Identifier
-
Mp00069:
Permutations
—complement⟶
Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St000024: Dyck paths ⟶ ℤ (values match St000443The number of long tunnels of a Dyck path., St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path., St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra., St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra.)
Values
=>
Cc0005;cc-rep-2
Cc0005;cc-rep
[1]=>[1]=>[1,0]=>[1,0]=>0
[1,2]=>[2,1]=>[1,1,0,0]=>[1,0,1,0]=>0
[2,1]=>[1,2]=>[1,0,1,0]=>[1,1,0,0]=>1
[1,2,3]=>[3,2,1]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>0
[1,3,2]=>[3,1,2]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>0
[2,1,3]=>[2,3,1]=>[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>1
[2,3,1]=>[2,1,3]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>1
[3,1,2]=>[1,3,2]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>1
[3,2,1]=>[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>2
[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[1,2,4,3]=>[4,3,1,2]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[1,3,2,4]=>[4,2,3,1]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[1,3,4,2]=>[4,2,1,3]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[1,4,2,3]=>[4,1,3,2]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[1,4,3,2]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>0
[2,1,3,4]=>[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>1
[2,1,4,3]=>[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>1
[2,3,1,4]=>[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>1
[2,3,4,1]=>[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>1
[2,4,1,3]=>[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>1
[2,4,3,1]=>[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>1
[3,1,2,4]=>[2,4,3,1]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>1
[3,1,4,2]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>1
[3,2,1,4]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>2
[3,2,4,1]=>[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>2
[3,4,1,2]=>[2,1,4,3]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>1
[3,4,2,1]=>[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>2
[4,1,2,3]=>[1,4,3,2]=>[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>1
[4,1,3,2]=>[1,4,2,3]=>[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>1
[4,2,1,3]=>[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>2
[4,2,3,1]=>[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>2
[4,3,1,2]=>[1,2,4,3]=>[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>2
[4,3,2,1]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>3
[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,4]=>[5,4,3,1,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,5]=>[5,4,2,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,3]=>[5,4,2,1,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,4]=>[5,4,1,3,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,3]=>[5,4,1,2,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,5]=>[5,3,4,2,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,4]=>[5,3,4,1,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,5]=>[5,3,2,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,2]=>[5,3,2,1,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,4]=>[5,3,1,4,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,2]=>[5,3,1,2,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,5]=>[5,2,4,3,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,3]=>[5,2,4,1,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,5]=>[5,2,3,4,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,2]=>[5,2,3,1,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,3]=>[5,2,1,4,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,2]=>[5,2,1,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,4]=>[5,1,4,3,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,3]=>[5,1,4,2,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,4]=>[5,1,3,4,2]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,2]=>[5,1,3,2,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,3]=>[5,1,2,4,3]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,2]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>0
[2,1,3,4,5]=>[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,4]=>[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,5]=>[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,3]=>[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,4]=>[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,3]=>[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,5]=>[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[2,3,1,5,4]=>[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,5,1]=>[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,1,4]=>[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,4,1]=>[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[2,4,1,3,5]=>[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[2,4,1,5,3]=>[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,1,5]=>[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,5,1]=>[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,1,3]=>[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,3,1]=>[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[2,5,1,3,4]=>[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[2,5,1,4,3]=>[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,1,4]=>[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,4,1]=>[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,1,3]=>[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,3,1]=>[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>1
[3,1,2,4,5]=>[3,5,4,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,4]=>[3,5,4,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,5]=>[3,5,2,4,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,2]=>[3,5,2,1,4]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,4]=>[3,5,1,4,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,2]=>[3,5,1,2,4]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[3,2,1,4,5]=>[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,4]=>[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,5]=>[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,5,1]=>[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,1,4]=>[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,4,1]=>[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>2
[3,4,1,2,5]=>[3,2,5,4,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>1
[3,4,1,5,2]=>[3,2,5,1,4]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>1
[3,4,2,1,5]=>[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>2
[3,4,2,5,1]=>[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>2
[3,4,5,1,2]=>[3,2,1,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>1
[3,4,5,2,1]=>[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>2
[3,5,1,2,4]=>[3,1,5,4,2]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>1
[3,5,1,4,2]=>[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>1
[3,5,2,1,4]=>[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>2
[3,5,2,4,1]=>[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>2
[3,5,4,1,2]=>[3,1,2,5,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>1
[3,5,4,2,1]=>[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>2
[4,1,2,3,5]=>[2,5,4,3,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,3]=>[2,5,4,1,3]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,5]=>[2,5,3,4,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,2]=>[2,5,3,1,4]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,3]=>[2,5,1,4,3]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,2]=>[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[4,2,1,3,5]=>[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,3]=>[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,5]=>[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,5,1]=>[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,1,3]=>[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,3,1]=>[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>2
[4,3,1,2,5]=>[2,3,5,4,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,2]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>2
[4,3,2,1,5]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>3
[4,3,2,5,1]=>[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>3
[4,3,5,1,2]=>[2,3,1,5,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>2
[4,3,5,2,1]=>[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>3
[4,5,1,2,3]=>[2,1,5,4,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>1
[4,5,1,3,2]=>[2,1,5,3,4]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>1
[4,5,2,1,3]=>[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>2
[4,5,2,3,1]=>[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>2
[4,5,3,1,2]=>[2,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>2
[4,5,3,2,1]=>[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>3
[5,1,2,3,4]=>[1,5,4,3,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,3]=>[1,5,4,2,3]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,4]=>[1,5,3,4,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,2]=>[1,5,3,2,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,3]=>[1,5,2,4,3]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,2]=>[1,5,2,3,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[5,2,1,3,4]=>[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,3]=>[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,4]=>[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,4,1]=>[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,1,3]=>[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,3,1]=>[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>2
[5,3,1,2,4]=>[1,3,5,4,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,2]=>[1,3,5,2,4]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>2
[5,3,2,1,4]=>[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[5,3,2,4,1]=>[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>3
[5,3,4,1,2]=>[1,3,2,5,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>2
[5,3,4,2,1]=>[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>3
[5,4,1,2,3]=>[1,2,5,4,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,2]=>[1,2,5,3,4]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>2
[5,4,2,1,3]=>[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>3
[5,4,2,3,1]=>[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>3
[5,4,3,1,2]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>3
[5,4,3,2,1]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>4
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,5,3]=>[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,6,5,1]=>[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,4,6,1]=>[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,6,4,1]=>[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,4,1,5]=>[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,4,5,1]=>[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,5,1,4]=>[5,4,1,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,5,4,1]=>[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,6,5,1]=>[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,3,6,1]=>[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,6,3,1]=>[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,1,5,3]=>[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,3,1,5]=>[5,3,1,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,3,5,1]=>[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,5,1,3]=>[5,3,1,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,5,3,1]=>[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,6,3]=>[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,4,3]=>[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,4,1,6]=>[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,4,6,1]=>[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,3,6,1,4]=>[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,6,4,1]=>[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,3,1,6]=>[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,3,6,1]=>[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,6,1,3]=>[5,2,3,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,6,3,1]=>[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,3,1,4]=>[5,2,1,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,3,4,1]=>[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,4,1,3]=>[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,3,5,4]=>[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,5,3]=>[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,4,3]=>[5,1,6,2,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,4,5]=>[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,1,5,4]=>[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,4,5,1]=>[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,3,5,1,4]=>[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,5,4,1]=>[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,1,3,5]=>[5,1,3,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,1,5,3]=>[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,3,5,1]=>[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,5,1,3]=>[5,1,3,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,5,3,1]=>[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,1,3,4]=>[5,1,2,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,1,4,3]=>[5,1,2,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,3,1,4]=>[5,1,2,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,3,4,1]=>[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,4,1,3]=>[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,4,3,1]=>[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,5,2]=>[4,6,3,1,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,6,2]=>[4,6,2,3,1,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,4,2]=>[4,6,2,1,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,4,2]=>[4,6,1,2,3,5]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,6,5,1]=>[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,4,1,6]=>[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,6,1,4]=>[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,6,4,1]=>[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,4,1,5]=>[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,4,5,1]=>[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,5,1,4]=>[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,5,4,1]=>[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,6,2]=>[4,3,6,2,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,5,2]=>[4,3,6,1,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,6,5,1]=>[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,5,1,6,2]=>[4,3,2,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,6,2]=>[4,2,6,3,1,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,4,2]=>[4,2,6,1,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,2,6,1,4]=>[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,6,4,1]=>[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,4,1,6,2]=>[4,2,3,6,1,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,4,2,1,6]=>[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,4,2,6,1]=>[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,4,6,1,2]=>[4,2,3,1,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,4,6,2,1]=>[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,6,1,4,2]=>[4,2,1,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,6,2,1,4]=>[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,6,2,4,1]=>[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,6,4,1,2]=>[4,2,1,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,6,4,2,1]=>[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,2,5,4]=>[4,1,6,5,2,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,2,5]=>[4,1,6,3,5,2]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,5,2]=>[4,1,6,3,2,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,2,4]=>[4,1,6,2,5,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,1,5,4]=>[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,5,4,1]=>[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,4,1,5,2]=>[4,1,3,6,2,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,4,2,1,5]=>[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,4,2,5,1]=>[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,4,5,1,2]=>[4,1,3,2,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,4,5,2,1]=>[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,5,1,4,2]=>[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,5,2,4,1]=>[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,5,4,1,2]=>[4,1,2,3,6,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,5,4,2,1]=>[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,5,3]=>[3,6,5,1,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,2,6]=>[3,6,4,2,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,6,2]=>[3,6,4,2,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,2,5]=>[3,6,4,1,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,5,2]=>[3,6,4,1,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,2,6]=>[3,6,2,4,5,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,6,2]=>[3,6,2,4,1,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,2,3]=>[3,6,2,1,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,3,2]=>[3,6,2,1,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,5,3]=>[3,6,1,5,2,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,2,5]=>[3,6,1,4,5,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,5,2]=>[3,6,1,4,2,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,2,3]=>[3,6,1,2,5,4]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,3,2]=>[3,6,1,2,4,5]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,6,3]=>[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,6,5]=>[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,6,5,1]=>[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,1,6,3]=>[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,3,1,6]=>[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,3,6,1]=>[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,6,1,3]=>[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,6,3,1]=>[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,3,1,5]=>[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,3,5,1]=>[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,5,1,3]=>[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,5,3,1]=>[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,2,6]=>[3,4,6,2,5,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,6,2]=>[3,4,6,2,1,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,5,2]=>[3,4,6,1,2,5]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,6,5,1]=>[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,5,1,6,2]=>[3,4,2,6,1,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,2,6,3]=>[3,2,6,5,1,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,2,6]=>[3,2,6,4,5,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,6,2]=>[3,2,6,4,1,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,3,2]=>[3,2,6,1,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,1,6,3]=>[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,6,1,3]=>[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,6,3,1]=>[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,5,3,1,6,2]=>[3,2,4,6,1,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,5,6,1,3,2]=>[3,2,1,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,2,5,3]=>[3,1,6,5,2,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,2,5]=>[3,1,6,4,5,2]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,5,2]=>[3,1,6,4,2,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,2,3]=>[3,1,6,2,5,4]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,3,2]=>[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,2,1,3,5]=>[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,1,5,3]=>[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,3,1,5]=>[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,3,5,1]=>[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,5,3,1]=>[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,6,3,1,2,5]=>[3,1,4,6,5,2]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,6,3,1,5,2]=>[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,6,3,5,1,2]=>[3,1,4,2,6,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,6,5,1,2,3]=>[3,1,2,6,5,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,6,5,3,2,1]=>[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,6,3]=>[2,6,5,3,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,3,4]=>[2,6,5,1,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,4,3]=>[2,6,5,1,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,6,4]=>[2,6,4,5,1,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,2,6]=>[2,6,4,3,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,2,4]=>[2,6,4,1,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,4,2]=>[2,6,4,1,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,6,3]=>[2,6,3,5,1,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,2,3]=>[2,6,3,1,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,3,2]=>[2,6,3,1,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,3,4]=>[2,6,1,5,4,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,4,3]=>[2,6,1,5,3,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,2,4]=>[2,6,1,4,5,3]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,4,2]=>[2,6,1,4,3,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,2,3]=>[2,6,1,3,5,4]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,3,2]=>[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,3,6,4]=>[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,6,3]=>[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,3,4]=>[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,4,3]=>[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,3,6,1,4]=>[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,6,4,1]=>[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,1,6,3]=>[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,3,1,6]=>[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,6,1,3]=>[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,6,3,1]=>[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,3,1,4]=>[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,3,4,1]=>[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,4,1,3]=>[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,2,6]=>[2,4,6,3,5,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,6,2]=>[2,4,6,3,1,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,2,4]=>[2,4,6,1,5,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,1,6,4]=>[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,6,4,1]=>[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,4,1,6,2]=>[2,4,3,6,1,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,3,6,1,2,4]=>[2,4,1,6,5,3]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,6,2,1,4]=>[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,6,4,1,2]=>[2,4,1,3,6,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,6,4,2,1]=>[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,2,6,3]=>[2,3,6,5,1,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,6,2]=>[2,3,6,4,1,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,2,3]=>[2,3,6,1,5,4]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,1,6,3]=>[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,2,6,1,3]=>[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,6,3,1]=>[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,1,6,2]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>4
[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>4
[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>3
[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>4
[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>3
[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>3
[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>4
[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,2,4,3]=>[2,1,6,5,3,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,2,4]=>[2,1,6,4,5,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,4,2]=>[2,1,6,4,3,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,2,3]=>[2,1,6,3,5,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,3,2]=>[2,1,6,3,4,5]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,1,4,3]=>[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[5,6,2,4,1,3]=>[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,4,3,1]=>[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>2
[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>2
[5,6,3,1,4,2]=>[2,1,4,6,3,5]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>2
[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>3
[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>3
[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>2
[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>3
[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[5,6,4,1,3,2]=>[2,1,3,6,4,5]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>2
[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>3
[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>3
[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>3
[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>4
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,5,3]=>[1,6,5,3,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,2,5]=>[1,6,4,3,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,2,4]=>[1,6,4,2,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,4,2]=>[1,6,4,2,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,5,3]=>[1,6,3,5,2,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,2,3]=>[1,6,3,2,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,3,2]=>[1,6,3,2,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,4,2]=>[1,6,2,4,3,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,5,3]=>[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,1,5,4]=>[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,5,4,1]=>[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,1,5,3]=>[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,3,1,5]=>[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,5,1,3]=>[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,5,3,1]=>[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,1,4,3]=>[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,3,1,4]=>[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,3,4,1]=>[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,4,1,3]=>[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,4,3,1]=>[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,2,5]=>[1,4,6,3,5,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,5,2]=>[1,4,6,3,2,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,4,2]=>[1,4,6,2,3,5]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,4,1,5,2]=>[1,4,3,6,2,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,5,1,4,2]=>[1,4,2,6,3,5]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,5,4,2,1]=>[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,2,5,3]=>[1,3,6,5,2,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,5,2]=>[1,3,6,4,2,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,2,3]=>[1,3,6,2,5,4]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,3,2]=>[1,3,6,2,4,5]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,1,5,3]=>[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,2,5,1,3]=>[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>4
[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>3
[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>4
[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,4,5,1,3,2]=>[1,3,2,6,4,5]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>3
[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>3
[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,4,2]=>[1,2,6,4,3,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,4,3,1]=>[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,1,4,2]=>[1,2,4,6,3,5]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>4
[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>4
[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>4
[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>4
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>5
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,4,6,7,5]=>[6,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,6,4,7]=>[6,7,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,6,7,4]=>[6,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,7,4,6]=>[6,7,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,5,7,6,4]=>[6,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,4,7,5]=>[6,7,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,5,7,4]=>[6,7,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,7,4,5]=>[6,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,6,7,5,4]=>[6,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,7,5,6,4]=>[6,7,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,6,7,5]=>[6,7,4,5,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,3,6,7]=>[6,7,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,6,3,7]=>[6,7,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,6,7,3]=>[6,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,7,3,6]=>[6,7,4,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,5,7,6,3]=>[6,7,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,3,5,7]=>[6,7,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,3,7,5]=>[6,7,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,5,3,7]=>[6,7,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,5,7,3]=>[6,7,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,7,3,5]=>[6,7,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,6,7,5,3]=>[6,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,7,3,5,6]=>[6,7,4,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,7,3,6,5]=>[6,7,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,7,5,3,6]=>[6,7,4,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,7,5,6,3]=>[6,7,4,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,7,6,3,5]=>[6,7,4,1,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,4,7,6,5,3]=>[6,7,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,6,4,7]=>[6,7,3,5,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,6,7,4]=>[6,7,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,7,4,6]=>[6,7,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,3,7,6,4]=>[6,7,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,6,3,7]=>[6,7,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,6,7,3]=>[6,7,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,7,3,6]=>[6,7,3,4,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,4,7,6,3]=>[6,7,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,3,4,7]=>[6,7,3,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,3,7,4]=>[6,7,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,4,3,7]=>[6,7,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,4,7,3]=>[6,7,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,7,3,4]=>[6,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,6,7,4,3]=>[6,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,7,3,4,6]=>[6,7,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,7,3,6,4]=>[6,7,3,1,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,7,4,3,6]=>[6,7,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,7,4,6,3]=>[6,7,3,1,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,7,6,3,4]=>[6,7,3,1,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,5,7,6,4,3]=>[6,7,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,4,7,5]=>[6,7,2,5,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,5,7,4]=>[6,7,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,7,4,5]=>[6,7,2,5,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,3,7,5,4]=>[6,7,2,5,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,3,7,5]=>[6,7,2,4,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,5,3,7]=>[6,7,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,5,7,3]=>[6,7,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,7,3,5]=>[6,7,2,4,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,4,7,5,3]=>[6,7,2,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,3,7,4]=>[6,7,2,3,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,4,7,3]=>[6,7,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,7,3,4]=>[6,7,2,3,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,5,7,4,3]=>[6,7,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,7,3,4,5]=>[6,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,7,3,5,4]=>[6,7,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,7,4,3,5]=>[6,7,2,1,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,7,4,5,3]=>[6,7,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,7,5,3,4]=>[6,7,2,1,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,6,7,5,4,3]=>[6,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,3,5,6,4]=>[6,7,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,4,5,3,6]=>[6,7,1,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,4,5,6,3]=>[6,7,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,4,6,3,5]=>[6,7,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,4,6,5,3]=>[6,7,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,5,3,6,4]=>[6,7,1,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,5,4,6,3]=>[6,7,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,5,6,3,4]=>[6,7,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,5,6,4,3]=>[6,7,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,6,4,5,3]=>[6,7,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,5,7,6]=>[6,5,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,6,5,7]=>[6,5,7,4,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,4,7,6,5]=>[6,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,4,6,7]=>[6,5,7,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,4,7,6]=>[6,5,7,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,6,4,7]=>[6,5,7,3,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,6,7,4]=>[6,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,7,4,6]=>[6,5,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,5,7,6,4]=>[6,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,4,5,7]=>[6,5,7,2,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,4,7,5]=>[6,5,7,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,5,4,7]=>[6,5,7,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,5,7,4]=>[6,5,7,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,7,4,5]=>[6,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,6,7,5,4]=>[6,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,7,4,5,6]=>[6,5,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,7,4,6,5]=>[6,5,7,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,7,5,4,6]=>[6,5,7,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,7,5,6,4]=>[6,5,7,1,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,7,6,4,5]=>[6,5,7,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,1,7,6,5,4]=>[6,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,5,7,6]=>[6,5,4,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,6,5,7]=>[6,5,4,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,6,7,5]=>[6,5,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,7,5,6]=>[6,5,4,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,1,7,6,5]=>[6,5,4,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,5,1,7,6]=>[6,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,5,7,6,1]=>[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,6,5,1,7]=>[6,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,6,5,7,1]=>[6,5,4,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,4,6,7,1,5]=>[6,5,4,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,6,7,5,1]=>[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,7,1,6,5]=>[6,5,4,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,4,7,5,1,6]=>[6,5,4,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,7,5,6,1]=>[6,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,4,7,6,5,1]=>[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,5,1,4,7,6]=>[6,5,3,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,5,1,6,4,7]=>[6,5,3,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,5,1,7,6,4]=>[6,5,3,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,5,4,1,6,7]=>[6,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,4,1,7,6]=>[6,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,4,6,1,7]=>[6,5,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,4,6,7,1]=>[6,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,4,7,1,6]=>[6,5,3,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,4,7,6,1]=>[6,5,3,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,6,1,4,7]=>[6,5,3,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,6,1,7,4]=>[6,5,3,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,6,4,1,7]=>[6,5,3,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,6,4,7,1]=>[6,5,3,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,7,1,4,6]=>[6,5,3,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,7,1,6,4]=>[6,5,3,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,5,7,4,1,6]=>[6,5,3,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,7,4,6,1]=>[6,5,3,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,5,7,6,1,4]=>[6,5,3,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,5,7,6,4,1]=>[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,6,1,5,4,7]=>[6,5,2,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,6,1,5,7,4]=>[6,5,2,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,6,1,7,4,5]=>[6,5,2,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,6,1,7,5,4]=>[6,5,2,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,6,4,1,5,7]=>[6,5,2,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,4,1,7,5]=>[6,5,2,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,4,5,1,7]=>[6,5,2,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,4,5,7,1]=>[6,5,2,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,4,7,1,5]=>[6,5,2,4,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,4,7,5,1]=>[6,5,2,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,5,1,4,7]=>[6,5,2,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,5,4,1,7]=>[6,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,5,4,7,1]=>[6,5,2,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,5,7,1,4]=>[6,5,2,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,5,7,4,1]=>[6,5,2,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,7,1,4,5]=>[6,5,2,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,7,1,5,4]=>[6,5,2,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,6,7,4,1,5]=>[6,5,2,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,7,4,5,1]=>[6,5,2,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,6,7,5,1,4]=>[6,5,2,1,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,6,7,5,4,1]=>[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,7,1,4,6,5]=>[6,5,1,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,7,1,5,4,6]=>[6,5,1,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,7,1,5,6,4]=>[6,5,1,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,7,1,6,5,4]=>[6,5,1,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,7,4,1,6,5]=>[6,5,1,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,7,4,5,1,6]=>[6,5,1,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,7,4,5,6,1]=>[6,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,7,4,6,1,5]=>[6,5,1,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,7,4,6,5,1]=>[6,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,7,5,1,6,4]=>[6,5,1,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,7,5,4,1,6]=>[6,5,1,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,7,5,4,6,1]=>[6,5,1,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,7,5,6,4,1]=>[6,5,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,7,6,1,5,4]=>[6,5,1,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,3,7,6,4,1,5]=>[6,5,1,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,7,6,4,5,1]=>[6,5,1,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,3,7,6,5,1,4]=>[6,5,1,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,3,7,6,5,4,1]=>[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,3,5,7,6]=>[6,4,7,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,3,6,5,7]=>[6,4,7,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,3,6,7,5]=>[6,4,7,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,3,7,5,6]=>[6,4,7,5,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,3,7,6,5]=>[6,4,7,5,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,3,6,7]=>[6,4,7,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,3,7,6]=>[6,4,7,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,6,3,7]=>[6,4,7,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,5,7,6,3]=>[6,4,7,3,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,3,5,7]=>[6,4,7,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,5,3,7]=>[6,4,7,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,5,7,3]=>[6,4,7,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,7,3,5]=>[6,4,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,6,7,5,3]=>[6,4,7,2,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,7,3,6,5]=>[6,4,7,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,7,5,3,6]=>[6,4,7,1,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,7,5,6,3]=>[6,4,7,1,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,1,7,6,5,3]=>[6,4,7,1,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,5,6,7]=>[6,4,5,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,5,7,6]=>[6,4,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,6,5,7]=>[6,4,5,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,6,7,5]=>[6,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,7,5,6]=>[6,4,5,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,1,7,6,5]=>[6,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,3,5,1,6,7]=>[6,4,5,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,5,1,7,6]=>[6,4,5,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,5,6,1,7]=>[6,4,5,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,5,6,7,1]=>[6,4,5,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,3,5,7,1,6]=>[6,4,5,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,5,7,6,1]=>[6,4,5,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,3,6,1,5,7]=>[6,4,5,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,6,1,7,5]=>[6,4,5,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,6,5,1,7]=>[6,4,5,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,6,5,7,1]=>[6,4,5,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,3,6,7,1,5]=>[6,4,5,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,6,7,5,1]=>[6,4,5,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,3,7,1,5,6]=>[6,4,5,1,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,7,1,6,5]=>[6,4,5,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,3,7,5,1,6]=>[6,4,5,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,7,5,6,1]=>[6,4,5,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,3,7,6,1,5]=>[6,4,5,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,3,7,6,5,1]=>[6,4,5,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,1,3,6,7]=>[6,4,3,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,5,1,3,7,6]=>[6,4,3,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,5,1,6,3,7]=>[6,4,3,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,5,1,6,7,3]=>[6,4,3,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,5,1,7,3,6]=>[6,4,3,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,5,1,7,6,3]=>[6,4,3,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,5,3,1,6,7]=>[6,4,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,3,1,7,6]=>[6,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,3,6,1,7]=>[6,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,3,7,1,6]=>[6,4,3,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,3,7,6,1]=>[6,4,3,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,6,1,3,7]=>[6,4,3,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,6,1,7,3]=>[6,4,3,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,6,3,1,7]=>[6,4,3,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,6,3,7,1]=>[6,4,3,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,6,7,1,3]=>[6,4,3,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,6,7,3,1]=>[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,7,1,3,6]=>[6,4,3,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,7,1,6,3]=>[6,4,3,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,5,7,3,1,6]=>[6,4,3,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,7,3,6,1]=>[6,4,3,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,5,7,6,1,3]=>[6,4,3,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,5,7,6,3,1]=>[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,6,1,3,7,5]=>[6,4,2,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,6,1,5,3,7]=>[6,4,2,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,6,1,5,7,3]=>[6,4,2,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,6,1,7,3,5]=>[6,4,2,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,6,1,7,5,3]=>[6,4,2,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,6,3,1,5,7]=>[6,4,2,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,3,1,7,5]=>[6,4,2,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,3,5,1,7]=>[6,4,2,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,3,5,7,1]=>[6,4,2,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,3,7,1,5]=>[6,4,2,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,3,7,5,1]=>[6,4,2,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,5,1,3,7]=>[6,4,2,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,5,1,7,3]=>[6,4,2,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,5,3,1,7]=>[6,4,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,5,3,7,1]=>[6,4,2,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,5,7,1,3]=>[6,4,2,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,5,7,3,1]=>[6,4,2,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,6,7,3,1,5]=>[6,4,2,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,7,3,5,1]=>[6,4,2,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,6,7,5,1,3]=>[6,4,2,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,7,1,3,6,5]=>[6,4,1,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,7,1,5,3,6]=>[6,4,1,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,7,1,5,6,3]=>[6,4,1,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,7,1,6,3,5]=>[6,4,1,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,7,1,6,5,3]=>[6,4,1,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,4,7,3,1,5,6]=>[6,4,1,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,7,3,1,6,5]=>[6,4,1,5,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,7,3,5,1,6]=>[6,4,1,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,7,3,5,6,1]=>[6,4,1,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,7,3,6,1,5]=>[6,4,1,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,7,3,6,5,1]=>[6,4,1,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,7,5,1,3,6]=>[6,4,1,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,7,5,1,6,3]=>[6,4,1,3,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,7,5,3,1,6]=>[6,4,1,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,7,5,3,6,1]=>[6,4,1,3,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,7,5,6,1,3]=>[6,4,1,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,7,5,6,3,1]=>[6,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,7,6,1,3,5]=>[6,4,1,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,7,6,1,5,3]=>[6,4,1,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,4,7,6,3,1,5]=>[6,4,1,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,7,6,3,5,1]=>[6,4,1,2,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,4,7,6,5,1,3]=>[6,4,1,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,4,7,6,5,3,1]=>[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,3,4,7,6]=>[6,3,7,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,3,6,4,7]=>[6,3,7,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,3,7,6,4]=>[6,3,7,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,3,6,7]=>[6,3,7,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,3,7,6]=>[6,3,7,4,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,6,3,7]=>[6,3,7,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,6,7,3]=>[6,3,7,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,7,3,6]=>[6,3,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,4,7,6,3]=>[6,3,7,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,3,4,7]=>[6,3,7,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,3,7,4]=>[6,3,7,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,4,3,7]=>[6,3,7,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,4,7,3]=>[6,3,7,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,7,3,4]=>[6,3,7,2,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,6,7,4,3]=>[6,3,7,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,7,3,4,6]=>[6,3,7,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,7,3,6,4]=>[6,3,7,1,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,7,4,3,6]=>[6,3,7,1,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,7,4,6,3]=>[6,3,7,1,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,7,6,3,4]=>[6,3,7,1,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,1,7,6,4,3]=>[6,3,7,1,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,4,6,7]=>[6,3,5,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,4,7,6]=>[6,3,5,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,6,4,7]=>[6,3,5,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,6,7,4]=>[6,3,5,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,7,4,6]=>[6,3,5,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,1,7,6,4]=>[6,3,5,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,3,4,1,6,7]=>[6,3,5,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,4,1,7,6]=>[6,3,5,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,4,6,1,7]=>[6,3,5,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,3,4,7,1,6]=>[6,3,5,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,4,7,6,1]=>[6,3,5,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,3,6,1,4,7]=>[6,3,5,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,6,1,7,4]=>[6,3,5,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,6,4,1,7]=>[6,3,5,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,6,4,7,1]=>[6,3,5,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,3,7,1,4,6]=>[6,3,5,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,7,1,6,4]=>[6,3,5,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,3,7,4,1,6]=>[6,3,5,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,7,4,6,1]=>[6,3,5,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,3,7,6,1,4]=>[6,3,5,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,3,7,6,4,1]=>[6,3,5,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,1,3,6,7]=>[6,3,4,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,4,1,3,7,6]=>[6,3,4,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,4,1,6,3,7]=>[6,3,4,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,4,1,7,6,3]=>[6,3,4,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,4,3,1,6,7]=>[6,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,3,1,7,6]=>[6,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,3,6,1,7]=>[6,3,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,3,7,1,6]=>[6,3,4,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,3,7,6,1]=>[6,3,4,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,6,1,3,7]=>[6,3,4,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,6,1,7,3]=>[6,3,4,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,6,3,1,7]=>[6,3,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,6,3,7,1]=>[6,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,6,7,1,3]=>[6,3,4,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,6,7,3,1]=>[6,3,4,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,7,1,3,6]=>[6,3,4,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,7,1,6,3]=>[6,3,4,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,4,7,3,1,6]=>[6,3,4,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,7,3,6,1]=>[6,3,4,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,4,7,6,1,3]=>[6,3,4,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,4,7,6,3,1]=>[6,3,4,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,6,1,3,7,4]=>[6,3,2,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,6,1,4,3,7]=>[6,3,2,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,6,1,4,7,3]=>[6,3,2,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,6,1,7,3,4]=>[6,3,2,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,6,1,7,4,3]=>[6,3,2,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,6,3,1,4,7]=>[6,3,2,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,3,1,7,4]=>[6,3,2,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,3,4,1,7]=>[6,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,3,4,7,1]=>[6,3,2,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,3,7,1,4]=>[6,3,2,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,3,7,4,1]=>[6,3,2,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,4,1,3,7]=>[6,3,2,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,4,1,7,3]=>[6,3,2,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,4,3,1,7]=>[6,3,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,4,3,7,1]=>[6,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,4,7,1,3]=>[6,3,2,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,4,7,3,1]=>[6,3,2,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,7,1,3,4]=>[6,3,2,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,7,1,4,3]=>[6,3,2,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,6,7,3,1,4]=>[6,3,2,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,7,3,4,1]=>[6,3,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,6,7,4,1,3]=>[6,3,2,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,6,7,4,3,1]=>[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,7,1,3,6,4]=>[6,3,1,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,7,1,4,3,6]=>[6,3,1,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,7,1,4,6,3]=>[6,3,1,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,7,1,6,3,4]=>[6,3,1,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,7,1,6,4,3]=>[6,3,1,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,5,7,3,1,4,6]=>[6,3,1,5,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,7,3,1,6,4]=>[6,3,1,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,7,3,4,1,6]=>[6,3,1,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,7,3,4,6,1]=>[6,3,1,5,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,7,3,6,1,4]=>[6,3,1,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,7,3,6,4,1]=>[6,3,1,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,7,4,1,6,3]=>[6,3,1,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,7,4,3,1,6]=>[6,3,1,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,7,4,3,6,1]=>[6,3,1,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,7,4,6,1,3]=>[6,3,1,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,7,4,6,3,1]=>[6,3,1,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,7,6,1,3,4]=>[6,3,1,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,7,6,1,4,3]=>[6,3,1,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,5,7,6,3,1,4]=>[6,3,1,2,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,7,6,3,4,1]=>[6,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,5,7,6,4,1,3]=>[6,3,1,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,5,7,6,4,3,1]=>[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,3,5,4,7]=>[6,2,7,5,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,3,5,7,4]=>[6,2,7,5,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,3,7,4,5]=>[6,2,7,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,3,7,5,4]=>[6,2,7,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,3,5,7]=>[6,2,7,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,3,7,5]=>[6,2,7,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,5,3,7]=>[6,2,7,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,5,7,3]=>[6,2,7,4,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,7,3,5]=>[6,2,7,4,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,4,7,5,3]=>[6,2,7,4,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,3,4,7]=>[6,2,7,3,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,4,3,7]=>[6,2,7,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,4,7,3]=>[6,2,7,3,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,5,7,4,3]=>[6,2,7,3,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,7,3,4,5]=>[6,2,7,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,7,3,5,4]=>[6,2,7,1,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,7,4,3,5]=>[6,2,7,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,7,4,5,3]=>[6,2,7,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,7,5,3,4]=>[6,2,7,1,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,1,7,5,4,3]=>[6,2,7,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,4,5,7]=>[6,2,5,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,4,7,5]=>[6,2,5,7,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,5,4,7]=>[6,2,5,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,5,7,4]=>[6,2,5,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,7,4,5]=>[6,2,5,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,1,7,5,4]=>[6,2,5,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,3,4,1,5,7]=>[6,2,5,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,4,1,7,5]=>[6,2,5,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,4,5,1,7]=>[6,2,5,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,4,5,7,1]=>[6,2,5,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,3,4,7,1,5]=>[6,2,5,4,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,4,7,5,1]=>[6,2,5,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,3,5,1,4,7]=>[6,2,5,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,5,1,7,4]=>[6,2,5,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,5,4,1,7]=>[6,2,5,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,5,4,7,1]=>[6,2,5,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,3,5,7,1,4]=>[6,2,5,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,5,7,4,1]=>[6,2,5,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,3,7,1,4,5]=>[6,2,5,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,7,1,5,4]=>[6,2,5,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,3,7,4,1,5]=>[6,2,5,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,7,4,5,1]=>[6,2,5,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,3,7,5,1,4]=>[6,2,5,1,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,3,7,5,4,1]=>[6,2,5,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,1,3,5,7]=>[6,2,4,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,4,1,5,3,7]=>[6,2,4,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,4,1,5,7,3]=>[6,2,4,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,4,1,7,3,5]=>[6,2,4,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,4,1,7,5,3]=>[6,2,4,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,4,3,1,5,7]=>[6,2,4,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,3,1,7,5]=>[6,2,4,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,3,5,1,7]=>[6,2,4,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,3,5,7,1]=>[6,2,4,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,3,7,1,5]=>[6,2,4,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,3,7,5,1]=>[6,2,4,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,5,1,3,7]=>[6,2,4,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,5,3,1,7]=>[6,2,4,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,5,3,7,1]=>[6,2,4,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,5,7,1,3]=>[6,2,4,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,5,7,3,1]=>[6,2,4,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,7,1,3,5]=>[6,2,4,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,7,1,5,3]=>[6,2,4,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,4,7,3,1,5]=>[6,2,4,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,7,3,5,1]=>[6,2,4,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,4,7,5,1,3]=>[6,2,4,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,4,7,5,3,1]=>[6,2,4,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,1,3,4,7]=>[6,2,3,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,1,4,3,7]=>[6,2,3,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,1,4,7,3]=>[6,2,3,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,1,7,3,4]=>[6,2,3,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,1,7,4,3]=>[6,2,3,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,5,3,1,4,7]=>[6,2,3,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,3,1,7,4]=>[6,2,3,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,3,4,1,7]=>[6,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,3,4,7,1]=>[6,2,3,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,3,7,1,4]=>[6,2,3,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,3,7,4,1]=>[6,2,3,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,4,1,3,7]=>[6,2,3,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,4,1,7,3]=>[6,2,3,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,4,3,1,7]=>[6,2,3,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,4,3,7,1]=>[6,2,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,4,7,1,3]=>[6,2,3,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,4,7,3,1]=>[6,2,3,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,7,1,3,4]=>[6,2,3,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,7,1,4,3]=>[6,2,3,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,5,7,3,1,4]=>[6,2,3,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,7,3,4,1]=>[6,2,3,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,5,7,4,1,3]=>[6,2,3,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,5,7,4,3,1]=>[6,2,3,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,7,1,3,5,4]=>[6,2,1,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,7,1,4,3,5]=>[6,2,1,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,6,7,3,1,4,5]=>[6,2,1,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,7,3,1,5,4]=>[6,2,1,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,7,3,4,1,5]=>[6,2,1,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,7,3,4,5,1]=>[6,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,7,3,5,1,4]=>[6,2,1,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,7,3,5,4,1]=>[6,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,7,4,3,1,5]=>[6,2,1,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,7,4,3,5,1]=>[6,2,1,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,7,4,5,1,3]=>[6,2,1,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,7,4,5,3,1]=>[6,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,7,5,1,3,4]=>[6,2,1,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,7,5,1,4,3]=>[6,2,1,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,7,5,3,4,1]=>[6,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,6,7,5,4,1,3]=>[6,2,1,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,3,4,6,5]=>[6,1,7,5,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,3,5,4,6]=>[6,1,7,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,3,5,6,4]=>[6,1,7,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,3,6,5,4]=>[6,1,7,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,4,3,5,6]=>[6,1,7,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,4,3,6,5]=>[6,1,7,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,4,5,3,6]=>[6,1,7,4,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,4,5,6,3]=>[6,1,7,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,4,6,3,5]=>[6,1,7,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,4,6,5,3]=>[6,1,7,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,5,3,6,4]=>[6,1,7,3,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,5,4,3,6]=>[6,1,7,3,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,5,4,6,3]=>[6,1,7,3,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,5,6,4,3]=>[6,1,7,3,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,6,3,5,4]=>[6,1,7,2,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,6,4,3,5]=>[6,1,7,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,6,4,5,3]=>[6,1,7,2,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,6,5,3,4]=>[6,1,7,2,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,1,6,5,4,3]=>[6,1,7,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,1,4,5,6]=>[6,1,5,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,1,4,6,5]=>[6,1,5,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,1,5,4,6]=>[6,1,5,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,1,5,6,4]=>[6,1,5,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,1,6,4,5]=>[6,1,5,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,1,6,5,4]=>[6,1,5,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,3,4,1,5,6]=>[6,1,5,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,3,4,1,6,5]=>[6,1,5,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,3,4,5,6,1]=>[6,1,5,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,3,4,6,1,5]=>[6,1,5,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,3,4,6,5,1]=>[6,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,3,5,1,4,6]=>[6,1,5,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,3,5,1,6,4]=>[6,1,5,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,3,5,4,1,6]=>[6,1,5,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,3,5,4,6,1]=>[6,1,5,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,3,5,6,1,4]=>[6,1,5,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,3,5,6,4,1]=>[6,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,3,6,1,4,5]=>[6,1,5,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,3,6,1,5,4]=>[6,1,5,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,3,6,4,1,5]=>[6,1,5,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,3,6,4,5,1]=>[6,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,3,6,5,1,4]=>[6,1,5,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,3,6,5,4,1]=>[6,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,4,1,3,6,5]=>[6,1,4,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,4,1,5,3,6]=>[6,1,4,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,4,1,5,6,3]=>[6,1,4,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,4,1,6,5,3]=>[6,1,4,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,4,3,1,5,6]=>[6,1,4,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,4,3,1,6,5]=>[6,1,4,5,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,4,3,5,1,6]=>[6,1,4,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,4,3,5,6,1]=>[6,1,4,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,4,3,6,1,5]=>[6,1,4,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,4,3,6,5,1]=>[6,1,4,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,4,5,1,6,3]=>[6,1,4,3,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,4,5,3,1,6]=>[6,1,4,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,4,5,3,6,1]=>[6,1,4,3,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,4,5,6,3,1]=>[6,1,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,4,6,1,5,3]=>[6,1,4,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,4,6,3,1,5]=>[6,1,4,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,4,6,3,5,1]=>[6,1,4,2,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,4,6,5,1,3]=>[6,1,4,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,4,6,5,3,1]=>[6,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,5,1,3,6,4]=>[6,1,3,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,5,1,4,3,6]=>[6,1,3,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,5,1,4,6,3]=>[6,1,3,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,5,1,6,4,3]=>[6,1,3,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,5,3,1,4,6]=>[6,1,3,5,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,5,3,1,6,4]=>[6,1,3,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,5,3,4,1,6]=>[6,1,3,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,5,3,4,6,1]=>[6,1,3,5,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,5,3,6,1,4]=>[6,1,3,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,5,3,6,4,1]=>[6,1,3,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,5,4,1,3,6]=>[6,1,3,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,5,4,1,6,3]=>[6,1,3,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,5,4,3,1,6]=>[6,1,3,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,5,4,3,6,1]=>[6,1,3,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,5,4,6,1,3]=>[6,1,3,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,5,4,6,3,1]=>[6,1,3,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,5,6,1,3,4]=>[6,1,3,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,5,6,1,4,3]=>[6,1,3,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,5,6,3,1,4]=>[6,1,3,2,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,5,6,3,4,1]=>[6,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,5,6,4,1,3]=>[6,1,3,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,5,6,4,3,1]=>[6,1,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,6,1,3,4,5]=>[6,1,2,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,6,1,3,5,4]=>[6,1,2,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,6,1,4,3,5]=>[6,1,2,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,6,1,4,5,3]=>[6,1,2,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,6,1,5,3,4]=>[6,1,2,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,6,1,5,4,3]=>[6,1,2,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>1
[2,7,6,3,1,4,5]=>[6,1,2,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,6,3,1,5,4]=>[6,1,2,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,6,3,4,1,5]=>[6,1,2,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,6,3,4,5,1]=>[6,1,2,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,6,3,5,1,4]=>[6,1,2,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,6,3,5,4,1]=>[6,1,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,6,4,1,3,5]=>[6,1,2,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,6,4,1,5,3]=>[6,1,2,4,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,6,4,3,1,5]=>[6,1,2,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,6,4,3,5,1]=>[6,1,2,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,6,4,5,1,3]=>[6,1,2,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,6,4,5,3,1]=>[6,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,6,5,1,4,3]=>[6,1,2,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>1
[2,7,6,5,3,1,4]=>[6,1,2,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,6,5,3,4,1]=>[6,1,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[2,7,6,5,4,1,3]=>[6,1,2,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>1
[2,7,6,5,4,3,1]=>[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>1
[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,6,4,7]=>[5,7,6,3,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,6,7,4]=>[5,7,6,3,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,7,4,6]=>[5,7,6,3,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,5,7,6,4]=>[5,7,6,3,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,4,7,5]=>[5,7,6,2,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,5,7,4]=>[5,7,6,2,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,7,4,5]=>[5,7,6,2,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,6,7,5,4]=>[5,7,6,2,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,7,5,6,4]=>[5,7,6,1,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,5,6,7]=>[5,7,4,6,3,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,5,7,6]=>[5,7,4,6,3,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,6,5,7]=>[5,7,4,6,2,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,6,7,5]=>[5,7,4,6,2,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,7,5,6]=>[5,7,4,6,1,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,2,7,6,5]=>[5,7,4,6,1,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,2,6,7]=>[5,7,4,3,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,2,7,6]=>[5,7,4,3,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,6,2,7]=>[5,7,4,3,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,5,7,6,2]=>[5,7,4,3,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,2,5,7]=>[5,7,4,2,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,5,2,7]=>[5,7,4,2,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,5,7,2]=>[5,7,4,2,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,7,2,5]=>[5,7,4,2,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,6,7,5,2]=>[5,7,4,2,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,7,2,6,5]=>[5,7,4,1,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,7,5,2,6]=>[5,7,4,1,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,4,7,6,5,2]=>[5,7,4,1,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,4,6,7]=>[5,7,3,6,4,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,4,7,6]=>[5,7,3,6,4,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,6,4,7]=>[5,7,3,6,2,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,2,7,6,4]=>[5,7,3,6,1,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,2,6,7]=>[5,7,3,4,6,2,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,2,7,6]=>[5,7,3,4,6,1,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,6,2,7]=>[5,7,3,4,2,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,6,7,2]=>[5,7,3,4,2,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,7,2,6]=>[5,7,3,4,1,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,4,7,6,2]=>[5,7,3,4,1,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,2,4,7]=>[5,7,3,2,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,2,7,4]=>[5,7,3,2,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,4,2,7]=>[5,7,3,2,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,4,7,2]=>[5,7,3,2,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,7,2,4]=>[5,7,3,2,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,6,7,4,2]=>[5,7,3,2,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,7,2,4,6]=>[5,7,3,1,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,7,2,6,4]=>[5,7,3,1,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,7,4,2,6]=>[5,7,3,1,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,7,4,6,2]=>[5,7,3,1,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,7,6,2,4]=>[5,7,3,1,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,5,7,6,4,2]=>[5,7,3,1,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,4,5,7]=>[5,7,2,6,4,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,5,4,7]=>[5,7,2,6,3,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,5,7,4]=>[5,7,2,6,3,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,7,4,5]=>[5,7,2,6,1,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,2,7,5,4]=>[5,7,2,6,1,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,2,5,7]=>[5,7,2,4,6,3,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,5,2,7]=>[5,7,2,4,3,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,5,7,2]=>[5,7,2,4,3,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,7,2,5]=>[5,7,2,4,1,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,4,7,5,2]=>[5,7,2,4,1,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,2,4,7]=>[5,7,2,3,6,4,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,4,2,7]=>[5,7,2,3,4,6,1]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,4,7,2]=>[5,7,2,3,4,1,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,7,2,4]=>[5,7,2,3,1,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,5,7,4,2]=>[5,7,2,3,1,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,7,2,4,5]=>[5,7,2,1,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,7,2,5,4]=>[5,7,2,1,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,7,4,2,5]=>[5,7,2,1,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,7,4,5,2]=>[5,7,2,1,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,7,5,2,4]=>[5,7,2,1,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,6,7,5,4,2]=>[5,7,2,1,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,2,4,6,5]=>[5,7,1,6,4,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,2,5,4,6]=>[5,7,1,6,3,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,2,5,6,4]=>[5,7,1,6,3,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,2,6,5,4]=>[5,7,1,6,2,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,4,2,5,6]=>[5,7,1,4,6,3,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,4,2,6,5]=>[5,7,1,4,6,2,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,4,5,2,6]=>[5,7,1,4,3,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,4,5,6,2]=>[5,7,1,4,3,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,4,6,2,5]=>[5,7,1,4,2,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,4,6,5,2]=>[5,7,1,4,2,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,5,2,6,4]=>[5,7,1,3,6,2,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,5,4,2,6]=>[5,7,1,3,4,6,2]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,5,4,6,2]=>[5,7,1,3,4,2,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,6,2,5,4]=>[5,7,1,2,6,3,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,6,4,2,5]=>[5,7,1,2,4,6,3]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,6,4,5,2]=>[5,7,1,2,4,3,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,6,5,2,4]=>[5,7,1,2,3,6,4]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,1,7,6,5,4,2]=>[5,7,1,2,3,4,6]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,4,6,7,5]=>[5,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,6,4,7]=>[5,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,6,7,4]=>[5,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,7,4,6]=>[5,6,7,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,5,7,6,4]=>[5,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,4,7,5]=>[5,6,7,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,5,7,4]=>[5,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,7,4,5]=>[5,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,6,7,5,4]=>[5,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,7,5,6,4]=>[5,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,5,7,6]=>[5,6,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,6,5,7]=>[5,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,6,7,5]=>[5,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,7,5,6]=>[5,6,4,7,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,1,7,6,5]=>[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,5,1,7,6]=>[5,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,5,7,6,1]=>[5,6,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,6,1,7,5]=>[5,6,4,2,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,6,5,1,7]=>[5,6,4,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,4,6,7,1,5]=>[5,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,6,7,5,1]=>[5,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,7,1,6,5]=>[5,6,4,1,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,4,7,5,1,6]=>[5,6,4,1,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,7,5,6,1]=>[5,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,4,7,6,1,5]=>[5,6,4,1,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,4,7,6,5,1]=>[5,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,5,1,4,7,6]=>[5,6,3,7,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,5,1,6,4,7]=>[5,6,3,7,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,5,1,6,7,4]=>[5,6,3,7,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,5,1,7,4,6]=>[5,6,3,7,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,5,1,7,6,4]=>[5,6,3,7,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,5,4,1,6,7]=>[5,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,4,1,7,6]=>[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,4,6,1,7]=>[5,6,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,4,6,7,1]=>[5,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,4,7,1,6]=>[5,6,3,4,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,4,7,6,1]=>[5,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,6,1,4,7]=>[5,6,3,2,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,6,1,7,4]=>[5,6,3,2,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,6,4,1,7]=>[5,6,3,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,6,4,7,1]=>[5,6,3,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,6,7,1,4]=>[5,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,6,7,4,1]=>[5,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,7,1,4,6]=>[5,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,7,1,6,4]=>[5,6,3,1,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,5,7,4,1,6]=>[5,6,3,1,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,7,4,6,1]=>[5,6,3,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,5,7,6,1,4]=>[5,6,3,1,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,5,7,6,4,1]=>[5,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,6,1,4,7,5]=>[5,6,2,7,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,6,1,5,4,7]=>[5,6,2,7,3,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,6,1,5,7,4]=>[5,6,2,7,3,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,6,1,7,4,5]=>[5,6,2,7,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,6,1,7,5,4]=>[5,6,2,7,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,6,4,1,5,7]=>[5,6,2,4,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,4,1,7,5]=>[5,6,2,4,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,4,5,1,7]=>[5,6,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,4,5,7,1]=>[5,6,2,4,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,4,7,1,5]=>[5,6,2,4,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,4,7,5,1]=>[5,6,2,4,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,5,1,4,7]=>[5,6,2,3,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,5,1,7,4]=>[5,6,2,3,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,5,4,1,7]=>[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,5,4,7,1]=>[5,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,7,1,4,5]=>[5,6,2,1,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,7,1,5,4]=>[5,6,2,1,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,6,7,4,1,5]=>[5,6,2,1,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,7,4,5,1]=>[5,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,6,7,5,1,4]=>[5,6,2,1,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,6,7,5,4,1]=>[5,6,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,7,1,4,6,5]=>[5,6,1,7,4,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,7,1,5,4,6]=>[5,6,1,7,3,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,7,1,5,6,4]=>[5,6,1,7,3,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,7,1,6,4,5]=>[5,6,1,7,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,7,1,6,5,4]=>[5,6,1,7,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,2,7,4,1,5,6]=>[5,6,1,4,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,7,4,5,1,6]=>[5,6,1,4,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,7,4,5,6,1]=>[5,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,7,4,6,1,5]=>[5,6,1,4,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,7,4,6,5,1]=>[5,6,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,7,5,1,4,6]=>[5,6,1,3,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,7,5,1,6,4]=>[5,6,1,3,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,7,5,4,1,6]=>[5,6,1,3,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,7,5,4,6,1]=>[5,6,1,3,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,7,5,6,1,4]=>[5,6,1,3,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,7,5,6,4,1]=>[5,6,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,7,6,1,4,5]=>[5,6,1,2,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,7,6,1,5,4]=>[5,6,1,2,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,2,7,6,4,1,5]=>[5,6,1,2,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,7,6,4,5,1]=>[5,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,2,7,6,5,1,4]=>[5,6,1,2,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,2,7,6,5,4,1]=>[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,2,5,7,6]=>[5,4,7,6,3,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,2,6,5,7]=>[5,4,7,6,2,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,2,6,7,5]=>[5,4,7,6,2,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,2,7,5,6]=>[5,4,7,6,1,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,2,7,6,5]=>[5,4,7,6,1,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,2,6,7]=>[5,4,7,3,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,2,7,6]=>[5,4,7,3,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,6,2,7]=>[5,4,7,3,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,6,7,2]=>[5,4,7,3,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,7,2,6]=>[5,4,7,3,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,5,7,6,2]=>[5,4,7,3,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,2,5,7]=>[5,4,7,2,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,2,7,5]=>[5,4,7,2,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,5,2,7]=>[5,4,7,2,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,5,7,2]=>[5,4,7,2,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,7,2,5]=>[5,4,7,2,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,6,7,5,2]=>[5,4,7,2,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,7,2,5,6]=>[5,4,7,1,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,7,2,6,5]=>[5,4,7,1,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,7,5,2,6]=>[5,4,7,1,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,7,5,6,2]=>[5,4,7,1,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,7,6,2,5]=>[5,4,7,1,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,1,7,6,5,2]=>[5,4,7,1,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,4,2,1,5,7,6]=>[5,4,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,4,2,1,6,5,7]=>[5,4,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,4,2,1,6,7,5]=>[5,4,6,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,4,2,1,7,5,6]=>[5,4,6,7,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,4,2,1,7,6,5]=>[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,5,1,7,6]=>[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,5,7,6,1]=>[5,4,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,6,1,7,5]=>[5,4,6,2,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,6,5,1,7]=>[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,6,5,7,1]=>[5,4,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,2,6,7,1,5]=>[5,4,6,2,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,6,7,5,1]=>[5,4,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,7,1,6,5]=>[5,4,6,1,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,4,2,7,5,1,6]=>[5,4,6,1,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,7,5,6,1]=>[5,4,6,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,2,7,6,1,5]=>[5,4,6,1,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,4,2,7,6,5,1]=>[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,5,1,2,7,6]=>[5,4,3,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,5,1,6,2,7]=>[5,4,3,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,5,1,6,7,2]=>[5,4,3,7,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,5,1,7,2,6]=>[5,4,3,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,5,1,7,6,2]=>[5,4,3,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,5,2,1,7,6]=>[5,4,3,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,5,2,7,6,1]=>[5,4,3,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,5,6,1,7,2]=>[5,4,3,2,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,6,1,2,7,5]=>[5,4,2,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,6,1,5,2,7]=>[5,4,2,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,6,1,5,7,2]=>[5,4,2,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,6,1,7,2,5]=>[5,4,2,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,6,1,7,5,2]=>[5,4,2,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,6,2,1,7,5]=>[5,4,2,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,6,2,7,1,5]=>[5,4,2,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,6,2,7,5,1]=>[5,4,2,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,6,5,1,7,2]=>[5,4,2,3,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,6,5,2,1,7]=>[5,4,2,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,6,5,2,7,1]=>[5,4,2,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,6,5,7,1,2]=>[5,4,2,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,6,5,7,2,1]=>[5,4,2,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,4,6,7,1,2,5]=>[5,4,2,1,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,6,7,1,5,2]=>[5,4,2,1,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,6,7,2,1,5]=>[5,4,2,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,6,7,2,5,1]=>[5,4,2,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,6,7,5,1,2]=>[5,4,2,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,6,7,5,2,1]=>[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,7,1,2,6,5]=>[5,4,1,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,7,1,5,2,6]=>[5,4,1,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,7,1,5,6,2]=>[5,4,1,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,7,1,6,2,5]=>[5,4,1,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,7,1,6,5,2]=>[5,4,1,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,7,2,1,6,5]=>[5,4,1,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,4,7,2,6,5,1]=>[5,4,1,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,7,5,1,6,2]=>[5,4,1,3,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,7,5,2,1,6]=>[5,4,1,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,7,5,2,6,1]=>[5,4,1,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,7,5,6,1,2]=>[5,4,1,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,7,5,6,2,1]=>[5,4,1,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,7,6,1,5,2]=>[5,4,1,2,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,4,7,6,2,1,5]=>[5,4,1,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,4,7,6,2,5,1]=>[5,4,1,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,4,7,6,5,1,2]=>[5,4,1,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,4,7,6,5,2,1]=>[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,2,4,7,6]=>[5,3,7,6,4,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,2,6,4,7]=>[5,3,7,6,2,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,2,6,7,4]=>[5,3,7,6,2,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,2,7,4,6]=>[5,3,7,6,1,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,2,7,6,4]=>[5,3,7,6,1,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,2,6,7]=>[5,3,7,4,6,2,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,2,7,6]=>[5,3,7,4,6,1,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,6,2,7]=>[5,3,7,4,2,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,6,7,2]=>[5,3,7,4,2,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,7,2,6]=>[5,3,7,4,1,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,4,7,6,2]=>[5,3,7,4,1,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,2,4,7]=>[5,3,7,2,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,2,7,4]=>[5,3,7,2,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,4,2,7]=>[5,3,7,2,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,4,7,2]=>[5,3,7,2,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,7,2,4]=>[5,3,7,2,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,6,7,4,2]=>[5,3,7,2,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,7,2,4,6]=>[5,3,7,1,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,7,2,6,4]=>[5,3,7,1,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,7,4,2,6]=>[5,3,7,1,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,7,4,6,2]=>[5,3,7,1,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,7,6,2,4]=>[5,3,7,1,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,1,7,6,4,2]=>[5,3,7,1,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,5,2,1,4,7,6]=>[5,3,6,7,4,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,5,2,1,6,4,7]=>[5,3,6,7,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,5,2,1,6,7,4]=>[5,3,6,7,2,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,5,2,1,7,4,6]=>[5,3,6,7,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,5,2,1,7,6,4]=>[5,3,6,7,1,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,4,1,7,6]=>[5,3,6,4,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,4,7,6,1]=>[5,3,6,4,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,5,2,6,1,4,7]=>[5,3,6,2,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,6,1,7,4]=>[5,3,6,2,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,6,4,1,7]=>[5,3,6,2,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,6,4,7,1]=>[5,3,6,2,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,5,2,6,7,1,4]=>[5,3,6,2,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,6,7,4,1]=>[5,3,6,2,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,5,2,7,1,4,6]=>[5,3,6,1,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,7,1,6,4]=>[5,3,6,1,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,5,2,7,4,1,6]=>[5,3,6,1,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,7,4,6,1]=>[5,3,6,1,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,5,2,7,6,1,4]=>[5,3,6,1,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,5,2,7,6,4,1]=>[5,3,6,1,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,4,1,2,7,6]=>[5,3,4,7,6,1,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,4,1,6,2,7]=>[5,3,4,7,2,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,4,1,6,7,2]=>[5,3,4,7,2,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,4,1,7,2,6]=>[5,3,4,7,1,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,4,1,7,6,2]=>[5,3,4,7,1,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,4,2,1,6,7]=>[5,3,4,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,4,2,1,7,6]=>[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,4,2,6,1,7]=>[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,4,2,6,7,1]=>[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,4,2,7,1,6]=>[5,3,4,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,4,2,7,6,1]=>[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,4,6,1,2,7]=>[5,3,4,2,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,4,6,1,7,2]=>[5,3,4,2,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,4,6,2,1,7]=>[5,3,4,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,4,6,2,7,1]=>[5,3,4,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,4,6,7,1,2]=>[5,3,4,2,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,4,6,7,2,1]=>[5,3,4,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,4,7,1,2,6]=>[5,3,4,1,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,4,7,1,6,2]=>[5,3,4,1,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,4,7,2,1,6]=>[5,3,4,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,4,7,2,6,1]=>[5,3,4,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,4,7,6,1,2]=>[5,3,4,1,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,4,7,6,2,1]=>[5,3,4,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,6,1,2,7,4]=>[5,3,2,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,6,1,4,2,7]=>[5,3,2,7,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,6,1,4,7,2]=>[5,3,2,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,6,1,7,2,4]=>[5,3,2,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,6,1,7,4,2]=>[5,3,2,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,6,2,1,4,7]=>[5,3,2,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,6,2,1,7,4]=>[5,3,2,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,6,2,4,1,7]=>[5,3,2,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,6,4,1,2,7]=>[5,3,2,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,6,4,1,7,2]=>[5,3,2,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,6,4,2,1,7]=>[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,6,4,7,1,2]=>[5,3,2,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,6,4,7,2,1]=>[5,3,2,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,6,7,1,2,4]=>[5,3,2,1,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,6,7,1,4,2]=>[5,3,2,1,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,6,7,2,1,4]=>[5,3,2,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,6,7,2,4,1]=>[5,3,2,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,6,7,4,1,2]=>[5,3,2,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,6,7,4,2,1]=>[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,7,1,2,6,4]=>[5,3,1,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,7,1,4,2,6]=>[5,3,1,7,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,5,7,2,1,4,6]=>[5,3,1,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,7,2,1,6,4]=>[5,3,1,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,5,7,2,4,1,6]=>[5,3,1,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,7,2,4,6,1]=>[5,3,1,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,7,2,6,1,4]=>[5,3,1,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,5,7,2,6,4,1]=>[5,3,1,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,7,4,2,1,6]=>[5,3,1,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,7,4,2,6,1]=>[5,3,1,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,7,4,6,1,2]=>[5,3,1,4,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,7,4,6,2,1]=>[5,3,1,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,5,7,6,1,2,4]=>[5,3,1,2,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,7,6,1,4,2]=>[5,3,1,2,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,5,7,6,2,4,1]=>[5,3,1,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,5,7,6,4,1,2]=>[5,3,1,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,2,4,7,5]=>[5,2,7,6,4,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,2,5,4,7]=>[5,2,7,6,3,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,2,5,7,4]=>[5,2,7,6,3,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,2,7,4,5]=>[5,2,7,6,1,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,2,7,5,4]=>[5,2,7,6,1,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,2,5,7]=>[5,2,7,4,6,3,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,2,7,5]=>[5,2,7,4,6,1,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,5,2,7]=>[5,2,7,4,3,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,5,7,2]=>[5,2,7,4,3,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,4,7,5,2]=>[5,2,7,4,1,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,2,4,7]=>[5,2,7,3,6,4,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,2,7,4]=>[5,2,7,3,6,1,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,4,2,7]=>[5,2,7,3,4,6,1]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,4,7,2]=>[5,2,7,3,4,1,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,7,2,4]=>[5,2,7,3,1,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,5,7,4,2]=>[5,2,7,3,1,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,7,2,4,5]=>[5,2,7,1,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,7,2,5,4]=>[5,2,7,1,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,7,4,2,5]=>[5,2,7,1,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,7,4,5,2]=>[5,2,7,1,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,7,5,2,4]=>[5,2,7,1,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,1,7,5,4,2]=>[5,2,7,1,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,6,2,1,4,7,5]=>[5,2,6,7,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,6,2,1,5,4,7]=>[5,2,6,7,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,6,2,1,5,7,4]=>[5,2,6,7,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,6,2,1,7,4,5]=>[5,2,6,7,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,6,2,1,7,5,4]=>[5,2,6,7,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,4,1,7,5]=>[5,2,6,4,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,6,2,4,7,1,5]=>[5,2,6,4,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,4,7,5,1]=>[5,2,6,4,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,5,1,7,4]=>[5,2,6,3,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,5,4,1,7]=>[5,2,6,3,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,5,4,7,1]=>[5,2,6,3,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,6,2,5,7,1,4]=>[5,2,6,3,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,5,7,4,1]=>[5,2,6,3,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,6,2,7,1,4,5]=>[5,2,6,1,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,7,1,5,4]=>[5,2,6,1,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,6,2,7,4,1,5]=>[5,2,6,1,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,7,4,5,1]=>[5,2,6,1,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,6,2,7,5,1,4]=>[5,2,6,1,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,6,2,7,5,4,1]=>[5,2,6,1,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,4,1,2,7,5]=>[5,2,4,7,6,1,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,4,1,5,2,7]=>[5,2,4,7,3,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,4,1,5,7,2]=>[5,2,4,7,3,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,4,1,7,2,5]=>[5,2,4,7,1,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,4,1,7,5,2]=>[5,2,4,7,1,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,4,2,1,5,7]=>[5,2,4,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,4,2,1,7,5]=>[5,2,4,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,4,2,5,1,7]=>[5,2,4,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,4,2,5,7,1]=>[5,2,4,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,4,2,7,1,5]=>[5,2,4,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,4,2,7,5,1]=>[5,2,4,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,4,5,1,2,7]=>[5,2,4,3,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,4,5,1,7,2]=>[5,2,4,3,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,4,5,2,1,7]=>[5,2,4,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,4,5,2,7,1]=>[5,2,4,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,4,5,7,1,2]=>[5,2,4,3,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,4,5,7,2,1]=>[5,2,4,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,4,7,1,2,5]=>[5,2,4,1,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,4,7,1,5,2]=>[5,2,4,1,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,4,7,2,1,5]=>[5,2,4,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,4,7,2,5,1]=>[5,2,4,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,4,7,5,1,2]=>[5,2,4,1,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,4,7,5,2,1]=>[5,2,4,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,5,1,2,7,4]=>[5,2,3,7,6,1,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,5,1,4,2,7]=>[5,2,3,7,4,6,1]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,5,1,4,7,2]=>[5,2,3,7,4,1,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,5,1,7,2,4]=>[5,2,3,7,1,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,5,1,7,4,2]=>[5,2,3,7,1,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,5,2,1,4,7]=>[5,2,3,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,5,2,1,7,4]=>[5,2,3,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,5,2,4,1,7]=>[5,2,3,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,5,2,4,7,1]=>[5,2,3,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,5,2,7,1,4]=>[5,2,3,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,5,2,7,4,1]=>[5,2,3,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,5,4,1,2,7]=>[5,2,3,4,7,6,1]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,5,4,1,7,2]=>[5,2,3,4,7,1,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,5,4,2,1,7]=>[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,5,4,2,7,1]=>[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,5,4,7,1,2]=>[5,2,3,4,1,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,5,4,7,2,1]=>[5,2,3,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,5,7,1,2,4]=>[5,2,3,1,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,5,7,1,4,2]=>[5,2,3,1,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,5,7,2,1,4]=>[5,2,3,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,5,7,2,4,1]=>[5,2,3,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,5,7,4,1,2]=>[5,2,3,1,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,5,7,4,2,1]=>[5,2,3,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,7,1,2,5,4]=>[5,2,1,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,7,1,4,2,5]=>[5,2,1,7,4,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,7,1,4,5,2]=>[5,2,1,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,7,1,5,2,4]=>[5,2,1,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,7,1,5,4,2]=>[5,2,1,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,6,7,2,1,4,5]=>[5,2,1,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,7,2,1,5,4]=>[5,2,1,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,6,7,2,4,1,5]=>[5,2,1,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,7,2,4,5,1]=>[5,2,1,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,7,2,5,1,4]=>[5,2,1,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,6,7,2,5,4,1]=>[5,2,1,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,7,4,1,5,2]=>[5,2,1,4,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,7,4,2,1,5]=>[5,2,1,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,7,4,2,5,1]=>[5,2,1,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,7,4,5,1,2]=>[5,2,1,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,7,4,5,2,1]=>[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,6,7,5,1,2,4]=>[5,2,1,3,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,7,5,1,4,2]=>[5,2,1,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,6,7,5,2,1,4]=>[5,2,1,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,6,7,5,2,4,1]=>[5,2,1,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,6,7,5,4,1,2]=>[5,2,1,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,6,7,5,4,2,1]=>[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,2,4,6,5]=>[5,1,7,6,4,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,2,5,4,6]=>[5,1,7,6,3,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,2,5,6,4]=>[5,1,7,6,3,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,2,6,4,5]=>[5,1,7,6,2,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,2,6,5,4]=>[5,1,7,6,2,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,4,2,5,6]=>[5,1,7,4,6,3,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,4,2,6,5]=>[5,1,7,4,6,2,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,4,5,2,6]=>[5,1,7,4,3,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,4,5,6,2]=>[5,1,7,4,3,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,4,6,2,5]=>[5,1,7,4,2,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,4,6,5,2]=>[5,1,7,4,2,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,5,2,4,6]=>[5,1,7,3,6,4,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,5,2,6,4]=>[5,1,7,3,6,2,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,5,4,2,6]=>[5,1,7,3,4,6,2]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,5,4,6,2]=>[5,1,7,3,4,2,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,5,6,2,4]=>[5,1,7,3,2,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,5,6,4,2]=>[5,1,7,3,2,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,6,2,4,5]=>[5,1,7,2,6,4,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,6,2,5,4]=>[5,1,7,2,6,3,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,6,4,2,5]=>[5,1,7,2,4,6,3]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,6,4,5,2]=>[5,1,7,2,4,3,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,6,5,2,4]=>[5,1,7,2,3,6,4]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,1,6,5,4,2]=>[5,1,7,2,3,4,6]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>1
[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,7,2,1,4,6,5]=>[5,1,6,7,4,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,7,2,1,5,4,6]=>[5,1,6,7,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,7,2,1,5,6,4]=>[5,1,6,7,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,7,2,1,6,4,5]=>[5,1,6,7,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,7,2,1,6,5,4]=>[5,1,6,7,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>2
[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,7,2,4,1,6,5]=>[5,1,6,4,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,7,2,4,6,5,1]=>[5,1,6,4,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,7,2,5,1,6,4]=>[5,1,6,3,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,7,2,5,4,1,6]=>[5,1,6,3,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,7,2,5,4,6,1]=>[5,1,6,3,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,7,2,5,6,1,4]=>[5,1,6,3,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,7,2,5,6,4,1]=>[5,1,6,3,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,7,2,6,1,5,4]=>[5,1,6,2,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>2
[3,7,2,6,4,1,5]=>[5,1,6,2,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,7,2,6,4,5,1]=>[5,1,6,2,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,7,2,6,5,1,4]=>[5,1,6,2,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>2
[3,7,2,6,5,4,1]=>[5,1,6,2,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>2
[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,4,1,2,6,5]=>[5,1,4,7,6,2,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,4,1,5,2,6]=>[5,1,4,7,3,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,4,1,5,6,2]=>[5,1,4,7,3,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,4,1,6,2,5]=>[5,1,4,7,2,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,4,1,6,5,2]=>[5,1,4,7,2,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,4,2,1,5,6]=>[5,1,4,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,7,4,2,1,6,5]=>[5,1,4,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,7,4,2,5,1,6]=>[5,1,4,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,7,4,2,5,6,1]=>[5,1,4,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,7,4,2,6,1,5]=>[5,1,4,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,7,4,2,6,5,1]=>[5,1,4,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,7,4,5,1,2,6]=>[5,1,4,3,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,4,5,1,6,2]=>[5,1,4,3,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,4,5,2,1,6]=>[5,1,4,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,7,4,5,2,6,1]=>[5,1,4,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,7,4,5,6,1,2]=>[5,1,4,3,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,7,4,5,6,2,1]=>[5,1,4,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,7,4,6,1,2,5]=>[5,1,4,2,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,4,6,1,5,2]=>[5,1,4,2,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,4,6,2,1,5]=>[5,1,4,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,7,4,6,2,5,1]=>[5,1,4,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,7,4,6,5,1,2]=>[5,1,4,2,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,7,4,6,5,2,1]=>[5,1,4,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,5,1,2,6,4]=>[5,1,3,7,6,2,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,5,1,4,2,6]=>[5,1,3,7,4,6,2]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,5,1,4,6,2]=>[5,1,3,7,4,2,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,5,1,6,2,4]=>[5,1,3,7,2,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,5,1,6,4,2]=>[5,1,3,7,2,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,5,2,1,4,6]=>[5,1,3,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,7,5,2,1,6,4]=>[5,1,3,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,7,5,2,4,1,6]=>[5,1,3,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,7,5,2,4,6,1]=>[5,1,3,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,7,5,2,6,1,4]=>[5,1,3,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,7,5,2,6,4,1]=>[5,1,3,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,7,5,4,1,2,6]=>[5,1,3,4,7,6,2]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,5,4,1,6,2]=>[5,1,3,4,7,2,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,5,4,2,1,6]=>[5,1,3,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,7,5,4,2,6,1]=>[5,1,3,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,7,5,4,6,1,2]=>[5,1,3,4,2,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,7,5,4,6,2,1]=>[5,1,3,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,7,5,6,1,2,4]=>[5,1,3,2,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,5,6,1,4,2]=>[5,1,3,2,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,5,6,2,1,4]=>[5,1,3,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,7,5,6,2,4,1]=>[5,1,3,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,7,5,6,4,1,2]=>[5,1,3,2,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,7,5,6,4,2,1]=>[5,1,3,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,6,1,2,5,4]=>[5,1,2,7,6,3,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,6,1,4,2,5]=>[5,1,2,7,4,6,3]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,6,1,4,5,2]=>[5,1,2,7,4,3,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,6,1,5,2,4]=>[5,1,2,7,3,6,4]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,6,1,5,4,2]=>[5,1,2,7,3,4,6]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>1
[3,7,6,2,1,4,5]=>[5,1,2,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,7,6,2,1,5,4]=>[5,1,2,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>2
[3,7,6,2,4,1,5]=>[5,1,2,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,7,6,2,4,5,1]=>[5,1,2,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,7,6,2,5,1,4]=>[5,1,2,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>2
[3,7,6,2,5,4,1]=>[5,1,2,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>2
[3,7,6,4,1,2,5]=>[5,1,2,4,7,6,3]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,6,4,1,5,2]=>[5,1,2,4,7,3,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,6,4,2,1,5]=>[5,1,2,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,7,6,4,2,5,1]=>[5,1,2,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,7,6,4,5,1,2]=>[5,1,2,4,3,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,7,6,4,5,2,1]=>[5,1,2,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[3,7,6,5,1,2,4]=>[5,1,2,3,7,6,4]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,6,5,1,4,2]=>[5,1,2,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>1
[3,7,6,5,2,1,4]=>[5,1,2,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>2
[3,7,6,5,2,4,1]=>[5,1,2,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>2
[3,7,6,5,4,1,2]=>[5,1,2,3,4,7,6]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>1
[3,7,6,5,4,2,1]=>[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>2
[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,3,6,7,5]=>[4,7,6,5,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,3,6,7]=>[4,7,6,3,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,3,7,6]=>[4,7,6,3,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,6,3,7]=>[4,7,6,3,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,5,7,6,3]=>[4,7,6,3,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,3,5,7]=>[4,7,6,2,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,5,3,7]=>[4,7,6,2,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,5,7,3]=>[4,7,6,2,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,7,3,5]=>[4,7,6,2,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,6,7,5,3]=>[4,7,6,2,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,7,3,6,5]=>[4,7,6,1,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,7,5,3,6]=>[4,7,6,1,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,7,5,6,3]=>[4,7,6,1,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,2,7,6,5,3]=>[4,7,6,1,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,6,7,5]=>[4,7,5,6,2,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,2,6,7]=>[4,7,5,3,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,2,7,6]=>[4,7,5,3,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,6,2,7]=>[4,7,5,3,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,6,7,2]=>[4,7,5,3,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,7,2,6]=>[4,7,5,3,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,5,7,6,2]=>[4,7,5,3,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,2,5,7]=>[4,7,5,2,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,2,7,5]=>[4,7,5,2,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,5,2,7]=>[4,7,5,2,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,5,7,2]=>[4,7,5,2,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,7,2,5]=>[4,7,5,2,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,6,7,5,2]=>[4,7,5,2,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,7,2,5,6]=>[4,7,5,1,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,7,2,6,5]=>[4,7,5,1,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,7,5,2,6]=>[4,7,5,1,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,7,5,6,2]=>[4,7,5,1,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,7,6,2,5]=>[4,7,5,1,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,3,7,6,5,2]=>[4,7,5,1,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,3,6,7]=>[4,7,3,6,5,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,3,7,6]=>[4,7,3,6,5,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,6,3,7]=>[4,7,3,6,2,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,6,7,3]=>[4,7,3,6,2,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,7,3,6]=>[4,7,3,6,1,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,2,7,6,3]=>[4,7,3,6,1,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,2,6,7]=>[4,7,3,5,6,2,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,2,7,6]=>[4,7,3,5,6,1,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,6,2,7]=>[4,7,3,5,2,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,6,7,2]=>[4,7,3,5,2,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,7,2,6]=>[4,7,3,5,1,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,3,7,6,2]=>[4,7,3,5,1,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,2,3,7]=>[4,7,3,2,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,2,7,3]=>[4,7,3,2,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,3,2,7]=>[4,7,3,2,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,3,7,2]=>[4,7,3,2,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,7,2,3]=>[4,7,3,2,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,6,7,3,2]=>[4,7,3,2,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,7,2,3,6]=>[4,7,3,1,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,7,2,6,3]=>[4,7,3,1,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,7,3,2,6]=>[4,7,3,1,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,7,3,6,2]=>[4,7,3,1,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,7,6,2,3]=>[4,7,3,1,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,5,7,6,3,2]=>[4,7,3,1,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,3,5,7]=>[4,7,2,6,5,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,3,7,5]=>[4,7,2,6,5,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,5,3,7]=>[4,7,2,6,3,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,5,7,3]=>[4,7,2,6,3,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,7,3,5]=>[4,7,2,6,1,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,2,7,5,3]=>[4,7,2,6,1,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,2,5,7]=>[4,7,2,5,6,3,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,2,7,5]=>[4,7,2,5,6,1,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,5,2,7]=>[4,7,2,5,3,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,5,7,2]=>[4,7,2,5,3,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,7,2,5]=>[4,7,2,5,1,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,3,7,5,2]=>[4,7,2,5,1,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,2,3,7]=>[4,7,2,3,6,5,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,2,7,3]=>[4,7,2,3,6,1,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,3,2,7]=>[4,7,2,3,5,6,1]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,3,7,2]=>[4,7,2,3,5,1,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,7,2,3]=>[4,7,2,3,1,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,5,7,3,2]=>[4,7,2,3,1,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,7,2,3,5]=>[4,7,2,1,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,7,2,5,3]=>[4,7,2,1,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,7,3,2,5]=>[4,7,2,1,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,7,3,5,2]=>[4,7,2,1,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,7,5,2,3]=>[4,7,2,1,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,6,7,5,3,2]=>[4,7,2,1,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,2,3,5,6]=>[4,7,1,6,5,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,2,3,6,5]=>[4,7,1,6,5,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,2,5,3,6]=>[4,7,1,6,3,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,2,5,6,3]=>[4,7,1,6,3,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,2,6,3,5]=>[4,7,1,6,2,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,2,6,5,3]=>[4,7,1,6,2,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,3,2,5,6]=>[4,7,1,5,6,3,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,3,2,6,5]=>[4,7,1,5,6,2,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,3,5,2,6]=>[4,7,1,5,3,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,3,5,6,2]=>[4,7,1,5,3,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,3,6,2,5]=>[4,7,1,5,2,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,3,6,5,2]=>[4,7,1,5,2,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,5,2,3,6]=>[4,7,1,3,6,5,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,5,2,6,3]=>[4,7,1,3,6,2,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,5,3,2,6]=>[4,7,1,3,5,6,2]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,5,3,6,2]=>[4,7,1,3,5,2,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,5,6,2,3]=>[4,7,1,3,2,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,5,6,3,2]=>[4,7,1,3,2,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,6,2,3,5]=>[4,7,1,2,6,5,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,6,2,5,3]=>[4,7,1,2,6,3,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,6,3,2,5]=>[4,7,1,2,5,6,3]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,6,3,5,2]=>[4,7,1,2,5,3,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,6,5,2,3]=>[4,7,1,2,3,6,5]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,1,7,6,5,3,2]=>[4,7,1,2,3,5,6]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,3,6,7,5]=>[4,6,7,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,3,6,7]=>[4,6,7,3,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,3,7,6]=>[4,6,7,3,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,6,3,7]=>[4,6,7,3,2,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,6,7,3]=>[4,6,7,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,7,3,6]=>[4,6,7,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,5,7,6,3]=>[4,6,7,3,1,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,3,5,7]=>[4,6,7,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,3,7,5]=>[4,6,7,2,5,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,5,3,7]=>[4,6,7,2,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,5,7,3]=>[4,6,7,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,7,3,5]=>[4,6,7,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,6,7,5,3]=>[4,6,7,2,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,7,3,5,6]=>[4,6,7,1,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,7,3,6,5]=>[4,6,7,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,7,5,3,6]=>[4,6,7,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,7,5,6,3]=>[4,6,7,1,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,7,6,3,5]=>[4,6,7,1,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,1,7,6,5,3]=>[4,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,5,7,6]=>[4,6,5,7,3,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,6,5,7]=>[4,6,5,7,2,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,6,7,5]=>[4,6,5,7,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,7,5,6]=>[4,6,5,7,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,1,7,6,5]=>[4,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,5,1,7,6]=>[4,6,5,3,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,5,7,6,1]=>[4,6,5,3,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,6,1,7,5]=>[4,6,5,2,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,6,5,1,7]=>[4,6,5,2,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,6,5,7,1]=>[4,6,5,2,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,3,6,7,1,5]=>[4,6,5,2,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,6,7,5,1]=>[4,6,5,2,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,7,1,6,5]=>[4,6,5,1,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,3,7,5,1,6]=>[4,6,5,1,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,7,5,6,1]=>[4,6,5,1,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,3,7,6,1,5]=>[4,6,5,1,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,3,7,6,5,1]=>[4,6,5,1,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,1,3,6,7]=>[4,6,3,7,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,5,1,3,7,6]=>[4,6,3,7,5,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,5,1,6,3,7]=>[4,6,3,7,2,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,5,1,6,7,3]=>[4,6,3,7,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,5,1,7,3,6]=>[4,6,3,7,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,5,1,7,6,3]=>[4,6,3,7,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,5,3,1,6,7]=>[4,6,3,5,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,3,1,7,6]=>[4,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,3,6,1,7]=>[4,6,3,5,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,3,6,7,1]=>[4,6,3,5,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,3,7,1,6]=>[4,6,3,5,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,3,7,6,1]=>[4,6,3,5,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,6,1,3,7]=>[4,6,3,2,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,6,1,7,3]=>[4,6,3,2,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,6,3,1,7]=>[4,6,3,2,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,6,3,7,1]=>[4,6,3,2,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,6,7,1,3]=>[4,6,3,2,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,6,7,3,1]=>[4,6,3,2,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,7,1,3,6]=>[4,6,3,1,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,7,1,6,3]=>[4,6,3,1,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,5,7,3,1,6]=>[4,6,3,1,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,7,3,6,1]=>[4,6,3,1,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,5,7,6,1,3]=>[4,6,3,1,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,5,7,6,3,1]=>[4,6,3,1,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,1,3,5,7]=>[4,6,2,7,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,6,1,3,7,5]=>[4,6,2,7,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,6,1,5,3,7]=>[4,6,2,7,3,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,6,1,5,7,3]=>[4,6,2,7,3,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,6,1,7,3,5]=>[4,6,2,7,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,6,1,7,5,3]=>[4,6,2,7,1,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,6,3,1,5,7]=>[4,6,2,5,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,3,1,7,5]=>[4,6,2,5,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,3,5,1,7]=>[4,6,2,5,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,3,5,7,1]=>[4,6,2,5,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,3,7,1,5]=>[4,6,2,5,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,3,7,5,1]=>[4,6,2,5,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,5,1,3,7]=>[4,6,2,3,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,5,1,7,3]=>[4,6,2,3,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,5,3,1,7]=>[4,6,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,5,3,7,1]=>[4,6,2,3,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,5,7,1,3]=>[4,6,2,3,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,5,7,3,1]=>[4,6,2,3,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,7,1,3,5]=>[4,6,2,1,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,7,1,5,3]=>[4,6,2,1,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,6,7,3,1,5]=>[4,6,2,1,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,7,3,5,1]=>[4,6,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,6,7,5,1,3]=>[4,6,2,1,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,6,7,5,3,1]=>[4,6,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,7,1,3,5,6]=>[4,6,1,7,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,7,1,3,6,5]=>[4,6,1,7,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,7,1,5,3,6]=>[4,6,1,7,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,7,1,5,6,3]=>[4,6,1,7,3,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,7,1,6,3,5]=>[4,6,1,7,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,7,1,6,5,3]=>[4,6,1,7,2,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,2,7,3,1,5,6]=>[4,6,1,5,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,7,3,1,6,5]=>[4,6,1,5,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,7,3,5,1,6]=>[4,6,1,5,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,7,3,5,6,1]=>[4,6,1,5,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,7,3,6,1,5]=>[4,6,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,7,3,6,5,1]=>[4,6,1,5,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,7,5,1,3,6]=>[4,6,1,3,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,7,5,1,6,3]=>[4,6,1,3,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,7,5,3,1,6]=>[4,6,1,3,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,7,5,3,6,1]=>[4,6,1,3,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,7,5,6,1,3]=>[4,6,1,3,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,7,5,6,3,1]=>[4,6,1,3,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,7,6,1,3,5]=>[4,6,1,2,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,7,6,1,5,3]=>[4,6,1,2,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,2,7,6,3,1,5]=>[4,6,1,2,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,7,6,3,5,1]=>[4,6,1,2,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,2,7,6,5,1,3]=>[4,6,1,2,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,2,7,6,5,3,1]=>[4,6,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,2,6,7,5]=>[4,5,7,6,2,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,2,6,7]=>[4,5,7,3,6,2,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,2,7,6]=>[4,5,7,3,6,1,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,6,2,7]=>[4,5,7,3,2,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,5,7,6,2]=>[4,5,7,3,1,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,2,5,7]=>[4,5,7,2,6,3,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,5,2,7]=>[4,5,7,2,3,6,1]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,5,7,2]=>[4,5,7,2,3,1,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,7,2,5]=>[4,5,7,2,1,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,6,7,5,2]=>[4,5,7,2,1,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,7,2,6,5]=>[4,5,7,1,6,2,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,7,5,2,6]=>[4,5,7,1,3,6,2]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,7,5,6,2]=>[4,5,7,1,3,2,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,1,7,6,5,2]=>[4,5,7,1,2,3,6]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,1,6,7,5]=>[4,5,6,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,5,1,7,6]=>[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,5,7,6,1]=>[4,5,6,3,1,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,6,1,7,5]=>[4,5,6,2,7,1,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,6,5,1,7]=>[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,6,5,7,1]=>[4,5,6,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,2,6,7,1,5]=>[4,5,6,2,1,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,6,7,5,1]=>[4,5,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,7,1,6,5]=>[4,5,6,1,7,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,2,7,5,1,6]=>[4,5,6,1,3,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,7,5,6,1]=>[4,5,6,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,2,7,6,1,5]=>[4,5,6,1,2,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,2,7,6,5,1]=>[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,5,1,2,7,6]=>[4,5,3,7,6,1,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,5,1,6,2,7]=>[4,5,3,7,2,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,5,1,6,7,2]=>[4,5,3,7,2,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,5,1,7,2,6]=>[4,5,3,7,1,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,5,1,7,6,2]=>[4,5,3,7,1,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,5,2,1,7,6]=>[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,5,2,7,6,1]=>[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,5,6,1,7,2]=>[4,5,3,2,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,3,5,7,1,2,6]=>[4,5,3,1,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,5,7,1,6,2]=>[4,5,3,1,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,5,7,6,2,1]=>[4,5,3,1,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,3,6,1,2,5,7]=>[4,5,2,7,6,3,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,6,1,2,7,5]=>[4,5,2,7,6,1,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,6,1,5,2,7]=>[4,5,2,7,3,6,1]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,6,1,5,7,2]=>[4,5,2,7,3,1,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,6,1,7,2,5]=>[4,5,2,7,1,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,6,1,7,5,2]=>[4,5,2,7,1,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,6,2,1,7,5]=>[4,5,2,6,7,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,6,2,7,1,5]=>[4,5,2,6,1,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,6,2,7,5,1]=>[4,5,2,6,1,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,6,5,1,7,2]=>[4,5,2,3,7,1,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,6,5,2,1,7]=>[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,6,5,2,7,1]=>[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,6,5,7,1,2]=>[4,5,2,3,1,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,6,5,7,2,1]=>[4,5,2,3,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,3,6,7,1,2,5]=>[4,5,2,1,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,6,7,1,5,2]=>[4,5,2,1,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,6,7,2,1,5]=>[4,5,2,1,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,6,7,2,5,1]=>[4,5,2,1,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,6,7,5,1,2]=>[4,5,2,1,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,6,7,5,2,1]=>[4,5,2,1,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,3,7,1,2,5,6]=>[4,5,1,7,6,3,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,7,1,2,6,5]=>[4,5,1,7,6,2,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,7,1,5,2,6]=>[4,5,1,7,3,6,2]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,7,1,5,6,2]=>[4,5,1,7,3,2,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,7,1,6,2,5]=>[4,5,1,7,2,6,3]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,7,1,6,5,2]=>[4,5,1,7,2,3,6]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,7,2,1,6,5]=>[4,5,1,6,7,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,3,7,2,6,5,1]=>[4,5,1,6,2,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,7,5,1,6,2]=>[4,5,1,3,7,2,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,7,5,2,1,6]=>[4,5,1,3,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,7,5,2,6,1]=>[4,5,1,3,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,7,5,6,1,2]=>[4,5,1,3,2,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,7,5,6,2,1]=>[4,5,1,3,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,7,6,1,5,2]=>[4,5,1,2,7,3,6]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,3,7,6,2,1,5]=>[4,5,1,2,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,3,7,6,2,5,1]=>[4,5,1,2,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,3,7,6,5,1,2]=>[4,5,1,2,3,7,6]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,3,7,6,5,2,1]=>[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,2,3,7,6]=>[4,3,7,6,5,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,2,6,3,7]=>[4,3,7,6,2,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,2,6,7,3]=>[4,3,7,6,2,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,2,7,3,6]=>[4,3,7,6,1,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,2,7,6,3]=>[4,3,7,6,1,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,2,6,7]=>[4,3,7,5,6,2,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,2,7,6]=>[4,3,7,5,6,1,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,6,2,7]=>[4,3,7,5,2,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,6,7,2]=>[4,3,7,5,2,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,7,2,6]=>[4,3,7,5,1,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,3,7,6,2]=>[4,3,7,5,1,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,2,3,7]=>[4,3,7,2,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,2,7,3]=>[4,3,7,2,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,3,2,7]=>[4,3,7,2,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,3,7,2]=>[4,3,7,2,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,7,2,3]=>[4,3,7,2,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,6,7,3,2]=>[4,3,7,2,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,7,2,3,6]=>[4,3,7,1,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,7,2,6,3]=>[4,3,7,1,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,7,3,2,6]=>[4,3,7,1,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,7,3,6,2]=>[4,3,7,1,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,7,6,2,3]=>[4,3,7,1,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,1,7,6,3,2]=>[4,3,7,1,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,5,2,1,3,7,6]=>[4,3,6,7,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,5,2,1,6,3,7]=>[4,3,6,7,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,5,2,1,6,7,3]=>[4,3,6,7,2,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,5,2,1,7,3,6]=>[4,3,6,7,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,5,2,1,7,6,3]=>[4,3,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,3,1,7,6]=>[4,3,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,3,7,1,6]=>[4,3,6,5,1,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,3,7,6,1]=>[4,3,6,5,1,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,6,1,3,7]=>[4,3,6,2,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,6,1,7,3]=>[4,3,6,2,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,6,3,1,7]=>[4,3,6,2,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,6,3,7,1]=>[4,3,6,2,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,6,7,1,3]=>[4,3,6,2,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,6,7,3,1]=>[4,3,6,2,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,7,1,3,6]=>[4,3,6,1,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,7,1,6,3]=>[4,3,6,1,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,5,2,7,3,1,6]=>[4,3,6,1,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,7,3,6,1]=>[4,3,6,1,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,5,2,7,6,1,3]=>[4,3,6,1,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,5,2,7,6,3,1]=>[4,3,6,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,5,3,1,2,7,6]=>[4,3,5,7,6,1,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,5,3,1,6,2,7]=>[4,3,5,7,2,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,5,3,1,6,7,2]=>[4,3,5,7,2,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,5,3,1,7,2,6]=>[4,3,5,7,1,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,5,3,1,7,6,2]=>[4,3,5,7,1,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,5,3,2,1,7,6]=>[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,5,3,2,7,6,1]=>[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,5,3,6,1,7,2]=>[4,3,5,2,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,6,1,2,7,3]=>[4,3,2,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,6,1,3,2,7]=>[4,3,2,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,6,1,3,7,2]=>[4,3,2,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,6,1,7,2,3]=>[4,3,2,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,6,1,7,3,2]=>[4,3,2,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,5,6,2,1,7,3]=>[4,3,2,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,5,6,2,7,1,3]=>[4,3,2,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,5,6,2,7,3,1]=>[4,3,2,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,5,6,3,1,7,2]=>[4,3,2,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,5,6,7,1,3,2]=>[4,3,2,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,7,1,2,6,3]=>[4,3,1,7,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,7,1,3,2,6]=>[4,3,1,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,7,1,3,6,2]=>[4,3,1,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,7,1,6,2,3]=>[4,3,1,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,7,1,6,3,2]=>[4,3,1,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,5,7,2,1,3,6]=>[4,3,1,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,5,7,2,1,6,3]=>[4,3,1,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,5,7,2,3,1,6]=>[4,3,1,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,5,7,2,3,6,1]=>[4,3,1,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,5,7,2,6,1,3]=>[4,3,1,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,5,7,2,6,3,1]=>[4,3,1,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,5,7,3,1,2,6]=>[4,3,1,5,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,5,7,3,1,6,2]=>[4,3,1,5,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,5,7,3,6,1,2]=>[4,3,1,5,2,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,5,7,6,1,2,3]=>[4,3,1,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,5,7,6,1,3,2]=>[4,3,1,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,5,7,6,3,2,1]=>[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,2,3,7,5]=>[4,2,7,6,5,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,2,5,3,7]=>[4,2,7,6,3,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,2,5,7,3]=>[4,2,7,6,3,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,2,7,3,5]=>[4,2,7,6,1,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,2,7,5,3]=>[4,2,7,6,1,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,2,5,7]=>[4,2,7,5,6,3,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,2,7,5]=>[4,2,7,5,6,1,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,5,2,7]=>[4,2,7,5,3,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,5,7,2]=>[4,2,7,5,3,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,7,2,5]=>[4,2,7,5,1,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,3,7,5,2]=>[4,2,7,5,1,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,2,3,7]=>[4,2,7,3,6,5,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,2,7,3]=>[4,2,7,3,6,1,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,3,2,7]=>[4,2,7,3,5,6,1]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,3,7,2]=>[4,2,7,3,5,1,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,7,2,3]=>[4,2,7,3,1,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,5,7,3,2]=>[4,2,7,3,1,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,7,2,3,5]=>[4,2,7,1,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,7,2,5,3]=>[4,2,7,1,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,7,3,2,5]=>[4,2,7,1,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,7,3,5,2]=>[4,2,7,1,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,7,5,2,3]=>[4,2,7,1,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,1,7,5,3,2]=>[4,2,7,1,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,6,2,1,3,5,7]=>[4,2,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,6,2,1,3,7,5]=>[4,2,6,7,5,1,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,6,2,1,5,3,7]=>[4,2,6,7,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,6,2,1,5,7,3]=>[4,2,6,7,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,6,2,1,7,3,5]=>[4,2,6,7,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,6,2,1,7,5,3]=>[4,2,6,7,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,6,2,3,1,5,7]=>[4,2,6,5,7,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,3,5,1,7]=>[4,2,6,5,3,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,6,2,3,7,1,5]=>[4,2,6,5,1,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,3,7,5,1]=>[4,2,6,5,1,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,6,2,5,1,3,7]=>[4,2,6,3,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,5,1,7,3]=>[4,2,6,3,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,5,3,1,7]=>[4,2,6,3,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,6,2,5,7,1,3]=>[4,2,6,3,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,5,7,3,1]=>[4,2,6,3,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,6,2,7,3,1,5]=>[4,2,6,1,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,7,3,5,1]=>[4,2,6,1,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,6,2,7,5,1,3]=>[4,2,6,1,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,6,3,1,2,5,7]=>[4,2,5,7,6,3,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,6,3,1,2,7,5]=>[4,2,5,7,6,1,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,6,3,1,5,2,7]=>[4,2,5,7,3,6,1]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,6,3,1,5,7,2]=>[4,2,5,7,3,1,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,6,3,1,7,2,5]=>[4,2,5,7,1,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,6,3,1,7,5,2]=>[4,2,5,7,1,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,6,3,2,1,7,5]=>[4,2,5,6,7,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,6,3,2,7,1,5]=>[4,2,5,6,1,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,6,3,2,7,5,1]=>[4,2,5,6,1,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,6,3,5,1,2,7]=>[4,2,5,3,7,6,1]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,6,3,5,1,7,2]=>[4,2,5,3,7,1,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,6,3,5,7,1,2]=>[4,2,5,3,1,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,6,3,7,1,2,5]=>[4,2,5,1,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,6,3,7,1,5,2]=>[4,2,5,1,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,6,3,7,2,1,5]=>[4,2,5,1,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,6,3,7,2,5,1]=>[4,2,5,1,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,6,3,7,5,1,2]=>[4,2,5,1,3,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,6,3,7,5,2,1]=>[4,2,5,1,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,6,5,1,2,3,7]=>[4,2,3,7,6,5,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,5,1,2,7,3]=>[4,2,3,7,6,1,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,5,1,3,2,7]=>[4,2,3,7,5,6,1]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,5,1,3,7,2]=>[4,2,3,7,5,1,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,5,1,7,2,3]=>[4,2,3,7,1,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,5,1,7,3,2]=>[4,2,3,7,1,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,6,5,2,1,7,3]=>[4,2,3,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,6,5,2,7,1,3]=>[4,2,3,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,6,5,2,7,3,1]=>[4,2,3,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,6,5,3,1,7,2]=>[4,2,3,5,7,1,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,6,5,3,2,1,7]=>[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,6,5,3,7,1,2]=>[4,2,3,5,1,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,6,5,3,7,2,1]=>[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,6,5,7,1,2,3]=>[4,2,3,1,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,6,5,7,1,3,2]=>[4,2,3,1,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,6,5,7,2,1,3]=>[4,2,3,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,6,5,7,2,3,1]=>[4,2,3,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,6,5,7,3,1,2]=>[4,2,3,1,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,6,5,7,3,2,1]=>[4,2,3,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,7,1,2,5,3]=>[4,2,1,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,7,1,3,2,5]=>[4,2,1,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,7,1,3,5,2]=>[4,2,1,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,7,1,5,2,3]=>[4,2,1,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,7,1,5,3,2]=>[4,2,1,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,6,7,2,1,3,5]=>[4,2,1,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,6,7,2,1,5,3]=>[4,2,1,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,6,7,2,3,1,5]=>[4,2,1,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,6,7,2,3,5,1]=>[4,2,1,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,6,7,2,5,1,3]=>[4,2,1,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,6,7,2,5,3,1]=>[4,2,1,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,6,7,3,1,2,5]=>[4,2,1,5,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,6,7,3,1,5,2]=>[4,2,1,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,6,7,3,2,1,5]=>[4,2,1,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,6,7,3,2,5,1]=>[4,2,1,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,6,7,3,5,1,2]=>[4,2,1,5,3,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,6,7,3,5,2,1]=>[4,2,1,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,6,7,5,1,2,3]=>[4,2,1,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,6,7,5,1,3,2]=>[4,2,1,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,6,7,5,2,1,3]=>[4,2,1,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,6,7,5,2,3,1]=>[4,2,1,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,6,7,5,3,1,2]=>[4,2,1,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,6,7,5,3,2,1]=>[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,2,3,6,5]=>[4,1,7,6,5,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,2,5,6,3]=>[4,1,7,6,3,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,2,6,3,5]=>[4,1,7,6,2,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,2,6,5,3]=>[4,1,7,6,2,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,3,2,5,6]=>[4,1,7,5,6,3,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,3,5,2,6]=>[4,1,7,5,3,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,3,6,2,5]=>[4,1,7,5,2,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,3,6,5,2]=>[4,1,7,5,2,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,5,2,3,6]=>[4,1,7,3,6,5,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,5,2,6,3]=>[4,1,7,3,6,2,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,5,3,2,6]=>[4,1,7,3,5,6,2]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,5,6,2,3]=>[4,1,7,3,2,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,5,6,3,2]=>[4,1,7,3,2,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,6,3,2,5]=>[4,1,7,2,5,6,3]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,6,3,5,2]=>[4,1,7,2,5,3,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,6,5,2,3]=>[4,1,7,2,3,6,5]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>1
[4,7,2,1,3,5,6]=>[4,1,6,7,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,7,2,1,3,6,5]=>[4,1,6,7,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,7,2,1,5,3,6]=>[4,1,6,7,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,7,2,1,5,6,3]=>[4,1,6,7,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,7,2,1,6,3,5]=>[4,1,6,7,2,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,7,2,1,6,5,3]=>[4,1,6,7,2,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>2
[4,7,2,3,1,5,6]=>[4,1,6,5,7,3,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,7,2,3,1,6,5]=>[4,1,6,5,7,2,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,7,2,3,5,1,6]=>[4,1,6,5,3,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,7,2,3,5,6,1]=>[4,1,6,5,3,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,7,2,3,6,1,5]=>[4,1,6,5,2,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,7,2,3,6,5,1]=>[4,1,6,5,2,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,7,2,5,1,3,6]=>[4,1,6,3,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,7,2,5,1,6,3]=>[4,1,6,3,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,7,2,5,3,1,6]=>[4,1,6,3,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,7,2,5,3,6,1]=>[4,1,6,3,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,7,2,5,6,1,3]=>[4,1,6,3,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,7,2,5,6,3,1]=>[4,1,6,3,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,7,2,6,1,3,5]=>[4,1,6,2,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,7,2,6,1,5,3]=>[4,1,6,2,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>2
[4,7,2,6,3,1,5]=>[4,1,6,2,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,7,2,6,3,5,1]=>[4,1,6,2,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,7,2,6,5,1,3]=>[4,1,6,2,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>2
[4,7,2,6,5,3,1]=>[4,1,6,2,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>2
[4,7,3,1,2,5,6]=>[4,1,5,7,6,3,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,7,3,1,2,6,5]=>[4,1,5,7,6,2,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,7,3,1,5,2,6]=>[4,1,5,7,3,6,2]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,7,3,1,5,6,2]=>[4,1,5,7,3,2,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,7,3,1,6,2,5]=>[4,1,5,7,2,6,3]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,7,3,1,6,5,2]=>[4,1,5,7,2,3,6]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>2
[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,7,3,2,1,6,5]=>[4,1,5,6,7,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>3
[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>3
[4,7,3,2,6,5,1]=>[4,1,5,6,2,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>3
[4,7,3,5,1,2,6]=>[4,1,5,3,7,6,2]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,7,3,5,1,6,2]=>[4,1,5,3,7,2,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,7,3,5,6,1,2]=>[4,1,5,3,2,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,7,3,6,1,2,5]=>[4,1,5,2,7,6,3]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,7,3,6,1,5,2]=>[4,1,5,2,7,3,6]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>2
[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>3
[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>3
[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>2
[4,7,3,6,5,2,1]=>[4,1,5,2,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>3
[4,7,5,1,2,3,6]=>[4,1,3,7,6,5,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,5,1,2,6,3]=>[4,1,3,7,6,2,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,5,1,3,2,6]=>[4,1,3,7,5,6,2]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,5,1,3,6,2]=>[4,1,3,7,5,2,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,5,1,6,2,3]=>[4,1,3,7,2,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,5,1,6,3,2]=>[4,1,3,7,2,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,7,5,2,1,6,3]=>[4,1,3,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,7,5,2,6,1,3]=>[4,1,3,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,7,5,2,6,3,1]=>[4,1,3,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,7,5,3,2,1,6]=>[4,1,3,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,7,5,3,2,6,1]=>[4,1,3,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,7,5,3,6,1,2]=>[4,1,3,5,2,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,7,5,3,6,2,1]=>[4,1,3,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,7,5,6,1,2,3]=>[4,1,3,2,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,7,5,6,1,3,2]=>[4,1,3,2,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,7,5,6,2,1,3]=>[4,1,3,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,7,5,6,2,3,1]=>[4,1,3,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,7,5,6,3,1,2]=>[4,1,3,2,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,7,5,6,3,2,1]=>[4,1,3,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[4,7,6,1,2,3,5]=>[4,1,2,7,6,5,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,6,1,2,5,3]=>[4,1,2,7,6,3,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,6,1,3,2,5]=>[4,1,2,7,5,6,3]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,6,1,3,5,2]=>[4,1,2,7,5,3,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,6,1,5,2,3]=>[4,1,2,7,3,6,5]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,6,1,5,3,2]=>[4,1,2,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>1
[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>2
[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>2
[4,7,6,2,5,3,1]=>[4,1,2,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>2
[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,7,6,3,1,5,2]=>[4,1,2,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>2
[4,7,6,3,2,1,5]=>[4,1,2,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>3
[4,7,6,3,2,5,1]=>[4,1,2,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>3
[4,7,6,3,5,1,2]=>[4,1,2,5,3,7,6]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>2
[4,7,6,3,5,2,1]=>[4,1,2,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>3
[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,7,6,5,1,3,2]=>[4,1,2,3,7,5,6]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>1
[4,7,6,5,2,1,3]=>[4,1,2,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>2
[4,7,6,5,2,3,1]=>[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>2
[4,7,6,5,3,1,2]=>[4,1,2,3,5,7,6]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>2
[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>3
[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,3,6,4,7]=>[3,7,6,5,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,3,7,6,4]=>[3,7,6,5,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,6,3,7]=>[3,7,6,4,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,7,3,6]=>[3,7,6,4,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,4,7,6,3]=>[3,7,6,4,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,3,4,7]=>[3,7,6,2,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,3,7,4]=>[3,7,6,2,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,4,3,7]=>[3,7,6,2,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,4,7,3]=>[3,7,6,2,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,7,3,4]=>[3,7,6,2,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,6,7,4,3]=>[3,7,6,2,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,7,3,4,6]=>[3,7,6,1,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,7,3,6,4]=>[3,7,6,1,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,7,4,3,6]=>[3,7,6,1,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,7,4,6,3]=>[3,7,6,1,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,7,6,3,4]=>[3,7,6,1,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,2,7,6,4,3]=>[3,7,6,1,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,6,4,7]=>[3,7,5,6,2,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,6,7,4]=>[3,7,5,6,2,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,7,4,6]=>[3,7,5,6,1,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,2,7,6,4]=>[3,7,5,6,1,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,2,6,7]=>[3,7,5,4,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,2,7,6]=>[3,7,5,4,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,6,2,7]=>[3,7,5,4,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,6,7,2]=>[3,7,5,4,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,7,2,6]=>[3,7,5,4,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,4,7,6,2]=>[3,7,5,4,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,2,4,7]=>[3,7,5,2,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,2,7,4]=>[3,7,5,2,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,4,2,7]=>[3,7,5,2,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,4,7,2]=>[3,7,5,2,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,7,2,4]=>[3,7,5,2,1,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,6,7,4,2]=>[3,7,5,2,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,7,2,4,6]=>[3,7,5,1,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,7,2,6,4]=>[3,7,5,1,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,7,4,2,6]=>[3,7,5,1,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,7,4,6,2]=>[3,7,5,1,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,7,6,2,4]=>[3,7,5,1,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,3,7,6,4,2]=>[3,7,5,1,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,6,3,7]=>[3,7,4,6,2,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,2,7,6,3]=>[3,7,4,6,1,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,6,2,7]=>[3,7,4,5,2,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,6,7,2]=>[3,7,4,5,2,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,7,2,6]=>[3,7,4,5,1,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,3,7,6,2]=>[3,7,4,5,1,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,2,3,7]=>[3,7,4,2,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,2,7,3]=>[3,7,4,2,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,3,2,7]=>[3,7,4,2,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,3,7,2]=>[3,7,4,2,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,7,2,3]=>[3,7,4,2,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,6,7,3,2]=>[3,7,4,2,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,7,2,3,6]=>[3,7,4,1,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,7,2,6,3]=>[3,7,4,1,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,7,3,2,6]=>[3,7,4,1,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,7,3,6,2]=>[3,7,4,1,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,7,6,2,3]=>[3,7,4,1,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,4,7,6,3,2]=>[3,7,4,1,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,3,4,7]=>[3,7,2,6,5,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,3,7,4]=>[3,7,2,6,5,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,4,3,7]=>[3,7,2,6,4,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,4,7,3]=>[3,7,2,6,4,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,7,3,4]=>[3,7,2,6,1,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,2,7,4,3]=>[3,7,2,6,1,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,2,4,7]=>[3,7,2,5,6,4,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,2,7,4]=>[3,7,2,5,6,1,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,4,2,7]=>[3,7,2,5,4,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,4,7,2]=>[3,7,2,5,4,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,7,2,4]=>[3,7,2,5,1,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,3,7,4,2]=>[3,7,2,5,1,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,2,3,7]=>[3,7,2,4,6,5,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,3,2,7]=>[3,7,2,4,5,6,1]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,3,7,2]=>[3,7,2,4,5,1,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,7,2,3]=>[3,7,2,4,1,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,4,7,3,2]=>[3,7,2,4,1,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,7,2,3,4]=>[3,7,2,1,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,7,2,4,3]=>[3,7,2,1,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,7,3,2,4]=>[3,7,2,1,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,7,3,4,2]=>[3,7,2,1,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,7,4,2,3]=>[3,7,2,1,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,6,7,4,3,2]=>[3,7,2,1,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,2,3,4,6]=>[3,7,1,6,5,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,2,3,6,4]=>[3,7,1,6,5,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,2,4,3,6]=>[3,7,1,6,4,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,2,4,6,3]=>[3,7,1,6,4,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,2,6,3,4]=>[3,7,1,6,2,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,2,6,4,3]=>[3,7,1,6,2,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,3,2,4,6]=>[3,7,1,5,6,4,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,3,2,6,4]=>[3,7,1,5,6,2,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,3,4,2,6]=>[3,7,1,5,4,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,3,4,6,2]=>[3,7,1,5,4,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,3,6,2,4]=>[3,7,1,5,2,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,3,6,4,2]=>[3,7,1,5,2,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,4,2,3,6]=>[3,7,1,4,6,5,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,4,2,6,3]=>[3,7,1,4,6,2,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,4,3,2,6]=>[3,7,1,4,5,6,2]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,4,3,6,2]=>[3,7,1,4,5,2,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,4,6,2,3]=>[3,7,1,4,2,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,4,6,3,2]=>[3,7,1,4,2,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,6,2,3,4]=>[3,7,1,2,6,5,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,6,2,4,3]=>[3,7,1,2,6,4,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,6,3,2,4]=>[3,7,1,2,5,6,4]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,6,3,4,2]=>[3,7,1,2,5,4,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,6,4,2,3]=>[3,7,1,2,4,6,5]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,1,7,6,4,3,2]=>[3,7,1,2,4,5,6]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,3,6,4,7]=>[3,6,7,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,3,6,7,4]=>[3,6,7,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,3,7,4,6]=>[3,6,7,5,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,3,7,6,4]=>[3,6,7,5,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,6,3,7]=>[3,6,7,4,2,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,6,7,3]=>[3,6,7,4,2,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,7,3,6]=>[3,6,7,4,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,3,4,7]=>[3,6,7,2,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,3,7,4]=>[3,6,7,2,5,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,4,3,7]=>[3,6,7,2,4,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,4,7,3]=>[3,6,7,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,7,3,4]=>[3,6,7,2,1,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,6,7,4,3]=>[3,6,7,2,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,7,3,4,6]=>[3,6,7,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,7,3,6,4]=>[3,6,7,1,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,7,4,3,6]=>[3,6,7,1,4,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,7,4,6,3]=>[3,6,7,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,7,6,3,4]=>[3,6,7,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,1,7,6,4,3]=>[3,6,7,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,4,7,6]=>[3,6,5,7,4,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,6,4,7]=>[3,6,5,7,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,6,7,4]=>[3,6,5,7,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,7,4,6]=>[3,6,5,7,1,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,1,7,6,4]=>[3,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,4,1,7,6]=>[3,6,5,4,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,4,7,6,1]=>[3,6,5,4,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,3,6,1,4,7]=>[3,6,5,2,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,6,1,7,4]=>[3,6,5,2,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,6,4,1,7]=>[3,6,5,2,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,6,4,7,1]=>[3,6,5,2,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,3,6,7,1,4]=>[3,6,5,2,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,6,7,4,1]=>[3,6,5,2,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,3,7,1,4,6]=>[3,6,5,1,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,7,1,6,4]=>[3,6,5,1,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,3,7,4,1,6]=>[3,6,5,1,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,7,4,6,1]=>[3,6,5,1,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,3,7,6,1,4]=>[3,6,5,1,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,3,7,6,4,1]=>[3,6,5,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,4,1,3,7,6]=>[3,6,4,7,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,4,1,6,3,7]=>[3,6,4,7,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,4,1,6,7,3]=>[3,6,4,7,2,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,4,1,7,3,6]=>[3,6,4,7,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,4,1,7,6,3]=>[3,6,4,7,1,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,4,3,1,6,7]=>[3,6,4,5,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,3,1,7,6]=>[3,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,3,6,1,7]=>[3,6,4,5,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,3,6,7,1]=>[3,6,4,5,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,3,7,1,6]=>[3,6,4,5,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,3,7,6,1]=>[3,6,4,5,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,6,1,3,7]=>[3,6,4,2,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,6,1,7,3]=>[3,6,4,2,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,6,3,1,7]=>[3,6,4,2,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,6,3,7,1]=>[3,6,4,2,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,6,7,1,3]=>[3,6,4,2,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,6,7,3,1]=>[3,6,4,2,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,7,1,3,6]=>[3,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,7,1,6,3]=>[3,6,4,1,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,4,7,3,1,6]=>[3,6,4,1,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,7,3,6,1]=>[3,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,4,7,6,1,3]=>[3,6,4,1,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,4,7,6,3,1]=>[3,6,4,1,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,1,3,4,7]=>[3,6,2,7,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,6,1,3,7,4]=>[3,6,2,7,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,6,1,4,3,7]=>[3,6,2,7,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,6,1,4,7,3]=>[3,6,2,7,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,6,1,7,3,4]=>[3,6,2,7,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,6,1,7,4,3]=>[3,6,2,7,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,6,3,1,4,7]=>[3,6,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,3,1,7,4]=>[3,6,2,5,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,3,4,1,7]=>[3,6,2,5,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,3,4,7,1]=>[3,6,2,5,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,3,7,1,4]=>[3,6,2,5,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,3,7,4,1]=>[3,6,2,5,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,4,1,3,7]=>[3,6,2,4,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,4,1,7,3]=>[3,6,2,4,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,4,3,1,7]=>[3,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,4,3,7,1]=>[3,6,2,4,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,4,7,1,3]=>[3,6,2,4,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,4,7,3,1]=>[3,6,2,4,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,7,1,3,4]=>[3,6,2,1,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,7,1,4,3]=>[3,6,2,1,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,6,7,3,1,4]=>[3,6,2,1,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,7,3,4,1]=>[3,6,2,1,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,6,7,4,1,3]=>[3,6,2,1,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,6,7,4,3,1]=>[3,6,2,1,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,7,1,3,4,6]=>[3,6,1,7,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,7,1,3,6,4]=>[3,6,1,7,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,7,1,4,3,6]=>[3,6,1,7,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,7,1,4,6,3]=>[3,6,1,7,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,7,1,6,3,4]=>[3,6,1,7,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,7,1,6,4,3]=>[3,6,1,7,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,2,7,3,1,4,6]=>[3,6,1,5,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,7,3,1,6,4]=>[3,6,1,5,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,7,3,4,1,6]=>[3,6,1,5,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,7,3,4,6,1]=>[3,6,1,5,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,7,3,6,1,4]=>[3,6,1,5,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,7,3,6,4,1]=>[3,6,1,5,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,7,4,1,3,6]=>[3,6,1,4,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,7,4,1,6,3]=>[3,6,1,4,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,7,4,3,1,6]=>[3,6,1,4,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,7,4,3,6,1]=>[3,6,1,4,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,7,4,6,1,3]=>[3,6,1,4,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,7,4,6,3,1]=>[3,6,1,4,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,7,6,1,3,4]=>[3,6,1,2,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,7,6,1,4,3]=>[3,6,1,2,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,2,7,6,3,1,4]=>[3,6,1,2,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,7,6,3,4,1]=>[3,6,1,2,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,2,7,6,4,1,3]=>[3,6,1,2,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,2,7,6,4,3,1]=>[3,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,2,6,4,7]=>[3,5,7,6,2,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,2,7,6,4]=>[3,5,7,6,1,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,2,6,7]=>[3,5,7,4,6,2,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,2,7,6]=>[3,5,7,4,6,1,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,6,2,7]=>[3,5,7,4,2,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,6,7,2]=>[3,5,7,4,2,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,7,2,6]=>[3,5,7,4,1,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,4,7,6,2]=>[3,5,7,4,1,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,2,4,7]=>[3,5,7,2,6,4,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,2,7,4]=>[3,5,7,2,6,1,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,4,2,7]=>[3,5,7,2,4,6,1]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,4,7,2]=>[3,5,7,2,4,1,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,7,2,4]=>[3,5,7,2,1,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,6,7,4,2]=>[3,5,7,2,1,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,7,2,4,6]=>[3,5,7,1,6,4,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,7,2,6,4]=>[3,5,7,1,6,2,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,7,4,2,6]=>[3,5,7,1,4,6,2]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,7,4,6,2]=>[3,5,7,1,4,2,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,7,6,2,4]=>[3,5,7,1,2,6,4]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,1,7,6,4,2]=>[3,5,7,1,2,4,6]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,1,6,4,7]=>[3,5,6,7,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,1,6,7,4]=>[3,5,6,7,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,1,7,4,6]=>[3,5,6,7,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,1,7,6,4]=>[3,5,6,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,4,1,7,6]=>[3,5,6,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,4,7,6,1]=>[3,5,6,4,1,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,2,6,1,4,7]=>[3,5,6,2,7,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,6,1,7,4]=>[3,5,6,2,7,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,6,4,1,7]=>[3,5,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,6,4,7,1]=>[3,5,6,2,4,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,2,6,7,1,4]=>[3,5,6,2,1,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,6,7,4,1]=>[3,5,6,2,1,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,2,7,1,4,6]=>[3,5,6,1,7,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,7,1,6,4]=>[3,5,6,1,7,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,2,7,4,1,6]=>[3,5,6,1,4,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,7,4,6,1]=>[3,5,6,1,4,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,2,7,6,1,4]=>[3,5,6,1,2,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,2,7,6,4,1]=>[3,5,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,4,1,2,7,6]=>[3,5,4,7,6,1,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,4,1,6,2,7]=>[3,5,4,7,2,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,4,1,7,6,2]=>[3,5,4,7,1,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,4,2,1,7,6]=>[3,5,4,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,4,2,7,6,1]=>[3,5,4,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,4,6,1,7,2]=>[3,5,4,2,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,3,6,1,2,4,7]=>[3,5,2,7,6,4,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,6,1,2,7,4]=>[3,5,2,7,6,1,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,6,1,4,2,7]=>[3,5,2,7,4,6,1]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,6,1,4,7,2]=>[3,5,2,7,4,1,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,6,1,7,2,4]=>[3,5,2,7,1,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,6,1,7,4,2]=>[3,5,2,7,1,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,6,2,1,4,7]=>[3,5,2,6,7,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,6,2,1,7,4]=>[3,5,2,6,7,1,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,6,2,4,1,7]=>[3,5,2,6,4,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,6,4,1,2,7]=>[3,5,2,4,7,6,1]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,6,4,1,7,2]=>[3,5,2,4,7,1,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,6,4,2,1,7]=>[3,5,2,4,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,6,4,7,1,2]=>[3,5,2,4,1,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,6,4,7,2,1]=>[3,5,2,4,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,3,6,7,1,2,4]=>[3,5,2,1,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,6,7,1,4,2]=>[3,5,2,1,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,6,7,2,1,4]=>[3,5,2,1,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,6,7,2,4,1]=>[3,5,2,1,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,6,7,4,1,2]=>[3,5,2,1,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,6,7,4,2,1]=>[3,5,2,1,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,7,1,2,6,4]=>[3,5,1,7,6,2,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,7,1,4,2,6]=>[3,5,1,7,4,6,2]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,3,7,2,1,4,6]=>[3,5,1,6,7,4,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,7,2,1,6,4]=>[3,5,1,6,7,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,3,7,2,4,1,6]=>[3,5,1,6,4,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,7,2,4,6,1]=>[3,5,1,6,4,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,7,2,6,1,4]=>[3,5,1,6,2,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,3,7,2,6,4,1]=>[3,5,1,6,2,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,7,4,2,1,6]=>[3,5,1,4,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,7,4,2,6,1]=>[3,5,1,4,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,7,4,6,1,2]=>[3,5,1,4,2,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,7,4,6,2,1]=>[3,5,1,4,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,3,7,6,1,2,4]=>[3,5,1,2,7,6,4]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,7,6,1,4,2]=>[3,5,1,2,7,4,6]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,3,7,6,2,4,1]=>[3,5,1,2,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,3,7,6,4,1,2]=>[3,5,1,2,4,7,6]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,2,6,3,7]=>[3,4,7,6,2,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,2,7,6,3]=>[3,4,7,6,1,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,6,2,7]=>[3,4,7,5,2,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,6,7,2]=>[3,4,7,5,2,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,7,2,6]=>[3,4,7,5,1,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,3,7,6,2]=>[3,4,7,5,1,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,2,3,7]=>[3,4,7,2,6,5,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,2,7,3]=>[3,4,7,2,6,1,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,3,2,7]=>[3,4,7,2,5,6,1]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,3,7,2]=>[3,4,7,2,5,1,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,7,2,3]=>[3,4,7,2,1,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,6,7,3,2]=>[3,4,7,2,1,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,7,2,3,6]=>[3,4,7,1,6,5,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,7,2,6,3]=>[3,4,7,1,6,2,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,7,3,2,6]=>[3,4,7,1,5,6,2]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,7,3,6,2]=>[3,4,7,1,5,2,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,7,6,2,3]=>[3,4,7,1,2,6,5]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,1,7,6,3,2]=>[3,4,7,1,2,5,6]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,1,6,3,7]=>[3,4,6,7,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,1,6,7,3]=>[3,4,6,7,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,1,7,3,6]=>[3,4,6,7,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,1,7,6,3]=>[3,4,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,3,1,7,6]=>[3,4,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,3,7,6,1]=>[3,4,6,5,1,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,2,6,1,3,7]=>[3,4,6,2,7,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,6,1,7,3]=>[3,4,6,2,7,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,6,3,1,7]=>[3,4,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,6,3,7,1]=>[3,4,6,2,5,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,2,6,7,1,3]=>[3,4,6,2,1,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,6,7,3,1]=>[3,4,6,2,1,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,2,7,1,3,6]=>[3,4,6,1,7,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,7,1,6,3]=>[3,4,6,1,7,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,2,7,3,1,6]=>[3,4,6,1,5,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,7,3,6,1]=>[3,4,6,1,5,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,2,7,6,1,3]=>[3,4,6,1,2,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,2,7,6,3,1]=>[3,4,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,1,6,2,7]=>[3,4,5,7,2,6,1]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,1,6,7,2]=>[3,4,5,7,2,1,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,1,7,2,6]=>[3,4,5,7,1,6,2]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,1,7,6,2]=>[3,4,5,7,1,2,6]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>4
[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>4
[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>4
[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>4
[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>4
[5,4,3,2,7,6,1]=>[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>4
[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,6,1,7,2]=>[3,4,5,2,7,1,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>4
[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>4
[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3
[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>4
[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>4
[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>4
[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>3
[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>4
[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,6,1,2,7,3]=>[3,4,2,7,6,1,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,6,1,3,2,7]=>[3,4,2,7,5,6,1]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,6,1,3,7,2]=>[3,4,2,7,5,1,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,6,1,7,2,3]=>[3,4,2,7,1,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,6,1,7,3,2]=>[3,4,2,7,1,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,6,2,1,7,3]=>[3,4,2,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,6,2,7,1,3]=>[3,4,2,6,1,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,6,2,7,3,1]=>[3,4,2,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,6,3,1,7,2]=>[3,4,2,5,7,1,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>4
[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>4
[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>4
[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,4,6,7,1,3,2]=>[3,4,2,1,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>3
[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>3
[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>4
[5,4,7,1,2,3,6]=>[3,4,1,7,6,5,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,7,1,2,6,3]=>[3,4,1,7,6,2,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,7,1,3,2,6]=>[3,4,1,7,5,6,2]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,7,1,3,6,2]=>[3,4,1,7,5,2,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,7,1,6,2,3]=>[3,4,1,7,2,6,5]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,7,1,6,3,2]=>[3,4,1,7,2,5,6]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,4,7,2,1,3,6]=>[3,4,1,6,7,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,7,2,1,6,3]=>[3,4,1,6,7,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,4,7,2,3,1,6]=>[3,4,1,6,5,7,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,7,2,3,6,1]=>[3,4,1,6,5,2,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,7,2,6,1,3]=>[3,4,1,6,2,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,4,7,2,6,3,1]=>[3,4,1,6,2,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,4,7,3,1,2,6]=>[3,4,1,5,7,6,2]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,7,3,1,6,2]=>[3,4,1,5,7,2,6]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>4
[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>4
[5,4,7,3,6,1,2]=>[3,4,1,5,2,7,6]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>3
[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>4
[5,4,7,6,1,2,3]=>[3,4,1,2,7,6,5]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,4,7,6,1,3,2]=>[3,4,1,2,7,5,6]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>3
[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>3
[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>3
[5,4,7,6,3,2,1]=>[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>4
[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,2,4,3,7]=>[3,2,7,6,4,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,2,4,7,3]=>[3,2,7,6,4,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,2,7,3,4]=>[3,2,7,6,1,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,2,7,4,3]=>[3,2,7,6,1,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,2,4,7]=>[3,2,7,5,6,4,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,2,7,4]=>[3,2,7,5,6,1,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,4,2,7]=>[3,2,7,5,4,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,4,7,2]=>[3,2,7,5,4,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,7,2,4]=>[3,2,7,5,1,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,3,7,4,2]=>[3,2,7,5,1,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,2,3,7]=>[3,2,7,4,6,5,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,2,7,3]=>[3,2,7,4,6,1,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,3,2,7]=>[3,2,7,4,5,6,1]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,3,7,2]=>[3,2,7,4,5,1,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,4,7,3,2]=>[3,2,7,4,1,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,7,2,3,4]=>[3,2,7,1,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,7,2,4,3]=>[3,2,7,1,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,7,3,2,4]=>[3,2,7,1,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,7,3,4,2]=>[3,2,7,1,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,7,4,2,3]=>[3,2,7,1,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,1,7,4,3,2]=>[3,2,7,1,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,6,2,1,3,7,4]=>[3,2,6,7,5,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,6,2,1,4,3,7]=>[3,2,6,7,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,6,2,1,4,7,3]=>[3,2,6,7,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,6,2,1,7,3,4]=>[3,2,6,7,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,6,2,1,7,4,3]=>[3,2,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,3,1,7,4]=>[3,2,6,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,6,2,3,7,1,4]=>[3,2,6,5,1,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,3,7,4,1]=>[3,2,6,5,1,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,6,2,4,1,3,7]=>[3,2,6,4,7,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,4,1,7,3]=>[3,2,6,4,7,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,4,3,1,7]=>[3,2,6,4,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,4,3,7,1]=>[3,2,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,6,2,4,7,1,3]=>[3,2,6,4,1,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,4,7,3,1]=>[3,2,6,4,1,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,6,2,7,1,3,4]=>[3,2,6,1,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,7,1,4,3]=>[3,2,6,1,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,6,2,7,3,1,4]=>[3,2,6,1,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,7,3,4,1]=>[3,2,6,1,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,6,2,7,4,1,3]=>[3,2,6,1,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,6,2,7,4,3,1]=>[3,2,6,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,6,3,1,2,7,4]=>[3,2,5,7,6,1,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,6,3,1,4,2,7]=>[3,2,5,7,4,6,1]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,6,3,1,4,7,2]=>[3,2,5,7,4,1,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,6,3,1,7,2,4]=>[3,2,5,7,1,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,6,3,1,7,4,2]=>[3,2,5,7,1,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,6,3,2,1,7,4]=>[3,2,5,6,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,6,3,2,7,1,4]=>[3,2,5,6,1,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,6,3,2,7,4,1]=>[3,2,5,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,6,3,4,1,7,2]=>[3,2,5,4,7,1,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,6,3,7,1,2,4]=>[3,2,5,1,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,6,3,7,1,4,2]=>[3,2,5,1,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,6,3,7,2,1,4]=>[3,2,5,1,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,6,3,7,2,4,1]=>[3,2,5,1,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,6,3,7,4,1,2]=>[3,2,5,1,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,6,3,7,4,2,1]=>[3,2,5,1,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,6,4,1,2,7,3]=>[3,2,4,7,6,1,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,6,4,1,3,2,7]=>[3,2,4,7,5,6,1]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,6,4,1,3,7,2]=>[3,2,4,7,5,1,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,6,4,1,7,2,3]=>[3,2,4,7,1,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,6,4,1,7,3,2]=>[3,2,4,7,1,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,6,4,2,1,7,3]=>[3,2,4,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,6,4,2,7,1,3]=>[3,2,4,6,1,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,6,4,2,7,3,1]=>[3,2,4,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,6,4,3,1,7,2]=>[3,2,4,5,7,1,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>4
[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4
[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>4
[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,6,4,7,1,3,2]=>[3,2,4,1,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4
[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,7,1,2,4,3]=>[3,2,1,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,7,1,3,2,4]=>[3,2,1,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,7,1,3,4,2]=>[3,2,1,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,7,1,4,2,3]=>[3,2,1,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,7,1,4,3,2]=>[3,2,1,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[5,6,7,2,1,4,3]=>[3,2,1,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[5,6,7,2,4,1,3]=>[3,2,1,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[5,6,7,2,4,3,1]=>[3,2,1,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[5,6,7,3,1,4,2]=>[3,2,1,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[5,6,7,4,1,3,2]=>[3,2,1,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3
[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4
[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,2,3,6,4]=>[3,1,7,6,5,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,2,4,3,6]=>[3,1,7,6,4,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,2,4,6,3]=>[3,1,7,6,4,2,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,2,6,4,3]=>[3,1,7,6,2,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,3,2,4,6]=>[3,1,7,5,6,4,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,3,2,6,4]=>[3,1,7,5,6,2,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,3,4,2,6]=>[3,1,7,5,4,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,3,4,6,2]=>[3,1,7,5,4,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,3,6,2,4]=>[3,1,7,5,2,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,3,6,4,2]=>[3,1,7,5,2,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,4,2,3,6]=>[3,1,7,4,6,5,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,4,2,6,3]=>[3,1,7,4,6,2,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,4,3,2,6]=>[3,1,7,4,5,6,2]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,4,3,6,2]=>[3,1,7,4,5,2,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,4,6,2,3]=>[3,1,7,4,2,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,4,6,3,2]=>[3,1,7,4,2,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,6,2,3,4]=>[3,1,7,2,6,5,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,6,2,4,3]=>[3,1,7,2,6,4,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,6,3,2,4]=>[3,1,7,2,5,6,4]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,6,3,4,2]=>[3,1,7,2,5,4,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,6,4,2,3]=>[3,1,7,2,4,6,5]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,1,6,4,3,2]=>[3,1,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>1
[5,7,2,1,3,4,6]=>[3,1,6,7,5,4,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,7,2,1,3,6,4]=>[3,1,6,7,5,2,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,7,2,1,4,3,6]=>[3,1,6,7,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,7,2,1,4,6,3]=>[3,1,6,7,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,7,2,1,6,3,4]=>[3,1,6,7,2,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,7,2,1,6,4,3]=>[3,1,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>2
[5,7,2,3,1,4,6]=>[3,1,6,5,7,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,7,2,3,1,6,4]=>[3,1,6,5,7,2,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,7,2,3,4,1,6]=>[3,1,6,5,4,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,7,2,3,4,6,1]=>[3,1,6,5,4,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,7,2,3,6,1,4]=>[3,1,6,5,2,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,7,2,3,6,4,1]=>[3,1,6,5,2,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,7,2,4,1,3,6]=>[3,1,6,4,7,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,7,2,4,1,6,3]=>[3,1,6,4,7,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,7,2,4,3,1,6]=>[3,1,6,4,5,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,7,2,4,3,6,1]=>[3,1,6,4,5,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,7,2,4,6,3,1]=>[3,1,6,4,2,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,7,2,6,1,3,4]=>[3,1,6,2,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,7,2,6,1,4,3]=>[3,1,6,2,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>2
[5,7,2,6,3,1,4]=>[3,1,6,2,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,7,2,6,3,4,1]=>[3,1,6,2,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,7,2,6,4,1,3]=>[3,1,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,7,2,6,4,3,1]=>[3,1,6,2,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,7,3,1,2,4,6]=>[3,1,5,7,6,4,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,7,3,1,2,6,4]=>[3,1,5,7,6,2,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,7,3,1,4,2,6]=>[3,1,5,7,4,6,2]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,7,3,1,4,6,2]=>[3,1,5,7,4,2,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,7,3,1,6,2,4]=>[3,1,5,7,2,6,4]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,7,3,1,6,4,2]=>[3,1,5,7,2,4,6]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,7,3,2,1,4,6]=>[3,1,5,6,7,4,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,7,3,2,1,6,4]=>[3,1,5,6,7,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>3
[5,7,3,2,4,1,6]=>[3,1,5,6,4,7,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,7,3,2,4,6,1]=>[3,1,5,6,4,2,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,7,3,2,6,1,4]=>[3,1,5,6,2,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>3
[5,7,3,2,6,4,1]=>[3,1,5,6,2,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>3
[5,7,3,4,1,2,6]=>[3,1,5,4,7,6,2]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,7,3,4,1,6,2]=>[3,1,5,4,7,2,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,7,3,4,2,1,6]=>[3,1,5,4,6,7,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,7,3,4,2,6,1]=>[3,1,5,4,6,2,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,7,3,4,6,1,2]=>[3,1,5,4,2,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,7,3,4,6,2,1]=>[3,1,5,4,2,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,7,3,6,1,2,4]=>[3,1,5,2,7,6,4]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,7,3,6,1,4,2]=>[3,1,5,2,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,7,3,6,2,1,4]=>[3,1,5,2,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>3
[5,7,3,6,2,4,1]=>[3,1,5,2,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>3
[5,7,3,6,4,1,2]=>[3,1,5,2,4,7,6]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>2
[5,7,3,6,4,2,1]=>[3,1,5,2,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>3
[5,7,4,1,2,3,6]=>[3,1,4,7,6,5,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,7,4,1,2,6,3]=>[3,1,4,7,6,2,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,7,4,1,3,2,6]=>[3,1,4,7,5,6,2]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,7,4,1,3,6,2]=>[3,1,4,7,5,2,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,7,4,1,6,2,3]=>[3,1,4,7,2,6,5]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,7,4,1,6,3,2]=>[3,1,4,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>2
[5,7,4,2,1,3,6]=>[3,1,4,6,7,5,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,7,4,2,1,6,3]=>[3,1,4,6,7,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>3
[5,7,4,2,3,1,6]=>[3,1,4,6,5,7,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,7,4,2,3,6,1]=>[3,1,4,6,5,2,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,7,4,2,6,1,3]=>[3,1,4,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>3
[5,7,4,2,6,3,1]=>[3,1,4,6,2,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>3
[5,7,4,3,1,2,6]=>[3,1,4,5,7,6,2]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,7,4,3,1,6,2]=>[3,1,4,5,7,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>3
[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>4
[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>4
[5,7,4,3,6,1,2]=>[3,1,4,5,2,7,6]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>3
[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>4
[5,7,4,6,1,2,3]=>[3,1,4,2,7,6,5]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,7,4,6,1,3,2]=>[3,1,4,2,7,5,6]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>2
[5,7,4,6,2,1,3]=>[3,1,4,2,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>3
[5,7,4,6,2,3,1]=>[3,1,4,2,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>3
[5,7,4,6,3,1,2]=>[3,1,4,2,5,7,6]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>3
[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>4
[5,7,6,1,2,3,4]=>[3,1,2,7,6,5,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,7,6,1,2,4,3]=>[3,1,2,7,6,4,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,7,6,1,3,2,4]=>[3,1,2,7,5,6,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,7,6,1,3,4,2]=>[3,1,2,7,5,4,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,7,6,1,4,2,3]=>[3,1,2,7,4,6,5]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,7,6,1,4,3,2]=>[3,1,2,7,4,5,6]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,7,6,2,1,3,4]=>[3,1,2,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[5,7,6,2,1,4,3]=>[3,1,2,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>2
[5,7,6,2,3,1,4]=>[3,1,2,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[5,7,6,2,3,4,1]=>[3,1,2,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[5,7,6,2,4,1,3]=>[3,1,2,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>2
[5,7,6,2,4,3,1]=>[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>2
[5,7,6,3,1,2,4]=>[3,1,2,5,7,6,4]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[5,7,6,3,1,4,2]=>[3,1,2,5,7,4,6]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>2
[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>3
[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>3
[5,7,6,3,4,1,2]=>[3,1,2,5,4,7,6]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>2
[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>3
[5,7,6,4,1,2,3]=>[3,1,2,4,7,6,5]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[5,7,6,4,1,3,2]=>[3,1,2,4,7,5,6]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>2
[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>3
[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>3
[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>3
[5,7,6,4,3,2,1]=>[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>4
[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,3,5,7,4]=>[2,7,6,5,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,3,7,4,5]=>[2,7,6,5,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,3,7,5,4]=>[2,7,6,5,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,3,7,5]=>[2,7,6,4,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,5,3,7]=>[2,7,6,4,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,5,7,3]=>[2,7,6,4,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,7,3,5]=>[2,7,6,4,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,4,7,5,3]=>[2,7,6,4,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,4,7,3]=>[2,7,6,3,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,7,3,4]=>[2,7,6,3,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,5,7,4,3]=>[2,7,6,3,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,7,3,4,5]=>[2,7,6,1,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,7,3,5,4]=>[2,7,6,1,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,7,4,3,5]=>[2,7,6,1,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,7,4,5,3]=>[2,7,6,1,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,7,5,3,4]=>[2,7,6,1,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,2,7,5,4,3]=>[2,7,6,1,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,4,7,5]=>[2,7,5,6,4,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,5,7,4]=>[2,7,5,6,3,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,7,4,5]=>[2,7,5,6,1,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,2,7,5,4]=>[2,7,5,6,1,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,2,5,7]=>[2,7,5,4,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,2,7,5]=>[2,7,5,4,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,5,2,7]=>[2,7,5,4,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,5,7,2]=>[2,7,5,4,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,7,2,5]=>[2,7,5,4,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,4,7,5,2]=>[2,7,5,4,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,2,4,7]=>[2,7,5,3,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,2,7,4]=>[2,7,5,3,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,4,2,7]=>[2,7,5,3,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,4,7,2]=>[2,7,5,3,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,7,2,4]=>[2,7,5,3,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,5,7,4,2]=>[2,7,5,3,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,7,2,4,5]=>[2,7,5,1,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,7,2,5,4]=>[2,7,5,1,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,7,4,2,5]=>[2,7,5,1,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,7,4,5,2]=>[2,7,5,1,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,7,5,2,4]=>[2,7,5,1,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,3,7,5,4,2]=>[2,7,5,1,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,5,3,7]=>[2,7,4,6,3,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,5,7,3]=>[2,7,4,6,3,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,7,3,5]=>[2,7,4,6,1,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,2,7,5,3]=>[2,7,4,6,1,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,2,7,5]=>[2,7,4,5,6,1,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,5,2,7]=>[2,7,4,5,3,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,5,7,2]=>[2,7,4,5,3,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,7,2,5]=>[2,7,4,5,1,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,3,7,5,2]=>[2,7,4,5,1,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,2,3,7]=>[2,7,4,3,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,3,2,7]=>[2,7,4,3,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,3,7,2]=>[2,7,4,3,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,7,2,3]=>[2,7,4,3,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,5,7,3,2]=>[2,7,4,3,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,7,2,3,5]=>[2,7,4,1,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,7,2,5,3]=>[2,7,4,1,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,7,3,2,5]=>[2,7,4,1,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,7,3,5,2]=>[2,7,4,1,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,7,5,2,3]=>[2,7,4,1,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,4,7,5,3,2]=>[2,7,4,1,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,4,7,3]=>[2,7,3,6,4,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,7,3,4]=>[2,7,3,6,1,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,2,7,4,3]=>[2,7,3,6,1,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,2,7,4]=>[2,7,3,5,6,1,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,4,2,7]=>[2,7,3,5,4,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,4,7,2]=>[2,7,3,5,4,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,7,2,4]=>[2,7,3,5,1,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,3,7,4,2]=>[2,7,3,5,1,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,2,7,3]=>[2,7,3,4,6,1,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,3,7,2]=>[2,7,3,4,5,1,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,7,2,3]=>[2,7,3,4,1,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,4,7,3,2]=>[2,7,3,4,1,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,7,2,3,4]=>[2,7,3,1,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,7,2,4,3]=>[2,7,3,1,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,7,3,2,4]=>[2,7,3,1,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,7,3,4,2]=>[2,7,3,1,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,7,4,2,3]=>[2,7,3,1,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,5,7,4,3,2]=>[2,7,3,1,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,2,3,5,4]=>[2,7,1,6,5,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,2,4,3,5]=>[2,7,1,6,4,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,2,4,5,3]=>[2,7,1,6,4,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,2,5,3,4]=>[2,7,1,6,3,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,2,5,4,3]=>[2,7,1,6,3,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,3,2,4,5]=>[2,7,1,5,6,4,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,3,2,5,4]=>[2,7,1,5,6,3,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,3,4,2,5]=>[2,7,1,5,4,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,3,4,5,2]=>[2,7,1,5,4,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,3,5,2,4]=>[2,7,1,5,3,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,3,5,4,2]=>[2,7,1,5,3,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,4,2,3,5]=>[2,7,1,4,6,5,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,4,2,5,3]=>[2,7,1,4,6,3,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,4,3,2,5]=>[2,7,1,4,5,6,3]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,4,3,5,2]=>[2,7,1,4,5,3,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,4,5,2,3]=>[2,7,1,4,3,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,4,5,3,2]=>[2,7,1,4,3,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,5,2,3,4]=>[2,7,1,3,6,5,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,5,2,4,3]=>[2,7,1,3,6,4,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,5,3,2,4]=>[2,7,1,3,5,6,4]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,5,3,4,2]=>[2,7,1,3,5,4,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,5,4,2,3]=>[2,7,1,3,4,6,5]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,1,7,5,4,3,2]=>[2,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,3,4,7,5]=>[2,6,7,5,4,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,3,5,7,4]=>[2,6,7,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,3,7,4,5]=>[2,6,7,5,1,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,3,7,5,4]=>[2,6,7,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,3,7,5]=>[2,6,7,4,5,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,5,3,7]=>[2,6,7,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,5,7,3]=>[2,6,7,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,7,3,5]=>[2,6,7,4,1,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,4,7,5,3]=>[2,6,7,4,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,3,7,4]=>[2,6,7,3,5,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,4,7,3]=>[2,6,7,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,5,7,4,3]=>[2,6,7,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,7,3,4,5]=>[2,6,7,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,7,3,5,4]=>[2,6,7,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,7,4,3,5]=>[2,6,7,1,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,7,4,5,3]=>[2,6,7,1,4,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,7,5,3,4]=>[2,6,7,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,1,7,5,4,3]=>[2,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,5,4,7]=>[2,6,5,7,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,5,7,4]=>[2,6,5,7,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,7,4,5]=>[2,6,5,7,1,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,1,7,5,4]=>[2,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,4,1,7,5]=>[2,6,5,4,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,3,4,7,1,5]=>[2,6,5,4,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,4,7,5,1]=>[2,6,5,4,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,5,1,7,4]=>[2,6,5,3,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,5,4,1,7]=>[2,6,5,3,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,5,4,7,1]=>[2,6,5,3,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,3,7,1,4,5]=>[2,6,5,1,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,7,1,5,4]=>[2,6,5,1,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,3,7,4,1,5]=>[2,6,5,1,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,7,4,5,1]=>[2,6,5,1,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,3,7,5,1,4]=>[2,6,5,1,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,3,7,5,4,1]=>[2,6,5,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,4,1,3,7,5]=>[2,6,4,7,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,4,1,5,3,7]=>[2,6,4,7,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,4,1,5,7,3]=>[2,6,4,7,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,4,1,7,3,5]=>[2,6,4,7,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,4,1,7,5,3]=>[2,6,4,7,1,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,4,3,1,5,7]=>[2,6,4,5,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,3,1,7,5]=>[2,6,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,3,5,1,7]=>[2,6,4,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,3,5,7,1]=>[2,6,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,3,7,1,5]=>[2,6,4,5,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,3,7,5,1]=>[2,6,4,5,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,5,1,3,7]=>[2,6,4,3,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,5,1,7,3]=>[2,6,4,3,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,5,3,1,7]=>[2,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,5,7,1,3]=>[2,6,4,3,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,5,7,3,1]=>[2,6,4,3,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,4,7,3,1,5]=>[2,6,4,1,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,7,3,5,1]=>[2,6,4,1,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,4,7,5,1,3]=>[2,6,4,1,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,5,1,3,7,4]=>[2,6,3,7,5,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,5,1,4,3,7]=>[2,6,3,7,4,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,5,1,4,7,3]=>[2,6,3,7,4,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,5,1,7,3,4]=>[2,6,3,7,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,5,1,7,4,3]=>[2,6,3,7,1,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,5,3,1,4,7]=>[2,6,3,5,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,3,1,7,4]=>[2,6,3,5,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,3,4,1,7]=>[2,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,4,1,3,7]=>[2,6,3,4,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,4,1,7,3]=>[2,6,3,4,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,4,3,1,7]=>[2,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,4,7,1,3]=>[2,6,3,4,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,4,7,3,1]=>[2,6,3,4,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,7,1,3,4]=>[2,6,3,1,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,7,1,4,3]=>[2,6,3,1,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,5,7,3,1,4]=>[2,6,3,1,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,7,3,4,1]=>[2,6,3,1,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,5,7,4,1,3]=>[2,6,3,1,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,5,7,4,3,1]=>[2,6,3,1,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,7,1,3,5,4]=>[2,6,1,7,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,7,1,4,3,5]=>[2,6,1,7,4,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,2,7,3,1,4,5]=>[2,6,1,5,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,7,3,1,5,4]=>[2,6,1,5,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,7,3,4,1,5]=>[2,6,1,5,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,7,3,4,5,1]=>[2,6,1,5,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,7,3,5,1,4]=>[2,6,1,5,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,7,3,5,4,1]=>[2,6,1,5,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,7,4,3,1,5]=>[2,6,1,4,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,7,4,3,5,1]=>[2,6,1,4,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,7,4,5,1,3]=>[2,6,1,4,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,7,4,5,3,1]=>[2,6,1,4,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,7,5,1,3,4]=>[2,6,1,3,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,7,5,1,4,3]=>[2,6,1,3,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,7,5,3,4,1]=>[2,6,1,3,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,2,7,5,4,1,3]=>[2,6,1,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,5,7,4]=>[2,5,7,6,3,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,7,4,5]=>[2,5,7,6,1,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,2,7,5,4]=>[2,5,7,6,1,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,2,5,7]=>[2,5,7,4,6,3,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,2,7,5]=>[2,5,7,4,6,1,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,5,2,7]=>[2,5,7,4,3,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,5,7,2]=>[2,5,7,4,3,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,7,2,5]=>[2,5,7,4,1,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,2,4,7]=>[2,5,7,3,6,4,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,4,2,7]=>[2,5,7,3,4,6,1]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,4,7,2]=>[2,5,7,3,4,1,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,7,2,4]=>[2,5,7,3,1,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,5,7,4,2]=>[2,5,7,3,1,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,7,2,4,5]=>[2,5,7,1,6,4,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,7,2,5,4]=>[2,5,7,1,6,3,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,7,4,2,5]=>[2,5,7,1,4,6,3]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,7,4,5,2]=>[2,5,7,1,4,3,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,7,5,2,4]=>[2,5,7,1,3,6,4]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,1,7,5,4,2]=>[2,5,7,1,3,4,6]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,1,4,7,5]=>[2,5,6,7,4,1,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,1,5,7,4]=>[2,5,6,7,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,1,7,4,5]=>[2,5,6,7,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,1,7,5,4]=>[2,5,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,4,1,7,5]=>[2,5,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,2,4,7,1,5]=>[2,5,6,4,1,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,4,7,5,1]=>[2,5,6,4,1,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,5,1,7,4]=>[2,5,6,3,7,1,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,5,4,1,7]=>[2,5,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,5,4,7,1]=>[2,5,6,3,4,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,2,5,7,1,4]=>[2,5,6,3,1,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,5,7,4,1]=>[2,5,6,3,1,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,2,7,1,4,5]=>[2,5,6,1,7,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,7,1,5,4]=>[2,5,6,1,7,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,2,7,4,1,5]=>[2,5,6,1,4,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,7,4,5,1]=>[2,5,6,1,4,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,2,7,5,1,4]=>[2,5,6,1,3,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,2,7,5,4,1]=>[2,5,6,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,4,1,5,2,7]=>[2,5,4,7,3,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,4,1,5,7,2]=>[2,5,4,7,3,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,4,1,7,2,5]=>[2,5,4,7,1,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,4,1,7,5,2]=>[2,5,4,7,1,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,4,2,1,7,5]=>[2,5,4,6,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,4,2,7,1,5]=>[2,5,4,6,1,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,4,2,7,5,1]=>[2,5,4,6,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,3,4,7,1,2,5]=>[2,5,4,1,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,4,7,1,5,2]=>[2,5,4,1,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,4,7,2,1,5]=>[2,5,4,1,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,4,7,2,5,1]=>[2,5,4,1,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,4,7,5,1,2]=>[2,5,4,1,3,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,4,7,5,2,1]=>[2,5,4,1,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,3,5,1,2,4,7]=>[2,5,3,7,6,4,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,5,1,4,2,7]=>[2,5,3,7,4,6,1]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,5,1,4,7,2]=>[2,5,3,7,4,1,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,5,1,7,2,4]=>[2,5,3,7,1,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,5,1,7,4,2]=>[2,5,3,7,1,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,5,2,1,7,4]=>[2,5,3,6,7,1,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,5,2,7,1,4]=>[2,5,3,6,1,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,5,2,7,4,1]=>[2,5,3,6,1,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,5,4,1,7,2]=>[2,5,3,4,7,1,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,5,4,2,1,7]=>[2,5,3,4,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,5,4,2,7,1]=>[2,5,3,4,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,5,4,7,1,2]=>[2,5,3,4,1,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,5,4,7,2,1]=>[2,5,3,4,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,3,5,7,1,2,4]=>[2,5,3,1,7,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,5,7,1,4,2]=>[2,5,3,1,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,5,7,2,1,4]=>[2,5,3,1,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,5,7,2,4,1]=>[2,5,3,1,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,5,7,4,1,2]=>[2,5,3,1,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,5,7,4,2,1]=>[2,5,3,1,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,7,1,2,5,4]=>[2,5,1,7,6,3,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,7,1,4,2,5]=>[2,5,1,7,4,6,3]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,7,1,4,5,2]=>[2,5,1,7,4,3,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,7,1,5,2,4]=>[2,5,1,7,3,6,4]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,7,1,5,4,2]=>[2,5,1,7,3,4,6]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,3,7,2,1,4,5]=>[2,5,1,6,7,4,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,7,2,1,5,4]=>[2,5,1,6,7,3,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,3,7,2,4,1,5]=>[2,5,1,6,4,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,7,2,4,5,1]=>[2,5,1,6,4,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,7,2,5,1,4]=>[2,5,1,6,3,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,3,7,2,5,4,1]=>[2,5,1,6,3,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,3,7,4,1,2,5]=>[2,5,1,4,7,6,3]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,7,4,2,1,5]=>[2,5,1,4,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,7,4,2,5,1]=>[2,5,1,4,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,7,4,5,1,2]=>[2,5,1,4,3,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,7,4,5,2,1]=>[2,5,1,4,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,3,7,5,1,2,4]=>[2,5,1,3,7,6,4]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,7,5,1,4,2]=>[2,5,1,3,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,3,7,5,2,1,4]=>[2,5,1,3,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,3,7,5,2,4,1]=>[2,5,1,3,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,3,7,5,4,1,2]=>[2,5,1,3,4,7,6]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,3,7,5,4,2,1]=>[2,5,1,3,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,2,5,3,7]=>[2,4,7,6,3,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,2,5,7,3]=>[2,4,7,6,3,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,2,7,3,5]=>[2,4,7,6,1,5,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,2,7,5,3]=>[2,4,7,6,1,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,2,7,5]=>[2,4,7,5,6,1,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,5,2,7]=>[2,4,7,5,3,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,5,7,2]=>[2,4,7,5,3,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,7,2,5]=>[2,4,7,5,1,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,3,7,5,2]=>[2,4,7,5,1,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,2,3,7]=>[2,4,7,3,6,5,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,3,2,7]=>[2,4,7,3,5,6,1]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,3,7,2]=>[2,4,7,3,5,1,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,7,2,3]=>[2,4,7,3,1,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,5,7,3,2]=>[2,4,7,3,1,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,7,2,3,5]=>[2,4,7,1,6,5,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,7,2,5,3]=>[2,4,7,1,6,3,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,7,3,2,5]=>[2,4,7,1,5,6,3]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,7,3,5,2]=>[2,4,7,1,5,3,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,7,5,2,3]=>[2,4,7,1,3,6,5]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,1,7,5,3,2]=>[2,4,7,1,3,5,6]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,1,3,7,5]=>[2,4,6,7,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,1,5,3,7]=>[2,4,6,7,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,1,5,7,3]=>[2,4,6,7,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,1,7,3,5]=>[2,4,6,7,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,1,7,5,3]=>[2,4,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,2,3,7,1,5]=>[2,4,6,5,1,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,3,7,5,1]=>[2,4,6,5,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,2,5,1,3,7]=>[2,4,6,3,7,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,5,1,7,3]=>[2,4,6,3,7,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,5,3,1,7]=>[2,4,6,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,2,5,7,1,3]=>[2,4,6,3,1,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,5,7,3,1]=>[2,4,6,3,1,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,2,7,3,1,5]=>[2,4,6,1,5,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,7,3,5,1]=>[2,4,6,1,5,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,2,7,5,1,3]=>[2,4,6,1,3,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,1,2,7,5]=>[2,4,5,7,6,1,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,1,5,2,7]=>[2,4,5,7,3,6,1]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,1,5,7,2]=>[2,4,5,7,3,1,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,1,7,2,5]=>[2,4,5,7,1,6,3]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,1,7,5,2]=>[2,4,5,7,1,3,6]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>4
[6,4,3,2,1,7,5]=>[2,4,5,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>4
[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4
[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[6,4,3,2,7,1,5]=>[2,4,5,6,1,7,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>4
[6,4,3,2,7,5,1]=>[2,4,5,6,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>4
[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,5,1,7,2]=>[2,4,5,3,7,1,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>4
[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>4
[6,4,3,7,1,2,5]=>[2,4,5,1,7,6,3]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,7,1,5,2]=>[2,4,5,1,7,3,6]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,3,7,2,1,5]=>[2,4,5,1,6,7,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>4
[6,4,3,7,2,5,1]=>[2,4,5,1,6,3,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>4
[6,4,3,7,5,1,2]=>[2,4,5,1,3,7,6]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>3
[6,4,3,7,5,2,1]=>[2,4,5,1,3,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>4
[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,5,1,2,7,3]=>[2,4,3,7,6,1,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,5,1,3,2,7]=>[2,4,3,7,5,6,1]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,5,1,3,7,2]=>[2,4,3,7,5,1,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,5,1,7,2,3]=>[2,4,3,7,1,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,5,1,7,3,2]=>[2,4,3,7,1,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,5,2,1,7,3]=>[2,4,3,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,5,2,7,1,3]=>[2,4,3,6,1,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,5,2,7,3,1]=>[2,4,3,6,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,5,3,1,7,2]=>[2,4,3,5,7,1,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4
[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4
[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3
[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,4,5,7,1,3,2]=>[2,4,3,1,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3
[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>3
[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[6,4,7,1,2,3,5]=>[2,4,1,7,6,5,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,7,1,2,5,3]=>[2,4,1,7,6,3,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,7,1,3,2,5]=>[2,4,1,7,5,6,3]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,7,1,3,5,2]=>[2,4,1,7,5,3,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,7,1,5,2,3]=>[2,4,1,7,3,6,5]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,7,1,5,3,2]=>[2,4,1,7,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,4,7,2,1,3,5]=>[2,4,1,6,7,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,7,2,1,5,3]=>[2,4,1,6,7,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,4,7,2,3,1,5]=>[2,4,1,6,5,7,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,7,2,3,5,1]=>[2,4,1,6,5,3,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,7,2,5,1,3]=>[2,4,1,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,4,7,2,5,3,1]=>[2,4,1,6,3,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,4,7,3,1,2,5]=>[2,4,1,5,7,6,3]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,7,3,1,5,2]=>[2,4,1,5,7,3,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,4,7,3,2,1,5]=>[2,4,1,5,6,7,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>4
[6,4,7,3,2,5,1]=>[2,4,1,5,6,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>4
[6,4,7,3,5,1,2]=>[2,4,1,5,3,7,6]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>3
[6,4,7,3,5,2,1]=>[2,4,1,5,3,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>4
[6,4,7,5,1,2,3]=>[2,4,1,3,7,6,5]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,4,7,5,1,3,2]=>[2,4,1,3,7,5,6]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,4,7,5,2,1,3]=>[2,4,1,3,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>3
[6,4,7,5,2,3,1]=>[2,4,1,3,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[6,4,7,5,3,1,2]=>[2,4,1,3,5,7,6]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>3
[6,4,7,5,3,2,1]=>[2,4,1,3,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>4
[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,2,3,7,4]=>[2,3,7,6,5,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,2,4,7,3]=>[2,3,7,6,4,1,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,2,7,3,4]=>[2,3,7,6,1,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,2,7,4,3]=>[2,3,7,6,1,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,2,7,4]=>[2,3,7,5,6,1,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,4,2,7]=>[2,3,7,5,4,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,4,7,2]=>[2,3,7,5,4,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,7,2,4]=>[2,3,7,5,1,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,3,7,4,2]=>[2,3,7,5,1,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,2,7,3]=>[2,3,7,4,6,1,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,3,7,2]=>[2,3,7,4,5,1,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,7,2,3]=>[2,3,7,4,1,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,7,2,3,4]=>[2,3,7,1,6,5,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,7,2,4,3]=>[2,3,7,1,6,4,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,7,3,2,4]=>[2,3,7,1,5,6,4]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,7,3,4,2]=>[2,3,7,1,5,4,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,7,4,2,3]=>[2,3,7,1,4,6,5]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,1,7,4,3,2]=>[2,3,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,1,3,7,4]=>[2,3,6,7,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,1,4,7,3]=>[2,3,6,7,4,1,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,1,7,3,4]=>[2,3,6,7,1,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,1,7,4,3]=>[2,3,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,3,1,7,4]=>[2,3,6,5,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,2,3,7,1,4]=>[2,3,6,5,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,3,7,4,1]=>[2,3,6,5,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,4,1,7,3]=>[2,3,6,4,7,1,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,4,3,1,7]=>[2,3,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,4,3,7,1]=>[2,3,6,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,2,4,7,1,3]=>[2,3,6,4,1,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,4,7,3,1]=>[2,3,6,4,1,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,2,7,1,3,4]=>[2,3,6,1,7,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,7,1,4,3]=>[2,3,6,1,7,4,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,2,7,3,1,4]=>[2,3,6,1,5,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,7,3,4,1]=>[2,3,6,1,5,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,2,7,4,1,3]=>[2,3,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,2,7,4,3,1]=>[2,3,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,1,2,7,4]=>[2,3,5,7,6,1,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,1,4,2,7]=>[2,3,5,7,4,6,1]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,1,4,7,2]=>[2,3,5,7,4,1,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,1,7,2,4]=>[2,3,5,7,1,6,4]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,1,7,4,2]=>[2,3,5,7,1,4,6]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>4
[6,5,3,2,1,7,4]=>[2,3,5,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>4
[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>4
[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>4
[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>4
[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>4
[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,4,1,7,2]=>[2,3,5,4,7,1,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>4
[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4
[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3
[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>4
[6,5,3,7,1,2,4]=>[2,3,5,1,7,6,4]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,7,1,4,2]=>[2,3,5,1,7,4,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,3,7,2,1,4]=>[2,3,5,1,6,7,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>4
[6,5,3,7,2,4,1]=>[2,3,5,1,6,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>4
[6,5,3,7,4,1,2]=>[2,3,5,1,4,7,6]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>3
[6,5,3,7,4,2,1]=>[2,3,5,1,4,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>4
[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,1,3,7,2]=>[2,3,4,7,5,1,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,1,7,2,3]=>[2,3,4,7,1,6,5]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,1,7,3,2]=>[2,3,4,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>4
[6,5,4,2,1,7,3]=>[2,3,4,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>4
[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4
[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>4
[6,5,4,2,7,1,3]=>[2,3,4,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>4
[6,5,4,2,7,3,1]=>[2,3,4,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>4
[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4
[6,5,4,3,1,7,2]=>[2,3,4,5,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4
[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>5
[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>5
[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>4
[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>5
[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,7,1,3,2]=>[2,3,4,1,7,5,6]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>3
[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>4
[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>4
[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>4
[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>5
[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,7,1,2,4,3]=>[2,3,1,7,6,4,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,7,1,3,2,4]=>[2,3,1,7,5,6,4]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,7,1,3,4,2]=>[2,3,1,7,5,4,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,7,1,4,2,3]=>[2,3,1,7,4,6,5]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,7,1,4,3,2]=>[2,3,1,7,4,5,6]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,7,2,1,4,3]=>[2,3,1,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>3
[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,7,2,4,1,3]=>[2,3,1,6,4,7,5]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>3
[6,5,7,2,4,3,1]=>[2,3,1,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>3
[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,7,3,1,4,2]=>[2,3,1,5,7,4,6]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>3
[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>4
[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>4
[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>4
[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>3
[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>3
[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>4
[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>4
[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>4
[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>5
[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,2,3,5,4]=>[2,1,7,6,5,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,2,4,3,5]=>[2,1,7,6,4,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,2,4,5,3]=>[2,1,7,6,4,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,2,5,3,4]=>[2,1,7,6,3,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,2,5,4,3]=>[2,1,7,6,3,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,3,2,4,5]=>[2,1,7,5,6,4,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,3,2,5,4]=>[2,1,7,5,6,3,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,3,4,2,5]=>[2,1,7,5,4,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,3,4,5,2]=>[2,1,7,5,4,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,3,5,2,4]=>[2,1,7,5,3,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,3,5,4,2]=>[2,1,7,5,3,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,4,2,3,5]=>[2,1,7,4,6,5,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,4,2,5,3]=>[2,1,7,4,6,3,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,4,3,2,5]=>[2,1,7,4,5,6,3]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,4,3,5,2]=>[2,1,7,4,5,3,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,4,5,2,3]=>[2,1,7,4,3,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,4,5,3,2]=>[2,1,7,4,3,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,5,2,4,3]=>[2,1,7,3,6,4,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,5,3,2,4]=>[2,1,7,3,5,6,4]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,5,3,4,2]=>[2,1,7,3,5,4,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,5,4,2,3]=>[2,1,7,3,4,6,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,1,5,4,3,2]=>[2,1,7,3,4,5,6]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,7,2,1,3,5,4]=>[2,1,6,7,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,7,2,1,4,3,5]=>[2,1,6,7,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,7,2,1,4,5,3]=>[2,1,6,7,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,7,2,1,5,3,4]=>[2,1,6,7,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,7,2,1,5,4,3]=>[2,1,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>2
[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,7,2,3,1,5,4]=>[2,1,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,7,2,3,5,1,4]=>[2,1,6,5,3,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,7,2,3,5,4,1]=>[2,1,6,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,7,2,4,1,3,5]=>[2,1,6,4,7,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,7,2,4,1,5,3]=>[2,1,6,4,7,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,7,2,4,3,1,5]=>[2,1,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,7,2,4,3,5,1]=>[2,1,6,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,7,2,4,5,1,3]=>[2,1,6,4,3,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,7,2,4,5,3,1]=>[2,1,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,7,2,5,1,3,4]=>[2,1,6,3,7,5,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,7,2,5,1,4,3]=>[2,1,6,3,7,4,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>2
[6,7,2,5,3,1,4]=>[2,1,6,3,5,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,7,2,5,3,4,1]=>[2,1,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,7,2,5,4,1,3]=>[2,1,6,3,4,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>2
[6,7,2,5,4,3,1]=>[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>2
[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,7,3,1,2,5,4]=>[2,1,5,7,6,3,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,7,3,1,4,2,5]=>[2,1,5,7,4,6,3]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,7,3,1,4,5,2]=>[2,1,5,7,4,3,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,7,3,1,5,2,4]=>[2,1,5,7,3,6,4]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,7,3,1,5,4,2]=>[2,1,5,7,3,4,6]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,7,3,2,1,5,4]=>[2,1,5,6,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>3
[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,7,3,2,5,1,4]=>[2,1,5,6,3,7,4]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>3
[6,7,3,2,5,4,1]=>[2,1,5,6,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>3
[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,7,3,4,1,5,2]=>[2,1,5,4,7,3,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,7,3,5,1,2,4]=>[2,1,5,3,7,6,4]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,7,3,5,1,4,2]=>[2,1,5,3,7,4,6]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,7,3,5,2,1,4]=>[2,1,5,3,6,7,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>3
[6,7,3,5,2,4,1]=>[2,1,5,3,6,4,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>3
[6,7,3,5,4,1,2]=>[2,1,5,3,4,7,6]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,7,3,5,4,2,1]=>[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>3
[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,7,4,1,2,5,3]=>[2,1,4,7,6,3,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,7,4,1,3,2,5]=>[2,1,4,7,5,6,3]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,7,4,1,3,5,2]=>[2,1,4,7,5,3,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,7,4,1,5,2,3]=>[2,1,4,7,3,6,5]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,7,4,1,5,3,2]=>[2,1,4,7,3,5,6]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>2
[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,7,4,2,1,5,3]=>[2,1,4,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>3
[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,7,4,2,5,1,3]=>[2,1,4,6,3,7,5]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>3
[6,7,4,2,5,3,1]=>[2,1,4,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>3
[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,7,4,3,1,5,2]=>[2,1,4,5,7,3,6]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>3
[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>4
[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>4
[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>3
[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>4
[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,7,4,5,1,3,2]=>[2,1,4,3,7,5,6]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>2
[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>3
[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>3
[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>3
[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>4
[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,7,5,1,2,4,3]=>[2,1,3,7,6,4,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,7,5,1,3,2,4]=>[2,1,3,7,5,6,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,7,5,1,3,4,2]=>[2,1,3,7,5,4,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,7,5,1,4,2,3]=>[2,1,3,7,4,6,5]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,7,5,1,4,3,2]=>[2,1,3,7,4,5,6]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>2
[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3
[6,7,5,2,1,4,3]=>[2,1,3,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>3
[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[6,7,5,2,4,1,3]=>[2,1,3,6,4,7,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>3
[6,7,5,2,4,3,1]=>[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>3
[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[6,7,5,3,1,4,2]=>[2,1,3,5,7,4,6]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>3
[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>4
[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>4
[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>3
[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>4
[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[6,7,5,4,1,3,2]=>[2,1,3,4,7,5,6]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>3
[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>4
[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>4
[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>4
[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,3,5,6,4]=>[1,7,6,5,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,4,5,6,3]=>[1,7,6,4,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,4,6,3,5]=>[1,7,6,4,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,4,6,5,3]=>[1,7,6,4,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,5,3,6,4]=>[1,7,6,3,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,5,4,6,3]=>[1,7,6,3,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,5,6,4,3]=>[1,7,6,3,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,6,4,5,3]=>[1,7,6,2,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,2,5,6,4]=>[1,7,5,6,3,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,4,2,5,6]=>[1,7,5,4,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,4,2,6,5]=>[1,7,5,4,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,4,5,2,6]=>[1,7,5,4,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,4,6,2,5]=>[1,7,5,4,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,4,6,5,2]=>[1,7,5,4,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,5,2,4,6]=>[1,7,5,3,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,5,2,6,4]=>[1,7,5,3,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,5,4,2,6]=>[1,7,5,3,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,5,4,6,2]=>[1,7,5,3,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,6,2,4,5]=>[1,7,5,2,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,6,2,5,4]=>[1,7,5,2,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,6,4,2,5]=>[1,7,5,2,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,6,4,5,2]=>[1,7,5,2,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,6,5,2,4]=>[1,7,5,2,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,3,6,5,4,2]=>[1,7,5,2,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,2,5,3,6]=>[1,7,4,6,3,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,2,5,6,3]=>[1,7,4,6,3,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,2,6,5,3]=>[1,7,4,6,2,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,3,5,2,6]=>[1,7,4,5,3,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,3,5,6,2]=>[1,7,4,5,3,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,3,6,2,5]=>[1,7,4,5,2,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,3,6,5,2]=>[1,7,4,5,2,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,5,2,6,3]=>[1,7,4,3,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,5,3,2,6]=>[1,7,4,3,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,5,6,3,2]=>[1,7,4,3,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,6,3,2,5]=>[1,7,4,2,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,6,3,5,2]=>[1,7,4,2,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,6,5,2,3]=>[1,7,4,2,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,2,3,6,4]=>[1,7,3,6,5,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,2,4,6,3]=>[1,7,3,6,4,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,2,6,4,3]=>[1,7,3,6,2,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,3,2,6,4]=>[1,7,3,5,6,2,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,3,4,2,6]=>[1,7,3,5,4,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,4,2,6,3]=>[1,7,3,4,6,2,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,4,6,2,3]=>[1,7,3,4,2,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,4,6,3,2]=>[1,7,3,4,2,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,6,2,3,4]=>[1,7,3,2,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,6,2,4,3]=>[1,7,3,2,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,6,3,2,4]=>[1,7,3,2,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,6,3,4,2]=>[1,7,3,2,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,6,4,2,3]=>[1,7,3,2,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,5,6,4,3,2]=>[1,7,3,2,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,3,4,2,5]=>[1,7,2,5,4,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,3,4,5,2]=>[1,7,2,5,4,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,3,5,2,4]=>[1,7,2,5,3,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,3,5,4,2]=>[1,7,2,5,3,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,4,3,5,2]=>[1,7,2,4,5,3,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,4,5,2,3]=>[1,7,2,4,3,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,4,5,3,2]=>[1,7,2,4,3,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,5,3,4,2]=>[1,7,2,3,5,4,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,3,5,6,4]=>[1,6,7,5,3,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,4,5,3,6]=>[1,6,7,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,4,5,6,3]=>[1,6,7,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,4,6,3,5]=>[1,6,7,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,4,6,5,3]=>[1,6,7,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,5,3,6,4]=>[1,6,7,3,5,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,5,4,6,3]=>[1,6,7,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,5,6,3,4]=>[1,6,7,3,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,5,6,4,3]=>[1,6,7,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,6,4,5,3]=>[1,6,7,2,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,1,4,6,5]=>[1,6,5,7,4,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,1,5,4,6]=>[1,6,5,7,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,1,5,6,4]=>[1,6,5,7,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,1,6,4,5]=>[1,6,5,7,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,1,6,5,4]=>[1,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,3,4,1,6,5]=>[1,6,5,4,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,3,4,6,5,1]=>[1,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,3,5,1,6,4]=>[1,6,5,3,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,3,5,4,1,6]=>[1,6,5,3,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,3,5,4,6,1]=>[1,6,5,3,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,3,5,6,1,4]=>[1,6,5,3,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,3,5,6,4,1]=>[1,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,3,6,1,5,4]=>[1,6,5,2,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,3,6,4,1,5]=>[1,6,5,2,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,3,6,4,5,1]=>[1,6,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,3,6,5,1,4]=>[1,6,5,2,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,3,6,5,4,1]=>[1,6,5,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,4,1,3,6,5]=>[1,6,4,7,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,4,1,5,3,6]=>[1,6,4,7,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,4,1,5,6,3]=>[1,6,4,7,3,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,4,1,6,3,5]=>[1,6,4,7,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,4,1,6,5,3]=>[1,6,4,7,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,4,3,1,5,6]=>[1,6,4,5,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,4,3,1,6,5]=>[1,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,4,3,5,1,6]=>[1,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,4,3,5,6,1]=>[1,6,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,4,3,6,1,5]=>[1,6,4,5,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,4,3,6,5,1]=>[1,6,4,5,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,4,5,1,3,6]=>[1,6,4,3,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,4,5,1,6,3]=>[1,6,4,3,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,4,5,3,1,6]=>[1,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,4,5,3,6,1]=>[1,6,4,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,4,5,6,1,3]=>[1,6,4,3,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,4,5,6,3,1]=>[1,6,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,4,6,1,3,5]=>[1,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,4,6,1,5,3]=>[1,6,4,2,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,4,6,3,1,5]=>[1,6,4,2,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,4,6,3,5,1]=>[1,6,4,2,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,4,6,5,1,3]=>[1,6,4,2,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,4,6,5,3,1]=>[1,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,5,1,3,6,4]=>[1,6,3,7,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,5,1,4,3,6]=>[1,6,3,7,4,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,5,1,4,6,3]=>[1,6,3,7,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,5,1,6,3,4]=>[1,6,3,7,2,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,5,1,6,4,3]=>[1,6,3,7,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,5,3,1,4,6]=>[1,6,3,5,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,5,3,1,6,4]=>[1,6,3,5,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,5,3,4,1,6]=>[1,6,3,5,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,5,3,4,6,1]=>[1,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,5,3,6,1,4]=>[1,6,3,5,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,5,3,6,4,1]=>[1,6,3,5,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,5,4,1,3,6]=>[1,6,3,4,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,5,4,1,6,3]=>[1,6,3,4,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,5,4,3,1,6]=>[1,6,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,5,4,6,1,3]=>[1,6,3,4,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,5,4,6,3,1]=>[1,6,3,4,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,5,6,1,3,4]=>[1,6,3,2,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,5,6,1,4,3]=>[1,6,3,2,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,5,6,3,1,4]=>[1,6,3,2,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,5,6,3,4,1]=>[1,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,5,6,4,1,3]=>[1,6,3,2,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,5,6,4,3,1]=>[1,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,6,1,3,5,4]=>[1,6,2,7,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,6,1,4,3,5]=>[1,6,2,7,4,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,6,1,4,5,3]=>[1,6,2,7,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,6,1,5,3,4]=>[1,6,2,7,3,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,6,1,5,4,3]=>[1,6,2,7,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>2
[7,2,6,3,1,4,5]=>[1,6,2,5,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,6,3,1,5,4]=>[1,6,2,5,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,6,3,4,1,5]=>[1,6,2,5,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,6,3,4,5,1]=>[1,6,2,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,6,3,5,1,4]=>[1,6,2,5,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,6,3,5,4,1]=>[1,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,6,4,1,3,5]=>[1,6,2,4,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,6,4,1,5,3]=>[1,6,2,4,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,6,4,3,1,5]=>[1,6,2,4,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,6,4,3,5,1]=>[1,6,2,4,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,6,4,5,1,3]=>[1,6,2,4,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,6,4,5,3,1]=>[1,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,6,5,1,3,4]=>[1,6,2,3,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,6,5,1,4,3]=>[1,6,2,3,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>2
[7,2,6,5,3,1,4]=>[1,6,2,3,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,6,5,3,4,1]=>[1,6,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,2,6,5,4,1,3]=>[1,6,2,3,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>2
[7,2,6,5,4,3,1]=>[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>2
[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,2,5,6,4]=>[1,5,7,6,3,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,4,2,5,6]=>[1,5,7,4,6,3,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,4,2,6,5]=>[1,5,7,4,6,2,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,4,5,2,6]=>[1,5,7,4,3,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,4,5,6,2]=>[1,5,7,4,3,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,4,6,2,5]=>[1,5,7,4,2,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,4,6,5,2]=>[1,5,7,4,2,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,5,2,6,4]=>[1,5,7,3,6,2,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,5,4,2,6]=>[1,5,7,3,4,6,2]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,5,4,6,2]=>[1,5,7,3,4,2,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,5,6,4,2]=>[1,5,7,3,2,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,6,2,5,4]=>[1,5,7,2,6,3,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,6,4,2,5]=>[1,5,7,2,4,6,3]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,6,4,5,2]=>[1,5,7,2,4,3,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,6,5,2,4]=>[1,5,7,2,3,6,4]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,1,6,5,4,2]=>[1,5,7,2,3,4,6]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>2
[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[7,3,2,1,5,6,4]=>[1,5,6,7,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>3
[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[7,3,2,4,1,6,5]=>[1,5,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[7,3,2,5,1,6,4]=>[1,5,6,3,7,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[7,3,2,5,4,1,6]=>[1,5,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[7,3,2,5,4,6,1]=>[1,5,6,3,4,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[7,3,2,5,6,1,4]=>[1,5,6,3,2,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[7,3,2,5,6,4,1]=>[1,5,6,3,2,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[7,3,2,6,1,5,4]=>[1,5,6,2,7,3,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>3
[7,3,2,6,4,1,5]=>[1,5,6,2,4,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[7,3,2,6,4,5,1]=>[1,5,6,2,4,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[7,3,2,6,5,1,4]=>[1,5,6,2,3,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>3
[7,3,2,6,5,4,1]=>[1,5,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>3
[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,4,1,2,6,5]=>[1,5,4,7,6,2,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,4,1,5,2,6]=>[1,5,4,7,3,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,4,1,5,6,2]=>[1,5,4,7,3,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,4,1,6,5,2]=>[1,5,4,7,2,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[7,3,4,2,1,6,5]=>[1,5,4,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[7,3,4,2,6,5,1]=>[1,5,4,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,4,5,1,6,2]=>[1,5,4,3,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,4,6,1,5,2]=>[1,5,4,2,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[7,3,4,6,5,2,1]=>[1,5,4,2,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,5,1,2,6,4]=>[1,5,3,7,6,2,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,5,1,4,2,6]=>[1,5,3,7,4,6,2]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,5,1,4,6,2]=>[1,5,3,7,4,2,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,5,1,6,4,2]=>[1,5,3,7,2,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[7,3,5,2,1,6,4]=>[1,5,3,6,7,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[7,3,5,2,6,1,4]=>[1,5,3,6,2,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[7,3,5,2,6,4,1]=>[1,5,3,6,2,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,5,4,1,6,2]=>[1,5,3,4,7,2,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,5,4,2,1,6]=>[1,5,3,4,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[7,3,5,4,2,6,1]=>[1,5,3,4,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[7,3,5,4,6,1,2]=>[1,5,3,4,2,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[7,3,5,4,6,2,1]=>[1,5,3,4,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[7,3,5,6,1,2,4]=>[1,5,3,2,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,5,6,1,4,2]=>[1,5,3,2,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,5,6,2,1,4]=>[1,5,3,2,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[7,3,5,6,2,4,1]=>[1,5,3,2,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[7,3,5,6,4,1,2]=>[1,5,3,2,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[7,3,5,6,4,2,1]=>[1,5,3,2,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[7,3,6,1,2,4,5]=>[1,5,2,7,6,4,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,6,1,2,5,4]=>[1,5,2,7,6,3,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,6,1,4,2,5]=>[1,5,2,7,4,6,3]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,6,1,4,5,2]=>[1,5,2,7,4,3,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,6,1,5,2,4]=>[1,5,2,7,3,6,4]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,6,1,5,4,2]=>[1,5,2,7,3,4,6]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>2
[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[7,3,6,2,1,5,4]=>[1,5,2,6,7,3,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>3
[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>3
[7,3,6,2,5,4,1]=>[1,5,2,6,3,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>3
[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,6,4,1,5,2]=>[1,5,2,4,7,3,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,6,4,2,1,5]=>[1,5,2,4,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[7,3,6,4,5,1,2]=>[1,5,2,4,3,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[7,3,6,4,5,2,1]=>[1,5,2,4,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,6,5,1,4,2]=>[1,5,2,3,7,4,6]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>2
[7,3,6,5,2,1,4]=>[1,5,2,3,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>3
[7,3,6,5,2,4,1]=>[1,5,2,3,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>3
[7,3,6,5,4,1,2]=>[1,5,2,3,4,7,6]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>2
[7,3,6,5,4,2,1]=>[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>3
[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,2,5,6,3]=>[1,4,7,6,3,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,2,6,5,3]=>[1,4,7,6,2,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,3,5,2,6]=>[1,4,7,5,3,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,3,6,2,5]=>[1,4,7,5,2,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,3,6,5,2]=>[1,4,7,5,2,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,5,2,6,3]=>[1,4,7,3,6,2,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,5,3,2,6]=>[1,4,7,3,5,6,2]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,5,6,3,2]=>[1,4,7,3,2,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,6,3,2,5]=>[1,4,7,2,5,6,3]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,6,3,5,2]=>[1,4,7,2,5,3,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,6,5,2,3]=>[1,4,7,2,3,6,5]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[7,4,2,1,5,3,6]=>[1,4,6,7,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[7,4,2,1,5,6,3]=>[1,4,6,7,3,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[7,4,2,1,6,3,5]=>[1,4,6,7,2,5,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[7,4,2,1,6,5,3]=>[1,4,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>3
[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[7,4,2,3,1,6,5]=>[1,4,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[7,4,2,3,6,5,1]=>[1,4,6,5,2,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[7,4,2,5,1,3,6]=>[1,4,6,3,7,5,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[7,4,2,5,1,6,3]=>[1,4,6,3,7,2,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[7,4,2,5,3,1,6]=>[1,4,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[7,4,2,5,3,6,1]=>[1,4,6,3,5,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[7,4,2,5,6,1,3]=>[1,4,6,3,2,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[7,4,2,5,6,3,1]=>[1,4,6,3,2,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[7,4,2,6,1,3,5]=>[1,4,6,2,7,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[7,4,2,6,1,5,3]=>[1,4,6,2,7,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>3
[7,4,2,6,3,1,5]=>[1,4,6,2,5,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[7,4,2,6,3,5,1]=>[1,4,6,2,5,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[7,4,2,6,5,1,3]=>[1,4,6,2,3,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>3
[7,4,2,6,5,3,1]=>[1,4,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>3
[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[7,4,3,1,5,2,6]=>[1,4,5,7,3,6,2]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[7,4,3,1,5,6,2]=>[1,4,5,7,3,2,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[7,4,3,1,6,2,5]=>[1,4,5,7,2,6,3]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[7,4,3,1,6,5,2]=>[1,4,5,7,2,3,6]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>3
[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>4
[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>4
[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>4
[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>4
[7,4,3,2,6,5,1]=>[1,4,5,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>4
[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[7,4,3,5,1,6,2]=>[1,4,5,3,7,2,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4
[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4
[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>3
[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4
[7,4,3,6,1,2,5]=>[1,4,5,2,7,6,3]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[7,4,3,6,1,5,2]=>[1,4,5,2,7,3,6]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>3
[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>4
[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>4
[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>3
[7,4,3,6,5,2,1]=>[1,4,5,2,3,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>4
[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,5,1,2,6,3]=>[1,4,3,7,6,2,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,5,1,3,2,6]=>[1,4,3,7,5,6,2]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,5,1,3,6,2]=>[1,4,3,7,5,2,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,5,1,6,2,3]=>[1,4,3,7,2,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,5,1,6,3,2]=>[1,4,3,7,2,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[7,4,5,2,1,6,3]=>[1,4,3,6,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[7,4,5,2,6,1,3]=>[1,4,3,6,2,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[7,4,5,2,6,3,1]=>[1,4,3,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[7,4,5,3,1,6,2]=>[1,4,3,5,7,2,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>4
[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[7,4,5,6,1,3,2]=>[1,4,3,2,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[7,4,6,1,2,3,5]=>[1,4,2,7,6,5,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,6,1,2,5,3]=>[1,4,2,7,6,3,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,6,1,3,2,5]=>[1,4,2,7,5,6,3]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,6,1,3,5,2]=>[1,4,2,7,5,3,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,6,1,5,2,3]=>[1,4,2,7,3,6,5]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,6,1,5,3,2]=>[1,4,2,7,3,5,6]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[7,4,6,2,1,3,5]=>[1,4,2,6,7,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[7,4,6,2,1,5,3]=>[1,4,2,6,7,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>3
[7,4,6,2,3,1,5]=>[1,4,2,6,5,7,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[7,4,6,2,3,5,1]=>[1,4,2,6,5,3,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[7,4,6,2,5,1,3]=>[1,4,2,6,3,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>3
[7,4,6,2,5,3,1]=>[1,4,2,6,3,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>3
[7,4,6,3,1,2,5]=>[1,4,2,5,7,6,3]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[7,4,6,3,1,5,2]=>[1,4,2,5,7,3,6]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>3
[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>4
[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>4
[7,4,6,3,5,1,2]=>[1,4,2,5,3,7,6]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>3
[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>4
[7,4,6,5,1,2,3]=>[1,4,2,3,7,6,5]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[7,4,6,5,1,3,2]=>[1,4,2,3,7,5,6]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>3
[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>3
[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>3
[7,4,6,5,3,2,1]=>[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>4
[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,2,3,6,4]=>[1,3,7,6,5,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,2,4,6,3]=>[1,3,7,6,4,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,2,6,3,4]=>[1,3,7,6,2,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,2,6,4,3]=>[1,3,7,6,2,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,3,2,6,4]=>[1,3,7,5,6,2,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,3,4,2,6]=>[1,3,7,5,4,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,3,4,6,2]=>[1,3,7,5,4,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,3,6,2,4]=>[1,3,7,5,2,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,3,6,4,2]=>[1,3,7,5,2,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,4,2,6,3]=>[1,3,7,4,6,2,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,4,3,6,2]=>[1,3,7,4,5,2,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,4,6,2,3]=>[1,3,7,4,2,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,4,6,3,2]=>[1,3,7,4,2,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,6,2,3,4]=>[1,3,7,2,6,5,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,6,2,4,3]=>[1,3,7,2,6,4,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,6,3,2,4]=>[1,3,7,2,5,6,4]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,6,3,4,2]=>[1,3,7,2,5,4,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,6,4,2,3]=>[1,3,7,2,4,6,5]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,1,6,4,3,2]=>[1,3,7,2,4,5,6]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>2
[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[7,5,2,1,3,6,4]=>[1,3,6,7,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[7,5,2,1,4,6,3]=>[1,3,6,7,4,2,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[7,5,2,1,6,3,4]=>[1,3,6,7,2,5,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[7,5,2,1,6,4,3]=>[1,3,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>3
[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[7,5,2,3,1,6,4]=>[1,3,6,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[7,5,2,3,6,1,4]=>[1,3,6,5,2,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[7,5,2,3,6,4,1]=>[1,3,6,5,2,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[7,5,2,4,1,6,3]=>[1,3,6,4,7,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[7,5,2,4,3,1,6]=>[1,3,6,4,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[7,5,2,4,3,6,1]=>[1,3,6,4,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[7,5,2,4,6,1,3]=>[1,3,6,4,2,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[7,5,2,6,1,3,4]=>[1,3,6,2,7,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[7,5,2,6,1,4,3]=>[1,3,6,2,7,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>3
[7,5,2,6,3,1,4]=>[1,3,6,2,5,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[7,5,2,6,3,4,1]=>[1,3,6,2,5,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[7,5,2,6,4,1,3]=>[1,3,6,2,4,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[7,5,2,6,4,3,1]=>[1,3,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>3
[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[7,5,3,1,2,6,4]=>[1,3,5,7,6,2,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[7,5,3,1,4,2,6]=>[1,3,5,7,4,6,2]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>3
[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>4
[7,5,3,2,1,6,4]=>[1,3,5,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>4
[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[7,5,3,2,6,1,4]=>[1,3,5,6,2,7,4]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>4
[7,5,3,2,6,4,1]=>[1,3,5,6,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>4
[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[7,5,3,4,1,6,2]=>[1,3,5,4,7,2,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4
[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>4
[7,5,3,6,1,2,4]=>[1,3,5,2,7,6,4]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[7,5,3,6,1,4,2]=>[1,3,5,2,7,4,6]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[7,5,3,6,2,1,4]=>[1,3,5,2,6,7,4]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>4
[7,5,3,6,2,4,1]=>[1,3,5,2,6,4,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>4
[7,5,3,6,4,1,2]=>[1,3,5,2,4,7,6]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[7,5,3,6,4,2,1]=>[1,3,5,2,4,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>4
[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[7,5,4,1,2,6,3]=>[1,3,4,7,6,2,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[7,5,4,1,3,6,2]=>[1,3,4,7,5,2,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[7,5,4,1,6,3,2]=>[1,3,4,7,2,5,6]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>3
[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>4
[7,5,4,2,1,6,3]=>[1,3,4,6,7,2,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>4
[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4
[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[7,5,4,2,6,1,3]=>[1,3,4,6,2,7,5]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>4
[7,5,4,2,6,3,1]=>[1,3,4,6,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>4
[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4
[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4
[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>5
[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>5
[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>4
[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>5
[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[7,5,4,6,1,3,2]=>[1,3,4,2,7,5,6]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>3
[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>4
[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4
[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>4
[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>5
[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[7,5,6,1,2,4,3]=>[1,3,2,7,6,4,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[7,5,6,1,3,2,4]=>[1,3,2,7,5,6,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[7,5,6,1,3,4,2]=>[1,3,2,7,5,4,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[7,5,6,1,4,2,3]=>[1,3,2,7,4,6,5]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[7,5,6,1,4,3,2]=>[1,3,2,7,4,5,6]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>2
[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3
[7,5,6,2,1,4,3]=>[1,3,2,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>3
[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[7,5,6,2,4,1,3]=>[1,3,2,6,4,7,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>3
[7,5,6,2,4,3,1]=>[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>3
[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[7,5,6,3,1,4,2]=>[1,3,2,5,7,4,6]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>3
[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>4
[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>4
[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>4
[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[7,5,6,4,1,3,2]=>[1,3,2,4,7,5,6]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>3
[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>4
[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>4
[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>4
[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>5
[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,2,4,5,3]=>[1,2,7,6,4,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,3,4,2,5]=>[1,2,7,5,4,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,3,4,5,2]=>[1,2,7,5,4,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,3,5,2,4]=>[1,2,7,5,3,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,3,5,4,2]=>[1,2,7,5,3,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,4,2,5,3]=>[1,2,7,4,6,3,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,4,3,5,2]=>[1,2,7,4,5,3,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,4,5,2,3]=>[1,2,7,4,3,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,4,5,3,2]=>[1,2,7,4,3,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,5,3,4,2]=>[1,2,7,3,5,4,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>2
[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>3
[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[7,6,2,3,1,5,4]=>[1,2,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[7,6,2,3,5,4,1]=>[1,2,6,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[7,6,2,4,1,5,3]=>[1,2,6,4,7,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[7,6,2,4,3,1,5]=>[1,2,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[7,6,2,4,3,5,1]=>[1,2,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[7,6,2,4,5,1,3]=>[1,2,6,4,3,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[7,6,2,4,5,3,1]=>[1,2,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[7,6,2,5,1,4,3]=>[1,2,6,3,7,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>3
[7,6,2,5,3,1,4]=>[1,2,6,3,5,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[7,6,2,5,3,4,1]=>[1,2,6,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[7,6,2,5,4,1,3]=>[1,2,6,3,4,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>3
[7,6,2,5,4,3,1]=>[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>3
[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[7,6,3,1,4,2,5]=>[1,2,5,7,4,6,3]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[7,6,3,1,4,5,2]=>[1,2,5,7,4,3,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[7,6,3,1,5,2,4]=>[1,2,5,7,3,6,4]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[7,6,3,1,5,4,2]=>[1,2,5,7,3,4,6]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>3
[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>4
[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>4
[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4
[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>4
[7,6,3,2,5,4,1]=>[1,2,5,6,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>4
[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[7,6,3,4,1,5,2]=>[1,2,5,4,7,3,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>4
[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>4
[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>4
[7,6,3,5,1,2,4]=>[1,2,5,3,7,6,4]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[7,6,3,5,1,4,2]=>[1,2,5,3,7,4,6]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>3
[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>4
[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>4
[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>3
[7,6,3,5,4,2,1]=>[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>4
[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[7,6,4,1,2,5,3]=>[1,2,4,7,6,3,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[7,6,4,1,3,5,2]=>[1,2,4,7,5,3,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[7,6,4,1,5,2,3]=>[1,2,4,7,3,6,5]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[7,6,4,1,5,3,2]=>[1,2,4,7,3,5,6]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>3
[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>4
[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>4
[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4
[7,6,4,2,5,1,3]=>[1,2,4,6,3,7,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>4
[7,6,4,2,5,3,1]=>[1,2,4,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>4
[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>4
[7,6,4,3,1,5,2]=>[1,2,4,5,7,3,6]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>4
[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>5
[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>5
[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>4
[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>5
[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[7,6,4,5,1,3,2]=>[1,2,4,3,7,5,6]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>3
[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>4
[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>4
[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>4
[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>5
[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[7,6,5,1,3,4,2]=>[1,2,3,7,5,4,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>3
[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>4
[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>4
[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4
[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>4
[7,6,5,2,4,3,1]=>[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>4
[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>4
[7,6,5,3,1,4,2]=>[1,2,3,5,7,4,6]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>4
[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>5
[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>5
[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>4
[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>5
[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4
[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>4
[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>5
[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>5
[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>5
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[]=>[]=>[]=>[]=>0
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Description
The number of double up and double down steps of a Dyck path.
In other words, this is the number of double rises (and, equivalently, the number of double falls) of a Dyck path.
In other words, this is the number of double rises (and, equivalently, the number of double falls) of a Dyck path.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let (c1,…,ck) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c1,c1+c2,…,c1+⋯+ck.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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