,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,5,2,7,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,5,4,2,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,5,4,7,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,5,7,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,5,7,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,7,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,7,2,5,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,7,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,7,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,1,7,5,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,1,7,5,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,1,4,7,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,1,5,4,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,1,5,7,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,1,7,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,1,7,5,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,4,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,4,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,5,1,4,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,5,1,7,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,5,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,5,4,7,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,5,7,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,5,7,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,7,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,7,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,7,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,2,7,5,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,4,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,1,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,1,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,1,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,1,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,1,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,2,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,2,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,2,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,7,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,7,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,7,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,7,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,4,7,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,4,7,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,5,1,2,4,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,1,2,7,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,1,4,2,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,1,4,7,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,1,7,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,1,7,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,2,1,4,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,2,1,7,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,2,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,2,4,7,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,2,7,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,2,7,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,4,1,2,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,4,1,7,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,4,2,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,4,2,7,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,4,7,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,4,7,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,7,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,7,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,7,2,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,7,2,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,5,7,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,5,7,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,7,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,7,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,7,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,7,1,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,7,1,5,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,7,1,5,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,7,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,7,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,7,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,7,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,7,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,7,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,7,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,7,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,7,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,7,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,7,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,3,7,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,3,7,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,7,5,2,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,7,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,3,7,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,3,7,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,2,3,7,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,2,5,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,2,5,7,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,2,7,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,2,7,5,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,3,2,5,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,3,2,7,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,3,5,2,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,3,5,7,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,3,7,2,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,3,7,5,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,5,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,5,2,7,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,5,3,2,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,5,3,7,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,5,7,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,5,7,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,7,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,7,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,7,3,2,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,7,3,5,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,1,7,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,1,7,5,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,1,3,7,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,1,5,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,1,5,7,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,1,7,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,1,7,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,3,1,7,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,3,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,3,5,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,3,7,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,3,7,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,5,1,7,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,5,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,5,3,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,5,7,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,5,7,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,7,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,7,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,7,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,7,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,2,7,5,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,1,2,7,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,1,5,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,1,5,7,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,1,7,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,1,7,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,2,7,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,5,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,5,1,7,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,7,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,7,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,7,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,3,7,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,3,7,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,5,1,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,5,1,2,7,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,5,1,3,2,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,1,3,7,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,1,7,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,5,1,7,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,2,1,7,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,2,7,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,2,7,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,3,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,3,1,7,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,5,3,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,5,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,5,7,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,5,7,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,7,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,7,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,5,7,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,7,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,7,1,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,7,1,3,2,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,1,3,5,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,7,1,5,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,2,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,2,5,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,7,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,7,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,4,7,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,4,7,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,4,7,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,4,7,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[6,5,1,2,3,7,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[6,5,1,2,4,3,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,2,4,7,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,2,7,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[6,5,1,2,7,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,3,2,4,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,3,2,7,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,3,4,2,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,3,4,7,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,3,7,2,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,3,7,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,4,2,3,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,4,2,7,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,4,3,2,7]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,1,4,3,7,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,1,4,7,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,4,7,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,1,7,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[6,5,1,7,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,7,3,2,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,7,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,1,7,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,1,7,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,1,3,7,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,1,4,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,1,4,7,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,1,7,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,1,7,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,3,1,7,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,3,4,7,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,3,7,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,3,7,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,4,1,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,4,1,7,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,4,3,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,4,3,7,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,4,7,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,4,7,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,7,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,7,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,7,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,7,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,2,7,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,2,7,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,1,2,7,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,1,4,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,1,4,7,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,1,7,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,1,7,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,2,4,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,2,7,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,2,7,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,4,1,7,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,7,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,7,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,7,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,3,7,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,3,7,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,4,1,2,7,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,4,1,3,2,7]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,1,3,7,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,1,7,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,4,1,7,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,2,7,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,2,7,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[6,5,4,3,7,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[6,5,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,4,7,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,7,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[6,5,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[6,5,7,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,7,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,7,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,7,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,7,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,5,7,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,7,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,7,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,5,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,5,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,5,7,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,5,7,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[6,7,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[6,7,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,7,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[6,7,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[6,7,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[6,7,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,1,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,1,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,1,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,7,1,4,2,5,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,7,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,1,4,3,5,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[6,7,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[6,7,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,7,1,5,3,2,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[6,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[6,7,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,7,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,7,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[6,7,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,4,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,4,1,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,2,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,2,5,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[6,7,2,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,3,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,3,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,3,1,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,3,1,5,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,3,1,5,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,7,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,7,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,7,3,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,3,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,7,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[6,7,3,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,3,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,3,5,2,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,3,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[6,7,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,7,4,1,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,7,4,1,3,2,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,1,3,5,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,7,4,1,5,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,2,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,2,5,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,7,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[6,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[6,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,7,5,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,7,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,7,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,7,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[6,7,5,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,7,5,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,7,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[6,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,7,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]
[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]
[7,1,2,3,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]
[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]
[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]
[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]
[7,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]
[7,1,2,4,3,6,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]
[7,1,2,4,5,3,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]
[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]
[7,1,2,4,6,3,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]
[7,1,2,4,6,5,3]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]
[7,1,2,5,3,4,6]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]
[7,1,2,5,3,6,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]
[7,1,2,5,4,3,6]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]
[7,1,2,5,4,6,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]
[7,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]
[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]
[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]
[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]
[7,1,2,6,4,3,5]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]
[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]
[7,1,3,2,4,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]
[7,1,3,2,4,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,2,5,6,4]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,2,6,4,5]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,2,6,5,4]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]
[7,1,3,4,2,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]
[7,1,3,4,2,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,4,5,2,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]
[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]
[7,1,3,4,6,2,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,4,6,5,2]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,5,2,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,5,2,6,4]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,5,4,2,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,5,4,6,2]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,5,6,2,4]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,5,6,4,2]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[7,1,3,6,2,4,5]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,6,2,5,4]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]
[7,1,3,6,4,2,5]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,6,4,5,2]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,1,3,6,5,2,4]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]
[7,1,3,6,5,4,2]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]
[7,1,4,2,3,5,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[7,1,4,2,3,6,5]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,4,2,5,3,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[7,1,4,2,5,6,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[7,1,4,2,6,3,5]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,4,2,6,5,3]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,4,3,2,5,6]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[7,1,4,3,2,6,5]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[7,1,4,3,5,2,6]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[7,1,4,3,5,6,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[7,1,4,3,6,2,5]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[7,1,4,3,6,5,2]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[7,1,4,5,2,3,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[7,1,4,5,2,6,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[7,1,4,5,3,2,6]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[7,1,4,5,3,6,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[7,1,4,5,6,2,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[7,1,4,5,6,3,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[7,1,4,6,2,3,5]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,4,6,2,5,3]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,4,6,3,2,5]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[7,1,4,6,3,5,2]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[7,1,4,6,5,2,3]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[7,1,4,6,5,3,2]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[7,1,5,2,3,4,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]
[7,1,5,2,3,6,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]
[7,1,5,2,4,3,6]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,2,4,6,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,2,6,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]
[7,1,5,2,6,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,3,2,4,6]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,3,2,6,4]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,3,4,2,6]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,3,4,6,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,3,6,2,4]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,3,6,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,4,2,3,6]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,4,2,6,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,4,3,2,6]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]
[7,1,5,4,3,6,2]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]
[7,1,5,4,6,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,4,6,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]
[7,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]
[7,1,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,6,3,2,4]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,6,3,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,1,5,6,4,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[7,1,5,6,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]
[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]
[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]
[7,1,6,2,4,3,5]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]
[7,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]
[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]
[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]
[7,1,6,3,2,4,5]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,1,6,3,2,5,4]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,1,6,3,4,2,5]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,1,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,1,6,3,5,2,4]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,1,6,3,5,4,2]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,1,6,4,2,3,5]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]
[7,1,6,4,2,5,3]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]
[7,1,6,4,3,2,5]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,1,6,4,3,5,2]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]
[7,1,6,4,5,3,2]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]
[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]
[7,1,6,5,3,2,4]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,1,6,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]
[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]
[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[7,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[7,2,1,3,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,1,3,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,1,3,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[7,2,1,3,6,5,4]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[7,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,1,4,5,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,1,4,5,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,1,4,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,1,4,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,1,5,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,1,5,3,6,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,1,5,4,3,6]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,1,5,4,6,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,1,5,6,3,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,1,5,6,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,1,6,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[7,2,1,6,3,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,1,6,4,3,5]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,1,6,4,5,3]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,1,6,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,1,6,5,4,3]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[7,2,3,1,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,1,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,1,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,1,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,1,6,5,4]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[7,2,3,4,1,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[7,2,3,4,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,5,1,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,5,1,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,5,4,1,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,5,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[7,2,3,6,1,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,6,1,5,4]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[7,2,3,6,4,1,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[7,2,3,6,5,1,4]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[7,2,4,1,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,1,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,1,5,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,1,5,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,1,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,1,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,3,1,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,3,1,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,3,5,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,5,1,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,5,1,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,5,3,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,5,3,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,5,6,3,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[7,2,4,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,6,1,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,6,3,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,6,3,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,6,5,1,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,4,6,5,3,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[7,2,5,1,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,1,3,6,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,1,4,3,6]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,1,4,6,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,1,6,3,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,1,6,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,3,1,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,3,1,6,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,3,4,1,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,3,4,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,3,6,1,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,3,6,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,4,1,3,6]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,4,1,6,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,4,3,1,6]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,4,6,1,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,4,6,3,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,6,1,3,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,6,1,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,6,3,1,4]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,6,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[7,2,5,6,4,1,3]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,5,6,4,3,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[7,2,6,1,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[7,2,6,1,3,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,1,4,3,5]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,1,4,5,3]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,1,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,1,5,4,3]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[7,2,6,3,1,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[7,2,6,3,1,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,3,4,1,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[7,2,6,3,4,5,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[7,2,6,3,5,1,4]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,3,5,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,4,1,3,5]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,4,1,5,3]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,4,3,1,5]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,4,3,5,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,4,5,1,3]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,2,6,5,1,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,5,1,4,3]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[7,2,6,5,3,1,4]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,5,3,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[7,2,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,1,2,4,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,1,2,5,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,2,5,6,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,2,6,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,1,2,6,5,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,1,4,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,1,4,2,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,1,4,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,1,4,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,1,4,6,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,1,4,6,5,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,1,5,2,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,5,2,6,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,5,4,2,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,5,4,6,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,5,6,2,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,5,6,4,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,1,6,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,1,6,2,5,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,1,6,4,2,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,1,6,4,5,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,1,6,5,2,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,1,6,5,4,2]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,2,1,4,6,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,1,5,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,1,5,6,4]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,1,6,4,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,2,4,1,6,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,2,4,6,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,4,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,5,1,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,5,1,6,4]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,5,4,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,5,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,5,6,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,5,6,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,2,6,1,4,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,6,1,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,2,6,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,6,4,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,2,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,4,1,2,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,4,1,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,4,1,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,4,1,6,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,4,1,6,5,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,4,2,1,6,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,4,2,6,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,4,2,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,4,5,1,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,4,5,2,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[7,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,4,6,1,5,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,4,6,2,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,4,6,2,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,4,6,5,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[7,3,4,6,5,2,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[7,3,5,1,2,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,1,2,6,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,1,4,2,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,1,4,6,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,1,6,2,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,1,6,4,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,2,1,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,2,1,6,4]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,2,4,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,2,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,2,6,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,2,6,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,4,1,2,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,4,1,6,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,4,2,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,4,2,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,4,6,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,4,6,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,6,1,2,4]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,6,1,4,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,6,2,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,6,2,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,5,6,4,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[7,3,5,6,4,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[7,3,6,1,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,6,1,2,5,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,6,1,4,2,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,6,1,4,5,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,6,1,5,2,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,6,1,5,4,2]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,6,2,1,4,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,6,2,1,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,6,2,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,6,2,4,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,6,2,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,6,2,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,6,4,1,2,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,6,4,1,5,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,6,4,2,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,6,4,2,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,6,4,5,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[7,3,6,4,5,2,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[7,3,6,5,1,2,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,6,5,1,4,2]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,6,5,2,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,6,5,2,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[7,3,6,5,4,2,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,1,2,3,6,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,1,2,5,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,1,2,5,6,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,1,2,6,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,1,2,6,5,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,1,3,2,5,6]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,1,3,2,6,5]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,1,3,5,2,6]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,1,3,5,6,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,1,3,6,2,5]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,1,3,6,5,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,1,5,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,1,5,2,6,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,1,5,3,2,6]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,1,5,3,6,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,1,5,6,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,1,5,6,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,1,6,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,1,6,2,5,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,1,6,3,2,5]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,1,6,3,5,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,1,6,5,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,1,6,5,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,1,3,6,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,1,5,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,1,5,6,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,1,6,3,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,1,6,5,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,3,1,6,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,3,5,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,3,6,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,3,6,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,5,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,5,1,6,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,5,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,5,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,5,6,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,5,6,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,2,6,1,3,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,6,1,5,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,6,3,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,6,3,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,2,6,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,3,1,2,6,5]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,3,1,5,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,3,1,5,6,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,3,1,6,2,5]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,3,1,6,5,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,3,5,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,3,5,1,6,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,3,5,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,3,6,1,2,5]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,3,6,1,5,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,3,6,2,1,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,3,6,2,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,3,6,5,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,5,1,2,6,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,5,1,3,2,6]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,1,3,6,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,1,6,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,5,1,6,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,2,1,6,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,2,6,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,2,6,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,3,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,3,1,6,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,5,3,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,3,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[7,4,5,6,1,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,6,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[7,4,6,1,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,6,1,2,5,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,6,1,3,2,5]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,1,3,5,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,1,5,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,6,1,5,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,2,1,3,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,2,1,5,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,2,3,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,2,3,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,3,1,2,5]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,3,1,5,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,3,2,1,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,6,3,2,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,6,3,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,3,5,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,4,6,5,1,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[7,4,6,5,1,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,5,2,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,5,2,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[7,4,6,5,3,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[7,4,6,5,3,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[7,5,1,2,3,6,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[7,5,1,2,4,3,6]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,2,4,6,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,2,6,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[7,5,1,2,6,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,3,2,4,6]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,3,2,6,4]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,3,4,2,6]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,3,4,6,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,3,6,2,4]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,3,6,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,4,2,3,6]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,4,2,6,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,4,3,2,6]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,1,4,3,6,2]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,1,4,6,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,4,6,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,1,6,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[7,5,1,6,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,6,3,2,4]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,6,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,1,6,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,1,6,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,1,3,6,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,1,4,3,6]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,1,4,6,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,1,6,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,1,6,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,3,1,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,3,1,6,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,3,4,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,3,6,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,3,6,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,4,1,3,6]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,4,1,6,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,4,3,1,6]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,4,3,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,4,6,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,4,6,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,6,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,6,1,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,6,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,6,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,2,6,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,2,6,4,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,1,2,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,1,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,1,6,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,2,1,6,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,2,4,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,2,6,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,4,1,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,6,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,6,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,3,6,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,3,6,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,4,1,2,6,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,4,1,3,2,6]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,1,3,6,2]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,1,6,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,4,1,6,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,2,1,6,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,2,3,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,2,3,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,3,1,6,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[7,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[7,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,4,6,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,6,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,6,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,4,6,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[7,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,6,1,3,2,4]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,6,2,1,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[7,5,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,6,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,6,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[7,5,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]
[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]
[7,6,1,2,4,3,5]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,1,2,4,5,3]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]
[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]
[7,6,1,3,2,4,5]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,1,3,2,5,4]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,1,3,4,2,5]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,1,3,5,2,4]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,1,3,5,4,2]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,1,4,2,3,5]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,1,4,2,5,3]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,1,4,3,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,1,4,3,5,2]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]
[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]
[7,6,1,5,3,2,4]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]
[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]
[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[7,6,2,1,3,5,4]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,1,4,3,5]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,1,4,5,3]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,1,5,3,4]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,1,5,4,3]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[7,6,2,3,1,5,4]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[7,6,2,3,5,1,4]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,3,5,4,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,4,1,3,5]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,4,1,5,3]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,4,3,1,5]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,4,3,5,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,4,5,1,3]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,4,5,3,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,2,5,1,3,4]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,5,1,4,3]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,2,5,3,1,4]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,5,3,4,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,2,5,4,1,3]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,2,5,4,3,1]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,3,1,2,5,4]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,3,1,4,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,3,1,4,5,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,3,1,5,2,4]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,3,1,5,4,2]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[7,6,3,2,1,5,4]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[7,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[7,6,3,2,5,1,4]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,3,2,5,4,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,3,4,1,5,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[7,6,3,5,1,2,4]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,3,5,1,4,2]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,3,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,3,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,3,5,4,1,2]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,4,1,2,5,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,4,1,3,2,5]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,1,3,5,2]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,1,5,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,4,1,5,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,2,1,5,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,2,5,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,3,1,5,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[7,6,4,3,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[7,6,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[7,6,5,1,3,2,4]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,5,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,5,2,1,4,3]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[7,6,5,2,4,1,3]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,5,3,1,4,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]
[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]
[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]
[7,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[7,6,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[6,7,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[7,8,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[8,5,6,7,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]
[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[6,7,5,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[7,5,6,8,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[6,5,7,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,6,7,8,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[8,6,7,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[7,6,8,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[8,6,5,4,7,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[8,5,6,4,7,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]
[8,6,4,5,7,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[7,6,5,4,8,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[6,7,5,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[7,5,6,4,8,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[6,5,7,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,6,7,4,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[7,6,4,5,8,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,4,5,8,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[7,5,4,6,8,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[7,4,5,6,8,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[6,5,4,7,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,6,4,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[6,4,5,7,8,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[5,4,6,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,6,7,8,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[8,7,6,5,3,4,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[7,8,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[7,6,8,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[7,8,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[8,5,6,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[7,6,5,8,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,7,5,8,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[5,6,7,8,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[8,7,6,4,3,5,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[7,8,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[7,6,8,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,8,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[7,8,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[8,6,7,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[7,6,8,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[6,7,8,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[7,8,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[7,8,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,6,5,4,3,8,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[7,5,6,4,3,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[7,4,5,6,3,8,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[6,4,5,7,3,8,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[5,4,6,7,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,6,7,3,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[7,6,3,4,5,8,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[7,5,4,3,6,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[7,5,3,4,6,8,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[6,5,4,3,7,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[7,6,8,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[8,5,6,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[7,6,5,8,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[6,7,5,8,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[7,5,6,8,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[5,6,7,8,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[8,7,6,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[7,6,8,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[6,7,8,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[8,7,5,4,6,2,3,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[8,7,4,5,6,2,3,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[8,6,5,4,7,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,5,6,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[8,6,4,5,7,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[7,5,6,4,8,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[6,5,7,4,8,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[4,5,6,7,8,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[8,7,6,5,3,2,4,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[7,8,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,6,7,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[7,6,8,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,7,8,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,5,6,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[7,6,5,8,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,7,5,8,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[5,6,7,8,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[8,7,6,5,2,3,4,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[8,6,7,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[7,6,8,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,8,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[8,7,5,6,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[7,8,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[8,6,5,7,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[7,6,5,8,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,5,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[6,5,7,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[5,6,7,8,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[7,8,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[8,6,7,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[7,6,8,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,8,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[8,7,6,3,4,2,5,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[8,6,7,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[7,6,8,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[7,6,8,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[6,7,8,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[8,6,7,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[6,7,8,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,7,6,2,3,4,5,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[7,8,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[8,6,7,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[7,6,8,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[6,7,8,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[8,7,5,3,4,2,6,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[7,8,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,8,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[8,7,5,3,2,4,6,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[7,8,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[7,8,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[7,8,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[8,5,6,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[8,4,5,3,6,2,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[8,6,4,2,3,5,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[8,5,4,2,3,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[7,4,5,6,3,2,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[4,5,6,7,3,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[7,5,6,3,4,2,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[6,5,7,3,4,2,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[7,4,5,3,6,2,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[6,4,5,3,7,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[5,4,6,3,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,6,3,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[6,5,3,4,7,2,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[5,6,3,4,7,2,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,4,3,6,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[6,7,5,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[7,5,6,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[6,5,7,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[5,6,7,4,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[6,7,4,5,2,3,8,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[7,4,5,6,2,3,8,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[6,5,4,7,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[5,6,4,7,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,4,6,7,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,5,6,7,2,3,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[6,7,5,3,2,4,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,5,7,3,2,4,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[7,6,5,2,3,4,8,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[5,6,7,2,3,4,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[6,7,4,3,2,5,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[7,6,4,2,3,5,8,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[6,7,3,2,4,5,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[6,7,2,3,4,5,8,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[7,5,2,3,4,6,8,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,4,6,3,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[3,4,5,6,2,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[6,4,5,2,3,7,8,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,3,5,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[5,4,2,3,6,7,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,5,2,3,6,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[4,3,2,5,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[3,4,2,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[3,2,4,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[2,3,4,5,6,7,8,1]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[8,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[8,7,5,6,4,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[7,8,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,6,5,8,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[6,7,5,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[7,5,6,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[5,6,7,8,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[8,6,7,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[8,7,5,4,6,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[7,8,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[8,5,6,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[6,5,7,4,8,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[7,6,4,5,8,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[6,7,4,5,8,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[5,6,4,7,8,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[4,5,6,7,8,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[8,7,6,5,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[7,8,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[6,7,8,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[8,7,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,5,6,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[7,6,5,8,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[6,7,5,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[7,5,6,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[6,5,7,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[8,7,6,3,4,5,1,2]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[7,8,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[8,7,4,5,3,6,1,2]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[7,8,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[7,8,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,7,4,3,5,6,1,2]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[7,8,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[8,5,4,6,3,7,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[8,5,4,3,6,7,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[8,5,3,4,6,7,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,4,3,5,6,7,1,2]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[7,6,5,4,3,8,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[5,6,7,4,3,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[6,7,4,5,3,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[7,5,4,6,3,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[6,5,4,7,3,8,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,6,4,7,3,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[4,5,6,7,3,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[7,6,3,4,5,8,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[7,5,4,3,6,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,4,5,3,6,8,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[7,5,3,4,6,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[6,5,4,3,7,8,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,4,6,3,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[4,5,6,3,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[5,6,3,4,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[6,4,3,5,7,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,3,4,5,7,8,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[5,4,3,6,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[4,5,3,6,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[5,3,4,6,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[4,3,5,6,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[6,7,8,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[8,7,5,6,4,2,1,3]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[7,8,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[7,6,5,8,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[6,7,5,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[7,5,6,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[6,5,7,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[5,6,7,8,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[6,7,5,4,8,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[7,6,4,5,8,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[4,5,6,7,8,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[8,7,6,5,4,1,2,3]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[7,8,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[8,5,6,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[7,6,5,8,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[6,7,5,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[7,5,6,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[6,5,7,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[5,6,7,8,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[8,6,7,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[8,7,5,4,6,1,2,3]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[8,6,5,4,7,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[8,5,6,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[8,6,4,5,7,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[7,6,5,4,8,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[6,7,5,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[7,5,6,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[6,5,7,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[5,6,7,4,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[7,6,4,5,8,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[6,7,4,5,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[7,5,4,6,8,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[7,4,5,6,8,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[6,5,4,7,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[5,6,4,7,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[6,4,5,7,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[5,4,6,7,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[4,5,6,7,8,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[7,8,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,6,7,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[7,6,8,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,7,8,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[8,7,5,6,3,2,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[7,8,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[8,6,5,7,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,5,6,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,7,5,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[7,5,6,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[6,5,7,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[5,6,7,8,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[8,7,6,5,2,3,1,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[7,8,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[8,6,7,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[7,6,8,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,8,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[8,7,5,6,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[7,8,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[8,6,5,7,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,6,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[7,6,5,8,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,5,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[6,5,7,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[5,6,7,8,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[8,7,6,5,3,1,2,4]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[7,8,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[7,8,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,6,5,8,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[7,5,6,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[6,5,7,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,6,7,8,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[8,7,6,5,2,1,3,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[7,6,8,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,8,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,8,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[8,6,5,7,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,6,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[7,6,5,8,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,5,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,5,6,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[5,6,7,8,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[8,7,6,5,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[7,8,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[8,6,7,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[7,6,8,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[6,7,8,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[8,7,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[8,6,5,7,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[8,5,6,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[7,6,5,8,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[6,7,5,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[7,5,6,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[6,5,7,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[7,8,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[8,6,7,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[7,6,8,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,8,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[8,7,6,3,4,2,1,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[7,8,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[6,7,8,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,7,6,4,2,3,1,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[7,6,8,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[6,7,8,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[8,7,6,3,2,4,1,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[8,6,7,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[6,7,8,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,7,6,2,3,4,1,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[6,7,8,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[8,7,6,4,3,1,2,5]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[6,7,8,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[8,7,6,3,4,1,2,5]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[6,7,8,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[8,7,6,4,2,1,3,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[7,8,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[8,6,7,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[6,7,8,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[8,7,6,4,1,2,3,5]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[7,8,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[7,6,8,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[6,7,8,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[7,6,8,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[6,7,8,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,7,6,2,3,1,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[7,6,8,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[6,7,8,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[8,7,6,3,1,2,4,5]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[7,8,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[6,7,8,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[8,7,6,2,1,3,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[7,8,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[6,7,8,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[8,7,6,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[7,8,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[8,6,7,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[7,6,8,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[6,7,8,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[7,8,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[8,7,5,3,4,2,1,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[7,8,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[8,7,4,5,2,3,1,6]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[7,8,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[8,7,5,3,2,4,1,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[8,7,4,3,2,5,1,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]
[7,8,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[7,8,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[8,7,5,4,3,1,2,6]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[7,8,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[8,7,5,3,4,1,2,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[7,8,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[7,8,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[8,7,4,5,1,2,3,6]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]
[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[7,8,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[8,7,5,3,1,2,4,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[7,8,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,7,5,2,1,3,4,6]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[7,8,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[8,7,5,1,2,3,4,6]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[7,8,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]
[7,8,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[8,7,3,4,2,1,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[7,8,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[7,8,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[8,7,3,2,4,1,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[7,8,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[7,8,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[7,8,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[8,7,3,4,1,2,5,6]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]
[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[7,8,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,8,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[7,8,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[7,8,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[8,7,2,1,3,4,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[7,8,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[8,5,6,4,3,2,1,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]
[8,4,5,6,3,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[8,6,5,3,4,2,1,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,5,6,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[8,4,5,3,6,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[8,3,4,5,6,2,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]
[8,6,5,4,2,3,1,7]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,5,6,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[8,6,5,3,2,4,1,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,6,5,2,3,4,1,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,6,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[8,6,4,2,3,5,1,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,6,3,2,4,5,1,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[8,5,2,3,4,6,1,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[8,6,4,5,3,1,2,7]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[8,5,6,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,6,3,4,5,1,2,7]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[8,4,5,3,6,1,2,7]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[8,4,3,5,6,1,2,7]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[8,3,4,5,6,1,2,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]
[8,6,5,4,2,1,3,7]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,5,6,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[8,5,6,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[8,4,5,6,1,2,3,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,5,6,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[8,6,5,2,3,1,4,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,6,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[8,5,6,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,6,5,2,1,3,4,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,6,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[8,6,5,1,2,3,4,7]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[8,5,6,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[8,6,3,4,2,1,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[8,6,4,2,3,1,5,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,6,3,2,4,1,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[8,6,3,4,1,2,5,7]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[8,6,4,2,1,3,5,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,6,4,1,2,3,5,7]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[8,4,5,3,2,1,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[8,4,3,5,2,1,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[8,3,4,5,2,1,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]
[8,4,5,2,3,1,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[8,5,2,3,4,1,6,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[8,4,2,3,5,1,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[8,5,3,4,1,2,6,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,5,4,2,1,3,6,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[8,5,3,1,2,4,6,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]
[8,3,4,1,2,5,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]
[8,4,2,1,3,5,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[8,3,2,1,4,5,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]
[8,2,3,1,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]
[8,3,1,2,4,5,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]
[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]
[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[6,7,5,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[7,5,6,4,3,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[6,5,7,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,6,7,4,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,6,4,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,6,7,3,2,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,7,5,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[7,5,6,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[6,5,7,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[5,6,7,3,4,2,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[5,4,6,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[5,6,7,4,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[7,6,4,5,2,3,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[6,7,4,5,2,3,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,5,4,7,2,3,1,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[5,6,4,7,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,4,6,7,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,5,6,7,2,3,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[5,6,7,3,2,4,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[7,6,5,2,3,4,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,5,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,5,6,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[6,5,7,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[5,6,7,2,3,4,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[6,7,4,3,2,5,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[6,7,3,4,2,5,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[7,6,4,2,3,5,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[7,6,3,2,4,5,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[6,7,3,2,4,5,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[7,6,2,3,4,5,1,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[6,7,2,3,4,5,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[7,4,5,3,2,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[7,4,5,2,3,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,5,3,2,4,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,4,2,3,5,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[5,4,6,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[5,6,3,4,2,7,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[6,3,4,5,2,7,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,3,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[3,4,5,6,2,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[6,5,3,2,4,7,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,4,2,3,5,7,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,3,2,4,5,7,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[6,2,3,4,5,7,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,2,3,6,7,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[5,4,6,7,3,1,2,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[4,5,6,7,3,1,2,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[6,5,7,3,4,1,2,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[6,5,4,3,7,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[6,4,5,3,7,1,2,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[3,4,5,6,7,1,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[4,5,6,7,2,1,3,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[7,6,5,4,1,2,3,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[5,6,4,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[5,4,6,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[4,5,6,7,1,2,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[7,6,5,2,3,1,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[6,7,5,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,5,6,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[6,5,7,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[5,6,7,2,3,1,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[5,6,7,3,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[7,6,5,2,1,3,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[5,6,7,2,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[7,6,5,1,2,3,4,8]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[6,7,5,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[7,5,6,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[6,5,7,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[5,6,7,1,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,4,3,2,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[6,7,3,4,2,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[7,6,4,2,3,1,5,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[7,6,3,2,4,1,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[7,6,2,3,4,1,5,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[6,7,2,3,4,1,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[7,6,4,2,1,3,5,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[6,7,3,2,1,4,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[7,6,2,3,1,4,5,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[6,7,3,1,2,4,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[6,7,1,2,3,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[7,5,2,3,4,1,6,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[7,4,2,3,5,1,6,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[7,4,5,1,2,3,6,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,5,3,1,2,4,6,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,1,2,3,4,6,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[7,4,3,1,2,5,6,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[7,3,4,1,2,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[7,3,1,2,4,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[7,1,2,3,4,5,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[5,6,4,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[5,4,6,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,6,3,2,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[5,4,3,6,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[3,4,5,6,2,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[5,4,6,2,3,1,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,6,3,2,4,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[6,5,2,3,4,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[5,6,2,3,4,1,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,3,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[5,3,2,4,6,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[6,5,4,3,1,2,7,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,6,4,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[5,4,6,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[6,4,3,5,1,2,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[5,4,3,6,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[5,6,4,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[6,4,5,2,1,3,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,4,6,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,6,3,2,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[6,3,4,2,1,5,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[6,4,3,1,2,5,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,4,2,1,3,5,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[4,5,3,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[5,3,4,2,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[4,3,5,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[3,4,5,2,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[5,4,2,3,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,5,2,3,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[4,3,2,5,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[3,4,2,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[4,2,3,5,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[3,2,4,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[2,3,4,5,1,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[5,4,3,1,2,6,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[5,4,2,1,3,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,4,1,2,3,6,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[4,5,1,2,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[5,3,2,1,4,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,3,1,2,4,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,2,1,3,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[5,1,2,3,4,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[3,4,2,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[3,2,4,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[2,3,4,1,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[4,3,1,2,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[4,2,1,3,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[4,1,2,3,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[2,3,1,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[3,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]
[6,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[5,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[5,7,8,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[6,5,8,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[5,6,8,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[5,7,6,8,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,8,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[4,5,6,8,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[5,7,6,4,8,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,7,6,5,8,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,6,7,5,8,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[5,4,7,6,8,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,5,7,6,8,3,2,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,6,5,7,8,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,8,7,6,5,4,2,1]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[3,5,8,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[3,5,7,8,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,7,6,5,8,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,5,6,7,8,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[4,3,6,7,8,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[5,4,3,7,8,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,5,3,7,8,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,3,5,7,8,6,2,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,5,6,3,8,7,2,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[4,3,6,5,8,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[5,4,3,6,8,7,2,1]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,5,3,6,8,7,2,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[4,3,5,6,8,7,2,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[5,7,6,4,3,8,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,7,6,5,3,8,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[3,4,7,6,5,8,2,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[4,5,3,7,6,8,2,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,3,5,7,6,8,2,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[3,4,6,5,7,8,2,1]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,8,7,6,5,4,3,1]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]
[2,7,6,8,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[2,5,6,7,8,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,4,6,8,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,5,4,8,7,6,3,1]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[2,5,6,4,8,7,3,1]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,7,6,5,4,8,3,1]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[2,6,5,4,7,8,3,1]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[3,2,8,7,6,5,4,1]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[3,2,6,8,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,2,5,6,7,8,4,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,3,8,7,6,5,4,1]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]
[2,3,5,8,7,6,4,1]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[2,3,5,7,8,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[2,3,7,6,5,8,4,1]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[2,3,5,6,7,8,4,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[4,3,2,8,7,6,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[4,3,2,7,8,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,2,6,8,7,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[3,4,2,8,7,6,5,1]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[3,4,2,7,8,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[2,4,3,8,7,6,5,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[3,2,4,8,7,6,5,1]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[2,3,4,8,7,6,5,1]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]
[2,3,4,6,7,8,5,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[5,4,3,2,8,7,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[5,4,3,2,7,8,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,5,3,2,8,7,6,1]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[4,3,5,2,8,7,6,1]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[2,5,4,3,8,7,6,1]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[2,5,4,3,7,8,6,1]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[2,4,5,3,8,7,6,1]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[2,3,5,4,8,7,6,1]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[4,3,2,5,8,7,6,1]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[2,3,4,5,8,7,6,1]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]
[6,5,4,3,2,8,7,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[4,6,5,3,2,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[5,4,6,3,2,8,7,1]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,5,6,3,2,8,7,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,6,5,4,2,8,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,5,6,4,2,8,7,1]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[4,3,6,5,2,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[5,4,3,6,2,8,7,1]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[2,4,6,5,3,8,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[4,3,2,6,5,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[3,4,2,6,5,8,7,1]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[2,4,3,6,5,8,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,3,4,6,5,8,7,1]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[5,4,3,2,6,8,7,1]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[2,5,4,3,6,8,7,1]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[4,3,2,5,6,8,7,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,4,2,5,6,8,7,1]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[2,4,3,5,6,8,7,1]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,3,4,5,6,8,7,1]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]
[4,7,6,5,3,2,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,6,5,7,3,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,5,7,6,4,2,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,5,6,7,4,2,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[4,3,7,6,5,2,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,6,7,5,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,4,7,6,5,2,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[5,4,3,7,6,2,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,6,5,3,7,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,6,5,4,7,2,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,5,6,4,7,2,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[4,3,6,5,7,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,5,4,6,7,2,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,5,4,7,6,3,8,1]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[2,4,6,5,7,3,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,5,6,7,3,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[3,2,6,7,5,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,2,6,5,7,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[2,3,7,6,5,4,8,1]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[2,3,5,7,6,4,8,1]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[4,3,2,7,6,5,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,2,6,7,5,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,4,2,7,6,5,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[2,4,3,7,6,5,8,1]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[3,2,4,7,6,5,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[2,3,4,7,6,5,8,1]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[5,4,3,2,7,6,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,3,5,2,7,6,8,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[2,5,4,3,7,6,8,1]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[3,2,5,4,7,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,3,5,4,7,6,8,1]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[4,3,2,5,7,6,8,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[2,4,3,5,7,6,8,1]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[3,2,4,5,7,6,8,1]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[2,3,4,5,7,6,8,1]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]
[3,6,5,4,2,7,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[2,3,6,5,4,7,8,1]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,3,5,6,4,7,8,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[4,3,2,6,5,7,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,4,2,6,5,7,8,1]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,4,3,6,5,7,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,3,4,6,5,7,8,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[3,5,4,2,6,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,5,4,3,6,7,8,1]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,4,5,3,6,7,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[3,2,5,4,6,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,3,5,4,6,7,8,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,4,3,5,6,7,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]
[1,7,8,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]
[1,6,8,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]
[1,7,6,8,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]
[1,6,7,8,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,7,6,5,8,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]
[1,6,7,5,8,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,5,7,6,8,4,3,2]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]
[1,6,5,7,8,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,5,6,7,8,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,4,7,8,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,4,6,8,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,4,6,7,8,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,4,6,5,8,7,3,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,4,7,6,5,8,3,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,6,5,4,7,8,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,5,4,6,7,8,3,2]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,3,8,7,6,5,4,2]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]
[1,3,6,8,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[1,3,6,7,8,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[1,3,5,8,7,6,4,2]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]
[1,3,5,7,8,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,3,6,5,7,8,4,2]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[1,3,5,6,7,8,4,2]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,4,3,8,7,6,5,2]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]
[1,4,3,7,8,6,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,4,3,6,8,7,5,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,4,3,7,6,8,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,3,4,8,7,6,5,2]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]
[1,3,4,7,6,8,5,2]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,3,4,6,7,8,5,2]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[1,5,4,3,8,7,6,2]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]
[1,4,3,5,8,7,6,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]
[1,4,3,5,7,8,6,2]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]
[1,3,4,5,8,7,6,2]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]
[1,6,5,4,3,8,7,2]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]
[1,5,6,4,3,8,7,2]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]
[1,4,6,5,3,8,7,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,3,6,5,4,8,7,2]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[1,4,3,6,5,8,7,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,5,4,3,6,8,7,2]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]
[1,6,7,5,4,3,8,2]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,3,4,7,6,5,8,2]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,3,5,4,7,6,8,2]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,4,3,6,5,7,8,2]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,5,4,3,6,7,8,2]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]
[2,1,7,8,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[2,1,6,8,7,5,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[2,1,7,6,8,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[2,1,6,7,8,5,4,3]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[2,1,5,8,7,6,4,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[2,1,5,7,8,6,4,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[2,1,6,5,8,7,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[2,1,7,6,5,8,4,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[2,1,6,7,5,8,4,3]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[2,1,6,5,7,8,4,3]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[2,1,5,6,7,8,4,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,1,4,8,7,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[2,1,4,7,8,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[2,1,4,6,8,7,5,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,4,6,7,8,5,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,1,4,5,8,7,6,3]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[2,1,4,5,7,8,6,3]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,1,4,6,5,8,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,4,5,6,8,7,3]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,1,6,5,7,4,8,3]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[2,1,5,6,7,4,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,1,4,7,6,5,8,3]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[2,1,4,6,7,5,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,1,5,4,7,6,8,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[2,1,5,6,4,7,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,1,4,5,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,2,8,7,6,5,4,3]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]
[1,2,6,7,8,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]
[1,2,6,5,8,7,4,3]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]
[1,2,7,6,5,8,4,3]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]
[1,2,5,7,6,8,4,3]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,2,6,5,7,8,4,3]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]
[1,2,5,6,7,8,4,3]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[1,2,4,8,7,6,5,3]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[1,2,4,7,8,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]
[1,2,4,6,8,7,5,3]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,2,4,6,7,8,5,3]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[1,2,5,4,8,7,6,3]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]
[1,2,5,4,7,8,6,3]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,2,4,5,7,8,6,3]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]
[1,2,6,5,4,8,7,3]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]
[1,2,4,6,5,8,7,3]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,2,5,4,6,8,7,3]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]
[1,2,5,7,6,4,8,3]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,2,5,6,7,4,8,3]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[1,2,4,7,6,5,8,3]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]
[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[3,2,1,7,8,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,2,1,6,8,7,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,2,1,7,6,8,5,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,2,1,6,7,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,2,1,5,8,7,6,4]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[3,2,1,5,7,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,2,1,6,5,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,2,1,5,6,8,7,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[3,2,1,7,6,5,8,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,2,1,6,7,5,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,3,1,8,7,6,5,4]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]
[2,3,1,6,8,7,5,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[2,3,1,7,6,8,5,4]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[2,3,1,6,7,8,5,4]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,3,1,6,5,8,7,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[2,3,1,5,7,6,8,4]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[2,3,1,5,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[1,3,2,8,7,6,5,4]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]
[1,3,2,6,8,7,5,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[1,3,2,6,5,8,7,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[1,3,2,7,6,5,8,4]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]
[1,3,2,6,5,7,8,4]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[2,1,3,8,7,6,5,4]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]
[2,1,3,7,8,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[2,1,3,6,8,7,5,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[1,2,3,8,7,6,5,4]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]
[1,2,3,7,8,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]
[1,2,3,6,8,7,5,4]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]
[1,2,3,7,6,8,5,4]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]
[1,2,3,6,7,8,5,4]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,2,3,5,8,7,6,4]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]
[1,2,3,5,7,8,6,4]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,2,3,6,5,8,7,4]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]
[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]
[1,2,3,7,6,5,8,4]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]
[1,2,3,6,7,5,8,4]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,2,3,6,5,7,8,4]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]
[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[4,3,2,1,7,8,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,2,1,6,8,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,3,2,1,7,6,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,2,1,6,7,8,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,4,2,1,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[3,4,2,1,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,4,2,1,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,4,2,1,6,7,8,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,4,3,1,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[2,4,3,1,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,3,1,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[2,4,3,1,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[3,2,4,1,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[3,2,4,1,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,2,4,1,6,8,7,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[3,2,4,1,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,2,4,1,6,7,8,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,3,4,1,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]
[2,3,4,1,7,8,6,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,3,4,1,6,8,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[2,3,4,1,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,4,3,2,8,7,6,5]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]
[1,4,3,2,7,6,8,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,4,3,2,6,7,8,5]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,3,4,2,8,7,6,5]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]
[1,3,4,2,7,8,6,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,3,4,2,6,8,7,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[1,3,4,2,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,3,4,2,6,7,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[2,1,4,3,7,8,6,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,4,3,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[1,2,4,3,8,7,6,5]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[1,2,4,3,7,8,6,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]
[1,2,4,3,6,8,7,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,2,4,3,7,6,8,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]
[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[3,2,1,4,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[3,2,1,4,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,2,1,4,6,8,7,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[3,2,1,4,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,2,1,4,6,7,8,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,3,1,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]
[2,3,1,4,7,8,6,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,3,1,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,3,1,4,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,3,2,4,8,7,6,5]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]
[1,3,2,4,6,8,7,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[1,3,2,4,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[2,1,3,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]
[2,1,3,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,2,3,4,8,7,6,5]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]
[1,2,3,4,7,8,6,5]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]
[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]
[1,2,3,4,7,6,8,5]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]
[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]
[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[5,4,3,2,1,7,8,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,5,3,2,1,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[3,5,4,2,1,8,7,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[3,5,4,2,1,7,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,3,5,2,1,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[3,4,5,2,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[2,5,4,3,1,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[2,5,4,3,1,7,8,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[2,4,5,3,1,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[3,2,5,4,1,8,7,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[3,2,5,4,1,7,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,3,5,4,1,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[4,3,2,5,1,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[3,4,2,5,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[3,4,2,5,1,7,8,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[2,4,3,5,1,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[3,2,4,5,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[2,3,4,5,1,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]
[1,2,5,4,3,7,8,6]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,2,4,5,3,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]
[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]
[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]
[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[4,3,2,1,5,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[4,3,2,1,5,7,8,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[3,2,4,1,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[3,2,4,1,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[2,3,4,1,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]
[2,3,4,1,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]
[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]
[1,3,4,2,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]
[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]
[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[3,2,1,4,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]
[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]
[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]
[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[5,6,4,3,2,1,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,6,5,3,2,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[5,4,6,3,2,1,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,5,6,3,2,1,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,6,5,4,2,1,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,5,6,4,2,1,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[4,3,6,5,2,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[5,4,3,6,2,1,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,5,3,6,2,1,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,4,5,6,2,1,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[2,6,5,4,3,1,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[2,5,6,4,3,1,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,4,6,5,3,1,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,3,6,5,4,1,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[2,3,5,6,4,1,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[5,4,3,2,6,1,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,5,3,2,6,1,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,5,4,2,6,1,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[4,3,5,2,6,1,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,4,5,2,6,1,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[2,5,4,3,6,1,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,4,5,3,6,1,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[3,2,5,4,6,1,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[3,4,2,5,6,1,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[2,3,4,5,6,1,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]
[1,5,4,6,3,2,8,7]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]
[1,3,6,5,4,2,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[2,1,5,6,4,3,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,1,4,6,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,5,4,6,3,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,1,4,5,6,3,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,3,1,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]
[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]
[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[3,4,2,1,6,5,8,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[2,4,3,1,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[3,2,4,1,6,5,8,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[2,3,4,1,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]
[5,4,3,2,1,6,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[4,5,3,2,1,6,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,5,4,2,1,6,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[2,5,4,3,1,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,4,5,3,1,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[3,2,5,4,1,6,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[1,3,5,4,2,6,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[2,1,4,5,3,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]
[2,1,3,5,4,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[4,3,2,1,5,6,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[3,2,4,1,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[2,3,4,1,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]
[1,4,3,2,5,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]
[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]
[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]
[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]
[5,7,6,4,3,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,7,6,5,3,2,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,6,7,5,3,2,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[4,5,7,6,3,2,1,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,6,5,7,3,2,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,5,7,6,4,2,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,5,6,7,4,2,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[3,5,4,7,6,2,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,5,6,7,4,3,1,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,4,6,7,5,3,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[3,2,7,6,5,4,1,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,2,6,7,5,4,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,2,5,7,6,4,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,3,7,6,5,4,1,8]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[2,3,6,7,5,4,1,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,3,5,7,6,4,1,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[2,3,6,5,7,4,1,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,3,5,6,7,4,1,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[3,2,4,6,7,5,1,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,3,4,7,6,5,1,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[5,4,3,2,7,6,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,5,3,2,7,6,1,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[3,5,4,2,7,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,2,5,4,7,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,3,2,5,7,6,1,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[3,6,5,4,2,7,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,4,6,5,2,7,1,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[3,5,4,6,2,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,5,4,6,3,7,1,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[3,2,6,5,4,7,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,4,2,6,5,7,1,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,4,3,6,5,7,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[3,5,4,2,6,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,5,4,3,6,7,1,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[1,5,6,7,4,3,2,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,4,6,5,7,3,2,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,3,5,7,6,4,2,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,3,5,6,7,4,2,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,3,5,4,7,6,2,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,4,3,5,7,6,2,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]
[1,5,4,6,3,7,2,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,3,6,5,4,7,2,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[1,4,3,6,5,7,2,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,5,4,3,6,7,2,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,3,4,5,6,7,2,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]
[2,1,5,6,7,4,3,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[1,2,5,7,6,4,3,8]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,2,5,6,7,4,3,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[1,2,5,6,4,7,3,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[1,2,5,4,6,7,3,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,2,1,6,5,7,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[2,3,1,6,7,5,4,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,3,1,6,5,7,4,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,3,1,5,6,7,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[1,3,2,6,5,7,4,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[2,1,3,6,7,5,4,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[1,2,3,7,6,5,4,8]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]
[1,2,3,6,7,5,4,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,2,3,6,5,7,4,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]
[4,3,2,1,7,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,2,1,6,7,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,2,4,1,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,2,4,1,6,7,5,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,3,4,1,7,6,5,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,3,4,1,6,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,4,3,2,6,7,5,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[2,1,4,3,6,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[2,3,1,4,6,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]
[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]
[5,4,3,2,1,7,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,5,3,2,1,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[3,5,4,2,1,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,5,4,3,1,7,6,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[2,4,5,3,1,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[3,2,5,4,1,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,4,2,5,1,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[2,4,3,5,1,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[1,4,3,5,2,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]
[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,3,1,5,4,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[4,3,2,1,5,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[3,2,4,1,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[2,3,4,1,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]
[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]
[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]
[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]
[3,6,5,4,2,1,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[4,3,6,5,2,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[2,4,6,5,3,1,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,5,6,3,1,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,3,6,5,4,1,7,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[4,3,2,6,5,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,5,4,2,6,1,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[1,5,6,4,3,2,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,4,6,5,3,2,7,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,5,4,6,3,2,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,4,5,6,3,2,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]
[1,3,5,6,4,2,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,4,3,6,5,2,7,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,5,4,3,6,2,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[2,1,5,6,4,3,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,1,4,6,5,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[1,2,6,5,4,3,7,8]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]
[1,2,4,5,6,3,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]
[3,2,1,5,6,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,3,1,6,5,4,7,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]
[4,3,2,1,6,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,2,4,1,6,5,7,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[2,3,4,1,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]
[3,5,4,2,1,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,5,4,3,1,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,4,5,3,1,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[3,2,5,4,1,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[2,3,5,4,1,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,4,3,5,1,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]
[2,4,3,1,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]
[1,3,4,2,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]
[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]
[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]
[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]
[1,2,3,5,8,6,7,4]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]
[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,2,3,7,5,6,8,4]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]
[1,2,3,8,5,7,6,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]
[1,2,3,8,6,5,7,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]
[1,2,3,8,6,7,5,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]
[1,2,4,5,8,6,7,3]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]
[1,2,4,8,5,6,7,3]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]
[1,2,4,8,6,5,7,3]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]
[1,2,5,4,8,6,7,3]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]
[1,2,6,4,5,3,7,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]
[1,2,8,4,6,7,5,3]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]
[1,2,8,4,7,6,5,3]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]
[1,2,7,5,4,6,8,3]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,2,8,5,4,6,7,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]
[1,2,8,5,4,7,6,3]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]
[1,2,8,6,5,4,7,3]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]
[1,3,2,7,5,6,8,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,3,2,8,5,7,6,4]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]
[1,3,4,5,8,6,7,2]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[1,3,4,8,5,6,7,2]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]
[1,3,6,4,5,2,8,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,3,6,4,5,7,2,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,3,6,4,5,8,7,2]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,3,8,4,5,6,7,2]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]
[1,3,8,4,6,5,7,2]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]
[1,3,8,4,6,7,5,2]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]
[1,3,8,5,4,6,7,2]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]
[1,3,8,5,6,7,4,2]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]
[1,3,8,5,7,6,4,2]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]
[1,3,8,6,5,7,4,2]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]
[1,3,8,7,5,6,4,2]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,4,3,8,5,6,7,2]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]
[1,4,3,8,5,7,6,2]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]
[1,4,3,8,6,7,5,2]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]
[1,5,3,4,2,7,8,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,5,3,4,8,6,7,2]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,8,3,4,6,7,5,2]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]
[1,6,3,5,4,2,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,6,3,5,4,8,7,2]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,8,3,5,6,4,7,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]
[1,8,3,5,7,6,4,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]
[1,8,3,6,5,4,7,2]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]
[1,8,3,7,5,6,4,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,8,3,7,6,5,4,2]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]
[1,6,4,3,5,2,7,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,8,4,3,5,6,7,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[1,8,4,3,5,7,6,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]
[1,7,4,3,6,5,8,2]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,6,4,5,3,8,7,2]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,8,4,5,6,3,7,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[1,8,4,5,6,7,3,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[1,8,4,6,5,7,3,2]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]
[1,8,4,7,6,5,3,2]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]
[1,7,5,4,3,6,8,2]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,8,5,4,3,6,7,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]
[1,8,5,4,6,3,7,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]
[1,8,5,4,6,7,3,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]
[1,8,5,4,7,6,3,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]
[1,8,6,4,5,7,3,2]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,8,6,5,4,7,3,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]
[1,8,7,5,6,4,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,4,5,8,6,7,3]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]
[2,1,4,8,5,6,7,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,1,4,8,5,7,6,3]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[2,1,4,8,6,5,7,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,5,4,8,6,7,3]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]
[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,6,4,5,7,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,1,6,4,5,8,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,8,4,5,7,6,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]
[2,1,8,4,7,6,5,3]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[2,1,8,5,4,6,7,3]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[2,1,8,5,4,7,6,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[2,1,7,5,6,4,8,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,1,8,5,6,4,7,3]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[2,1,8,5,7,6,4,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[2,1,8,7,5,6,4,3]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[2,3,1,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]
[2,3,1,8,6,7,5,4]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]
[2,3,4,1,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,4,5,8,6,7,1]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]
[2,3,4,7,5,6,1,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,4,7,5,6,8,1]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,4,8,5,6,7,1]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[2,3,4,8,5,7,6,1]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]
[2,3,4,8,6,5,7,1]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,4,8,6,7,5,1]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,6,4,5,1,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,6,4,5,7,8,1]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,3,7,4,5,6,8,1]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[2,3,8,4,5,6,7,1]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]
[2,3,7,4,6,5,8,1]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]
[2,3,7,5,4,6,1,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,3,7,5,4,6,8,1]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,3,7,5,6,4,1,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,3,7,5,6,4,8,1]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,3,8,5,7,6,4,1]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]
[2,4,3,5,8,6,7,1]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]
[2,4,3,8,5,6,7,1]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,5,3,4,1,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,3,4,1,8,7,6]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[2,5,3,4,6,7,1,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,3,4,8,7,6,1]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[2,6,3,4,5,8,7,1]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,6,3,5,4,1,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[2,7,3,5,4,6,8,1]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,7,3,5,6,4,8,1]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,8,3,5,7,6,4,1]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]
[2,7,3,6,5,4,1,8]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]
[2,8,3,7,5,6,4,1]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[2,5,4,3,8,6,7,1]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]
[2,8,4,3,5,6,7,1]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[2,8,4,3,7,6,5,1]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[2,6,4,5,3,1,7,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,7,4,5,6,3,1,8]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[2,7,4,5,6,3,8,1]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[2,7,5,4,3,6,8,1]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,8,5,4,3,6,7,1]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[2,8,5,4,3,7,6,1]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[2,7,5,4,6,3,8,1]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,8,5,4,7,6,3,1]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[2,8,7,5,4,6,3,1]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[2,8,7,5,6,4,3,1]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]
[3,2,1,5,8,6,7,4]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,1,7,5,6,8,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[3,2,1,8,5,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[3,2,1,8,6,5,7,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[3,2,1,8,6,7,5,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[3,2,4,1,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]
[3,2,4,8,5,6,7,1]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]
[3,2,5,4,8,6,7,1]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[3,2,6,4,5,1,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,2,6,4,5,1,8,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[3,2,7,4,6,5,1,8]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[3,2,7,4,6,5,8,1]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[3,2,8,5,4,6,7,1]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[3,2,7,5,6,4,1,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,7,5,6,4,8,1]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,8,5,6,4,7,1]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[3,2,8,5,7,6,4,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,3,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[4,2,3,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,2,3,1,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[4,2,3,5,1,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[4,2,3,5,6,1,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[4,2,3,5,6,8,7,1]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[4,2,3,7,5,6,1,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[4,2,3,8,5,6,7,1]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[4,2,3,7,6,5,8,1]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,2,3,8,7,6,5,1]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[5,2,3,4,8,7,6,1]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[6,2,3,5,4,1,7,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[6,2,3,5,4,1,8,7]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,2,3,5,4,7,1,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,2,3,5,6,4,1,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]
[8,2,3,5,6,7,4,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]
[7,2,3,6,5,4,1,8]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]
[8,2,3,7,5,6,4,1]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[5,2,4,3,1,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,2,4,3,1,6,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[5,2,4,3,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,2,4,3,1,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,2,4,3,6,1,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,2,4,3,6,1,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[5,2,4,3,7,6,1,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,2,4,3,7,6,8,1]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[7,2,4,3,6,5,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,2,4,3,6,5,8,1]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[6,2,4,5,3,1,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[7,2,4,5,3,6,1,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,2,4,5,3,6,8,1]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[8,2,4,7,5,6,3,1]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[8,2,4,7,6,5,3,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]
[6,2,5,4,3,1,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[7,2,5,4,3,6,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[8,2,5,4,7,6,3,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]
[8,2,6,4,5,7,3,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,2,7,4,6,5,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,2,7,5,6,4,3,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]
[4,3,2,1,8,6,7,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[4,3,2,7,5,6,8,1]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[4,3,2,8,5,6,7,1]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]
[4,3,2,8,6,7,5,1]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[5,3,2,4,1,6,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[5,3,2,4,1,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[5,3,2,4,6,1,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[6,3,2,5,4,1,7,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,3,2,5,4,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,3,2,5,4,7,1,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,3,2,5,4,7,8,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[8,3,2,5,4,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[8,3,2,5,6,4,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[8,3,2,5,7,6,4,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]
[5,3,4,2,1,7,8,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,3,4,2,1,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[5,3,4,2,6,1,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[5,3,4,2,7,6,1,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,3,4,2,7,6,8,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,3,4,2,8,6,7,1]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[6,3,4,2,5,1,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[7,3,4,2,6,5,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[7,3,4,2,6,5,8,1]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[6,3,5,4,2,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,3,5,4,2,7,1,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,3,5,4,2,7,8,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[8,3,5,4,2,6,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[8,3,5,4,7,6,2,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[7,3,6,4,5,2,8,1]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[8,3,6,4,5,2,7,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]
[8,3,7,4,5,6,2,1]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]
[7,3,6,5,4,2,1,8]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,3,7,5,6,4,2,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[5,4,3,2,8,6,7,1]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[7,4,3,2,6,5,8,1]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[8,4,3,2,6,7,5,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]
[6,4,3,5,2,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[8,4,3,5,7,6,2,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]
[7,4,3,6,5,2,1,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[7,4,3,6,5,2,8,1]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[8,4,3,7,5,6,2,1]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]
[6,5,3,4,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[8,5,3,4,7,6,2,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,7,3,5,6,4,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[8,5,4,3,7,6,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[2,4,1,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,4,6,3,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,1,6,3,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,6,1,3,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,4,3,6,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,1,3,6,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,1,4,6,3,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,1,6,3,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,6,1,3,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,1,6,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,6,1,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,6,8,1,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[2,4,1,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,1,6,3,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,6,1,3,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,6,7,1,3,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,1,3,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,1,4,6,3,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,1,6,3,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,1,6,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,6,1,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,6,7,1,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,1,6,7,8,3,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,4,6,7,8,1,3,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[2,1,4,3,7,5,8,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,1,3,7,5,8,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,1,7,3,5,8,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,1,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,1,7,3,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,1,7,8,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,7,1,8,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[2,4,1,5,3,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,4,5,1,7,3,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,4,1,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,4,1,5,3,7,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,4,5,1,3,7,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,1,4,5,7,3,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,4,1,5,7,3,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,4,5,1,7,3,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[2,1,4,3,8,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,4,1,3,8,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,1,4,8,3,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,4,1,8,3,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,4,1,5,3,8,6,7]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]
[2,1,4,5,8,3,6,7]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]
[2,4,1,5,6,3,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,1,4,5,6,8,3,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,4,5,1,6,8,3,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,4,5,6,1,8,3,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[2,4,1,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,1,5,6,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,5,1,6,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,5,6,1,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,5,6,7,1,3,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,1,5,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,5,6,1,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,4,5,6,7,1,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[2,1,5,3,6,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,1,5,3,6,8,4,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,5,1,3,6,8,4,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,5,1,6,8,3,4,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,1,5,6,3,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,6,3,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,3,6,7,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,6,3,7,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,6,3,7,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,6,1,3,7,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,6,7,3,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,6,7,3,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,3,6,7,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,3,6,7,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,6,3,7,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,6,3,7,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,6,1,3,7,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,6,7,3,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,6,7,3,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,6,7,8,3,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,1,6,7,8,3,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,5,6,1,7,8,3,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,1,5,3,7,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,1,3,7,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,1,5,7,3,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,1,7,3,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,7,1,3,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,1,5,3,7,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,1,3,7,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,1,5,7,8,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,1,7,8,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,1,5,7,3,4,6,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,3,5,1,4,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[2,3,5,7,1,4,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[2,3,5,7,1,4,8,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[2,1,5,3,8,4,6,7]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[2,3,5,1,4,8,6,7]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]
[2,1,5,3,4,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,3,5,1,6,4,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[2,3,5,6,1,8,4,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[2,3,5,6,8,1,4,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[2,5,1,3,4,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[2,3,5,6,1,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,3,5,6,1,7,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,3,5,1,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,3,5,6,1,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,3,5,6,7,8,1,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[2,1,6,3,7,4,8,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,1,3,7,4,8,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,7,1,3,4,8,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,1,6,3,7,8,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,1,7,3,8,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,1,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,7,8,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,1,7,3,4,5,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,6,7,1,3,4,5,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,3,1,6,4,7,5,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,3,6,1,4,7,5,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,1,6,3,4,7,8,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[2,3,6,1,4,7,8,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,1,3,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,3,1,6,7,8,4,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,3,6,7,8,1,4,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[2,6,1,8,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,1,6,3,4,8,5,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,3,1,6,4,8,5,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,1,6,8,4,5,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,6,1,8,4,5,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[2,1,6,3,4,5,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,6,1,3,4,5,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,3,6,1,4,5,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,4,1,6,8,5,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[2,3,4,6,1,8,5,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[2,3,4,6,7,8,1,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[2,7,1,3,8,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[2,1,7,8,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[2,7,1,8,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[2,7,8,1,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[2,1,7,3,4,8,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[2,1,3,7,4,8,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[2,3,1,7,4,8,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[2,3,1,7,8,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[2,1,7,3,4,5,8,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[2,3,1,7,4,5,8,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[2,3,7,1,4,5,8,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[2,3,4,1,7,5,8,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,4,7,1,5,8,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,1,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,4,1,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,4,1,7,5,6,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,3,4,7,1,5,6,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[2,1,8,3,4,5,6,7]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]
[2,8,1,3,4,5,6,7]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]
[2,1,3,8,4,5,6,7]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]
[2,3,1,8,4,5,6,7]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]
[2,3,8,1,4,5,6,7]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]
[2,1,3,4,8,5,6,7]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[2,3,1,4,8,5,6,7]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[2,3,4,1,8,5,6,7]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[2,3,4,8,1,5,6,7]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[2,3,4,1,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]
[2,3,4,5,8,1,6,7]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]
[3,1,4,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,4,6,1,2,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,1,4,2,6,8,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,4,1,2,6,8,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,1,4,6,2,8,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,1,4,6,8,2,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,4,1,6,8,2,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,1,4,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,1,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,4,2,6,7,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,1,2,6,7,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,1,6,2,7,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,6,1,2,7,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,4,2,6,7,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,1,2,6,7,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,6,1,2,7,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,6,1,7,2,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,4,6,7,8,2,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,6,1,7,8,2,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,6,7,1,8,2,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,6,7,8,1,2,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,4,2,7,5,8,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,1,2,7,5,8,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,7,1,2,5,8,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,1,4,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,7,1,8,2,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,1,4,2,7,5,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,1,2,7,5,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,1,4,5,2,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,4,1,5,2,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,4,1,5,7,2,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,1,4,2,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,4,1,2,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,1,4,5,2,7,8,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,4,1,5,7,2,8,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,1,4,5,7,8,2,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,4,1,5,7,8,2,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,4,5,1,7,8,2,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,1,4,2,8,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[3,4,1,2,8,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[3,1,4,8,2,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[3,4,1,8,2,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[3,4,8,1,2,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[3,1,4,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,1,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,1,5,2,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,5,1,2,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,1,5,8,2,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,1,4,5,6,2,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,4,5,1,6,2,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,4,5,6,1,2,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,4,1,5,6,8,2,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,4,5,6,1,8,2,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,4,5,6,8,1,2,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[3,1,4,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,4,1,5,6,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,4,5,1,6,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,4,1,5,6,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,4,5,6,1,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,1,4,5,6,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,4,5,1,6,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,4,5,6,1,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[3,1,5,2,6,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,5,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,6,1,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,1,2,6,8,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,5,6,2,8,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,6,1,2,8,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,5,6,8,2,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,6,1,8,2,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,5,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,1,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,6,1,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,1,6,2,7,4,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,6,1,2,7,4,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,6,1,7,2,4,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,1,5,2,6,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,1,2,6,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,1,5,6,2,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,1,6,2,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,6,1,2,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,1,5,6,7,2,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,1,6,7,2,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,6,1,7,2,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,1,5,6,7,8,2,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,1,6,7,8,2,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,5,6,1,7,8,2,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,1,5,2,7,4,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,1,2,7,4,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,5,7,2,4,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,7,1,2,4,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,5,2,7,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,1,2,7,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,5,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,5,7,8,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,1,7,8,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,7,8,1,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,5,2,7,4,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,5,7,2,4,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,1,7,2,4,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,7,1,2,4,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,2,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,3,5,7,2,4,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[3,5,1,2,4,7,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,1,2,5,7,4,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,3,5,2,7,4,8,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,3,5,7,2,4,8,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,3,5,2,7,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,3,5,7,8,2,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[3,1,5,2,8,4,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,5,1,2,8,4,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,1,5,8,2,4,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,5,1,8,2,4,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,1,5,2,4,8,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,5,1,2,4,8,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,3,2,5,4,8,6,7]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[1,3,5,2,4,8,6,7]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,2,5,8,4,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,3,2,5,8,4,6,7]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[1,3,5,2,8,4,6,7]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[1,3,5,8,2,4,6,7]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,1,2,4,6,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,2,5,4,6,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[1,3,5,2,4,6,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[1,3,5,2,6,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[1,3,5,6,2,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[3,1,2,5,6,8,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[1,3,5,2,6,8,4,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,3,5,6,2,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[3,1,2,5,6,7,4,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,3,5,2,6,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,3,5,6,2,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,3,5,6,7,2,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[3,1,2,5,6,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,3,5,6,2,7,8,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,3,5,6,7,8,2,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[3,1,6,2,7,4,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,1,2,7,4,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,1,7,2,4,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,7,1,2,4,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,1,6,7,2,8,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,1,7,2,8,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,7,1,2,8,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,7,8,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,1,6,7,2,4,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,7,1,2,4,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,1,6,2,4,7,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,1,2,4,7,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,1,2,6,4,7,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,3,2,6,4,7,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,3,6,2,4,7,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,6,2,4,7,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,6,1,2,4,7,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,1,2,6,4,7,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,3,6,2,4,7,8,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,2,6,7,4,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,3,6,2,7,4,8,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,3,6,7,2,4,8,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,3,6,2,7,8,4,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,6,2,8,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[3,1,6,8,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[3,6,1,8,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[3,1,6,2,4,8,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[3,6,1,2,4,8,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,3,2,6,4,8,5,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,3,6,2,4,8,5,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,1,6,2,4,5,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[3,1,2,6,4,5,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,3,4,6,2,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[3,1,2,4,6,8,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,3,2,4,6,8,5,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[1,3,4,6,8,2,5,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[3,1,6,2,4,5,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,3,2,6,4,5,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,3,6,2,4,5,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,2,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,1,2,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,7,1,2,8,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[3,1,7,8,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[3,7,1,2,4,8,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[3,1,2,7,4,8,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,3,2,7,4,8,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,3,7,2,4,8,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,1,2,7,8,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,3,7,2,8,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,7,1,2,4,5,8,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,3,7,2,4,5,8,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,1,2,4,7,5,8,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,3,2,4,7,5,8,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]
[1,3,4,7,2,5,8,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,1,2,4,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,3,2,4,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]
[1,3,4,2,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]
[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,3,2,7,4,5,6,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,1,2,4,7,5,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,3,4,5,7,8,2,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]
[3,1,8,2,4,5,6,7]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]
[3,1,2,8,4,5,6,7]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]
[1,3,2,8,4,5,6,7]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]
[1,3,8,2,4,5,6,7]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]
[3,1,2,4,8,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[1,3,2,4,8,5,6,7]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]
[1,3,4,2,8,5,6,7]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]
[1,3,4,8,2,5,6,7]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]
[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[1,3,2,4,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[1,3,4,2,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[1,3,4,5,2,8,6,7]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[1,3,4,5,8,2,6,7]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[4,1,5,2,6,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,5,1,2,6,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,1,5,6,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,1,5,2,6,8,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,5,1,2,6,8,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,1,5,6,2,8,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,5,1,6,2,8,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,1,5,6,8,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,5,6,8,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[4,1,5,6,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,6,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,6,2,7,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,1,5,6,7,2,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,6,7,2,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,1,5,2,6,7,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,2,6,7,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,6,2,7,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,1,5,6,7,2,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,6,7,2,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,6,1,7,2,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,6,7,1,2,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,1,5,6,7,8,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,1,6,7,8,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,5,6,7,1,8,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[4,1,5,2,7,3,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,2,7,3,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,7,2,3,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,5,2,7,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,2,7,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,5,7,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,7,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,7,8,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,5,2,7,3,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,2,7,3,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,2,3,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,2,5,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,2,5,7,3,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,2,5,7,3,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,2,7,3,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,7,2,3,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,5,2,3,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,2,5,3,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,5,2,3,7,8,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,2,5,7,3,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,2,5,7,3,8,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,2,7,3,8,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,7,2,3,8,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,2,5,7,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,2,5,7,8,3,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,2,7,8,3,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,5,7,8,2,3,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,5,2,8,3,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[4,5,1,2,8,3,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[4,5,1,8,2,3,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[4,1,5,2,3,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[4,5,1,2,3,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[4,1,2,5,3,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[1,4,2,5,3,8,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[1,4,5,2,3,8,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[4,1,2,5,8,3,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[1,4,2,5,8,3,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[1,4,5,2,8,3,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[1,4,2,5,3,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[4,1,2,5,6,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[1,4,5,2,6,3,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[4,1,2,5,6,8,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[1,4,5,2,6,8,3,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[1,4,5,6,8,2,3,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[1,4,2,5,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[4,1,2,5,6,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,4,5,2,6,3,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[4,1,2,5,6,7,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,4,2,5,6,7,3,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[1,4,5,6,7,2,3,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[4,1,2,5,6,7,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,4,5,2,6,7,8,3]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[1,4,5,6,7,2,8,3]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[4,1,6,2,7,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,6,7,2,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,6,7,1,2,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,6,7,1,2,8,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,6,7,8,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,6,2,7,3,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,6,7,2,3,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,6,1,7,2,3,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,6,2,3,7,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,6,1,2,3,7,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,2,6,3,7,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,2,6,3,7,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[4,1,2,6,7,3,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,2,6,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[4,1,6,2,3,7,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,2,6,3,7,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,6,2,3,7,8,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[4,1,2,6,7,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,6,2,7,3,8,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,4,2,6,7,8,3,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,4,6,2,7,8,3,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,4,6,7,2,8,3,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[4,1,6,2,8,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[4,6,1,2,8,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[4,1,6,8,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[4,6,1,8,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[4,6,1,2,3,8,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[4,1,2,6,3,8,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,4,2,6,3,8,5,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,4,6,2,3,8,5,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,4,2,6,8,3,5,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,4,6,2,8,3,5,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,4,6,8,2,3,5,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[4,1,2,6,3,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,4,2,6,3,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[4,1,2,3,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,4,2,3,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[4,1,2,3,6,8,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,2,4,3,6,8,5,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,2,4,6,3,8,5,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,2,4,6,8,3,5,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,4,2,6,3,5,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[4,1,2,3,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,2,3,6,5,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,2,4,6,3,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[4,1,2,3,6,7,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[4,1,2,3,6,7,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,2,3,6,7,8,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[4,1,7,2,8,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[4,7,1,2,8,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[4,7,1,8,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[4,1,7,2,3,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,4,2,7,3,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,7,2,3,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,2,7,8,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,4,2,7,8,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,7,2,3,5,8,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[4,1,2,7,3,5,8,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,4,2,7,3,5,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,7,2,3,5,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,2,3,7,5,8,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,2,4,3,7,5,8,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,2,3,7,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,4,2,3,7,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,2,4,7,3,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,2,4,7,8,3,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,4,2,7,3,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,2,3,7,5,6,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,2,3,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,2,3,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[4,1,2,3,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,4,2,3,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,2,4,5,7,3,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]
[4,8,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[4,1,2,8,3,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[1,4,2,8,3,5,6,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]
[1,4,8,2,3,5,6,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]
[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[1,4,2,3,8,5,6,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]
[1,2,4,3,8,5,6,7]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]
[1,2,4,8,3,5,6,7]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]
[4,1,2,3,5,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[1,4,2,3,5,8,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[1,2,4,3,5,8,6,7]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]
[1,2,4,5,3,8,6,7]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]
[1,2,4,5,8,3,6,7]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]
[4,1,2,3,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[1,4,2,3,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[1,2,4,5,6,8,3,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]
[1,4,2,3,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[5,1,6,2,7,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,1,2,7,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,6,7,2,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,1,7,2,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,7,1,2,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,6,7,2,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,7,1,2,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,6,7,8,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,1,7,8,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,7,1,8,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,6,2,7,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,6,2,3,7,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,2,6,3,7,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,2,6,3,7,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[5,1,2,6,7,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,2,6,7,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[5,1,6,2,3,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,6,1,2,3,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,2,6,3,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,2,6,3,7,8,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[1,5,6,2,3,7,8,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[5,1,2,6,7,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,6,7,2,3,8,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[5,1,2,6,7,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,6,7,8,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[5,1,6,2,8,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[5,6,1,2,8,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[5,6,8,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[5,1,6,2,3,8,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[5,6,1,2,3,8,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[5,1,2,6,3,8,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[1,5,2,6,3,8,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,5,6,2,3,8,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[5,1,2,6,8,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[1,5,2,6,8,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,5,6,2,8,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,5,6,8,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[5,1,2,6,3,4,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[1,5,2,6,3,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,5,6,2,3,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,5,2,3,6,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,2,5,3,6,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]
[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]
[5,1,2,3,6,8,4,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[1,5,2,3,6,8,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,2,5,6,3,8,4,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]
[1,2,5,6,8,3,4,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]
[5,1,6,2,3,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[5,1,2,6,3,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,2,6,3,4,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[5,1,2,3,6,7,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,2,5,6,3,7,4,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[5,1,2,3,6,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,5,2,3,6,7,8,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[1,2,5,3,6,7,8,4]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[1,2,5,6,3,7,8,4]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[1,2,5,6,7,8,3,4]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[5,1,7,2,8,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[5,7,1,2,8,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[5,7,8,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[5,1,2,7,3,8,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,5,2,7,3,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,5,7,2,3,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[5,1,2,7,8,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,5,2,7,8,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,5,7,2,8,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,5,7,8,2,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[5,1,7,2,3,4,8,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[5,1,2,7,3,4,8,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,5,2,7,3,4,8,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,5,7,2,3,4,8,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[5,1,2,3,7,4,8,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,5,2,3,7,4,8,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,2,5,3,7,4,8,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,2,5,7,3,4,8,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[5,1,2,3,7,8,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,5,2,3,7,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,2,5,3,7,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,2,5,7,8,3,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[5,7,1,2,3,4,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[5,1,2,7,3,4,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,5,2,7,3,4,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,2,5,7,3,4,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,5,2,3,4,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,2,3,5,7,4,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,5,2,3,4,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,2,5,3,4,7,8,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,2,3,5,7,4,8,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,2,3,5,7,8,4,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[5,1,2,8,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]
[1,5,2,8,3,4,6,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[1,5,2,3,8,4,6,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[1,2,5,3,8,4,6,7]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]
[1,2,5,8,3,4,6,7]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]
[1,5,2,3,4,8,6,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[1,2,5,3,4,8,6,7]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]
[1,2,3,5,4,8,6,7]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]
[1,2,3,5,8,4,6,7]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]
[1,5,2,3,4,6,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,2,3,5,6,8,4,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]
[1,5,2,3,4,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[6,1,7,2,8,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,1,7,8,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,7,1,8,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,1,7,2,3,8,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,7,1,2,3,8,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,1,2,7,3,8,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,6,2,7,3,8,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,7,2,3,8,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,7,2,8,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,7,8,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[6,1,7,2,3,4,8,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,7,1,2,3,4,8,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[6,1,2,7,3,4,8,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,6,2,7,3,4,8,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,7,2,3,4,8,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,2,3,7,4,8,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,2,6,3,7,4,8,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,2,6,7,3,4,8,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[6,1,2,3,7,8,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,2,6,3,7,8,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,2,6,7,3,8,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[6,1,7,2,3,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,6,2,7,3,4,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,7,2,3,4,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,6,2,3,4,7,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,2,6,3,4,7,5,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,2,3,6,4,7,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[6,1,2,3,4,7,8,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,6,2,3,4,7,8,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,2,6,3,4,7,8,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,2,3,6,4,7,8,5]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[1,2,3,6,7,4,8,5]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[1,2,3,6,7,8,4,5]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[6,1,8,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[6,1,2,8,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[1,6,2,8,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,6,8,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,6,2,3,8,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,2,6,3,8,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[1,2,6,8,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[1,6,2,3,4,8,5,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,2,6,3,4,8,5,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[1,2,3,6,4,8,5,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]
[6,1,2,3,4,5,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[1,6,2,3,4,5,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,2,6,3,4,5,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[1,2,3,6,4,5,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]
[1,2,3,4,6,8,5,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]
[1,6,2,3,4,5,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,2,6,3,4,5,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,2,3,6,4,5,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[7,1,2,8,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,7,2,8,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]
[1,7,8,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]
[7,1,2,3,8,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,2,7,8,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]
[1,2,7,3,4,8,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]
[1,2,3,7,4,8,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]
[1,2,3,7,8,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]
[1,2,7,3,4,5,8,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]
[1,2,3,7,4,5,8,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]
[1,2,3,4,7,5,8,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]
[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]
[1,2,7,3,4,5,6,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]
[1,2,3,7,4,5,6,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]
[1,2,3,4,7,5,6,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]
[1,8,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]
[1,2,8,3,4,5,6,7]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]
[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]
[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]
[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]
[5,3,2,6,1,4,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[7,3,2,5,4,8,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[8,4,5,2,3,7,6,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[7,4,5,2,3,8,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[6,4,5,2,3,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[5,4,6,2,1,3,8,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[3,6,1,5,4,2,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[4,6,5,1,3,2,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[5,6,4,3,1,2,8,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,4,3,8,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[5,7,4,3,1,8,2,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[4,7,5,1,3,8,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[3,7,1,5,4,8,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[2,1,7,5,4,8,3,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[3,8,1,5,4,7,6,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[4,8,5,1,3,7,6,2]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[4,8,6,1,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[3,8,1,6,7,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[2,1,8,6,7,4,5,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[2,1,7,6,8,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[3,7,1,6,8,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[4,7,6,1,8,3,2,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[5,7,6,8,1,3,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,4,7,2,1,8,3,6]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,4,7,2,8,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[7,4,6,2,8,3,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[8,4,6,2,7,3,5,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,3,2,6,7,4,5,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]
[7,3,2,6,8,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[5,3,2,7,1,8,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[4,3,2,1,7,8,5,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[3,4,1,2,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[4,5,8,1,2,7,6,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]
[3,5,1,8,2,7,6,4]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[2,1,5,8,3,7,6,4]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[2,1,6,8,7,3,5,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[3,6,1,8,7,2,5,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[4,6,8,1,7,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[5,7,8,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[4,7,8,1,6,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[3,7,1,8,6,5,2,4]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[2,1,7,8,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[3,2,5,1,4,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[3,2,6,1,4,5,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[6,3,5,1,2,4,7,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,4,7,1,2,3,6,8]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[6,2,7,1,3,4,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[6,3,7,1,2,4,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[6,4,7,1,2,3,5,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[7,3,5,1,2,4,6,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,4,6,1,2,3,5,8]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[3,2,8,1,4,5,6,7]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]
[5,4,8,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[6,2,8,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]
[6,5,8,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[7,5,8,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[8,3,5,1,2,4,6,7]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[8,3,6,1,2,4,5,7]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[8,4,7,1,2,3,5,6]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]
[8,5,7,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[3,2,5,7,1,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,2,6,7,1,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[5,3,6,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[3,2,5,8,1,4,6,7]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[4,2,5,8,1,3,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[4,3,5,8,1,2,6,7]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[5,2,4,8,1,3,6,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[3,2,6,8,1,4,5,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[6,2,4,8,1,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,2,5,8,1,3,4,7]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[3,2,7,8,1,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]
[4,3,7,8,1,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[5,4,7,8,1,2,3,6]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[6,2,7,8,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[6,3,7,8,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[6,4,7,8,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[7,2,4,8,1,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,3,5,8,1,2,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,4,5,8,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[8,2,4,7,1,3,5,6]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[8,2,5,7,1,3,4,6]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[8,3,5,7,1,2,4,6]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[8,2,6,7,1,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]
[8,4,6,7,1,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[4,6,2,5,1,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[4,6,3,5,1,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,6,2,4,1,3,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,7,3,5,1,2,6,8]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[5,7,2,4,1,3,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[3,7,2,6,1,4,5,8]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[5,7,2,6,1,3,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[6,7,2,5,1,3,4,8]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[4,8,2,5,1,3,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[5,8,3,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[6,8,3,5,1,2,4,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[3,8,2,7,1,4,5,6]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]
[4,8,2,7,1,3,5,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[4,8,3,7,1,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[5,8,2,7,1,3,4,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[5,8,3,7,1,2,4,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[6,8,2,7,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]
[6,8,3,7,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[6,8,5,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[7,8,2,4,1,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,8,2,5,1,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[7,8,3,5,1,2,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,4,6,1,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[4,3,2,6,1,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[5,3,2,6,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,4,2,6,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[6,5,2,4,1,3,7,8]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[4,3,2,7,1,5,6,8]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[5,3,2,7,1,4,6,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[6,3,2,7,1,4,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[6,4,3,7,1,2,5,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,5,3,7,1,2,4,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[7,3,2,5,1,4,6,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,4,2,5,1,3,6,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,3,2,6,1,4,5,8]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[7,4,3,6,1,2,5,8]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,5,2,6,1,3,4,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[7,5,3,6,1,2,4,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,6,3,5,1,2,4,8]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[4,3,2,8,1,5,6,7]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]
[5,3,2,8,1,4,6,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[6,3,2,8,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[6,4,3,8,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,5,2,8,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,5,3,8,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,3,2,8,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[7,4,2,8,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,5,3,8,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,6,2,8,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[8,4,2,5,1,3,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[8,3,2,6,1,4,5,7]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]
[8,4,2,6,1,3,5,7]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,5,3,6,1,2,4,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,6,2,4,1,3,5,7]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,6,2,5,1,3,4,7]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,3,2,7,1,4,5,6]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]
[8,4,2,7,1,3,5,6]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[8,4,3,7,1,2,5,6]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[8,5,2,7,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[8,5,3,7,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,6,3,7,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[8,7,2,4,1,3,5,6]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[8,7,2,5,1,3,4,6]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[8,7,3,5,1,2,4,6]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[8,7,2,6,1,3,4,5]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]
[8,7,3,6,1,2,4,5]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]
[8,7,4,6,1,2,3,5]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[5,6,2,4,8,1,3,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[4,7,3,5,8,1,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[4,7,3,6,8,1,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[5,7,4,6,8,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[3,8,2,5,7,1,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[4,8,3,5,7,1,2,6]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[3,8,2,6,7,1,4,5]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]
[6,8,2,5,7,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,8,4,5,7,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[7,8,2,4,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,8,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[7,8,2,5,6,1,3,4]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[7,8,3,5,6,1,2,4]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[4,3,2,6,8,1,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[5,4,2,6,8,1,3,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[5,4,3,6,8,1,2,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[6,3,2,5,8,1,4,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,4,3,5,8,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,5,2,4,8,1,3,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[4,3,2,7,8,1,5,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[5,3,2,7,8,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,4,2,7,8,1,3,6]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,4,3,7,8,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,5,2,7,8,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,4,2,5,8,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,5,3,6,8,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,4,2,5,7,1,3,6]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[8,5,2,6,7,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[8,5,3,6,7,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,6,2,5,7,1,3,4]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,6,3,5,7,1,2,4]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[8,7,2,4,6,1,3,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[8,7,3,4,6,1,2,5]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[8,7,2,5,6,1,3,4]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[4,3,7,2,6,1,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[5,3,7,2,6,1,4,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,4,7,2,6,1,3,8]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,3,7,2,5,1,4,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,4,7,2,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[7,3,6,2,5,1,4,8]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[4,3,8,2,6,1,5,7]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[5,3,8,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[5,4,8,2,6,1,3,7]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,4,8,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,4,8,3,5,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[4,3,8,2,7,1,5,6]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]
[5,3,8,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[5,4,8,2,7,1,3,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,4,8,2,7,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[7,3,8,2,5,1,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,4,8,3,5,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[7,5,8,2,4,1,3,6]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[7,5,8,2,6,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[7,5,8,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[8,3,6,2,5,1,4,7]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]
[8,4,6,2,5,1,3,7]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,3,7,2,5,1,4,6]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,4,7,3,5,1,2,6]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[8,3,7,2,6,1,4,5]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[8,4,7,2,6,1,3,5]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,4,7,3,6,1,2,5]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,5,7,2,6,1,3,4]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[8,6,7,2,4,1,3,5]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,6,7,2,5,1,3,4]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,6,7,3,5,1,2,4]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[6,5,3,2,7,1,4,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,5,4,2,7,1,3,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[7,5,3,2,6,1,4,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[5,4,3,2,8,1,6,7]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[6,5,3,2,8,1,4,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,5,4,3,8,1,2,7]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[7,5,3,2,8,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,6,4,3,8,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[8,5,3,2,6,1,4,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[8,5,4,2,6,1,3,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[8,6,3,2,5,1,4,7]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,6,5,2,4,1,3,7]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,5,3,2,7,1,4,6]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,6,3,2,7,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[8,7,3,2,5,1,4,6]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[8,7,3,2,6,1,4,5]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]
[8,7,4,2,6,1,3,5]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[8,7,4,3,6,1,2,5]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[8,7,5,2,6,1,3,4]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[8,7,6,2,4,1,3,5]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[8,7,6,2,5,1,3,4]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[8,7,6,3,5,1,2,4]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[4,8,3,7,2,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[5,8,3,7,2,6,1,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[5,8,4,7,2,6,1,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,8,4,7,3,6,1,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[6,8,3,7,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,8,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,8,4,7,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,8,5,7,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[6,8,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,8,3,6,2,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[7,8,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,8,4,6,3,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,8,5,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[6,4,3,8,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[6,5,3,8,2,7,1,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,4,3,8,2,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,5,4,8,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[7,6,3,8,2,5,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[7,6,4,8,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[7,6,5,8,2,4,1,3]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[8,5,3,7,2,6,1,4]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,6,4,7,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[8,6,4,7,3,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[8,6,5,7,2,4,1,3]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[8,7,4,6,3,5,1,2]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[8,7,5,6,2,4,1,3]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[8,7,4,3,2,6,1,5]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[8,7,5,3,2,6,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[8,7,5,4,2,6,1,3]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[8,7,6,3,2,5,1,4]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[8,7,6,5,2,4,1,3]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[8,1,2,3,7,4,5,6]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]
[8,1,2,5,3,4,6,7]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]
[6,1,2,5,3,8,4,7]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[8,1,2,6,3,7,4,5]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]
[4,1,2,8,7,3,5,6]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]
[4,1,2,7,6,3,8,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[8,1,2,5,6,3,4,7]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]
[8,1,2,7,6,3,4,5]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]
[7,1,2,5,6,3,8,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[4,1,2,5,8,7,3,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]
[8,1,2,5,6,7,3,4]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]
[3,1,7,2,6,4,8,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[3,1,8,2,6,7,4,5]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[8,1,4,2,3,5,6,7]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]
[7,1,4,2,3,5,8,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[6,1,4,2,3,8,5,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[7,1,5,2,3,4,8,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[6,1,5,2,3,8,4,7]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[6,1,8,2,3,7,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[6,1,5,2,3,7,8,4]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]
[5,1,4,2,8,3,6,7]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[5,1,4,2,7,3,8,6]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[8,1,4,2,6,3,5,7]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[7,1,4,2,6,3,8,5]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[8,1,5,2,6,3,4,7]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]
[8,1,5,2,7,3,4,6]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]
[7,1,8,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]
[7,1,5,2,6,3,8,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[5,1,4,2,8,7,3,6]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[8,1,4,2,6,7,3,5]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[8,1,5,2,6,7,3,4]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]
[5,1,4,2,6,7,8,3]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[3,1,8,6,2,4,5,7]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[3,1,6,5,2,8,4,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[3,1,8,5,2,7,4,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[3,1,8,6,2,7,4,5]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[8,1,4,5,2,3,6,7]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]
[7,1,8,5,2,3,4,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[7,1,8,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]
[7,1,6,5,2,3,8,4]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[3,1,4,8,6,2,5,7]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[3,1,8,5,7,2,4,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[3,1,7,5,6,2,8,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[8,1,4,5,7,2,3,6]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]
[8,1,4,7,6,2,3,5]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[3,1,8,5,6,7,2,4]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[8,1,4,5,6,7,2,3]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]
[2,8,1,3,7,4,5,6]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]
[2,8,1,3,6,7,4,5]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]
[2,4,1,8,3,7,5,6]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[2,6,1,5,3,8,4,7]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[2,6,1,5,3,7,8,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[2,4,1,8,6,3,5,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[2,8,1,7,6,3,4,5]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]
[2,4,1,5,8,7,3,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[7,3,1,2,4,5,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[6,3,1,2,4,8,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[6,3,1,2,4,7,8,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[5,3,1,2,8,4,6,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[8,3,1,2,6,4,5,7]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[8,3,1,2,7,4,5,6]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]
[7,3,1,2,6,4,8,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[5,3,1,2,8,7,4,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,3,1,2,6,7,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[8,4,1,2,3,7,5,6]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]
[7,6,1,2,3,4,8,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[8,6,1,2,3,7,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[5,4,1,2,8,3,6,7]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[7,4,1,2,6,3,8,5]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[5,8,1,2,7,3,4,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]
[8,7,1,2,6,3,4,5]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]
[5,7,1,2,6,3,8,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[8,4,1,2,6,7,3,5]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[5,8,1,2,6,7,3,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]
[5,4,1,2,6,7,8,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[4,3,1,8,2,5,6,7]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[4,3,1,7,2,5,8,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[4,3,1,6,2,8,5,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[4,3,1,6,2,7,8,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[8,3,1,5,2,4,6,7]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[8,3,1,6,2,4,5,7]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[7,3,1,6,2,4,8,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[8,3,1,5,2,7,4,6]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[8,3,1,6,2,7,4,5]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[6,3,1,5,2,7,8,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[7,4,1,5,2,3,8,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[8,4,1,6,2,3,5,7]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[7,4,1,8,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[7,4,1,6,2,3,8,5]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[8,7,1,6,2,3,4,5]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]
[6,7,1,5,2,3,8,4]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]
[6,4,1,5,2,8,3,7]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[8,4,1,6,2,7,3,5]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[6,8,1,5,2,7,3,4]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[6,4,1,5,2,7,8,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[4,3,1,8,7,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[4,3,1,7,6,2,8,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[8,3,1,5,6,2,4,7]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[8,3,1,5,7,2,4,6]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[8,3,1,7,6,2,4,5]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[7,3,1,5,6,2,8,4]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[4,3,1,5,6,8,2,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[8,4,1,5,6,7,2,3]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[4,3,1,5,6,7,8,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[2,3,7,1,6,4,8,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]
[2,3,5,1,8,7,4,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[2,3,8,1,6,7,4,5]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]
[2,8,4,1,3,5,6,7]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[2,6,4,1,3,8,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,6,4,1,3,7,8,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,6,5,1,3,7,8,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[2,8,4,1,7,3,5,6]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[2,7,4,1,6,3,8,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[2,8,5,1,7,3,4,6]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[2,7,5,1,6,3,8,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,5,4,1,6,7,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[6,3,4,1,2,7,8,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[7,3,5,1,2,4,8,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,3,7,1,2,4,8,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[8,3,5,1,2,7,4,6]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[6,3,8,1,2,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[6,7,4,1,2,3,8,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[6,8,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[8,5,4,1,2,7,3,6]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[6,8,4,1,2,7,3,5]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[6,8,5,1,2,7,3,4]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[8,3,4,1,7,2,5,6]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]
[7,3,4,1,6,2,8,5]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[8,3,5,1,6,2,4,7]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[7,3,8,1,6,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[7,3,5,1,6,2,8,4]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[8,5,4,1,6,2,3,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[7,8,4,1,6,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[7,8,5,1,6,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[7,5,4,1,6,2,8,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[5,3,4,1,6,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[2,3,4,8,1,7,5,6]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]
[2,3,7,6,1,4,8,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]
[2,3,6,5,1,8,4,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[2,3,6,5,1,7,8,4]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[2,7,4,8,1,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[2,7,4,6,1,3,8,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[2,8,6,5,1,3,4,7]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[2,7,8,5,1,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,7,6,5,1,3,8,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[2,6,4,5,1,8,3,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,8,4,6,1,7,3,5]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[7,3,8,5,1,2,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[8,6,4,5,1,7,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[2,3,4,8,6,1,5,7]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,4,8,7,1,5,6]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]
[2,3,4,7,6,1,8,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[2,3,8,5,7,1,4,6]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]
[2,3,7,5,6,1,8,4]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,8,4,7,6,1,3,5]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[2,8,7,5,6,1,3,4]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[8,3,4,7,6,1,2,5]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[8,3,7,5,6,1,2,4]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[2,3,4,5,8,7,1,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]
[2,3,4,8,6,7,1,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,8,4,5,6,7,1,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[6,5,8,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[4,6,7,3,8,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[3,6,7,4,5,8,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[2,6,7,4,5,1,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,5,4,7,6,2,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[2,5,4,7,6,1,8,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[3,5,4,7,6,8,1,2]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[4,5,3,7,8,6,1,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[5,4,3,8,7,6,1,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[6,4,8,3,7,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,3,8,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[5,3,4,8,6,7,1,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[4,3,5,6,8,7,1,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[3,2,5,6,1,8,7,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[4,2,5,6,8,1,7,3]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[5,2,4,8,6,1,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[7,8,2,4,5,1,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,8,1,4,5,2,3,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[6,1,8,4,5,2,3,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,1,4,8,6,2,3,7]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[4,1,3,2,8,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[5,1,3,8,2,6,4,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[6,1,8,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,8,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,2,3,1,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]
[6,2,8,3,1,5,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[6,3,8,2,1,7,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,8,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[7,8,4,2,6,1,5,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[5,4,2,8,7,1,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[4,5,2,7,8,1,6,3]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[3,5,2,7,1,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[2,5,3,7,1,6,8,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,6,7,3,2,5,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[2,6,7,3,1,5,8,4]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[3,6,7,2,1,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[4,6,7,2,8,1,5,3]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[5,6,7,8,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[7,8,5,6,2,1,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[6,5,8,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[5,4,1,8,7,2,3,6]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[6,4,8,1,7,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[7,8,3,1,2,6,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[5,3,1,8,2,7,4,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[4,3,1,2,8,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[4,2,1,3,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[5,2,1,8,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[6,2,8,1,3,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]
[7,8,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]
[4,5,2,3,7,6,1,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[6,4,3,7,2,5,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[8,4,3,6,5,1,2,7]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,5,6,3,4,8,7,2]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[4,6,2,7,3,5,1,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,2,6,7,4,5,1,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[8,7,5,4,1,3,2,6]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[5,8,6,2,4,1,3,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[4,8,2,6,5,1,3,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,1,2,6,5,8,7,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[5,1,6,2,4,8,7,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[6,1,5,4,2,8,7,3]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[8,1,5,4,7,6,2,3]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,8,6,7,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[8,1,6,7,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[6,1,7,8,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[5,1,7,2,8,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[4,1,2,7,8,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[3,2,1,7,8,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,8,7,1,5,4,6]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[4,8,2,7,1,5,3,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[5,8,7,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,8,7,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[7,8,6,1,4,2,3,5]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[8,7,6,1,4,3,2,5]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,6,7,8,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[8,6,7,1,3,4,2,5]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[7,6,8,1,3,2,4,5]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[5,7,8,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[4,7,2,8,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[3,2,6,8,4,1,5,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[4,6,2,8,3,1,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[5,6,8,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[7,5,8,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,5,7,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,5,7,3,8,4,6,2]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,4,3,7,8,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]
[6,4,3,8,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[4,5,2,3,8,1,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[3,2,5,4,8,1,6,7]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[4,5,2,3,1,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[6,4,3,1,2,8,7,5]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[8,4,3,1,7,6,2,5]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,5,8,3,7,6,4,2]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[7,5,1,3,8,2,6,4]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[5,6,1,2,3,8,7,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[4,6,2,1,3,8,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[3,2,6,1,4,8,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[3,2,7,1,8,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[5,7,1,2,8,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[6,7,1,8,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[7,6,1,8,3,2,5,4]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[8,7,1,6,5,3,2,4]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[7,8,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[6,8,1,7,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[5,8,1,2,7,6,3,4]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]
[3,2,8,1,7,6,4,5]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[4,1,2,8,7,6,5,3]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[5,1,8,2,7,6,4,3]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[6,1,8,7,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[8,1,7,6,5,4,2,3]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[3,2,5,1,6,4,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[3,2,5,4,7,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,2,5,3,7,6,8,1]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[4,2,5,3,7,1,8,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[4,2,5,3,6,1,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[4,2,5,1,6,3,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[3,1,5,4,6,2,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[4,1,5,3,6,2,8,7]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[4,1,5,3,7,2,8,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[3,1,5,4,7,2,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[2,1,5,4,7,3,8,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[3,1,5,4,7,6,8,2]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[4,1,5,3,7,6,8,2]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[4,3,6,5,7,1,8,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,3,6,4,7,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,1,6,3,7,4,8,2]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[4,1,6,3,7,5,8,2]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[3,1,6,4,7,5,8,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[2,1,6,4,7,5,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,1,6,4,7,3,8,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,1,6,4,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[4,1,6,3,7,2,8,5]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,1,6,3,7,2,8,4]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,3,6,2,7,4,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,2,6,3,7,4,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[5,2,6,3,7,1,8,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[5,2,6,1,7,3,8,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[4,2,5,1,7,3,8,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[4,2,6,1,7,3,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[4,2,6,3,7,1,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[4,2,6,3,7,5,8,1]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,2,6,4,7,5,8,1]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,2,6,4,7,1,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,2,6,1,7,4,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,2,5,1,7,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,2,4,1,7,5,8,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[3,1,4,2,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[3,2,5,1,7,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,2,6,1,7,5,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[4,2,6,1,7,5,8,3]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[4,2,5,1,7,6,8,3]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[4,1,5,2,7,6,8,3]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[3,1,5,2,7,6,8,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[2,1,5,3,7,6,8,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,1,6,3,7,5,8,4]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[3,1,6,2,7,5,8,4]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[4,1,6,2,7,5,8,3]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[5,1,6,2,7,4,8,3]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[5,2,6,1,7,4,8,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,4,6,2,7,1,8,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,1,6,4,7,2,8,3]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[3,1,6,5,7,2,8,4]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[3,1,6,5,7,4,8,2]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[4,1,6,5,7,3,8,2]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,1,6,4,7,3,8,2]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[8,6,1,3,4,2,5,7]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[8,3,5,2,1,6,4,7]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[8,6,3,5,2,4,1,7]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,3,7,5,2,4,6,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,2,4,5,7,3,6,1]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]
[2,4,5,7,3,1,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[8,2,4,6,5,3,1,7]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]
[8,1,2,4,5,6,3,7]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]
[8,2,5,1,3,6,4,7]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]
[8,6,1,4,5,3,2,7]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[8,1,5,6,4,3,2,7]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]
[8,5,7,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[8,5,7,4,2,1,6,3]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[4,6,3,8,7,1,5,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,7,4,8,6,3,5,2]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]
[8,4,7,6,3,5,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[4,8,1,6,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[3,6,4,1,8,7,5,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[8,2,6,1,4,7,5,3]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[2,7,6,8,1,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[3,7,6,5,8,2,1,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,6,8,5,7,2,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[2,1,6,5,7,8,3,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[5,2,7,1,3,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[5,3,1,7,8,2,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[3,7,2,6,4,8,1,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[3,2,6,1,4,7,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[5,3,7,2,1,8,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[4,7,3,2,1,5,8,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[1,7,3,4,2,5,8,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]
[4,7,2,1,3,5,8,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[8,7,6,1,3,4,2,5]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[8,5,7,3,2,1,6,4]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,7,6,3,5,2,4,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[2,7,4,8,1,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,6,8,2,1,7,5,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[8,5,3,7,1,6,2,4]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,5,7,2,1,3,6,4]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[4,6,1,8,7,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[8,1,2,5,6,7,4,3]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]
[8,2,6,5,7,4,1,3]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]
[2,1,7,8,5,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,7,6,8,5,4,1,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[1,7,2,5,8,6,4,3]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]
[3,7,8,1,6,5,2,4]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[8,7,6,3,5,1,4,2]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[8,4,7,6,5,1,3,2]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,7,1,5,6,4,3,2]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[8,1,6,7,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]
[3,2,5,1,6,8,4,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[3,6,2,5,4,8,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,5,2,4,7,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,5,8,2,4,7,6,1]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[4,2,6,5,3,8,1,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[5,3,1,6,8,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,6,2,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[5,4,3,2,7,1,8,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[5,4,3,8,2,7,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[4,3,6,2,8,7,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,3,7,6,2,1,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[6,4,3,1,7,2,8,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,4,7,5,8,3,2,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]
[2,8,5,7,4,6,1,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[3,5,8,7,1,4,6,2]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[4,3,7,1,8,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[4,8,3,7,6,5,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[7,5,3,1,8,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[1,5,8,6,3,7,4,2]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[6,2,8,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,1,7,5,3,2,8,4]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,2,6,3,8,7,4,1]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[6,5,2,1,7,3,8,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[6,1,7,4,2,8,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[6,7,2,1,8,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[7,5,8,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[5,7,3,1,8,2,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[4,7,1,5,2,8,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[2,4,8,6,3,7,5,1]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[3,8,6,2,4,7,5,1]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]
[7,3,6,2,4,1,8,5]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[3,5,2,7,1,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,3,7,8,2,1,5,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[8,3,7,1,4,6,2,5]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[3,8,2,5,7,1,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[7,8,3,6,2,1,5,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,7,3,6,2,5,4,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[4,2,6,8,1,7,5,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[5,8,3,7,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,8,7,2,6,1,3,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[8,6,2,7,5,1,3,4]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[6,4,8,1,7,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,1,6,8,2,7,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[6,5,2,8,1,7,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[5,2,7,1,8,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,8,2,7,6,4,3,1]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,2,8,7,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[6,1,7,2,8,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[4,7,1,8,6,2,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[8,7,4,6,1,5,3,2]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[8,5,7,1,6,4,3,2]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[6,8,1,7,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[7,1,8,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]
[4,1,3,2,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[6,3,5,1,2,4,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[4,3,5,6,1,2,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[8,3,7,5,2,1,4,6]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[6,3,7,5,1,8,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[6,5,2,7,1,8,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[3,5,2,6,4,1,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[6,1,2,4,5,3,8,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,6,3,2,1,4,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[2,1,6,3,5,4,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[6,4,3,5,1,2,8,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[5,3,1,4,6,2,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,7,4,6,2,8,3,1]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[3,4,7,8,5,2,1,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[2,1,8,5,7,3,4,6]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[8,6,3,5,1,7,4,2]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[3,4,8,6,5,7,1,2]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[5,1,4,6,8,2,7,3]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[2,5,4,6,7,1,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[2,4,6,3,7,5,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[4,1,6,3,8,5,7,2]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[3,7,4,2,8,6,5,1]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[2,1,5,7,4,8,6,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[3,1,8,2,7,6,5,4]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[4,3,7,2,6,8,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[2,8,1,3,6,5,7,4]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]
[8,1,2,3,5,6,7,4]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]
[7,8,2,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[6,8,3,2,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[2,1,8,3,4,6,7,5]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]
[2,1,7,8,5,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,7,3,8,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[7,1,8,4,5,3,2,6]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]
[8,7,1,6,3,4,2,5]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]
[5,3,8,7,4,2,6,1]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[8,3,6,1,4,2,7,5]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[7,3,5,8,2,4,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[2,3,4,1,8,5,7,6]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]
[4,1,3,2,8,5,7,6]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[2,1,4,3,8,5,7,6]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[4,1,3,2,6,7,8,5]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[8,3,5,6,2,7,1,4]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[5,3,6,1,8,7,2,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,6,2,8,7,4,1,3]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[7,8,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[8,1,6,4,5,7,2,3]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[5,8,3,6,1,7,2,4]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[2,1,8,6,5,7,3,4]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[2,1,7,5,3,6,8,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[7,1,4,2,5,6,8,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[2,7,4,1,6,5,8,3]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,1,2,5,8,6,7,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[7,3,5,4,6,1,8,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,3,4,1,5,7,8,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[3,1,4,5,6,8,7,2]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[4,5,2,6,3,1,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[6,5,2,1,4,3,8,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[8,5,2,7,4,1,6,3]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[8,3,7,5,2,1,6,4]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[6,3,7,5,2,8,4,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,3,1,5,2,4,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[3,1,6,5,4,2,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[5,4,3,6,1,2,8,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[5,6,3,2,4,1,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[6,7,2,3,4,8,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[8,7,2,3,4,1,6,5]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]
[5,1,7,3,8,4,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[2,5,7,3,8,6,4,1]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[3,6,7,4,1,8,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[5,6,3,7,4,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[2,1,6,7,4,8,5,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,1,8,7,4,3,6,5]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[5,8,3,7,4,2,6,1]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[5,8,7,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[2,8,6,3,1,5,7,4]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[8,1,6,3,2,5,4,7]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[2,8,4,1,6,3,7,5]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[4,8,1,2,7,6,3,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[6,8,3,5,2,7,4,1]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[2,1,8,5,3,7,4,6]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[6,5,3,2,8,7,1,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[2,4,1,8,7,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[4,1,2,8,7,5,6,3]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]
[8,4,2,1,7,5,3,6]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[4,3,1,8,6,7,5,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[3,1,4,8,6,5,7,2]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[7,3,5,4,8,6,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,4,3,5,8,1,7,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[2,1,7,6,5,8,3,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[5,7,3,6,1,8,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[2,7,6,4,5,8,1,3]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[3,7,5,6,8,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,1,6,8,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[8,6,2,5,1,7,4,3]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[7,5,2,6,3,8,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[4,1,2,3,6,8,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[2,4,3,1,8,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[7,5,2,8,3,4,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[4,7,2,8,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[8,7,2,1,4,5,6,3]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[3,6,8,7,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[5,7,8,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,7,3,8,1,4,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[2,1,7,8,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[7,5,8,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[2,4,8,3,5,6,1,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[4,1,8,3,6,5,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[8,4,1,3,7,2,6,5]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[4,3,8,2,5,1,7,6]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]
[2,1,4,8,3,5,7,6]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[6,8,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[4,8,2,3,5,1,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[7,8,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,8,4,2,1,5,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,8,2,1,6,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[6,4,1,2,5,7,3,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[4,3,8,1,7,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[6,3,1,4,7,2,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[7,8,1,4,6,2,5,3]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[7,8,3,5,4,2,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,8,4,1,2,3,6,5]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[7,8,2,6,4,1,3,5]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,8,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]
[2,1,8,7,5,4,3,6]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,3,8,2,6,4,7,5]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[5,3,7,1,6,4,8,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[6,1,2,5,8,7,4,3]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[6,3,1,8,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[6,4,2,1,5,3,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,4,3,7,5,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[4,3,8,7,5,6,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[2,4,7,1,5,3,6,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[3,7,2,8,6,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[3,8,1,7,6,4,5,2]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[2,7,5,8,3,6,1,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,5,6,8,2,4,7,3]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]
[2,6,1,4,7,3,5,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,6,8,4,7,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[5,6,7,3,8,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[4,5,6,7,2,8,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[4,5,7,6,1,8,3,2]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,5,8,6,2,7,3,4]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[4,7,5,6,3,1,8,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[5,1,6,3,4,2,8,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,7,1,4,2,3,8,6]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[5,7,6,4,3,8,1,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[6,3,4,5,8,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[6,2,4,1,8,3,7,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,2,3,5,4,8,1,7]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[5,1,4,2,7,6,8,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,6,2,4,7,8,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[5,7,2,4,1,6,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,1,4,2,8,5,3,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[6,7,5,8,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,8,7,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,8,7,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[4,1,7,2,6,5,3,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[4,8,2,1,5,6,3,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[4,2,7,8,1,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[2,1,8,7,6,5,3,4]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[4,2,7,1,6,3,8,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,3,7,5,6,8,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[3,8,6,5,2,4,1,7]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[3,8,5,6,1,4,7,2]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[5,3,7,8,2,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[3,6,7,8,5,1,4,2]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[3,7,8,5,1,2,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[4,1,8,6,2,3,5,7]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[3,8,7,6,5,4,1,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[2,8,6,7,5,1,3,4]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[5,3,7,8,2,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[7,6,1,2,5,8,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[2,1,7,8,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[7,8,1,2,5,4,6,3]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]
[8,4,1,3,7,6,2,5]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[6,5,2,1,8,7,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[4,7,2,8,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[3,4,7,1,8,2,6,5]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,8,2,4,3,5,6,7]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]
[1,7,2,4,3,5,6,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,5,2,4,3,6,7,8]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[1,7,2,5,3,4,6,8]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,8,2,5,3,4,6,7]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]
[1,8,2,6,3,4,5,7]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]
[1,8,2,7,3,4,5,6]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]
[1,8,2,7,3,5,4,6]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,7,2,8,3,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,6,2,8,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,5,2,8,3,6,4,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[1,4,2,8,3,6,5,7]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,3,2,8,4,6,5,7]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]
[1,2,3,8,4,6,5,7]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]
[1,2,3,7,4,6,5,8]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]
[1,3,2,7,4,6,5,8]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,4,2,7,3,6,5,8]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,5,2,7,3,6,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,6,2,7,3,5,4,8]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,7,2,6,3,5,4,8]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,8,2,6,3,5,4,7]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]
[1,8,2,5,3,6,4,7]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]
[1,7,2,5,3,6,4,8]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,6,2,5,3,7,4,8]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,5,2,4,3,7,6,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,6,2,4,3,7,5,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,7,2,4,3,6,5,8]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,8,2,4,3,6,5,7]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]
[1,8,2,4,3,7,5,6]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]
[1,7,2,4,3,8,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,6,2,4,3,8,5,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,5,2,4,3,8,6,7]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]
[1,6,2,5,3,8,4,7]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,7,2,5,3,8,4,6]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,8,2,5,3,7,4,6]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]
[1,8,2,6,3,7,4,5]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]
[1,7,2,6,3,8,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]
[1,2,3,8,4,7,5,6]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]
[1,3,2,8,4,7,5,6]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]
[1,4,2,8,3,7,5,6]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,5,2,8,3,7,4,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,6,2,8,3,7,4,5]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,7,2,8,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]
[1,8,2,7,3,6,4,5]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]
[2,8,4,1,6,5,3,7]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[2,8,4,1,5,6,7,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[2,8,7,4,1,6,3,5]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[7,2,8,5,1,6,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,3,7,5,2,6,4,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,3,7,5,4,2,6,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]
[7,2,8,5,4,1,6,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[2,8,5,3,4,1,6,7]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]
[2,8,7,6,1,4,5,3]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[2,8,6,5,7,3,1,4]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[6,2,3,8,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,3,2,8,5,1,4,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,4,8,5,2,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[6,4,8,5,1,3,7,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[4,3,7,1,5,6,8,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[3,6,1,7,5,2,8,4]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[3,4,1,2,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[3,5,2,6,4,8,7,1]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[4,3,2,1,8,6,5,7]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[4,2,1,3,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[7,1,6,8,4,3,5,2]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[6,1,2,8,4,5,7,3]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,6,8,2,3,1,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[6,5,8,2,4,3,1,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[6,5,8,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[7,5,3,8,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,6,5,7,3,4,2,8]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[5,2,1,8,7,6,3,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[7,1,3,8,4,6,2,5]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]
[5,7,8,4,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[4,1,8,3,5,6,7,2]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[4,1,8,3,6,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[2,3,4,8,6,1,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,3,4,8,6,5,1,7]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[2,7,3,5,8,6,1,4]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[3,2,4,7,8,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[1,5,4,6,2,7,3,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[5,2,4,7,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,3,6,4,1,8,7,2]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,3,6,1,4,8,2,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[7,3,5,6,8,4,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[6,3,5,1,8,2,7,4]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,7,1,6,3,8,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[3,2,4,1,7,8,5,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[2,5,4,6,1,7,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[7,3,4,1,2,6,5,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[7,4,3,2,1,6,5,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[6,7,3,2,5,4,8,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[1,8,3,2,5,4,7,6]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]
[1,8,4,5,2,3,7,6]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]
[1,8,5,4,3,2,7,6]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]
[6,4,7,5,1,3,8,2]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[3,2,1,8,5,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[2,3,8,1,5,4,7,6]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]
[2,4,8,5,1,3,7,6]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[2,6,8,4,3,7,1,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,7,8,4,3,6,5,1]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[2,7,8,5,6,3,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,5,8,6,7,1,3,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[2,4,8,6,1,7,3,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[3,2,1,8,6,7,4,5]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]
[5,3,7,1,6,8,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,4,7,6,1,8,3,2]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[4,5,7,6,8,1,3,2]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[4,6,7,5,8,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,8,5,6,7,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]
[4,6,5,7,8,2,1,3]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[5,4,6,7,1,8,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[5,3,6,1,7,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,2,1,6,7,8,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[6,2,1,5,7,3,8,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[6,3,5,1,7,2,8,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,6,4,7,2,8,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[1,8,4,6,2,7,3,5]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]
[1,8,3,2,6,7,4,5]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]
[5,7,3,2,6,8,4,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[6,5,3,2,7,1,8,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,4,3,2,1,7,8,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[6,2,1,4,3,7,8,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[4,5,3,2,8,1,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[4,6,3,2,8,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,7,3,2,8,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[1,8,3,2,7,6,5,4]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]
[1,8,4,7,2,6,5,3]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[3,6,4,8,2,7,1,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[3,4,5,8,1,2,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]
[4,2,1,5,8,3,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[4,2,1,6,8,7,3,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[3,4,6,8,1,7,2,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,5,6,8,7,1,2,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,6,5,8,7,2,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,6,7,8,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[3,5,7,8,6,1,4,2]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[4,2,1,7,8,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[2,3,8,1,7,6,5,4]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]
[2,4,8,7,1,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[8,1,6,7,3,2,5,4]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[8,1,6,7,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]
[8,1,2,4,3,6,5,7]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]
[8,1,4,3,2,7,6,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]
[8,1,5,3,7,2,6,4]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[8,1,3,5,6,2,7,4]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]
[6,3,2,1,4,5,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[4,7,8,5,6,1,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[3,7,8,5,6,2,1,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,7,8,4,2,6,1,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[3,7,8,2,4,5,1,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]
[3,6,2,8,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[2,3,6,7,4,5,8,1]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[3,5,2,4,8,6,1,7]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[3,5,4,2,8,7,1,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[6,4,5,1,7,8,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[5,4,2,3,1,8,6,7]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,5,3,1,8,2,7,4]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[6,5,4,1,8,7,2,3]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[7,5,1,4,8,6,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[7,4,1,3,2,8,6,5]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,4,1,2,3,8,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[6,4,2,1,3,8,5,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[2,6,4,8,3,7,5,1]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,6,5,8,7,3,4,1]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[6,5,2,1,8,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[7,5,1,2,8,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[7,6,1,8,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[7,6,1,8,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[6,7,8,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[6,7,8,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[4,2,6,7,3,1,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[4,7,8,2,3,1,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[4,7,8,3,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[5,7,8,3,1,2,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,7,8,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[4,6,3,8,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,2,5,3,7,1,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[5,3,6,7,1,2,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[3,5,6,7,8,2,1,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[7,4,6,1,8,3,5,2]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,3,5,1,8,4,6,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,3,4,1,8,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[4,5,7,3,1,8,6,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,6,5,2,7,4,3,8]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[7,4,3,1,8,6,5,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[3,6,7,5,1,8,4,2]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[7,5,6,1,8,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,6,5,1,8,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[6,4,2,1,8,7,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[2,6,5,1,7,8,4,3]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[4,5,7,1,6,8,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,7,1,3,8,2,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[6,4,1,2,8,5,3,7]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,3,1,2,8,6,4,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[4,3,1,2,8,6,5,7]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[6,1,2,5,8,3,4,7]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[7,1,3,4,8,2,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]
[2,6,1,5,7,8,3,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[7,6,1,5,8,3,2,4]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[3,6,7,1,5,8,2,4]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[7,1,6,5,8,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[7,5,1,6,8,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[7,4,1,6,8,5,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[5,2,3,1,8,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[7,3,1,5,8,6,2,4]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,2,4,1,8,5,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,2,5,1,8,4,7,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[7,1,6,4,8,2,5,3]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[7,1,5,3,8,2,6,4]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,1,5,2,8,3,7,4]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[7,3,1,4,8,6,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[6,2,1,4,8,7,3,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[5,2,1,3,8,7,4,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[7,4,1,3,8,5,2,6]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[6,1,4,2,8,3,7,5]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[7,1,4,3,8,2,6,5]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]
[3,6,7,1,4,8,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[7,6,1,4,8,3,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[5,1,3,2,8,4,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[4,2,1,3,8,7,5,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[2,6,1,4,7,8,3,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[7,1,3,5,8,2,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,1,3,6,2,5,4]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,3,8,4,7,2,5,6]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]
[4,6,1,2,5,7,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,8,2,5,7,3,6]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]
[7,8,4,2,5,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,8,1,5,4,6,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,8,2,1,6,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]
[7,8,3,5,6,4,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,4,5,3,1,6,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[2,6,4,8,3,7,1,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,4,6,8,3,7,5,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[2,4,8,5,3,1,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[2,5,8,1,4,7,6,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[2,1,8,4,7,3,6,5]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[3,5,8,4,7,6,1,2]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,6,2,4,7,3,8,5]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[5,6,2,1,4,7,8,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,7,5,1,3,6,8,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[5,7,3,6,1,4,8,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,3,6,7,2,1,8,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[6,3,1,2,4,5,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[1,4,7,2,5,3,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[6,4,7,3,5,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[3,5,6,7,8,1,4,2]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,6,5,7,8,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[2,7,5,6,8,4,1,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,1,6,8,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,7,1,8,5,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[3,7,6,8,5,4,1,2]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[4,3,8,5,6,7,1,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[4,2,8,1,6,3,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[3,1,8,5,4,6,7,2]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[3,4,2,8,6,1,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]
[1,7,3,8,5,2,6,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]
[4,1,8,3,6,2,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[5,7,8,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,8,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[7,6,5,8,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,6,4,3,8,2,5,7]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[2,6,3,4,5,8,1,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,6,4,1,8,3,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[3,6,4,5,8,7,1,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[7,2,1,4,8,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,1,6,5,3,8,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[7,2,5,6,3,8,1,4]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[5,6,2,7,3,1,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[5,7,6,4,1,8,3,2]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[6,7,1,5,2,8,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]
[6,1,5,2,8,3,4,7]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[7,5,2,4,3,1,6,8]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[6,8,1,3,7,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,4,2,6,5,1,3,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,2,3,5,4,1,6,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]
[6,8,1,2,3,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[2,5,1,7,8,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,3,6,8,4,7,1]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[2,5,7,8,1,4,6,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[3,5,7,4,1,6,2,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[5,2,8,4,6,1,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[5,2,1,8,6,3,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[4,2,8,5,7,6,3,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[4,1,2,8,5,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[1,4,2,7,5,8,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[5,8,4,7,6,2,1,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,8,7,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[6,4,8,3,1,7,2,5]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,3,1,8,7,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,1,8,4,6,2,7,3]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[5,8,7,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[6,8,5,3,1,2,7,4]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[4,5,1,2,7,6,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,5,1,2,6,8,7,3]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[3,5,6,1,8,4,7,2]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[4,2,6,1,7,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,5,2,7,8,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,1,4,7,5,6,2,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,1,4,5,8,6,7,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,6,8,5,2,7,1]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[4,2,5,6,1,8,7,3]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[2,1,7,5,8,6,4,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,2,7,5,3,8,6,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]
[4,1,2,7,3,8,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[7,1,4,2,5,3,8,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[6,1,3,7,5,2,4,8]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[3,7,1,2,5,4,8,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,3,7,2,4,8,6,5]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]
[3,2,7,8,1,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[2,4,1,7,8,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[2,6,8,3,1,5,7,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[3,6,4,8,5,1,7,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[6,3,7,4,5,1,8,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[2,6,3,7,5,8,1,4]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[5,2,1,7,8,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[5,7,4,6,2,8,1,3]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[4,2,8,3,6,7,1,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,8,3,1,7,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[5,2,8,4,7,1,6,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,8,4,7,3,1,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[4,6,8,3,1,7,5,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[6,3,8,2,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[3,5,1,8,2,7,4,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[7,5,1,3,6,2,4,8]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,5,4,1,2,6,3,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[5,1,8,4,2,7,3,6]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[4,1,6,2,8,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,6,2,8,5,3,7,4]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[6,8,5,3,1,7,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,6,7,3,1,8,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,6,2,1,7,8,4,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[8,4,5,1,2,6,3,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[5,6,3,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[1,6,3,7,2,8,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[6,4,7,2,8,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,7,4,8,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[4,5,7,8,3,1,6,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[4,7,2,5,8,1,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[5,7,3,8,2,6,1,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,4,7,8,2,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[8,1,3,4,6,2,5,7]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]
[3,8,2,4,6,7,1,5]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]
[2,4,5,6,8,1,7,3]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[8,4,3,6,5,1,7,2]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[8,6,5,4,3,1,7,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,8,6,5,2,7,3,4]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[8,7,5,4,1,6,3,2]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[7,8,5,4,1,3,6,2]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[6,8,5,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[3,2,8,6,5,1,7,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[5,1,7,3,6,2,4,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[8,1,6,5,2,3,7,4]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,2,8,3,7,4,5,6]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]
[8,1,7,2,6,3,5,4]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[7,1,8,2,6,4,3,5]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[5,1,8,3,2,7,4,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[3,2,1,8,4,7,5,6]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]
[3,2,8,7,1,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[4,8,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[5,8,7,2,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[8,7,6,1,5,4,3,2]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[8,6,7,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[7,6,8,1,4,3,5,2]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[6,7,8,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[5,7,8,2,1,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[4,7,2,8,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[3,2,7,8,1,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,6,8,4,1,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[4,6,2,8,3,1,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[6,5,8,3,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,5,8,3,1,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,4,3,7,1,6,5,2]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[6,4,3,8,2,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[5,4,3,2,8,1,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[4,5,2,3,8,1,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[3,2,5,4,8,1,7,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[6,4,3,1,5,2,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[7,4,3,1,2,6,5,8]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,5,4,2,3,6,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[8,5,1,4,2,3,7,6]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[7,5,1,4,2,6,3,8]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[4,6,2,1,5,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,2,6,1,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[5,7,1,3,2,6,4,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[6,7,1,2,4,5,3,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[7,6,1,2,5,4,3,8]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[8,6,1,2,5,3,7,4]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[7,8,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]
[4,8,2,1,3,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[3,2,8,1,4,5,7,6]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]
[4,1,3,2,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[5,8,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[6,7,3,8,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[6,7,4,5,1,8,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[5,4,7,6,2,3,8,1]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,4,7,6,8,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[5,3,7,8,6,1,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[4,3,8,7,6,1,2,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[4,8,3,7,5,1,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[4,5,6,7,1,8,3,2]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[3,5,6,2,7,4,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[3,5,6,1,7,8,4,2]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[2,5,6,8,1,7,3,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[8,2,4,5,1,6,3,7]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]
[1,4,8,6,2,3,7,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,5,6,8,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,5,6,2,8,4,7,3]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]
[1,4,2,6,8,5,7,3]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[8,1,3,2,5,4,6,7]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]
[4,3,1,7,6,8,5,2]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[3,8,2,1,7,5,4,6]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[8,3,2,1,6,5,4,7]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]
[8,4,2,6,1,5,3,7]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[4,2,8,7,1,6,3,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[5,3,7,2,6,4,8,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[6,7,3,1,5,8,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[6,7,2,1,8,5,4,3]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[6,7,2,8,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[6,7,8,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[8,5,6,2,1,4,3,7]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[5,8,7,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]
[6,7,1,2,8,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[6,7,1,3,4,8,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[5,1,7,3,4,8,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,1,7,8,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[4,8,1,7,2,3,5,6]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]
[3,8,1,2,7,4,5,6]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]
[3,1,8,2,7,4,6,5]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[3,1,2,8,7,5,6,4]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[4,1,3,7,5,8,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[2,1,8,3,4,7,6,5]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]
[1,8,2,3,4,5,7,6]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]
[1,2,8,3,4,6,7,5]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]
[6,3,8,5,2,7,4,1]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,3,4,5,8,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[3,6,4,8,5,7,1,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[5,1,4,8,6,3,7,2]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[3,4,7,1,8,6,5,2]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[6,3,8,4,2,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[3,6,8,7,1,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[5,3,7,1,6,8,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[4,6,1,2,7,8,5,3]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[3,6,4,2,8,7,5,1]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[6,3,7,5,2,8,1,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,5,2,7,4,8,1,3]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[5,8,1,4,6,7,2,3]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[6,3,7,4,2,8,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,7,1,6,2,4,5,3]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[3,6,4,5,7,2,8,1]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[5,4,2,7,3,6,8,1]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,4,1,5,3,8,2,7]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[8,2,6,3,4,7,5,1]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]
[4,2,5,7,3,6,8,1]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[1,6,5,3,4,8,2,7]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[6,8,3,1,7,2,5,4]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,8,6,3,7,5,2,4]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[8,7,5,2,6,4,3,1]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[8,7,1,6,2,5,4,3]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[7,8,1,6,3,2,5,4]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[2,8,1,7,3,5,6,4]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[4,8,1,3,7,2,6,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[4,2,8,5,7,3,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[6,7,3,1,8,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,7,3,8,4,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,7,2,8,5,3,4,6]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]
[7,6,1,8,4,3,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[7,1,2,8,3,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]
[6,3,7,2,1,8,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[8,2,6,1,7,3,5,4]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]
[4,2,1,5,8,3,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[5,4,3,1,6,8,2,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,5,3,4,6,8,2,7]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[4,3,5,1,6,8,2,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[4,7,5,6,8,3,2,1]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[6,5,1,8,7,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[8,6,4,7,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[5,7,3,8,2,6,4,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[2,3,8,7,4,5,6,1]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]
[7,2,8,6,4,3,5,1]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[2,1,8,7,5,6,3,4]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[7,1,8,6,5,3,2,4]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,3,8,7,4,6,2,5]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[4,7,1,8,6,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[6,8,7,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[6,7,4,8,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,7,4,5,2,8,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,7,4,6,2,3,1,8]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,7,4,6,3,8,1,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[5,7,4,8,3,6,1,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[6,8,4,5,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[5,8,4,6,3,7,1,2]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[5,6,4,8,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[5,6,3,7,2,4,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,6,3,7,2,8,1,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,6,3,8,2,7,1,4]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[5,6,4,8,2,7,1,3]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[5,8,4,6,2,7,1,3]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,8,4,5,2,7,1,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[7,8,4,5,2,6,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[6,8,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[5,8,4,6,2,3,1,7]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[5,6,4,8,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[5,6,3,8,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[5,6,3,4,2,8,1,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[4,6,3,5,2,7,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[4,6,3,5,2,8,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,6,3,8,2,5,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,8,3,6,2,5,1,7]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[5,8,3,6,2,4,1,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[6,8,3,5,2,4,1,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,8,3,5,2,4,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,8,3,5,2,6,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[6,8,3,5,2,7,1,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[5,8,3,6,2,7,1,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[4,8,3,6,2,7,1,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[4,6,3,8,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,6,3,7,2,8,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[4,6,3,7,2,5,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[4,7,3,6,2,5,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,7,3,6,2,8,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,7,3,8,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[5,7,4,8,2,6,1,3]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,7,3,6,2,8,1,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,3,6,2,4,1,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[6,7,3,5,2,4,1,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,7,3,5,2,8,1,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,7,3,8,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,7,4,8,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,7,5,8,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[6,8,5,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,7,4,8,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,7,3,8,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[6,7,3,4,2,8,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[5,7,3,4,2,6,1,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,3,4,2,8,1,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,3,8,2,4,1,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,4,8,2,3,1,6]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,8,4,7,2,3,1,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,8,4,7,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[7,8,4,6,2,3,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,8,3,6,2,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[6,8,3,7,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[5,8,3,7,2,4,1,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[4,8,3,7,2,5,1,6]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]
[4,7,3,8,2,5,1,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[4,7,3,5,2,8,1,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[4,7,3,5,2,6,1,8]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[4,5,3,7,2,6,1,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,5,3,7,2,8,1,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,5,3,8,2,7,1,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[4,8,3,5,2,7,1,6]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]
[5,8,3,4,2,7,1,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[6,8,3,4,2,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[7,8,3,4,2,6,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[6,8,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[5,8,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[4,8,3,5,2,6,1,7]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]
[4,5,3,8,2,6,1,7]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[4,5,3,6,2,8,1,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[4,7,5,2,1,8,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[4,6,5,2,1,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[5,6,4,2,3,1,8,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[6,4,5,3,1,2,8,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[5,4,6,1,3,2,8,7]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[4,6,8,1,7,3,2,5]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[7,4,8,1,6,5,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,4,5,3,1,8,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[6,4,8,1,7,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[6,4,7,1,8,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[8,5,7,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[2,1,6,8,7,4,3,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,7,8,6,4,5,3]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[8,4,7,3,6,2,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[7,6,8,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[5,7,8,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[5,8,7,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[6,8,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[7,8,4,2,6,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[3,6,1,8,7,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[4,7,6,2,8,1,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[6,8,4,2,7,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[5,7,4,2,3,8,1,6]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,1,8,6,7,5,3,4]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[8,6,4,3,7,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[5,8,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[6,7,5,8,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[7,6,5,8,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[8,6,5,7,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[2,1,7,6,8,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[7,5,6,8,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[4,1,7,3,6,5,8,2]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[5,1,8,4,7,6,2,3]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[8,1,3,7,4,6,5,2]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[5,2,8,7,4,6,1,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,1,5,4,3,8,7,2]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[6,1,4,5,3,7,8,2]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[5,1,7,8,6,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[6,1,8,3,4,5,7,2]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[8,5,2,1,4,3,7,6]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[5,6,2,1,4,8,3,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[3,6,1,8,5,2,4,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[3,4,1,2,8,6,5,7]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[6,3,8,5,2,1,4,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[8,5,2,7,3,1,6,4]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[2,3,8,5,6,1,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]
[7,4,5,6,3,1,8,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[8,5,6,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[7,5,3,6,2,8,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,7,5,6,3,2,4,8]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[8,7,5,4,1,6,2,3]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[2,6,4,1,8,5,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[6,1,2,3,8,5,7,4]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[7,1,2,3,6,5,8,4]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]
[7,2,1,3,8,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]
[1,5,7,3,2,4,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[5,2,7,3,1,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[5,8,2,4,1,3,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[8,7,2,6,3,4,1,5]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]
[4,8,1,6,3,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[3,1,8,6,4,2,7,5]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[8,1,6,7,4,3,2,5]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[3,5,8,7,2,4,1,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[4,2,1,3,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[8,6,1,3,7,2,4,5]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[5,2,7,8,6,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,4,2,7,8,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,6,2,4,8,5,3,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,6,2,4,7,5,3,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,7,3,2,8,6,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[7,8,3,6,5,2,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[4,7,2,8,6,1,5,3]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,2,5,7,8,6,1,3]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[8,2,5,1,7,3,4,6]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[1,3,6,4,8,5,7,2]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,3,6,4,7,5,8,2]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[6,2,4,7,5,8,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,2,7,3,5,1,8,4]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[6,2,1,3,7,8,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[7,2,5,1,8,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[7,8,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,5,4,2,6,8,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,7,5,3,4,6,8,2]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[8,2,5,4,6,7,1,3]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]
[8,2,6,4,3,1,7,5]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,2,7,4,1,3,5,6]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[1,2,8,4,3,5,6,7]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]
[1,8,7,4,3,2,5,6]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[5,8,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,8,7,5,4,3,6,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,6,8,4,3,7,5,2]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[6,8,7,3,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[5,3,8,1,2,7,4,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,1,8,3,2,6,4,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[5,7,3,1,2,6,4,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[1,4,6,2,8,3,7,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[5,2,6,7,8,4,1,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,3,6,1,2,8,4,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[1,6,3,2,7,8,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[6,7,3,8,5,2,1,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[4,6,2,7,8,1,5,3]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[1,6,4,7,8,3,5,2]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[4,5,7,2,1,8,6,3]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[7,8,3,4,2,1,6,5]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[6,3,4,1,2,5,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[6,3,1,4,2,7,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,8,3,2,4,5,6,7]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]
[8,6,3,2,4,1,7,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[8,5,3,2,6,7,1,4]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[4,5,2,6,8,1,7,3]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[4,2,5,6,7,8,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[6,2,3,4,1,7,8,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[7,2,3,1,4,5,8,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[7,8,3,5,4,6,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,7,3,8,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[7,8,4,6,1,5,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[7,8,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[6,8,1,7,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,8,6,7,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,8,6,7,3,5,2,4]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[6,8,1,7,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,8,1,6,3,5,2,4]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[7,8,3,6,1,5,2,4]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[7,8,3,6,4,5,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[7,8,2,6,4,5,1,3]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,8,2,6,3,5,1,4]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[7,8,2,6,1,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[7,8,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,8,6,7,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,8,5,7,2,6,3,4]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]
[5,8,1,7,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]
[5,8,2,7,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[6,8,2,7,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,8,2,7,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,8,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,8,3,7,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[3,8,6,7,4,5,1,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[2,8,6,7,4,5,1,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[2,8,6,7,3,5,1,4]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[2,8,6,7,1,5,3,4]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[2,8,5,7,1,6,3,4]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[2,8,1,7,5,6,3,4]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,8,2,7,5,6,3,4]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,8,2,7,4,6,3,5]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[2,8,1,7,4,6,3,5]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[2,8,4,7,1,6,3,5]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[2,8,4,7,3,6,1,5]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[2,8,5,7,3,6,1,4]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[3,8,5,7,4,6,1,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[5,8,3,7,4,6,1,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,8,2,7,4,6,1,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,8,2,7,3,6,1,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[4,8,2,7,3,6,1,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[4,8,2,7,1,6,3,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[4,8,1,7,2,6,3,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,8,4,7,2,6,3,5]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,8,4,7,3,6,2,5]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]
[4,8,1,7,3,6,2,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[4,8,3,7,1,6,2,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[6,8,3,7,1,5,2,4]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,8,1,7,3,6,2,4]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,8,5,7,3,6,2,4]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,8,5,7,4,6,2,3]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[5,8,1,7,4,6,2,3]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[5,8,4,7,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[6,8,4,7,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[6,8,5,7,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[5,8,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[5,8,6,7,2,4,1,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[5,8,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[4,8,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[4,8,5,7,1,6,2,3]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]
[4,8,1,7,5,6,2,3]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,8,4,7,5,6,2,3]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,8,3,7,5,6,2,4]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[3,8,1,7,5,6,2,4]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[3,8,5,7,1,6,2,4]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[3,8,6,7,1,5,2,4]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[3,8,6,7,2,5,1,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[4,8,6,7,2,5,1,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,8,6,7,3,5,1,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[4,8,5,7,3,6,1,2]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[4,8,5,7,2,6,1,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[3,8,5,7,2,6,1,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[3,8,4,7,2,6,1,5]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]
[3,8,4,7,1,6,2,5]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[3,8,1,7,4,6,2,5]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,8,3,7,4,6,2,5]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,8,3,7,2,6,4,5]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[3,8,1,7,2,6,4,5]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[3,8,2,7,1,6,4,5]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[3,8,2,7,4,6,1,5]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[3,8,2,7,5,6,1,4]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[4,8,2,7,5,6,1,3]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[4,8,3,7,5,6,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[3,8,4,7,5,6,1,2]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]
[2,8,4,7,5,6,1,3]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[2,8,3,7,5,6,1,4]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[2,8,3,7,4,6,1,5]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[2,8,3,7,1,6,4,5]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[2,8,1,7,3,6,4,5]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]
[7,5,2,8,6,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[7,4,8,6,1,5,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[7,1,8,4,5,2,6,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[1,6,7,4,2,8,5,3]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,6,7,3,8,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[7,1,8,3,5,6,2,4]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,3,8,6,2,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[6,8,1,7,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[1,5,7,8,2,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[2,6,3,7,8,5,4,1]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[2,5,3,7,8,1,6,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[2,5,4,1,3,7,8,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[3,1,5,4,7,8,2,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[5,3,1,4,8,2,6,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[5,2,4,8,6,1,3,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[4,8,1,3,6,7,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[5,4,3,8,1,2,7,6]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[6,4,3,1,2,8,5,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,4,2,8,1,3,7,5]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,3,8,1,4,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[1,5,7,3,6,8,4,2]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,5,7,4,2,6,8,3]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[5,8,1,4,2,6,3,7]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[6,5,1,2,8,7,3,4]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[6,5,3,1,4,2,8,7]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,3,1,6,4,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,2,6,4,1,7,3,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[3,5,6,1,2,8,7,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,7,1,8,6,2,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,6,2,7,5,1,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[4,3,1,5,7,2,6,8]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[3,4,5,8,2,7,1,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[3,4,6,2,8,1,5,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[3,5,2,6,8,1,7,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[5,3,6,8,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[3,7,2,5,4,8,6,1]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[4,2,6,5,8,3,7,1]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,1,6,5,8,3,2,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[5,1,6,8,4,3,2,7]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[6,7,8,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[4,7,1,5,8,3,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[8,3,1,5,4,7,2,6]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[8,4,1,5,7,3,2,6]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[8,4,6,1,7,3,2,5]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[8,3,6,1,4,7,2,5]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[8,2,6,1,4,3,7,5]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[3,7,6,1,4,8,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[6,7,8,5,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[6,7,8,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[4,7,6,2,8,3,5,1]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[3,7,6,2,4,8,5,1]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[5,7,3,8,4,6,2,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[4,7,3,5,8,6,2,1]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[8,7,2,1,4,3,6,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[8,7,3,1,4,6,2,5]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[8,7,6,3,2,5,4,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[8,7,3,5,1,6,2,4]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[8,7,2,5,1,3,6,4]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[8,4,6,5,7,1,2,3]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[4,7,6,5,8,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[8,7,6,5,2,1,4,3]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[3,6,4,8,7,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,6,2,4,7,8,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[3,6,2,4,8,1,5,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[3,4,7,2,8,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[7,3,8,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[3,8,7,5,4,6,1,2]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[4,3,6,7,8,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[3,5,6,4,8,7,1,2]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[4,6,8,5,3,7,1,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[6,5,2,1,4,7,8,3]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[4,2,7,5,1,8,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[2,1,6,4,8,7,5,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[7,8,1,4,2,6,5,3]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[6,5,1,3,4,2,8,7]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[4,8,5,3,1,7,2,6]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[7,4,5,3,2,8,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[5,8,3,6,1,4,2,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[1,6,8,7,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[7,6,1,8,3,2,4,5]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[7,1,8,6,3,4,2,5]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[1,8,7,6,4,3,2,5]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[2,1,7,5,6,3,8,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[3,1,6,7,5,8,2,4]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[7,8,1,6,5,3,2,4]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[7,8,2,1,4,5,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[4,2,6,1,8,5,7,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,8,1,5,4,6,7,3]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[1,2,8,3,6,5,7,4]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]
[6,1,3,2,7,5,8,4]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[2,6,4,1,7,5,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[7,6,5,8,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[5,8,6,7,3,2,1,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[1,6,4,3,7,2,8,5]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[4,6,3,8,1,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[4,1,6,3,8,2,7,5]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[7,8,1,3,4,2,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]
[2,8,5,7,4,3,1,6]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[7,2,5,8,3,4,1,6]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[5,3,8,7,1,2,6,4]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[3,5,7,8,4,1,2,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[5,4,7,3,6,8,1,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[3,4,7,2,5,1,6,8]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[1,4,7,2,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[3,6,2,4,7,1,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[7,6,3,5,4,8,1,2]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[4,5,6,3,8,7,1,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[6,3,7,5,8,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[4,8,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,3,6,2,5,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[7,8,3,2,5,1,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,8,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[4,1,6,2,5,7,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[2,1,8,6,4,7,3,5]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[7,1,3,6,8,4,2,5]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,8,3,6,7,4,5,2]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]
[7,1,5,8,3,6,2,4]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[3,1,6,4,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[5,8,7,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,5,7,8,2,4,6,3]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[6,8,5,1,3,4,2,7]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,6,5,1,4,3,2,8]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[2,6,4,5,1,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[3,5,6,4,1,8,2,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[7,8,5,4,1,3,2,6]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,8,2,3,4,1,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]
[4,2,6,3,8,1,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[7,2,3,5,4,1,8,6]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]
[6,2,4,3,1,5,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[4,2,8,3,1,7,5,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[1,3,7,4,8,2,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[5,3,7,4,1,6,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[2,4,7,3,6,1,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[5,8,7,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[7,5,6,8,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[2,4,7,1,6,5,3,8]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[5,2,7,1,8,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,3,1,2,8,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[4,2,1,3,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,6,1,8,5,3,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[7,8,2,1,4,5,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,8,4,1,5,3,6,2]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[7,5,1,6,4,3,8,2]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[5,8,1,6,3,4,7,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[6,8,1,7,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[5,6,1,7,4,8,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[7,8,5,1,6,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[2,6,5,7,3,4,8,1]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[1,6,4,7,5,8,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,3,7,4,6,8,2,5]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]
[5,2,4,7,3,6,8,1]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[8,1,6,5,7,2,4,3]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[7,1,6,5,8,3,2,4]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,2,7,6,8,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]
[3,8,6,4,2,7,5,1]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]
[7,8,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[2,8,1,7,4,3,6,5]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[3,7,4,1,8,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[6,7,1,4,8,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[2,7,1,8,4,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[6,1,2,8,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,1,2,4,8,3,6,7]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[4,1,3,2,8,5,6,7]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[3,2,1,4,8,5,6,7]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]
[4,3,6,1,5,8,2,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[2,6,1,4,5,8,3,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,6,2,5,8,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[8,4,2,1,7,3,6,5]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[7,4,2,1,8,5,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[1,5,4,2,8,3,6,7]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]
[6,4,3,1,5,8,2,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[5,4,3,2,1,8,6,7]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[2,5,3,4,1,8,6,7]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[4,3,5,2,1,8,6,7]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[3,7,6,8,4,5,2,1]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[1,7,6,8,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[2,4,8,6,7,3,5,1]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[6,3,5,8,4,7,2,1]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[5,4,3,8,6,7,2,1]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[3,2,8,5,7,4,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[2,1,8,7,4,6,3,5]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[3,1,8,5,7,6,2,4]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[5,8,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[4,8,7,5,6,3,2,1]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]
[4,2,1,6,3,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[6,2,1,4,3,8,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[8,2,1,4,3,6,5,7]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]
[6,2,4,1,3,8,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[2,1,6,4,3,5,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[6,4,2,1,3,5,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[8,4,2,1,3,6,5,7]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,4,2,1,6,3,5,7]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[6,4,2,1,8,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[4,6,2,1,3,8,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,6,1,4,3,8,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,6,4,3,8,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,8,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[8,6,2,1,4,3,5,7]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[2,8,1,4,6,3,5,7]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[2,6,1,4,8,3,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,6,4,1,8,3,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,6,4,8,1,3,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,6,2,8,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,6,1,8,3,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[6,2,4,1,8,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[4,2,1,6,8,3,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,1,6,3,8,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,1,3,6,8,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,1,4,3,8,6,5,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[2,4,1,3,8,6,5,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,1,3,8,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,2,1,8,3,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,2,1,8,6,3,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[8,2,1,6,4,3,5,7]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[2,4,8,1,6,3,5,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,8,6,1,3,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[2,1,8,6,4,3,5,7]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[2,8,6,1,4,3,5,7]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[2,8,6,4,1,3,5,7]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[4,8,6,2,1,3,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[3,2,6,1,5,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[6,1,5,2,4,3,8,7]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[6,1,3,2,5,4,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[4,3,6,1,5,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[4,3,7,2,6,5,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[4,3,8,2,6,1,7,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[4,3,8,1,7,2,6,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[4,3,8,1,5,2,7,6]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[2,1,5,4,8,3,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[5,4,7,6,8,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[4,3,7,6,8,1,5,2]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[4,3,7,1,8,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[4,3,6,5,8,1,7,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[6,3,5,4,7,2,8,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[6,3,5,4,8,1,7,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,1,6,3,8,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[7,1,6,5,8,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[7,4,6,5,8,1,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[8,4,6,1,3,2,7,5]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[8,1,6,3,4,2,7,5]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[8,3,5,2,6,1,7,4]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[7,3,5,2,6,4,8,1]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[8,2,7,1,5,3,6,4]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[8,1,7,2,4,3,6,5]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[8,1,3,2,7,4,6,5]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[2,1,8,3,7,4,6,5]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[2,1,8,3,5,4,7,6]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]
[8,1,3,2,5,4,7,6]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]
[8,1,5,2,4,3,7,6]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[8,2,4,1,5,3,7,6]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]
[8,2,4,1,7,3,6,5]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]
[3,2,8,4,6,1,7,5]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]
[3,2,8,1,7,4,6,5]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[3,2,8,1,5,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[3,2,4,1,8,5,7,6]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]
[4,1,3,2,7,6,8,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[3,2,7,6,8,1,5,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[3,2,7,1,8,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,2,6,5,8,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[7,2,4,1,8,5,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[7,6,8,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[7,6,8,1,3,2,5,4]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[7,1,8,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]
[7,1,8,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[7,2,8,1,5,4,6,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[5,4,7,2,6,3,8,1]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,4,8,2,6,1,7,3]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,1,8,4,7,2,5,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[6,5,8,1,3,2,7,4]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[2,1,6,5,8,3,7,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[6,5,7,4,8,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,4,6,3,8,1,7,2]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[3,2,1,5,8,4,6,7]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[2,8,3,1,5,4,6,7]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]
[2,4,8,3,5,7,6,1]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[4,2,5,3,1,8,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[1,8,4,2,5,3,6,7]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]
[8,1,5,3,2,4,6,7]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[3,8,1,5,2,4,6,7]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[5,4,1,3,8,2,6,7]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,5,7,3,8,4,2,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[5,1,4,7,8,3,2,6]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[8,1,5,3,7,4,6,2]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,4,3,8,7,5,6,2]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,6,8,5,3,7,4,2]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[6,4,8,1,7,3,5,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,4,8,7,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[7,1,6,8,4,3,2,5]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,6,7,2,8,4,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[6,7,1,4,2,8,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[6,3,7,1,4,8,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[3,7,8,1,5,2,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[7,1,2,8,5,3,4,6]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[1,7,2,8,4,5,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]
[4,2,1,7,8,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[7,2,6,3,4,1,8,5]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]
[2,7,1,8,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,1,7,3,5,8,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,2,7,5,8,3,4,6]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]
[8,7,1,3,6,2,4,5]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[8,2,1,7,3,5,6,4]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[7,8,2,6,3,1,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[2,8,4,1,6,7,5,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[2,1,8,4,7,5,6,3]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[8,3,7,1,5,6,2,4]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,1,6,2,7,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,8,5,2,6,7,4,3]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]
[5,2,1,8,6,7,4,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[7,8,1,6,4,2,5,3]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[8,7,6,5,1,4,2,3]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[8,7,6,1,5,3,4,2]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[8,1,7,5,6,4,3,2]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,8,6,7,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]
[6,3,5,2,1,4,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[8,3,5,7,2,4,1,6]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[8,5,2,7,4,3,1,6]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[6,5,3,1,2,4,8,7]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[4,5,3,6,1,2,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[3,5,1,4,6,2,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[8,1,4,7,3,6,2,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]
[8,5,1,4,7,3,2,6]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[8,5,3,7,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[6,3,4,7,5,8,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[5,1,4,6,8,3,7,2]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[4,7,1,3,5,8,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[4,8,3,7,1,2,6,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[8,7,1,4,2,6,3,5]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[8,6,3,1,2,4,7,5]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[2,1,8,7,5,3,4,6]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[8,1,7,4,5,2,3,6]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]
[2,8,7,5,4,1,3,6]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[8,7,2,6,4,1,3,5]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[5,3,7,6,2,1,8,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,8,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,7,3,5,1,8,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[2,1,6,7,5,8,3,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[2,1,5,7,3,6,8,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[4,1,7,2,5,6,8,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[2,4,7,1,6,5,8,3]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[3,4,6,2,7,8,5,1]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[4,6,1,2,5,8,7,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[3,5,6,4,7,1,8,2]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[3,4,6,1,5,7,8,2]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[3,4,1,5,7,6,8,2]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[4,2,1,7,3,5,8,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[7,3,1,5,4,2,8,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[6,3,1,4,2,8,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[8,4,1,5,2,7,6,3]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]
[7,2,5,1,4,3,8,6]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[3,6,2,7,1,4,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[2,7,5,4,1,3,8,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[6,4,3,2,1,8,5,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[1,7,6,2,4,8,3,5]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[2,7,3,6,4,8,1,5]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]
[6,2,7,5,3,8,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[7,1,8,5,3,6,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[5,8,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[8,7,2,6,1,5,4,3]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,8,5,7,4,3,6,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]
[1,8,5,7,2,4,6,3]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[3,8,6,1,7,2,5,4]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[5,8,4,6,7,1,3,2]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[7,2,8,5,6,1,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[3,6,5,8,1,4,2,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[4,3,6,7,8,1,2,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,4,6,7,2,8,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[3,5,7,1,4,8,2,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[8,1,5,2,7,4,6,3]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[5,4,1,6,8,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[5,3,1,7,2,8,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,3,6,4,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[6,3,7,4,8,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[6,3,1,8,4,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[5,4,8,1,7,6,2,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[5,2,8,1,7,3,6,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[6,4,7,8,1,5,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,3,7,8,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[4,6,8,2,7,1,5,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,5,8,7,1,3,6,4]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[8,3,7,6,1,5,4,2]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[8,2,7,6,5,1,4,3]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]
[4,3,8,7,6,2,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[2,4,8,7,6,1,3,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[3,5,8,7,2,6,1,4]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[4,7,3,8,6,5,1,2]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[7,5,8,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[5,8,7,3,6,4,2,1]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[3,8,7,6,5,1,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[2,8,7,6,5,4,1,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]
[7,8,5,6,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,5,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,5,3,1,6,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,5,3,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,8,5,3,6,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,3,1,2,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,3,4,1,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,6,3,4,1,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,1,6,4,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,6,4,1,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,4,1,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,1,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,1,8,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,1,8,2,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,1,8,6,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,3,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,8,6,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,6,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,8,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,6,8,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,6,3,8,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,6,3,1,8,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,6,1,8,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,1,2,8,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[7,5,3,4,1,6,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[4,6,8,3,5,7,1,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[6,8,1,2,4,5,7,3]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[3,6,8,2,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[8,3,5,2,4,1,6,7]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[3,5,7,2,4,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,2,5,7,3,6,1,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[4,5,2,8,3,1,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[2,1,6,8,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,2,5,8,3,6,7,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]
[5,3,6,8,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[3,1,2,6,8,5,7,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[4,3,6,2,7,5,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[4,3,1,7,8,2,6,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[5,4,7,3,8,6,1,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[5,8,4,7,6,3,1,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[5,8,7,1,4,2,6,3]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[8,3,5,1,2,7,6,4]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[4,7,3,6,5,2,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[5,3,7,6,4,2,1,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,3,1,6,4,2,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[1,3,8,5,4,2,7,6]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]
[1,8,3,6,2,7,5,4]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]
[1,6,8,7,4,2,5,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[6,4,8,7,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[3,1,2,7,6,4,8,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[5,2,6,3,7,4,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[2,8,5,3,1,6,4,7]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]
[2,1,7,3,8,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,6,2,3,7,8,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,6,7,2,8,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[6,3,7,4,8,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[5,7,1,8,2,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[5,1,2,7,8,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[4,2,1,7,3,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[6,2,8,4,3,1,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[6,4,2,7,3,5,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[7,3,2,1,8,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[3,7,2,8,6,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[7,8,3,2,5,6,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,1,8,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]
[8,7,6,1,2,4,5,3]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[8,3,6,5,2,1,4,7]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]
[8,2,4,1,6,5,3,7]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]
[8,2,4,1,7,6,3,5]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]
[8,5,1,2,7,3,6,4]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[6,8,3,7,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[6,1,8,2,3,7,5,4]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[8,1,2,6,4,3,7,5]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[2,8,1,7,5,4,3,6]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,7,2,8,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]
[7,3,8,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,8,7,6,5,2,4,3]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[8,1,7,3,2,6,5,4]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[4,3,1,2,8,7,6,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[5,1,4,3,2,8,7,6]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[8,6,4,3,1,5,7,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[8,6,4,1,5,2,7,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[8,6,5,3,2,1,7,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,7,2,4,5,3,1,6]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[8,5,1,2,6,7,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[8,5,1,6,4,2,7,3]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[8,5,1,3,6,4,7,2]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[8,6,5,1,7,3,2,4]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[7,4,8,3,1,6,2,5]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,1,5,8,3,2,6,4]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[5,7,4,1,8,2,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[5,7,4,3,1,8,6,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[8,5,7,4,6,1,3,2]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,8,7,2,5,4,6,3]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[4,3,1,8,7,5,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,3,5,6,8,4,2,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[1,6,2,4,8,7,5,3]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[8,4,1,6,7,5,3,2]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[7,1,6,4,8,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[7,3,6,8,5,1,2,4]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,3,7,2,6,8,4,5]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[3,6,5,2,8,1,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[6,1,2,7,8,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[6,1,2,7,4,8,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[3,1,6,4,7,8,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[5,7,1,3,8,4,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,7,1,8,4,2,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[5,7,1,2,8,6,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[4,2,6,3,8,1,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,6,7,3,5,1,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,6,2,4,7,5,1,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,6,2,4,1,8,5,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[7,1,4,5,2,8,6,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[4,7,3,1,5,8,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[8,7,6,4,1,5,2,3]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[3,8,2,7,1,5,4,6]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[3,6,8,2,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[2,4,8,1,6,5,3,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[4,2,8,1,5,7,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[8,5,7,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,8,2,4,6,7,3,5]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]
[2,1,5,8,6,4,3,7]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]
[1,2,5,7,8,4,3,6]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,2,7,4,8,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,2,7,8,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,8,5,7,4,3,2,6]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]
[1,6,8,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]
[7,1,5,8,3,4,6,2]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,1,5,8,4,3,2,6]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,1,2,5,8,3,6,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[7,1,6,4,2,3,5,8]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[2,7,1,4,8,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[7,1,4,6,5,8,3,2]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]
[7,1,2,3,8,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]
[7,1,5,4,3,8,2,6]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,1,3,4,2,6,8,5]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]
[3,6,7,1,4,8,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[3,5,1,4,8,6,2,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,6,2,4,7,8,1,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[6,5,8,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[3,4,7,2,5,8,1,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[4,3,8,1,2,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[5,6,7,8,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,7,8,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[2,8,3,1,5,6,4,7]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]
[3,8,7,1,5,4,2,6]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[4,3,1,7,6,8,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[3,4,1,7,5,6,8,2]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[3,4,1,5,7,6,2,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[2,4,6,1,7,5,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[4,2,1,5,6,3,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[5,8,1,6,4,3,2,7]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[5,8,1,6,3,7,2,4]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[7,6,5,1,3,8,2,4]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[7,6,5,1,3,4,8,2]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[7,2,6,4,1,3,8,5]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[8,4,5,3,7,2,6,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]
[4,7,5,2,8,1,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[4,6,3,8,5,1,7,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[2,6,4,3,1,5,7,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[3,6,4,8,1,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[7,3,8,4,1,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[4,2,8,3,6,1,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[6,7,5,8,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[6,8,5,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[4,8,5,2,7,1,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[6,3,5,2,1,7,4,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[3,6,5,4,2,8,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[7,4,5,3,8,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[1,6,4,7,2,5,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,3,7,2,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,5,7,2,4,8,3,6]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,6,5,7,2,4,3,8]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,7,6,2,8,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]
[1,4,2,3,5,8,7,6]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]
[1,5,2,3,4,8,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,6,5,2,3,8,7,4]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,7,6,5,2,8,4,3]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,6,5,2,3,8,4,7]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,6,7,5,2,3,8,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,7,5,2,8,4,3,6]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,7,5,6,2,8,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]
[1,5,7,6,2,4,8,3]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,4,7,6,2,5,8,3]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,2,6,5,3,7,4,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]
[1,3,7,5,2,6,8,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,7,4,6,2,8,3,5]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,7,3,5,2,8,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,3,7,4,2,6,8,5]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,4,7,3,2,5,8,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,5,7,3,2,4,8,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,7,3,4,2,8,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,7,4,2,8,5,3,6]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,6,7,4,2,3,8,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,4,3,2,5,8,6,7]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]
[1,5,3,2,4,8,6,7]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,6,4,2,3,8,5,7]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,7,6,4,2,8,5,3]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,7,5,3,2,8,6,4]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,6,4,2,3,8,7,5]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,5,3,2,4,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[6,8,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[2,8,5,4,3,7,1,6]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[7,6,1,4,3,8,5,2]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[7,6,5,1,3,8,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[7,3,5,4,8,1,6,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[5,6,8,4,3,1,7,2]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[6,8,2,4,3,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[1,8,3,4,7,2,6,5]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]
[7,5,8,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[4,8,5,7,3,2,1,6]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]
[7,8,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]
[7,8,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[3,4,6,5,7,8,1,2]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[4,3,6,5,8,7,1,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[4,2,6,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[6,7,3,8,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[6,7,4,5,1,8,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[4,7,5,6,1,8,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[4,5,3,8,6,7,1,2]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[4,8,3,6,5,7,1,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[5,6,3,8,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,6,2,7,3,4,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[4,5,1,8,6,7,2,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[7,8,4,5,1,6,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[4,5,2,3,1,8,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[5,6,2,3,1,8,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[5,6,3,4,1,8,2,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[3,6,4,5,2,7,1,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,6,4,5,1,8,2,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[2,6,4,8,1,5,3,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[2,8,3,6,1,5,4,7]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]
[2,8,3,4,1,6,5,7]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]
[7,8,1,5,3,6,2,4]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,8,3,6,5,7,2,4]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]
[1,6,4,7,3,8,2,5]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,7,3,6,4,8,2,5]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,7,2,8,4,6,3,5]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,7,5,8,2,6,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]
[6,7,1,5,3,8,2,4]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[6,7,1,8,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[6,7,1,8,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[6,7,5,8,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[5,8,6,7,2,3,1,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[6,7,2,3,1,8,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[6,7,2,8,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[6,7,3,4,1,8,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[3,4,2,7,5,6,1,8]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[2,7,5,8,1,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[2,3,1,8,4,7,5,6]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]
[2,3,1,8,6,7,4,5]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]
[7,8,2,3,1,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]
[2,8,1,4,3,7,5,6]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[2,8,1,7,3,5,4,6]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[4,5,1,7,3,8,2,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[3,8,1,5,2,7,4,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[3,4,1,8,6,7,2,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[7,8,3,4,1,6,2,5]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[3,4,2,5,1,8,6,7]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]
[3,6,5,4,1,2,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[2,5,4,1,6,3,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[3,6,5,1,2,4,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[5,2,3,6,4,1,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[6,1,4,5,3,2,8,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[5,6,7,8,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[2,1,5,8,7,6,3,4]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[2,1,4,7,6,3,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[4,2,8,6,7,3,1,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[7,4,3,8,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[4,7,5,8,1,6,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[2,1,5,8,7,3,4,6]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[8,5,7,3,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[4,2,5,1,6,7,8,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[7,2,3,4,8,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[6,1,8,5,2,7,4,3]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[2,1,7,4,5,8,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[2,1,8,3,6,7,5,4]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]
[6,8,7,2,5,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[8,2,1,6,4,7,5,3]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[7,8,2,5,6,1,4,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[7,8,4,2,5,1,6,3]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[6,1,2,3,7,5,8,4]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[7,6,8,4,2,5,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[8,5,7,1,6,3,2,4]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[4,1,2,3,7,6,8,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[3,2,4,1,8,5,6,7]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]
[4,1,6,3,5,8,7,2]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[8,6,7,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[2,1,6,5,8,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[4,1,8,5,6,2,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[2,6,4,8,7,3,5,1]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[3,1,8,2,7,5,4,6]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[8,2,3,1,7,4,6,5]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]
[5,8,4,3,2,7,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[7,4,8,6,3,2,5,1]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[2,1,8,4,3,7,5,6]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[5,8,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[7,3,5,8,1,4,2,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[3,8,7,6,1,4,2,5]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[5,1,8,3,6,7,2,4]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[3,6,1,4,7,8,5,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,6,8,4,7,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[6,8,1,3,5,7,2,4]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,6,1,4,3,8,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[8,4,2,6,7,5,3,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[7,4,1,6,8,2,5,3]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,8,6,2,5,3,4,7]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[4,7,1,2,5,3,8,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[8,7,3,6,4,5,2,1]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]
[5,7,8,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,8,6,4,5,2,3,7]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,4,7,2,6,8,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[2,5,4,3,6,8,1,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[3,8,5,4,6,2,1,7]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[4,8,2,1,3,7,5,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[1,8,3,2,5,6,7,4]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]
[6,4,1,2,7,5,8,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[4,3,7,8,5,1,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,2,7,3,6,5,8,4]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]
[2,8,7,6,3,4,1,5]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]
[5,8,2,6,3,4,1,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[4,1,7,5,8,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,2,4,5,8,3,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]
[4,8,1,5,2,3,7,6]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]
[2,4,6,3,7,1,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[6,5,8,7,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,5,2,7,4,3,8,6]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[7,6,1,2,8,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[6,7,8,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[5,7,8,4,1,2,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[4,7,8,5,6,1,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[5,6,4,8,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[6,5,4,1,2,3,8,7]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[7,5,1,6,2,3,8,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[4,5,6,7,8,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[8,1,3,6,7,4,5,2]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]
[4,2,6,7,3,1,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[7,3,1,5,4,8,2,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[4,5,3,2,8,1,6,7]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[7,4,1,5,3,2,6,8]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[8,1,5,4,3,2,6,7]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]
[8,1,6,4,2,5,3,7]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[6,5,3,1,2,7,4,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,6,3,8,1,4,2,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[4,6,3,8,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,7,8,3,2,1,5,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[5,7,8,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[8,1,7,2,5,4,3,6]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[8,1,7,2,4,5,6,3]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]
[7,6,1,2,4,5,8,3]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[7,5,1,3,2,6,8,4]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[8,1,6,3,2,5,7,4]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[8,1,5,3,4,2,7,6]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[5,4,2,3,1,6,8,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[6,3,2,1,5,7,4,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[8,1,4,3,5,6,2,7]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]
[3,6,5,8,2,4,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[6,2,4,5,8,3,1,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[4,8,1,2,5,6,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[8,1,3,5,2,6,4,7]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]
[5,2,1,6,3,8,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[6,1,4,5,8,3,2,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[6,5,4,3,8,2,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[4,6,8,3,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[4,7,8,5,3,1,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[8,5,4,7,6,2,1,3]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[5,8,7,3,1,4,6,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[8,5,7,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[4,7,8,3,6,1,5,2]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[8,4,6,1,7,3,5,2]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,3,8,6,4,7,5,2]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[7,6,2,1,4,3,8,5]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[7,6,8,1,4,3,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[3,2,6,8,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[1,6,4,7,2,3,8,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[3,1,7,5,2,8,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,7,4,5,2,8,3,6]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]
[3,2,6,8,7,4,5,1]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[6,3,2,1,7,8,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[5,7,3,8,2,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,7,1,8,4,2,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[4,2,1,3,7,5,8,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[8,4,2,1,3,7,6,5]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,4,3,7,6,2,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[3,6,2,8,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[7,3,2,8,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[3,8,7,2,6,5,4,1]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[4,2,7,8,6,1,5,3]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[5,8,4,2,7,1,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[8,5,3,1,7,2,6,4]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,2,1,6,3,7,5,4]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]
[1,4,6,8,2,7,5,3]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[2,1,7,3,8,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]
[8,2,1,7,6,5,4,3]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]
[8,6,7,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[6,4,7,3,2,1,8,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[4,8,7,3,2,1,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[6,4,3,7,2,1,8,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[4,8,3,6,2,1,7,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[5,3,7,6,2,1,4,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,8,7,6,2,1,4,5]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[5,8,4,2,6,1,3,7]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[4,8,7,2,5,1,3,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[5,8,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[4,3,7,2,5,1,8,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[6,4,2,7,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,4,2,6,7,1,3,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[2,8,7,6,5,1,3,4]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[6,4,7,3,1,5,8,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[4,8,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[6,5,3,7,1,4,8,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,8,3,6,1,4,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[4,8,3,6,1,5,7,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[5,3,7,6,1,4,8,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[4,3,7,6,1,5,8,2]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[3,8,7,6,1,4,5,2]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[5,8,4,2,1,7,3,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,4,7,2,1,5,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,8,3,2,1,4,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[6,3,7,2,1,4,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[5,8,2,6,1,4,3,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,4,2,7,1,5,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[2,8,7,6,1,4,3,5]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[5,8,4,1,6,7,3,2]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[6,4,7,1,5,8,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,5,3,1,8,4,7,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[5,8,3,1,6,4,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[6,4,3,1,5,8,7,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[5,8,2,1,6,4,3,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[6,4,2,1,5,8,3,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[3,8,2,1,5,4,6,7]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[6,2,7,1,5,4,3,8]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[4,2,7,1,5,6,3,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[3,2,7,1,5,4,6,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[2,8,7,1,5,4,3,6]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[6,5,1,7,8,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,4,1,6,7,8,3,2]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[4,3,1,6,5,7,8,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,2,1,6,7,4,3,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[4,2,1,6,5,7,3,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,8,1,6,5,4,3,7]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]
[6,1,7,8,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[5,1,7,6,8,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[4,1,7,6,5,8,3,2]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[4,5,8,1,7,2,3,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]
[4,5,8,1,2,6,3,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[8,1,3,5,7,2,4,6]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]
[3,6,8,1,7,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[3,4,5,6,8,1,7,2]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[8,2,3,5,6,7,1,4]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]
[8,1,2,3,5,4,6,7]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]
[4,5,8,1,7,6,3,2]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[8,7,2,1,6,3,4,5]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]
[8,7,2,1,3,5,4,6]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[8,6,4,1,7,5,3,2]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[2,3,6,7,8,1,5,4]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[7,4,2,6,8,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,3,2,5,8,6,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,3,1,8,6,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[3,1,7,2,5,4,8,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[7,1,4,2,8,3,6,5]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[7,1,8,2,5,3,6,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[7,3,8,4,5,1,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[8,3,7,4,6,1,5,2]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[8,2,7,1,6,4,5,3]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,1,7,5,4,2,3,6]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[8,1,2,6,5,4,3,7]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]
[8,1,7,6,3,2,4,5]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[8,2,7,5,6,1,4,3]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[3,6,8,1,7,5,4,2]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[8,2,6,7,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]
[8,6,7,2,3,1,5,4]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[2,7,8,6,3,1,5,4]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[8,1,7,6,5,4,3,2]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]
[2,1,8,6,3,7,4,5]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]
[8,6,1,5,2,7,4,3]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[8,5,1,7,4,2,6,3]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[2,1,8,4,5,3,6,7]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[2,1,7,8,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]
[7,8,1,5,2,6,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[6,4,1,5,2,3,8,7]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,3,7,4,6,8,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[5,8,3,7,6,2,1,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[4,2,6,3,8,5,1,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[8,5,2,7,4,6,1,3]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[5,8,2,1,7,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[8,3,2,4,1,7,5,6]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]
[6,3,4,2,1,7,8,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[7,8,3,1,5,4,6,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,2,8,1,4,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[6,2,3,1,4,5,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]
[5,6,1,4,3,2,8,7]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[5,7,1,8,3,6,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[6,8,1,4,5,3,2,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[8,2,6,1,4,7,3,5]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[4,2,1,3,6,7,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[2,3,4,1,8,6,5,7]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[6,3,5,4,1,2,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[8,7,3,6,5,1,4,2]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[3,4,7,2,8,1,5,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[4,2,3,5,8,1,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[3,8,4,7,1,6,5,2]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[3,2,4,6,1,5,8,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[6,8,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[6,5,4,3,1,8,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[8,7,5,4,3,1,6,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[3,4,6,2,8,5,1,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[3,4,6,8,1,5,2,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[3,4,7,2,1,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[3,4,7,2,8,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[3,4,8,2,1,5,6,7]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]
[3,5,2,6,8,4,1,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[3,5,2,7,4,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,5,6,2,7,8,1,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[3,5,6,8,4,1,2,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,7,2,4,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[3,5,7,8,4,1,6,2]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,5,8,2,4,1,6,7]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[3,6,2,1,8,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[3,6,2,7,4,8,5,1]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[3,6,2,7,8,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[3,6,8,2,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[3,7,2,1,4,8,6,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[3,7,2,8,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]
[3,8,2,1,4,5,6,7]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]
[4,1,5,6,7,8,3,2]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[4,1,5,7,8,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[4,1,5,8,3,2,6,7]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[4,1,6,3,7,8,5,2]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[4,1,6,3,8,5,2,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[4,1,6,7,3,8,5,2]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[4,1,6,8,3,5,2,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[4,1,7,3,8,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[4,1,8,3,2,5,6,7]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[4,5,2,7,3,8,6,1]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[4,5,7,3,2,8,6,1]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[4,5,8,3,2,1,6,7]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[4,6,2,8,3,5,1,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[4,6,7,3,2,8,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[4,7,2,8,3,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[4,7,8,3,2,5,6,1]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[4,8,2,3,1,5,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[5,1,2,6,8,4,3,7]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[5,1,6,3,7,8,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[5,1,6,3,8,4,2,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[5,1,6,7,4,8,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[5,6,2,3,8,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[5,6,2,7,4,8,1,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,6,2,7,8,4,1,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[5,6,8,3,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[5,7,8,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[6,1,2,3,7,8,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[6,1,2,3,8,5,4,7]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[6,1,2,7,8,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[6,1,7,8,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[6,7,2,8,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[7,1,2,3,4,8,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]
[7,1,2,3,8,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]
[7,1,2,8,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]
[7,1,8,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]
[2,4,6,1,8,5,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[6,4,1,8,2,3,7,5]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,8,1,2,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[5,8,1,6,2,4,3,7]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[3,5,8,6,1,2,4,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[3,5,1,8,2,4,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[3,1,6,8,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[2,3,5,6,8,1,7,4]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[5,6,4,8,2,1,7,3]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[7,1,8,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[7,6,5,2,4,8,1,3]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[6,7,4,5,2,1,8,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,1,7,8,6,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[2,5,7,8,6,3,1,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[7,1,8,6,3,2,4,5]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[7,8,1,6,4,2,3,5]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[2,4,8,1,5,6,7,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[8,4,1,2,5,6,3,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[8,3,1,6,5,2,4,7]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[2,5,3,8,7,6,1,4]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[5,8,7,4,2,6,1,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,1,8,4,7,6,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[7,3,2,6,5,1,8,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[8,2,3,6,5,1,7,4]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]
[2,8,7,6,3,4,5,1]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,8,7,6,5,2,3,4]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]
[6,3,2,8,5,1,7,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[5,8,6,4,1,3,7,2]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[3,6,1,8,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[3,4,1,2,8,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[6,8,3,5,4,1,7,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[7,2,5,8,3,6,1,4]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[4,2,3,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[6,8,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[5,2,8,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[4,1,3,6,8,2,5,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,6,3,2,5,8,4,7]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[8,3,2,1,5,4,7,6]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[2,5,1,8,4,3,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[5,3,6,2,4,8,1,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[1,6,2,4,5,8,3,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[5,3,2,1,6,8,4,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[2,6,5,8,1,3,4,7]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[4,3,1,6,5,8,2,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[8,3,4,1,5,2,7,6]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]
[3,4,6,5,7,1,8,2]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[8,2,6,4,1,7,3,5]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[5,4,6,8,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[3,4,7,8,6,2,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[7,5,8,2,4,6,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[8,2,7,4,6,1,3,5]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[4,7,3,2,8,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[3,8,1,7,2,5,6,4]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[8,3,2,5,7,6,1,4]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[2,8,6,1,5,7,3,4]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[1,2,8,3,5,6,7,4]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]
[4,2,3,7,1,8,6,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[3,2,6,4,8,1,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[8,2,1,6,7,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]
[2,7,8,5,4,1,3,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,7,5,3,8,4,2,6]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[4,7,5,3,1,2,8,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[5,6,7,3,8,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[5,7,3,2,4,1,8,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[8,4,1,3,7,2,5,6]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[2,8,4,7,1,3,5,6]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[3,5,2,8,6,1,7,4]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[1,7,6,3,2,5,8,4]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[3,8,1,5,6,2,7,4]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[4,3,5,6,7,1,8,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[7,1,5,2,8,6,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,8,5,3,6,2,7,4]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[6,5,8,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[4,7,2,6,5,8,1,3]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[6,8,1,4,2,7,3,5]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[6,3,4,7,1,8,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[3,4,7,8,2,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[1,8,2,4,5,6,7,3]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]
[3,2,5,7,6,1,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,3,5,6,1,8,7,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[3,1,4,6,5,7,8,2]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,2,3,4,8,6,5,7]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]
[1,2,3,8,5,4,6,7]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]
[1,2,3,8,5,6,4,7]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]
[1,2,3,8,6,5,4,7]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]
[1,8,3,4,2,5,6,7]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]
[1,2,8,5,4,3,6,7]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]
[1,8,4,3,2,5,6,7]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[8,5,7,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[8,4,7,6,5,3,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[8,4,7,5,6,3,2,1]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]
[8,5,7,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[8,7,6,3,5,4,2,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[8,6,7,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,5,7,3,6,4,2,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,4,7,3,6,5,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[8,1,7,4,6,5,3,2]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,3,7,2,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]
[8,5,7,2,6,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[8,6,7,2,5,4,3,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,7,6,2,5,4,3,1]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[8,4,7,1,6,5,3,2]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,3,7,1,6,5,4,2]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[8,2,7,1,6,5,4,3]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]
[8,1,7,2,6,5,4,3]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[8,1,7,2,6,4,5,3]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[8,3,7,1,6,4,5,2]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[8,4,7,1,6,3,5,2]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,5,7,1,6,3,4,2]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,6,7,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[8,7,6,2,5,3,4,1]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[8,6,7,2,5,3,4,1]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[8,5,7,2,6,3,4,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[8,4,7,2,6,3,5,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,3,7,2,6,4,5,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[8,2,7,3,6,4,5,1]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]
[8,1,7,3,6,4,5,2]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[8,1,7,4,6,3,5,2]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,2,7,4,6,3,5,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,3,7,4,6,2,5,1]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[8,5,7,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,6,7,3,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[8,5,7,4,6,2,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[8,4,7,5,6,2,3,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[8,3,7,5,6,2,4,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[8,2,7,5,6,3,4,1]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[8,1,7,5,6,3,4,2]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,3,7,6,5,2,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]
[8,4,7,6,5,2,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,5,7,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[8,7,6,5,4,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[8,6,7,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[8,5,7,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[8,3,7,6,5,1,4,2]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[8,1,7,5,6,2,4,3]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[8,3,7,5,6,1,4,2]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[8,4,7,5,6,1,3,2]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[8,6,7,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[8,7,6,4,5,1,3,2]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[8,6,7,3,5,1,4,2]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[8,4,7,3,6,1,5,2]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[8,2,7,4,6,1,5,3]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,1,7,4,6,2,5,3]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[8,1,7,3,6,2,5,4]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[8,2,7,3,6,1,5,4]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[8,3,7,2,6,1,5,4]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]
[8,4,7,2,6,1,5,3]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[8,5,7,2,6,1,4,3]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[8,6,7,2,5,1,4,3]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[8,7,6,2,5,1,4,3]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[8,7,6,1,5,2,4,3]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[8,6,7,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[8,5,7,1,6,2,4,3]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[8,4,7,1,6,2,5,3]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[8,3,7,1,6,2,5,4]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[8,2,7,1,6,3,5,4]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[4,6,7,3,8,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[1,4,8,2,6,3,5,7]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,6,2,4,8,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,5,2,3,8,4,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,7,2,3,5,4,8,6]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,8,2,3,5,4,6,7]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]
[1,7,8,2,4,5,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,2,8,3,6,4,5,7]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]
[1,5,8,2,3,7,4,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,6,8,2,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[5,7,2,6,3,8,1,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[5,7,1,6,8,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[4,8,1,2,5,7,3,6]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,7,8,4,6,2,5,3]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]
[3,7,5,4,8,2,1,6]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[4,7,1,3,2,8,6,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[2,7,3,1,5,8,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,7,5,8,6,4,1,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[3,8,7,1,6,4,5,2]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[3,4,2,7,8,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[4,3,2,1,5,8,6,7]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[4,1,3,7,5,6,8,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[3,4,6,1,5,8,2,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[6,5,8,7,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[4,1,7,3,8,5,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[6,1,7,3,5,4,8,2]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,6,8,7,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[6,8,5,7,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[7,1,3,4,2,8,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]
[7,6,1,4,3,5,8,2]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[3,5,4,1,6,7,8,2]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[2,5,3,4,8,6,1,7]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[2,4,8,3,6,1,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[8,2,4,3,7,5,6,1]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[6,8,2,1,5,7,3,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[7,2,8,4,1,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,2,4,8,6,5,3,7]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]
[7,1,5,6,8,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]
[7,3,5,6,1,4,8,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[3,7,6,5,1,4,8,2]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[2,7,6,5,3,8,1,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[2,7,8,1,4,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,8,2,5,7,1,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[4,1,6,8,5,3,7,2]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[5,2,6,4,8,3,1,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[1,2,6,3,4,8,7,5]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[5,3,6,1,4,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[6,7,1,3,4,5,8,2]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,7,3,2,4,8,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]
[6,1,4,2,8,3,5,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[5,8,6,7,2,1,4,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[7,4,1,5,8,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[6,3,4,2,8,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[4,3,8,7,5,2,6,1]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]
[6,8,7,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[8,6,1,3,5,4,2,7]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[2,7,6,3,4,5,8,1]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]
[5,3,8,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[2,4,8,7,3,5,6,1]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[2,5,3,6,8,7,4,1]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[3,8,7,2,6,4,5,1]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[4,5,8,7,2,6,3,1]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[8,5,2,7,1,4,3,6]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[5,1,7,2,4,3,8,6]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[8,2,3,7,6,4,5,1]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]
[3,7,5,8,2,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[1,6,7,4,8,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[8,2,1,3,5,6,7,4]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]
[4,1,3,8,2,6,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[3,6,1,4,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[6,2,7,4,5,8,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[2,1,8,4,5,7,3,6]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]
[1,8,5,7,3,2,4,6]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[3,2,1,6,4,8,5,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[2,1,8,5,4,3,6,7]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[2,7,4,1,5,3,8,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[7,4,8,6,2,3,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[7,3,2,4,8,6,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[7,1,3,2,8,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[5,1,7,4,2,3,8,6]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,3,4,8,6,5,2,7]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]
[4,1,8,6,5,3,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[4,8,5,3,6,2,7,1]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]
[7,5,2,8,4,6,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[5,7,4,3,6,2,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[6,7,5,1,2,8,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[7,5,1,4,2,6,8,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[5,2,6,8,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[6,2,7,5,8,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[2,1,5,6,8,3,7,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[1,2,7,4,8,3,6,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,6,8,3,2,7,4,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,6,7,5,2,8,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]
[7,5,1,2,8,4,6,3]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[5,4,8,3,6,2,7,1]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[5,8,2,7,4,3,6,1]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,7,3,8,2,4,6,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[5,7,3,6,4,8,2,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[3,6,2,4,7,1,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[4,2,8,5,1,6,7,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[1,2,8,3,7,5,4,6]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[1,6,3,8,7,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[4,3,8,1,2,6,7,5]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[3,8,5,7,1,4,2,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[4,7,2,5,1,3,8,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[5,1,7,4,8,6,3,2]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[3,6,5,2,1,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[5,2,8,4,7,3,1,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,2,7,4,1,3,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[5,2,6,4,1,8,7,3]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[6,3,2,1,4,8,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[3,1,4,6,2,8,7,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[6,3,5,1,7,4,2,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[5,4,7,6,3,8,1,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[4,6,3,7,5,8,1,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[5,7,4,3,8,1,2,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,5,7,4,8,6,3,2]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]
[1,8,2,7,6,5,4,3]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]
[3,8,1,6,7,5,4,2]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[3,7,2,6,8,5,1,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[8,2,4,3,6,1,5,7]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]
[1,7,8,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]
[7,3,8,1,4,2,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,8,4,5,3,2,6,7]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[3,8,7,4,2,6,1,5]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[3,7,8,1,2,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[3,5,6,2,7,1,4,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[3,7,1,6,8,2,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[8,1,7,6,2,4,3,5]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,6,4,5,7,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[8,3,6,1,7,2,4,5]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[7,3,5,2,1,8,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[7,4,1,6,5,8,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[6,4,2,8,7,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[4,2,1,5,8,7,3,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[1,5,3,6,8,7,4,2]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,5,4,6,1,8,2,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[3,1,5,7,6,8,2,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[6,4,5,7,2,8,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[5,3,6,4,2,8,1,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[4,1,5,3,8,2,7,6]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[2,6,3,5,4,8,1,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[3,7,4,5,6,8,1,2]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[2,5,7,3,6,8,1,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[7,6,4,5,2,8,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[5,4,3,1,8,2,7,6]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[8,2,6,4,7,3,1,5]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[8,6,1,7,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,2,8,3,5,4,6,7]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]
[1,7,8,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]
[3,1,6,8,4,5,7,2]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,4,5,8,3,6,7,2]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]
[2,5,7,1,8,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[6,2,7,1,8,4,5,3]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[4,7,1,3,8,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[3,7,2,1,8,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]
[2,1,5,8,3,6,7,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[4,2,7,1,8,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[4,3,1,6,8,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[5,3,4,6,8,2,7,1]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[3,5,1,6,8,2,7,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[5,1,8,7,4,2,3,6]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[5,8,3,2,6,4,1,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[7,3,8,2,6,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[3,8,7,4,5,6,1,2]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]
[2,7,6,3,5,4,1,8]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[3,8,7,4,6,2,5,1]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[5,8,3,7,6,2,4,1]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[8,7,2,5,4,3,1,6]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[5,8,7,4,3,6,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[5,8,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[6,5,8,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[2,6,4,7,1,5,3,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[5,3,8,1,7,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[5,4,8,7,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[4,8,6,7,5,3,1,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[4,8,6,5,7,2,1,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[6,2,1,5,8,3,7,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[6,5,4,8,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[5,8,4,7,2,6,3,1]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[5,8,3,2,7,6,4,1]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[5,8,3,2,6,7,1,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[6,5,3,2,8,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[6,4,3,2,1,8,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[6,3,4,1,2,8,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[4,6,3,2,5,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[3,5,7,4,2,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[4,3,6,1,5,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[4,2,1,5,7,6,3,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[3,5,4,7,1,6,2,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[3,4,5,8,6,7,1,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[3,4,6,5,8,1,7,2]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[4,3,5,1,6,8,7,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[2,1,5,3,8,4,7,6]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[3,1,8,2,5,4,7,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[8,1,3,2,6,4,7,5]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]
[3,1,8,2,6,4,7,5]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[2,1,8,3,6,4,7,5]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]
[2,1,6,3,8,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[2,1,7,3,5,4,8,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[2,1,7,3,6,4,8,5]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]
[2,1,7,3,8,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]
[8,1,4,2,7,3,6,5]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[4,1,8,2,7,3,6,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[4,1,7,2,8,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[3,1,7,2,8,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[3,1,6,2,5,4,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[7,1,3,2,5,4,8,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[7,1,3,2,6,4,8,5]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[7,1,3,2,8,4,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]
[7,1,8,2,4,3,6,5]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]
[8,1,7,2,5,3,6,4]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]
[7,1,5,2,8,3,6,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[6,1,4,2,5,3,8,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[4,1,6,2,5,3,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[4,1,7,2,5,3,8,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[1,