Identifier
-
Mp00297:
Parking functions
—ordered tree⟶
Ordered trees
St000084: Ordered trees ⟶ ℤ
Values
=>
Cc0021;cc-rep
[1]=>[[]]=>1
[1,1]=>[[],[]]=>2
[1,2]=>[[[]]]=>1
[2,1]=>[[[]]]=>1
[1,1,1]=>[[],[],[]]=>3
[1,1,2]=>[[],[[]]]=>2
[1,2,1]=>[[[[]]]]=>1
[2,1,1]=>[[],[[]]]=>2
[1,1,3]=>[[],[[]]]=>2
[1,3,1]=>[[[],[]]]=>1
[3,1,1]=>[[],[[]]]=>2
[1,2,2]=>[[],[[]]]=>2
[2,1,2]=>[[[[]]]]=>1
[2,2,1]=>[[],[[]]]=>2
[1,2,3]=>[[[],[]]]=>1
[1,3,2]=>[[[[]]]]=>1
[2,1,3]=>[[[[]]]]=>1
[2,3,1]=>[[[[]]]]=>1
[3,1,2]=>[[[[]]]]=>1
[3,2,1]=>[[[],[]]]=>1
[1,1,1,1]=>[[],[],[],[]]=>4
[1,1,1,2]=>[[],[],[[]]]=>3
[1,1,2,1]=>[[],[[[]]]]=>2
[1,2,1,1]=>[[],[[[]]]]=>2
[2,1,1,1]=>[[],[],[[]]]=>3
[1,1,1,3]=>[[],[],[[]]]=>3
[1,1,3,1]=>[[],[[[]]]]=>2
[1,3,1,1]=>[[],[[[]]]]=>2
[3,1,1,1]=>[[],[],[[]]]=>3
[1,1,1,4]=>[[],[],[[]]]=>3
[1,1,4,1]=>[[],[[[]]]]=>2
[1,4,1,1]=>[[],[[[]]]]=>2
[4,1,1,1]=>[[],[],[[]]]=>3
[1,1,2,2]=>[[],[],[[]]]=>3
[1,2,1,2]=>[[[],[[]]]]=>1
[1,2,2,1]=>[[[]],[[]]]=>2
[2,1,1,2]=>[[],[[[]]]]=>2
[2,1,2,1]=>[[[],[[]]]]=>1
[2,2,1,1]=>[[],[],[[]]]=>3
[1,1,2,3]=>[[],[[],[]]]=>2
[1,1,3,2]=>[[],[[[]]]]=>2
[1,2,1,3]=>[[[[[]]]]]=>1
[1,2,3,1]=>[[[],[[]]]]=>1
[1,3,1,2]=>[[[[[]]]]]=>1
[1,3,2,1]=>[[[[],[]]]]=>1
[2,1,1,3]=>[[],[[[]]]]=>2
[2,1,3,1]=>[[[[[]]]]]=>1
[2,3,1,1]=>[[],[[[]]]]=>2
[3,1,1,2]=>[[[]],[[]]]=>2
[3,1,2,1]=>[[[[[]]]]]=>1
[3,2,1,1]=>[[],[[],[]]]=>2
[1,1,2,4]=>[[],[[[]]]]=>2
[1,1,4,2]=>[[],[[],[]]]=>2
[1,2,1,4]=>[[[[[]]]]]=>1
[1,2,4,1]=>[[[[],[]]]]=>1
[1,4,1,2]=>[[[[[]]]]]=>1
[1,4,2,1]=>[[[],[[]]]]=>1
[2,1,1,4]=>[[],[[[]]]]=>2
[2,1,4,1]=>[[[[[]]]]]=>1
[2,4,1,1]=>[[],[[],[]]]=>2
[4,1,1,2]=>[[[]],[[]]]=>2
[4,1,2,1]=>[[[[[]]]]]=>1
[4,2,1,1]=>[[[]],[[]]]=>2
[1,1,3,3]=>[[],[],[[]]]=>3
[1,3,1,3]=>[[[],[[]]]]=>1
[1,3,3,1]=>[[[]],[[]]]=>2
[3,1,1,3]=>[[[]],[[]]]=>2
[3,1,3,1]=>[[[],[[]]]]=>1
[3,3,1,1]=>[[],[],[[]]]=>3
[1,1,3,4]=>[[],[[[]]]]=>2
[1,1,4,3]=>[[],[[[]]]]=>2
[1,3,1,4]=>[[[[],[]]]]=>1
[1,3,4,1]=>[[[],[[]]]]=>1
[1,4,1,3]=>[[[[],[]]]]=>1
[1,4,3,1]=>[[[],[[]]]]=>1
[3,1,1,4]=>[[],[[],[]]]=>2
[3,1,4,1]=>[[[],[[]]]]=>1
[3,4,1,1]=>[[],[[[]]]]=>2
[4,1,1,3]=>[[],[[],[]]]=>2
[4,1,3,1]=>[[[],[[]]]]=>1
[4,3,1,1]=>[[[]],[[]]]=>2
[1,2,2,2]=>[[],[],[[]]]=>3
[2,1,2,2]=>[[[]],[[]]]=>2
[2,2,1,2]=>[[],[[[]]]]=>2
[2,2,2,1]=>[[],[],[[]]]=>3
[1,2,2,3]=>[[],[[],[]]]=>2
[1,2,3,2]=>[[[],[[]]]]=>1
[1,3,2,2]=>[[],[[[]]]]=>2
[2,1,2,3]=>[[[[],[]]]]=>1
[2,1,3,2]=>[[[],[[]]]]=>1
[2,2,1,3]=>[[],[[[]]]]=>2
[2,2,3,1]=>[[],[[[]]]]=>2
[2,3,1,2]=>[[[],[[]]]]=>1
[2,3,2,1]=>[[[[],[]]]]=>1
[3,1,2,2]=>[[],[[[]]]]=>2
[3,2,1,2]=>[[[],[[]]]]=>1
[3,2,2,1]=>[[],[[],[]]]=>2
[1,2,2,4]=>[[[]],[[]]]=>2
[1,2,4,2]=>[[[[[]]]]]=>1
[1,4,2,2]=>[[],[[],[]]]=>2
[2,1,2,4]=>[[[[[]]]]]=>1
[2,1,4,2]=>[[[[],[]]]]=>1
[2,2,1,4]=>[[],[[[]]]]=>2
[2,2,4,1]=>[[],[[],[]]]=>2
[2,4,1,2]=>[[[],[[]]]]=>1
[2,4,2,1]=>[[[[[]]]]]=>1
[4,1,2,2]=>[[],[[[]]]]=>2
[4,2,1,2]=>[[[[[]]]]]=>1
[4,2,2,1]=>[[],[[[]]]]=>2
[1,2,3,3]=>[[],[[],[]]]=>2
[1,3,2,3]=>[[[[[]]]]]=>1
[1,3,3,2]=>[[[]],[[]]]=>2
[2,1,3,3]=>[[[]],[[]]]=>2
[2,3,1,3]=>[[[[[]]]]]=>1
[2,3,3,1]=>[[[]],[[]]]=>2
[3,1,2,3]=>[[[[],[]]]]=>1
[3,1,3,2]=>[[[[[]]]]]=>1
[3,2,1,3]=>[[[],[[]]]]=>1
[3,2,3,1]=>[[[[[]]]]]=>1
[3,3,1,2]=>[[],[[[]]]]=>2
[3,3,2,1]=>[[],[[],[]]]=>2
[1,2,3,4]=>[[[],[],[]]]=>1
[1,2,4,3]=>[[[[[]]]]]=>1
[1,3,2,4]=>[[[],[[]]]]=>1
[1,3,4,2]=>[[[[[]]]]]=>1
[1,4,2,3]=>[[[],[[]]]]=>1
[1,4,3,2]=>[[[[],[]]]]=>1
[2,1,3,4]=>[[[[[]]]]]=>1
[2,1,4,3]=>[[[],[[]]]]=>1
[2,3,1,4]=>[[[[],[]]]]=>1
[2,3,4,1]=>[[[],[[]]]]=>1
[2,4,1,3]=>[[[],[],[]]]=>1
[2,4,3,1]=>[[[[[]]]]]=>1
[3,1,2,4]=>[[[[[]]]]]=>1
[3,1,4,2]=>[[[],[],[]]]=>1
[3,2,1,4]=>[[[],[[]]]]=>1
[3,2,4,1]=>[[[[],[]]]]=>1
[3,4,1,2]=>[[[],[[]]]]=>1
[3,4,2,1]=>[[[[[]]]]]=>1
[4,1,2,3]=>[[[[],[]]]]=>1
[4,1,3,2]=>[[[],[[]]]]=>1
[4,2,1,3]=>[[[[[]]]]]=>1
[4,2,3,1]=>[[[],[[]]]]=>1
[4,3,1,2]=>[[[[[]]]]]=>1
[4,3,2,1]=>[[[],[],[]]]=>1
[1,1,1,1,1]=>[[],[],[],[],[]]=>5
[1,1,1,1,2]=>[[],[],[],[[]]]=>4
[1,1,1,2,1]=>[[],[],[[[]]]]=>3
[1,1,2,1,1]=>[[],[],[[[]]]]=>3
[1,2,1,1,1]=>[[],[],[[[]]]]=>3
[2,1,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,1,3]=>[[],[],[],[[]]]=>4
[1,1,1,3,1]=>[[],[],[[[]]]]=>3
[1,1,3,1,1]=>[[],[],[[[]]]]=>3
[1,3,1,1,1]=>[[],[],[[[]]]]=>3
[3,1,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,1,4]=>[[],[],[],[[]]]=>4
[1,1,1,4,1]=>[[],[],[[],[]]]=>3
[1,1,4,1,1]=>[[],[],[[],[]]]=>3
[1,4,1,1,1]=>[[],[],[[],[]]]=>3
[4,1,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,1,5]=>[[],[],[],[[]]]=>4
[1,1,1,5,1]=>[[],[],[[[]]]]=>3
[1,1,5,1,1]=>[[],[],[[[]]]]=>3
[1,5,1,1,1]=>[[],[[]],[[]]]=>3
[5,1,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,2,2]=>[[],[],[],[[]]]=>4
[1,1,2,1,2]=>[[],[[],[[]]]]=>2
[1,1,2,2,1]=>[[],[[]],[[]]]=>3
[1,2,1,1,2]=>[[],[[],[[]]]]=>2
[1,2,1,2,1]=>[[[],[[],[]]]]=>1
[1,2,2,1,1]=>[[],[[]],[[]]]=>3
[2,1,1,1,2]=>[[],[],[[[]]]]=>3
[2,1,1,2,1]=>[[],[[[],[]]]]=>2
[2,1,2,1,1]=>[[],[[],[[]]]]=>2
[2,2,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,2,3]=>[[],[],[[],[]]]=>3
[1,1,1,3,2]=>[[],[],[[[]]]]=>3
[1,1,2,1,3]=>[[],[[[[]]]]]=>2
[1,1,2,3,1]=>[[],[[],[[]]]]=>2
[1,1,3,1,2]=>[[],[[[[]]]]]=>2
[1,1,3,2,1]=>[[],[[[],[]]]]=>2
[1,2,1,1,3]=>[[],[[[[]]]]]=>2
[1,2,1,3,1]=>[[[[[[]]]]]]=>1
[1,2,3,1,1]=>[[],[[[],[]]]]=>2
[1,3,1,1,2]=>[[[]],[[[]]]]=>2
[1,3,1,2,1]=>[[[[[[]]]]]]=>1
[1,3,2,1,1]=>[[],[[],[[]]]]=>2
[2,1,1,1,3]=>[[],[],[[[]]]]=>3
[2,1,1,3,1]=>[[],[[[[]]]]]=>2
[2,1,3,1,1]=>[[[[]]],[[]]]=>2
[2,3,1,1,1]=>[[],[],[[[]]]]=>3
[3,1,1,1,2]=>[[],[[]],[[]]]=>3
[3,1,1,2,1]=>[[],[[[[]]]]]=>2
[3,1,2,1,1]=>[[[]],[[[]]]]=>2
[3,2,1,1,1]=>[[],[],[[],[]]]=>3
[1,1,1,2,4]=>[[],[],[[[]]]]=>3
[1,1,1,4,2]=>[[],[],[[[]]]]=>3
[1,1,2,1,4]=>[[],[[[[]]]]]=>2
[1,1,2,4,1]=>[[],[[[[]]]]]=>2
[1,1,4,1,2]=>[[],[[],[[]]]]=>2
[1,1,4,2,1]=>[[],[[[[]]]]]=>2
[1,2,1,1,4]=>[[],[[[[]]]]]=>2
[1,2,1,4,1]=>[[[[[],[]]]]]=>1
[1,2,4,1,1]=>[[],[[[[]]]]]=>2
[1,4,1,1,2]=>[[[]],[[],[]]]=>2
[1,4,1,2,1]=>[[[],[[[]]]]]=>1
[1,4,2,1,1]=>[[[]],[[[]]]]=>2
[2,1,1,1,4]=>[[],[],[[[]]]]=>3
[2,1,1,4,1]=>[[],[[],[[]]]]=>2
[2,1,4,1,1]=>[[[]],[[],[]]]=>2
[2,4,1,1,1]=>[[],[],[[[]]]]=>3
[4,1,1,1,2]=>[[],[[]],[[]]]=>3
[4,1,1,2,1]=>[[[[]]],[[]]]=>2
[4,1,2,1,1]=>[[],[[[[]]]]]=>2
[4,2,1,1,1]=>[[],[[]],[[]]]=>3
[1,1,1,2,5]=>[[],[],[[[]]]]=>3
[1,1,1,5,2]=>[[],[],[[[]]]]=>3
[1,1,2,1,5]=>[[],[[[[]]]]]=>2
[1,1,2,5,1]=>[[],[[[[]]]]]=>2
[1,1,5,1,2]=>[[],[[[[]]]]]=>2
[1,1,5,2,1]=>[[],[[[[]]]]]=>2
[1,2,1,1,5]=>[[],[[[[]]]]]=>2
[1,2,1,5,1]=>[[[[[[]]]]]]=>1
[1,2,5,1,1]=>[[],[[[[]]]]]=>2
[1,5,1,1,2]=>[[[]],[[[]]]]=>2
[1,5,1,2,1]=>[[[[[[]]]]]]=>1
[1,5,2,1,1]=>[[[]],[[[]]]]=>2
[2,1,1,1,5]=>[[],[],[[[]]]]=>3
[2,1,1,5,1]=>[[],[[[[]]]]]=>2
[2,1,5,1,1]=>[[[[]]],[[]]]=>2
[2,5,1,1,1]=>[[],[],[[[]]]]=>3
[5,1,1,1,2]=>[[],[[]],[[]]]=>3
[5,1,1,2,1]=>[[[[]]],[[]]]=>2
[5,1,2,1,1]=>[[],[[[[]]]]]=>2
[5,2,1,1,1]=>[[],[[]],[[]]]=>3
[1,1,1,3,3]=>[[],[],[],[[]]]=>4
[1,1,3,1,3]=>[[],[[],[[]]]]=>2
[1,1,3,3,1]=>[[],[[]],[[]]]=>3
[1,3,1,1,3]=>[[[]],[[],[]]]=>2
[1,3,1,3,1]=>[[[],[[],[]]]]=>1
[1,3,3,1,1]=>[[],[[]],[[]]]=>3
[3,1,1,1,3]=>[[],[[]],[[]]]=>3
[3,1,1,3,1]=>[[],[[[],[]]]]=>2
[3,1,3,1,1]=>[[],[[],[[]]]]=>2
[3,3,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,3,4]=>[[],[],[[[]]]]=>3
[1,1,1,4,3]=>[[],[],[[[]]]]=>3
[1,1,3,1,4]=>[[],[[[[]]]]]=>2
[1,1,3,4,1]=>[[],[[[[]]]]]=>2
[1,1,4,1,3]=>[[],[[],[[]]]]=>2
[1,1,4,3,1]=>[[],[[[[]]]]]=>2
[1,3,1,1,4]=>[[[]],[[[]]]]=>2
[1,3,1,4,1]=>[[[[],[[]]]]]=>1
[1,3,4,1,1]=>[[],[[[[]]]]]=>2
[1,4,1,1,3]=>[[[]],[[],[]]]=>2
[1,4,1,3,1]=>[[[],[[[]]]]]=>1
[1,4,3,1,1]=>[[[[]]],[[]]]=>2
[3,1,1,1,4]=>[[],[[]],[[]]]=>3
[3,1,1,4,1]=>[[],[[],[[]]]]=>2
[3,1,4,1,1]=>[[],[[],[[]]]]=>2
[3,4,1,1,1]=>[[],[],[[[]]]]=>3
[4,1,1,1,3]=>[[],[[]],[[]]]=>3
[4,1,1,3,1]=>[[[[]]],[[]]]=>2
[4,1,3,1,1]=>[[],[[[[]]]]]=>2
[4,3,1,1,1]=>[[],[[]],[[]]]=>3
[1,1,1,3,5]=>[[],[],[[],[]]]=>3
[1,1,1,5,3]=>[[],[],[[],[]]]=>3
[1,1,3,1,5]=>[[],[[[],[]]]]=>2
[1,1,3,5,1]=>[[],[[],[],[]]]=>2
[1,1,5,1,3]=>[[],[[[],[]]]]=>2
[1,1,5,3,1]=>[[],[[],[],[]]]=>2
[1,3,1,1,5]=>[[],[[],[[]]]]=>2
[1,3,1,5,1]=>[[[],[[],[]]]]=>1
[1,3,5,1,1]=>[[],[[],[],[]]]=>2
[1,5,1,1,3]=>[[[]],[[],[]]]=>2
[1,5,1,3,1]=>[[[],[[],[]]]]=>1
[1,5,3,1,1]=>[[],[[],[],[]]]=>2
[3,1,1,1,5]=>[[],[],[[],[]]]=>3
[3,1,1,5,1]=>[[],[[],[[]]]]=>2
[3,1,5,1,1]=>[[],[[[],[]]]]=>2
[3,5,1,1,1]=>[[],[],[[],[]]]=>3
[5,1,1,1,3]=>[[],[],[[],[]]]=>3
[5,1,1,3,1]=>[[],[[],[[]]]]=>2
[5,1,3,1,1]=>[[],[[[],[]]]]=>2
[5,3,1,1,1]=>[[],[],[[],[]]]=>3
[1,1,1,4,4]=>[[],[],[],[[]]]=>4
[1,1,4,1,4]=>[[],[[],[],[]]]=>2
[1,1,4,4,1]=>[[],[],[[],[]]]=>3
[1,4,1,1,4]=>[[],[[],[],[]]]=>2
[1,4,1,4,1]=>[[[],[],[],[]]]=>1
[1,4,4,1,1]=>[[],[],[[],[]]]=>3
[4,1,1,1,4]=>[[],[],[[],[]]]=>3
[4,1,1,4,1]=>[[],[[],[],[]]]=>2
[4,1,4,1,1]=>[[],[[],[],[]]]=>2
[4,4,1,1,1]=>[[],[],[],[[]]]=>4
[1,1,1,4,5]=>[[],[],[[[]]]]=>3
[1,1,1,5,4]=>[[],[],[[[]]]]=>3
[1,1,4,1,5]=>[[],[[],[[]]]]=>2
[1,1,4,5,1]=>[[],[[[[]]]]]=>2
[1,1,5,1,4]=>[[],[[[[]]]]]=>2
[1,1,5,4,1]=>[[],[[[[]]]]]=>2
[1,4,1,1,5]=>[[[]],[[],[]]]=>2
[1,4,1,5,1]=>[[[],[[[]]]]]=>1
[1,4,5,1,1]=>[[],[[[[]]]]]=>2
[1,5,1,1,4]=>[[[[]]],[[]]]=>2
[1,5,1,4,1]=>[[[[],[[]]]]]=>1
[1,5,4,1,1]=>[[[[]]],[[]]]=>2
[4,1,1,1,5]=>[[],[[]],[[]]]=>3
[4,1,1,5,1]=>[[[]],[[[]]]]=>2
[4,1,5,1,1]=>[[],[[[[]]]]]=>2
[4,5,1,1,1]=>[[],[],[[[]]]]=>3
[5,1,1,1,4]=>[[],[[]],[[]]]=>3
[5,1,1,4,1]=>[[[]],[[],[]]]=>2
[5,1,4,1,1]=>[[],[[],[[]]]]=>2
[5,4,1,1,1]=>[[],[[]],[[]]]=>3
[1,1,2,2,2]=>[[],[],[],[[]]]=>4
[1,2,1,2,2]=>[[[]],[[],[]]]=>2
[1,2,2,1,2]=>[[],[[[],[]]]]=>2
[1,2,2,2,1]=>[[],[[]],[[]]]=>3
[2,1,1,2,2]=>[[],[[]],[[]]]=>3
[2,1,2,1,2]=>[[[],[[],[]]]]=>1
[2,1,2,2,1]=>[[[]],[[],[]]]=>2
[2,2,1,1,2]=>[[],[],[[[]]]]=>3
[2,2,1,2,1]=>[[],[[],[[]]]]=>2
[2,2,2,1,1]=>[[],[],[],[[]]]=>4
[1,1,2,2,3]=>[[],[],[[],[]]]=>3
[1,1,2,3,2]=>[[],[[],[[]]]]=>2
[1,1,3,2,2]=>[[],[],[[[]]]]=>3
[1,2,1,2,3]=>[[[],[],[[]]]]=>1
[1,2,1,3,2]=>[[[[],[[]]]]]=>1
[1,2,2,1,3]=>[[[]],[[[]]]]=>2
[1,2,2,3,1]=>[[],[[],[[]]]]=>2
[1,2,3,1,2]=>[[[],[],[[]]]]=>1
[1,2,3,2,1]=>[[[],[[],[]]]]=>1
[1,3,1,2,2]=>[[],[[[[]]]]]=>2
[1,3,2,1,2]=>[[[[],[[]]]]]=>1
[1,3,2,2,1]=>[[],[[],[[]]]]=>2
[2,1,1,2,3]=>[[],[[],[[]]]]=>2
[2,1,1,3,2]=>[[],[[[],[]]]]=>2
[2,1,2,1,3]=>[[[[]],[[]]]]=>1
[2,1,2,3,1]=>[[[[[],[]]]]]=>1
[2,1,3,1,2]=>[[[[[[]]]]]]=>1
[2,1,3,2,1]=>[[[],[],[[]]]]=>1
[2,2,1,1,3]=>[[],[],[[[]]]]=>3
[2,2,1,3,1]=>[[],[[[[]]]]]=>2
[2,2,3,1,1]=>[[],[],[[[]]]]=>3
[2,3,1,1,2]=>[[[]],[[],[]]]=>2
[2,3,1,2,1]=>[[[],[[[]]]]]=>1
[2,3,2,1,1]=>[[],[[],[[]]]]=>2
[3,1,1,2,2]=>[[],[],[[[]]]]=>3
[3,1,2,1,2]=>[[[[],[[]]]]]=>1
[3,1,2,2,1]=>[[[]],[[[]]]]=>2
[3,2,1,1,2]=>[[],[[[],[]]]]=>2
[3,2,1,2,1]=>[[[],[],[[]]]]=>1
[3,2,2,1,1]=>[[],[],[[],[]]]=>3
[1,1,2,2,4]=>[[],[[]],[[]]]=>3
[1,1,2,4,2]=>[[],[[[[]]]]]=>2
[1,1,4,2,2]=>[[],[],[[[]]]]=>3
[1,2,1,2,4]=>[[[],[[[]]]]]=>1
[1,2,1,4,2]=>[[[[[[]]]]]]=>1
[1,2,2,1,4]=>[[[]],[[[]]]]=>2
[1,2,2,4,1]=>[[[]],[[[]]]]=>2
[1,2,4,1,2]=>[[[],[[[]]]]]=>1
[1,2,4,2,1]=>[[[[[[]]]]]]=>1
[1,4,1,2,2]=>[[],[[[],[]]]]=>2
[1,4,2,1,2]=>[[[[[[]]]]]]=>1
[1,4,2,2,1]=>[[[]],[[[]]]]=>2
[2,1,1,2,4]=>[[],[[[[]]]]]=>2
[2,1,1,4,2]=>[[],[[[[]]]]]=>2
[2,1,2,1,4]=>[[[[]],[[]]]]=>1
[2,1,2,4,1]=>[[[[[[]]]]]]=>1
[2,1,4,1,2]=>[[[[[],[]]]]]=>1
[2,1,4,2,1]=>[[[[]],[[]]]]=>1
[2,2,1,1,4]=>[[],[],[[[]]]]=>3
[2,2,1,4,1]=>[[],[[[],[]]]]=>2
[2,2,4,1,1]=>[[],[],[[[]]]]=>3
[2,4,1,1,2]=>[[[]],[[[]]]]=>2
[2,4,1,2,1]=>[[[[[[]]]]]]=>1
[2,4,2,1,1]=>[[[[]]],[[]]]=>2
[4,1,1,2,2]=>[[],[[]],[[]]]=>3
[4,1,2,1,2]=>[[[[[],[]]]]]=>1
[4,1,2,2,1]=>[[[[]]],[[]]]=>2
[4,2,1,1,2]=>[[[[]]],[[]]]=>2
[4,2,1,2,1]=>[[[[],[[]]]]]=>1
[4,2,2,1,1]=>[[],[[]],[[]]]=>3
[1,1,2,2,5]=>[[],[[]],[[]]]=>3
[1,1,2,5,2]=>[[],[[[],[]]]]=>2
[1,1,5,2,2]=>[[],[],[[[]]]]=>3
[1,2,1,2,5]=>[[[],[[[]]]]]=>1
[1,2,1,5,2]=>[[[[[[]]]]]]=>1
[1,2,2,1,5]=>[[[]],[[[]]]]=>2
[1,2,2,5,1]=>[[[]],[[[]]]]=>2
[1,2,5,1,2]=>[[[],[[[]]]]]=>1
[1,2,5,2,1]=>[[[[],[[]]]]]=>1
[1,5,1,2,2]=>[[],[[[[]]]]]=>2
[1,5,2,1,2]=>[[[[[[]]]]]]=>1
[1,5,2,2,1]=>[[[]],[[[]]]]=>2
[2,1,1,2,5]=>[[],[[[[]]]]]=>2
[2,1,1,5,2]=>[[],[[[[]]]]]=>2
[2,1,2,1,5]=>[[[[]],[[]]]]=>1
[2,1,2,5,1]=>[[[[[[]]]]]]=>1
[2,1,5,1,2]=>[[[[[[]]]]]]=>1
[2,1,5,2,1]=>[[[[]],[[]]]]=>1
[2,2,1,1,5]=>[[],[],[[[]]]]=>3
[2,2,1,5,1]=>[[],[[[[]]]]]=>2
[2,2,5,1,1]=>[[],[],[[[]]]]=>3
[2,5,1,1,2]=>[[[]],[[[]]]]=>2
[2,5,1,2,1]=>[[[[[[]]]]]]=>1
[2,5,2,1,1]=>[[],[[[],[]]]]=>2
[5,1,1,2,2]=>[[],[[]],[[]]]=>3
[5,1,2,1,2]=>[[[[],[[]]]]]=>1
[5,1,2,2,1]=>[[[[]]],[[]]]=>2
[5,2,1,1,2]=>[[],[[[[]]]]]=>2
[5,2,1,2,1]=>[[[[[],[]]]]]=>1
[5,2,2,1,1]=>[[],[],[[[]]]]=>3
[1,1,2,3,3]=>[[],[],[[],[]]]=>3
[1,1,3,2,3]=>[[],[[[[]]]]]=>2
[1,1,3,3,2]=>[[],[[]],[[]]]=>3
[1,2,1,3,3]=>[[[]],[[[]]]]=>2
[1,2,3,1,3]=>[[[],[[[]]]]]=>1
[1,2,3,3,1]=>[[[]],[[],[]]]=>2
[1,3,1,2,3]=>[[[[[],[]]]]]=>1
[1,3,1,3,2]=>[[[],[[[]]]]]=>1
[1,3,2,1,3]=>[[[],[[],[]]]]=>1
[1,3,2,3,1]=>[[[[[[]]]]]]=>1
[1,3,3,1,2]=>[[[]],[[[]]]]=>2
[1,3,3,2,1]=>[[[]],[[],[]]]=>2
[2,1,1,3,3]=>[[],[[]],[[]]]=>3
[2,1,3,1,3]=>[[[[],[[]]]]]=>1
[2,1,3,3,1]=>[[[]],[[[]]]]=>2
[2,3,1,1,3]=>[[[]],[[[]]]]=>2
[2,3,1,3,1]=>[[[[],[[]]]]]=>1
[2,3,3,1,1]=>[[],[[]],[[]]]=>3
[3,1,1,2,3]=>[[],[[],[[]]]]=>2
[3,1,1,3,2]=>[[],[[[[]]]]]=>2
[3,1,2,1,3]=>[[[[[[]]]]]]=>1
[3,1,2,3,1]=>[[[],[[],[]]]]=>1
[3,1,3,1,2]=>[[[[]],[[]]]]=>1
[3,1,3,2,1]=>[[[[],[[]]]]]=>1
[3,2,1,1,3]=>[[],[[[],[]]]]=>2
[3,2,1,3,1]=>[[[],[[[]]]]]=>1
[3,2,3,1,1]=>[[[[]]],[[]]]=>2
[3,3,1,1,2]=>[[],[[]],[[]]]=>3
[3,3,1,2,1]=>[[],[[[[]]]]]=>2
[3,3,2,1,1]=>[[],[],[[],[]]]=>3
[1,1,2,3,4]=>[[],[[],[],[]]]=>2
[1,1,2,4,3]=>[[],[[[[]]]]]=>2
[1,1,3,2,4]=>[[],[[],[[]]]]=>2
[1,1,3,4,2]=>[[],[[[[]]]]]=>2
[1,1,4,2,3]=>[[],[[[[]]]]]=>2
[1,1,4,3,2]=>[[],[[[],[]]]]=>2
[1,2,1,3,4]=>[[[[]],[[]]]]=>1
[1,2,1,4,3]=>[[[[],[[]]]]]=>1
[1,2,3,1,4]=>[[[],[[[]]]]]=>1
[1,2,3,4,1]=>[[[],[],[[]]]]=>1
[1,2,4,1,3]=>[[[[],[[]]]]]=>1
[1,2,4,3,1]=>[[[[[[]]]]]]=>1
[1,3,1,2,4]=>[[[],[[[]]]]]=>1
[1,3,1,4,2]=>[[[[[],[]]]]]=>1
[1,3,2,1,4]=>[[[[],[[]]]]]=>1
[1,3,2,4,1]=>[[[],[[[]]]]]=>1
[1,3,4,1,2]=>[[[[],[[]]]]]=>1
[1,3,4,2,1]=>[[[[[[]]]]]]=>1
[1,4,1,2,3]=>[[[],[[],[]]]]=>1
[1,4,1,3,2]=>[[[],[[[]]]]]=>1
[1,4,2,1,3]=>[[[[[[]]]]]]=>1
[1,4,2,3,1]=>[[[[[],[]]]]]=>1
[1,4,3,1,2]=>[[[[[[]]]]]]=>1
[1,4,3,2,1]=>[[[[],[],[]]]]=>1
[2,1,1,3,4]=>[[],[[[[]]]]]=>2
[2,1,1,4,3]=>[[],[[[],[]]]]=>2
[2,1,3,1,4]=>[[[[[[]]]]]]=>1
[2,1,3,4,1]=>[[[[[[]]]]]]=>1
[2,1,4,1,3]=>[[[[[],[]]]]]=>1
[2,1,4,3,1]=>[[[],[[[]]]]]=>1
[2,3,1,1,4]=>[[[]],[[[]]]]=>2
[2,3,1,4,1]=>[[[[[],[]]]]]=>1
[2,3,4,1,1]=>[[],[[[],[]]]]=>2
[2,4,1,1,3]=>[[[]],[[],[]]]=>2
[2,4,1,3,1]=>[[[[]],[[]]]]=>1
[2,4,3,1,1]=>[[[]],[[[]]]]=>2
[3,1,1,2,4]=>[[[[]]],[[]]]=>2
[3,1,1,4,2]=>[[],[[[],[]]]]=>2
[3,1,2,1,4]=>[[[[[[]]]]]]=>1
[3,1,2,4,1]=>[[[[[[]]]]]]=>1
[3,1,4,1,2]=>[[[[],[[]]]]]=>1
[3,1,4,2,1]=>[[[],[[[]]]]]=>1
[3,2,1,1,4]=>[[],[[[],[]]]]=>2
[3,2,1,4,1]=>[[[],[[],[]]]]=>1
[3,2,4,1,1]=>[[[[]]],[[]]]=>2
[3,4,1,1,2]=>[[[]],[[],[]]]=>2
[3,4,1,2,1]=>[[[[]],[[]]]]=>1
[3,4,2,1,1]=>[[[[]]],[[]]]=>2
[4,1,1,2,3]=>[[[]],[[],[]]]=>2
[4,1,1,3,2]=>[[[[]]],[[]]]=>2
[4,1,2,1,3]=>[[[[[[]]]]]]=>1
[4,1,2,3,1]=>[[[[],[[]]]]]=>1
[4,1,3,1,2]=>[[[[[[]]]]]]=>1
[4,1,3,2,1]=>[[[[],[[]]]]]=>1
[4,2,1,1,3]=>[[[[]]],[[]]]=>2
[4,2,1,3,1]=>[[[[]],[[]]]]=>1
[4,2,3,1,1]=>[[],[[],[[]]]]=>2
[4,3,1,1,2]=>[[[[]]],[[]]]=>2
[4,3,1,2,1]=>[[[[]],[[]]]]=>1
[4,3,2,1,1]=>[[],[[],[],[]]]=>2
[1,1,2,3,5]=>[[],[[],[[]]]]=>2
[1,1,2,5,3]=>[[],[[[[]]]]]=>2
[1,1,3,2,5]=>[[],[[[[]]]]]=>2
[1,1,3,5,2]=>[[],[[],[[]]]]=>2
[1,1,5,2,3]=>[[],[[[[]]]]]=>2
[1,1,5,3,2]=>[[],[[],[[]]]]=>2
[1,2,1,3,5]=>[[[[[],[]]]]]=>1
[1,2,1,5,3]=>[[[[[],[]]]]]=>1
[1,2,3,1,5]=>[[[],[[],[]]]]=>1
[1,2,3,5,1]=>[[[],[[],[]]]]=>1
[1,2,5,1,3]=>[[[[[],[]]]]]=>1
[1,2,5,3,1]=>[[[[[],[]]]]]=>1
[1,3,1,2,5]=>[[[[[[]]]]]]=>1
[1,3,1,5,2]=>[[[[],[[]]]]]=>1
[1,3,2,1,5]=>[[[[],[[]]]]]=>1
[1,3,2,5,1]=>[[[[]],[[]]]]=>1
[1,3,5,1,2]=>[[[],[],[[]]]]=>1
[1,3,5,2,1]=>[[[],[[[]]]]]=>1
[1,5,1,2,3]=>[[[[],[[]]]]]=>1
[1,5,1,3,2]=>[[[[[],[]]]]]=>1
[1,5,2,1,3]=>[[[[[[]]]]]]=>1
[1,5,2,3,1]=>[[[],[[[]]]]]=>1
[1,5,3,1,2]=>[[[],[],[[]]]]=>1
[1,5,3,2,1]=>[[[],[[],[]]]]=>1
[2,1,1,3,5]=>[[],[[],[[]]]]=>2
[2,1,1,5,3]=>[[],[[],[[]]]]=>2
[2,1,3,1,5]=>[[[[],[[]]]]]=>1
[2,1,3,5,1]=>[[[[],[],[]]]]=>1
[2,1,5,1,3]=>[[[[],[[]]]]]=>1
[2,1,5,3,1]=>[[[[],[],[]]]]=>1
[2,3,1,1,5]=>[[],[[],[[]]]]=>2
[2,3,1,5,1]=>[[[[],[[]]]]]=>1
[2,3,5,1,1]=>[[],[[],[[]]]]=>2
[2,5,1,1,3]=>[[],[[],[[]]]]=>2
[2,5,1,3,1]=>[[[[],[[]]]]]=>1
[2,5,3,1,1]=>[[],[[],[[]]]]=>2
[3,1,1,2,5]=>[[[[]]],[[]]]=>2
[3,1,1,5,2]=>[[],[[],[[]]]]=>2
[3,1,2,1,5]=>[[[],[[[]]]]]=>1
[3,1,2,5,1]=>[[[[[[]]]]]]=>1
[3,1,5,1,2]=>[[[],[[[]]]]]=>1
[3,1,5,2,1]=>[[[],[[[]]]]]=>1
[3,2,1,1,5]=>[[],[[[],[]]]]=>2
[3,2,1,5,1]=>[[[],[[[]]]]]=>1
[3,2,5,1,1]=>[[[[]]],[[]]]=>2
[3,5,1,1,2]=>[[[]],[[],[]]]=>2
[3,5,1,2,1]=>[[[],[[[]]]]]=>1
[3,5,2,1,1]=>[[],[[[[]]]]]=>2
[5,1,1,2,3]=>[[[]],[[],[]]]=>2
[5,1,1,3,2]=>[[],[[],[[]]]]=>2
[5,1,2,1,3]=>[[[],[[[]]]]]=>1
[5,1,2,3,1]=>[[[[],[[]]]]]=>1
[5,1,3,1,2]=>[[[],[[[]]]]]=>1
[5,1,3,2,1]=>[[[],[[],[]]]]=>1
[5,2,1,1,3]=>[[],[[[[]]]]]=>2
[5,2,1,3,1]=>[[[[[[]]]]]]=>1
[5,2,3,1,1]=>[[],[[[[]]]]]=>2
[5,3,1,1,2]=>[[[]],[[],[]]]=>2
[5,3,1,2,1]=>[[[],[[[]]]]]=>1
[5,3,2,1,1]=>[[[]],[[],[]]]=>2
[1,1,2,4,4]=>[[],[],[[[]]]]=>3
[1,1,4,2,4]=>[[],[[[[]]]]]=>2
[1,1,4,4,2]=>[[],[[]],[[]]]=>3
[1,2,1,4,4]=>[[[]],[[[]]]]=>2
[1,2,4,1,4]=>[[[[[],[]]]]]=>1
[1,2,4,4,1]=>[[[[]]],[[]]]=>2
[1,4,1,2,4]=>[[[],[[[]]]]]=>1
[1,4,1,4,2]=>[[[],[],[[]]]]=>1
[1,4,2,1,4]=>[[[[]],[[]]]]=>1
[1,4,2,4,1]=>[[[],[[[]]]]]=>1
[1,4,4,1,2]=>[[],[[],[[]]]]=>2
[1,4,4,2,1]=>[[],[[[[]]]]]=>2
[2,1,1,4,4]=>[[],[[]],[[]]]=>3
[2,1,4,1,4]=>[[[[],[],[]]]]=>1
[2,1,4,4,1]=>[[],[[],[[]]]]=>2
[2,4,1,1,4]=>[[],[[],[[]]]]=>2
[2,4,1,4,1]=>[[[[],[],[]]]]=>1
[2,4,4,1,1]=>[[],[[]],[[]]]=>3
[4,1,1,2,4]=>[[[[]]],[[]]]=>2
[4,1,1,4,2]=>[[],[[],[[]]]]=>2
[4,1,2,1,4]=>[[[],[[[]]]]]=>1
[4,1,2,4,1]=>[[[],[[[]]]]]=>1
[4,1,4,1,2]=>[[[],[],[[]]]]=>1
[4,1,4,2,1]=>[[[],[[[]]]]]=>1
[4,2,1,1,4]=>[[[[]]],[[]]]=>2
[4,2,1,4,1]=>[[[[],[[]]]]]=>1
[4,2,4,1,1]=>[[],[[[[]]]]]=>2
[4,4,1,1,2]=>[[],[[]],[[]]]=>3
[4,4,1,2,1]=>[[],[[[[]]]]]=>2
[4,4,2,1,1]=>[[],[[]],[[]]]=>3
[1,1,2,4,5]=>[[],[[],[[]]]]=>2
[1,1,2,5,4]=>[[],[[[[]]]]]=>2
[1,1,4,2,5]=>[[],[[],[[]]]]=>2
[1,1,4,5,2]=>[[],[[],[[]]]]=>2
[1,1,5,2,4]=>[[],[[[[]]]]]=>2
[1,1,5,4,2]=>[[],[[],[[]]]]=>2
[1,2,1,4,5]=>[[[[]],[[]]]]=>1
[1,2,1,5,4]=>[[[[],[[]]]]]=>1
[1,2,4,1,5]=>[[[[[[]]]]]]=>1
[1,2,4,5,1]=>[[[],[[],[]]]]=>1
[1,2,5,1,4]=>[[[[],[[]]]]]=>1
[1,2,5,4,1]=>[[[[],[[]]]]]=>1
[1,4,1,2,5]=>[[[],[],[[]]]]=>1
[1,4,1,5,2]=>[[[],[],[[]]]]=>1
[1,4,2,1,5]=>[[[[],[[]]]]]=>1
[1,4,2,5,1]=>[[[[]],[[]]]]=>1
[1,4,5,1,2]=>[[[[],[[]]]]]=>1
[1,4,5,2,1]=>[[[[]],[[]]]]=>1
[1,5,1,2,4]=>[[[[[],[]]]]]=>1
[1,5,1,4,2]=>[[[],[[[]]]]]=>1
[1,5,2,1,4]=>[[[[],[[]]]]]=>1
[1,5,2,4,1]=>[[[[[],[]]]]]=>1
[1,5,4,1,2]=>[[[[[[]]]]]]=>1
[1,5,4,2,1]=>[[[],[[],[]]]]=>1
[2,1,1,4,5]=>[[],[[[[]]]]]=>2
[2,1,1,5,4]=>[[],[[[],[]]]]=>2
[2,1,4,1,5]=>[[[[[],[]]]]]=>1
[2,1,4,5,1]=>[[[[[[]]]]]]=>1
[2,1,5,1,4]=>[[[[[[]]]]]]=>1
[2,1,5,4,1]=>[[[],[[[]]]]]=>1
[2,4,1,1,5]=>[[[[]]],[[]]]=>2
[2,4,1,5,1]=>[[[],[[[]]]]]=>1
[2,4,5,1,1]=>[[],[[],[[]]]]=>2
[2,5,1,1,4]=>[[[]],[[],[]]]=>2
[2,5,1,4,1]=>[[[],[],[[]]]]=>1
[2,5,4,1,1]=>[[[]],[[],[]]]=>2
[4,1,1,2,5]=>[[],[[[],[]]]]=>2
[4,1,1,5,2]=>[[],[[[],[]]]]=>2
[4,1,2,1,5]=>[[[[[[]]]]]]=>1
[4,1,2,5,1]=>[[[[]],[[]]]]=>1
[4,1,5,1,2]=>[[[[[[]]]]]]=>1
[4,1,5,2,1]=>[[[],[[[]]]]]=>1
[4,2,1,1,5]=>[[],[[],[[]]]]=>2
[4,2,1,5,1]=>[[[],[[[]]]]]=>1
[4,2,5,1,1]=>[[],[[[[]]]]]=>2
[4,5,1,1,2]=>[[[]],[[],[]]]=>2
[4,5,1,2,1]=>[[[[]],[[]]]]=>1
[4,5,2,1,1]=>[[],[[[[]]]]]=>2
[5,1,1,2,4]=>[[],[[[],[]]]]=>2
[5,1,1,4,2]=>[[[]],[[[]]]]=>2
[5,1,2,1,4]=>[[[[[[]]]]]]=>1
[5,1,2,4,1]=>[[[[]],[[]]]]=>1
[5,1,4,1,2]=>[[[[],[[]]]]]=>1
[5,1,4,2,1]=>[[[[[[]]]]]]=>1
[5,2,1,1,4]=>[[],[[],[[]]]]=>2
[5,2,1,4,1]=>[[[],[],[[]]]]=>1
[5,2,4,1,1]=>[[],[[],[[]]]]=>2
[5,4,1,1,2]=>[[[[]]],[[]]]=>2
[5,4,1,2,1]=>[[[],[[[]]]]]=>1
[5,4,2,1,1]=>[[[]],[[],[]]]=>2
[1,1,3,3,3]=>[[],[],[],[[]]]=>4
[1,3,1,3,3]=>[[],[[],[[]]]]=>2
[1,3,3,1,3]=>[[],[[[],[]]]]=>2
[1,3,3,3,1]=>[[],[[]],[[]]]=>3
[3,1,1,3,3]=>[[],[],[[[]]]]=>3
[3,1,3,1,3]=>[[[],[[],[]]]]=>1
[3,1,3,3,1]=>[[[]],[[],[]]]=>2
[3,3,1,1,3]=>[[],[[]],[[]]]=>3
[3,3,1,3,1]=>[[],[[],[[]]]]=>2
[3,3,3,1,1]=>[[],[],[],[[]]]=>4
[1,1,3,3,4]=>[[],[[]],[[]]]=>3
[1,1,3,4,3]=>[[],[[[[]]]]]=>2
[1,1,4,3,3]=>[[],[],[[[]]]]=>3
[1,3,1,3,4]=>[[[[]],[[]]]]=>1
[1,3,1,4,3]=>[[[[[[]]]]]]=>1
[1,3,3,1,4]=>[[[]],[[[]]]]=>2
[1,3,3,4,1]=>[[[[]]],[[]]]=>2
[1,3,4,1,3]=>[[[],[[[]]]]]=>1
[1,3,4,3,1]=>[[[[[[]]]]]]=>1
[1,4,1,3,3]=>[[],[[[],[]]]]=>2
[1,4,3,1,3]=>[[[[[[]]]]]]=>1
[1,4,3,3,1]=>[[[]],[[[]]]]=>2
[3,1,1,3,4]=>[[[[]]],[[]]]=>2
[3,1,1,4,3]=>[[],[[[[]]]]]=>2
[3,1,3,1,4]=>[[[[]],[[]]]]=>1
[3,1,3,4,1]=>[[[[[[]]]]]]=>1
[3,1,4,1,3]=>[[[[],[[]]]]]=>1
[3,1,4,3,1]=>[[[[]],[[]]]]=>1
[3,3,1,1,4]=>[[],[[]],[[]]]=>3
[3,3,1,4,1]=>[[],[[[],[]]]]=>2
[3,3,4,1,1]=>[[],[],[[[]]]]=>3
[3,4,1,1,3]=>[[[]],[[[]]]]=>2
[3,4,1,3,1]=>[[[[[[]]]]]]=>1
[3,4,3,1,1]=>[[[]],[[[]]]]=>2
[4,1,1,3,3]=>[[],[[]],[[]]]=>3
[4,1,3,1,3]=>[[[[[],[]]]]]=>1
[4,1,3,3,1]=>[[[[]]],[[]]]=>2
[4,3,1,1,3]=>[[[[]]],[[]]]=>2
[4,3,1,3,1]=>[[[[],[[]]]]]=>1
[4,3,3,1,1]=>[[],[[]],[[]]]=>3
[1,1,3,3,5]=>[[],[],[[],[]]]=>3
[1,1,3,5,3]=>[[],[[],[[]]]]=>2
[1,1,5,3,3]=>[[],[],[[],[]]]=>3
[1,3,1,3,5]=>[[[],[],[[]]]]=>1
[1,3,1,5,3]=>[[[[],[],[]]]]=>1
[1,3,3,1,5]=>[[[]],[[],[]]]=>2
[1,3,3,5,1]=>[[],[[],[],[]]]=>2
[1,3,5,1,3]=>[[[],[],[],[]]]=>1
[1,3,5,3,1]=>[[[],[[],[]]]]=>1
[1,5,1,3,3]=>[[],[[],[[]]]]=>2
[1,5,3,1,3]=>[[[],[],[[]]]]=>1
[1,5,3,3,1]=>[[],[[],[],[]]]=>2
[3,1,1,3,5]=>[[],[[],[[]]]]=>2
[3,1,1,5,3]=>[[],[[],[],[]]]=>2
[3,1,3,1,5]=>[[[],[],[[]]]]=>1
[3,1,3,5,1]=>[[[[],[],[]]]]=>1
[3,1,5,1,3]=>[[[],[[],[]]]]=>1
[3,1,5,3,1]=>[[[],[],[],[]]]=>1
[3,3,1,1,5]=>[[],[],[[],[]]]=>3
[3,3,1,5,1]=>[[],[[],[[]]]]=>2
[3,3,5,1,1]=>[[],[],[[],[]]]=>3
[3,5,1,1,3]=>[[],[[],[],[]]]=>2
[3,5,1,3,1]=>[[[],[],[[]]]]=>1
[3,5,3,1,1]=>[[],[[],[[]]]]=>2
[5,1,1,3,3]=>[[],[],[[],[]]]=>3
[5,1,3,1,3]=>[[[],[],[[]]]]=>1
[5,1,3,3,1]=>[[[]],[[],[]]]=>2
[5,3,1,1,3]=>[[[]],[[],[]]]=>2
[5,3,1,3,1]=>[[[],[],[[]]]]=>1
[5,3,3,1,1]=>[[],[],[[],[]]]=>3
[1,1,3,4,4]=>[[],[],[[[]]]]=>3
[1,1,4,3,4]=>[[],[[[[]]]]]=>2
[1,1,4,4,3]=>[[],[[]],[[]]]=>3
[1,3,1,4,4]=>[[],[[[[]]]]]=>2
[1,3,4,1,4]=>[[[[[],[]]]]]=>1
[1,3,4,4,1]=>[[[[]]],[[]]]=>2
[1,4,1,3,4]=>[[[],[[[]]]]]=>1
[1,4,1,4,3]=>[[[],[],[[]]]]=>1
[1,4,3,1,4]=>[[[[]],[[]]]]=>1
[1,4,3,4,1]=>[[[[]],[[]]]]=>1
[1,4,4,1,3]=>[[],[[],[[]]]]=>2
[1,4,4,3,1]=>[[],[[[[]]]]]=>2
[3,1,1,4,4]=>[[],[],[[[]]]]=>3
[3,1,4,1,4]=>[[[[],[],[]]]]=>1
[3,1,4,4,1]=>[[[]],[[],[]]]=>2
[3,4,1,1,4]=>[[],[[],[[]]]]=>2
[3,4,1,4,1]=>[[[[],[],[]]]]=>1
[3,4,4,1,1]=>[[],[[]],[[]]]=>3
[4,1,1,3,4]=>[[[[]]],[[]]]=>2
[4,1,1,4,3]=>[[],[[],[[]]]]=>2
[4,1,3,1,4]=>[[[],[[[]]]]]=>1
[4,1,3,4,1]=>[[[],[[[]]]]]=>1
[4,1,4,1,3]=>[[[],[],[[]]]]=>1
[4,1,4,3,1]=>[[[],[[[]]]]]=>1
[4,3,1,1,4]=>[[[[]]],[[]]]=>2
[4,3,1,4,1]=>[[[[],[[]]]]]=>1
[4,3,4,1,1]=>[[[[]]],[[]]]=>2
[4,4,1,1,3]=>[[],[[]],[[]]]=>3
[4,4,1,3,1]=>[[],[[[[]]]]]=>2
[4,4,3,1,1]=>[[],[[]],[[]]]=>3
[1,1,3,4,5]=>[[],[[[],[]]]]=>2
[1,1,3,5,4]=>[[],[[],[[]]]]=>2
[1,1,4,3,5]=>[[],[[[[]]]]]=>2
[1,1,4,5,3]=>[[],[[[[]]]]]=>2
[1,1,5,3,4]=>[[],[[],[[]]]]=>2
[1,1,5,4,3]=>[[],[[[],[]]]]=>2
[1,3,1,4,5]=>[[[[[[]]]]]]=>1
[1,3,1,5,4]=>[[[[],[[]]]]]=>1
[1,3,4,1,5]=>[[[[[[]]]]]]=>1
[1,3,4,5,1]=>[[[],[[],[]]]]=>1
[1,3,5,1,4]=>[[[],[],[[]]]]=>1
[1,3,5,4,1]=>[[[],[[[]]]]]=>1
[1,4,1,3,5]=>[[[],[[],[]]]]=>1
[1,4,1,5,3]=>[[[],[[],[]]]]=>1
[1,4,3,1,5]=>[[[[],[[]]]]]=>1
[1,4,3,5,1]=>[[[[],[[]]]]]=>1
[1,4,5,1,3]=>[[[[[],[]]]]]=>1
[1,4,5,3,1]=>[[[[],[[]]]]]=>1
[1,5,1,3,4]=>[[[[],[[]]]]]=>1
[1,5,1,4,3]=>[[[[[[]]]]]]=>1
[1,5,3,1,4]=>[[[],[],[[]]]]=>1
[1,5,3,4,1]=>[[[],[[[]]]]]=>1
[1,5,4,1,3]=>[[[[[[]]]]]]=>1
[1,5,4,3,1]=>[[[],[[],[]]]]=>1
[3,1,1,4,5]=>[[[[]]],[[]]]=>2
[3,1,1,5,4]=>[[],[[],[[]]]]=>2
[3,1,4,1,5]=>[[[],[[],[]]]]=>1
[3,1,4,5,1]=>[[[[[[]]]]]]=>1
[3,1,5,1,4]=>[[[],[[[]]]]]=>1
[3,1,5,4,1]=>[[[],[[[]]]]]=>1
[3,4,1,1,5]=>[[[[]]],[[]]]=>2
[3,4,1,5,1]=>[[[[[[]]]]]]=>1
[3,4,5,1,1]=>[[],[[[],[]]]]=>2
[3,5,1,1,4]=>[[[]],[[],[]]]=>2
[3,5,1,4,1]=>[[[],[[],[]]]]=>1
[3,5,4,1,1]=>[[[]],[[[]]]]=>2
[4,1,1,3,5]=>[[[]],[[],[]]]=>2
[4,1,1,5,3]=>[[],[[],[[]]]]=>2
[4,1,3,1,5]=>[[[[],[[]]]]]=>1
[4,1,3,5,1]=>[[[[],[],[]]]]=>1
[4,1,5,1,3]=>[[[[],[[]]]]]=>1
[4,1,5,3,1]=>[[[[],[],[]]]]=>1
[4,3,1,1,5]=>[[],[[],[[]]]]=>2
[4,3,1,5,1]=>[[[[[],[]]]]]=>1
[4,3,5,1,1]=>[[[]],[[],[]]]=>2
[4,5,1,1,3]=>[[],[[],[[]]]]=>2
[4,5,1,3,1]=>[[[[],[[]]]]]=>1
[4,5,3,1,1]=>[[],[[],[[]]]]=>2
[5,1,1,3,4]=>[[],[[],[[]]]]=>2
[5,1,1,4,3]=>[[[]],[[[]]]]=>2
[5,1,3,1,4]=>[[[],[[[]]]]]=>1
[5,1,3,4,1]=>[[[],[[[]]]]]=>1
[5,1,4,1,3]=>[[[],[[],[]]]]=>1
[5,1,4,3,1]=>[[[[[[]]]]]]=>1
[5,3,1,1,4]=>[[[]],[[],[]]]=>2
[5,3,1,4,1]=>[[[],[[],[]]]]=>1
[5,3,4,1,1]=>[[],[[[[]]]]]=>2
[5,4,1,1,3]=>[[[[]]],[[]]]=>2
[5,4,1,3,1]=>[[[[[[]]]]]]=>1
[5,4,3,1,1]=>[[[]],[[],[]]]=>2
[1,2,2,2,2]=>[[],[],[],[[]]]=>4
[2,1,2,2,2]=>[[],[[]],[[]]]=>3
[2,2,1,2,2]=>[[],[[]],[[]]]=>3
[2,2,2,1,2]=>[[],[],[[[]]]]=>3
[2,2,2,2,1]=>[[],[],[],[[]]]=>4
[1,2,2,2,3]=>[[],[],[[],[]]]=>3
[1,2,2,3,2]=>[[],[[],[[]]]]=>2
[1,2,3,2,2]=>[[],[[[],[]]]]=>2
[1,3,2,2,2]=>[[],[],[[[]]]]=>3
[2,1,2,2,3]=>[[],[[],[[]]]]=>2
[2,1,2,3,2]=>[[[],[[],[]]]]=>1
[2,1,3,2,2]=>[[],[[],[[]]]]=>2
[2,2,1,2,3]=>[[],[[[],[]]]]=>2
[2,2,1,3,2]=>[[],[[],[[]]]]=>2
[2,2,2,1,3]=>[[],[],[[[]]]]=>3
[2,2,2,3,1]=>[[],[],[[[]]]]=>3
[2,2,3,1,2]=>[[],[[],[[]]]]=>2
[2,2,3,2,1]=>[[],[[[],[]]]]=>2
[2,3,1,2,2]=>[[],[[],[[]]]]=>2
[2,3,2,1,2]=>[[[],[[],[]]]]=>1
[2,3,2,2,1]=>[[],[[],[[]]]]=>2
[3,1,2,2,2]=>[[],[[]],[[]]]=>3
[3,2,1,2,2]=>[[[]],[[],[]]]=>2
[3,2,2,1,2]=>[[],[[],[[]]]]=>2
[3,2,2,2,1]=>[[],[],[[],[]]]=>3
[1,2,2,2,4]=>[[],[[]],[[]]]=>3
[1,2,2,4,2]=>[[[]],[[[]]]]=>2
[1,2,4,2,2]=>[[],[[[[]]]]]=>2
[1,4,2,2,2]=>[[],[[]],[[]]]=>3
[2,1,2,2,4]=>[[[]],[[[]]]]=>2
[2,1,2,4,2]=>[[[[[[]]]]]]=>1
[2,1,4,2,2]=>[[[[]]],[[]]]=>2
[2,2,1,2,4]=>[[],[[[[]]]]]=>2
[2,2,1,4,2]=>[[],[[[[]]]]]=>2
[2,2,2,1,4]=>[[],[],[[[]]]]=>3
[2,2,2,4,1]=>[[],[],[[[]]]]=>3
[2,2,4,1,2]=>[[],[[[[]]]]]=>2
[2,2,4,2,1]=>[[],[[[[]]]]]=>2
[2,4,1,2,2]=>[[],[[[[]]]]]=>2
[2,4,2,1,2]=>[[[[[[]]]]]]=>1
[2,4,2,2,1]=>[[],[[[[]]]]]=>2
[4,1,2,2,2]=>[[],[],[[[]]]]=>3
[4,2,1,2,2]=>[[[[]]],[[]]]=>2
[4,2,2,1,2]=>[[],[[[[]]]]]=>2
[4,2,2,2,1]=>[[],[],[[[]]]]=>3
[1,2,2,2,5]=>[[],[[]],[[]]]=>3
[1,2,2,5,2]=>[[[]],[[],[]]]=>2
[1,2,5,2,2]=>[[],[[],[[]]]]=>2
[1,5,2,2,2]=>[[],[[]],[[]]]=>3
[2,1,2,2,5]=>[[[]],[[[]]]]=>2
[2,1,2,5,2]=>[[[[],[[]]]]]=>1
[2,1,5,2,2]=>[[[[]]],[[]]]=>2
[2,2,1,2,5]=>[[],[[[[]]]]]=>2
[2,2,1,5,2]=>[[],[[[[]]]]]=>2
[2,2,2,1,5]=>[[],[],[[[]]]]=>3
[2,2,2,5,1]=>[[],[],[[[]]]]=>3
[2,2,5,1,2]=>[[],[[[[]]]]]=>2
[2,2,5,2,1]=>[[],[[],[[]]]]=>2
[2,5,1,2,2]=>[[],[[[[]]]]]=>2
[2,5,2,1,2]=>[[[],[[[]]]]]=>1
[2,5,2,2,1]=>[[[]],[[],[]]]=>2
[5,1,2,2,2]=>[[],[],[[[]]]]=>3
[5,2,1,2,2]=>[[[]],[[[]]]]=>2
[5,2,2,1,2]=>[[[]],[[[]]]]=>2
[5,2,2,2,1]=>[[],[[]],[[]]]=>3
[1,2,2,3,3]=>[[],[],[[],[]]]=>3
[1,2,3,2,3]=>[[[],[],[[]]]]=>1
[1,2,3,3,2]=>[[[]],[[],[]]]=>2
[1,3,2,2,3]=>[[],[[[[]]]]]=>2
[1,3,2,3,2]=>[[[[],[[]]]]]=>1
[1,3,3,2,2]=>[[],[[]],[[]]]=>3
[2,1,2,3,3]=>[[[]],[[],[]]]=>2
[2,1,3,2,3]=>[[[[]],[[]]]]=>1
[2,1,3,3,2]=>[[[]],[[],[]]]=>2
[2,2,1,3,3]=>[[],[[]],[[]]]=>3
[2,2,3,1,3]=>[[],[[[[]]]]]=>2
[2,2,3,3,1]=>[[],[[]],[[]]]=>3
[2,3,1,2,3]=>[[[],[],[[]]]]=>1
[2,3,1,3,2]=>[[[[[[]]]]]]=>1
[2,3,2,1,3]=>[[[[],[[]]]]]=>1
[2,3,2,3,1]=>[[[],[[[]]]]]=>1
[2,3,3,1,2]=>[[],[[[],[]]]]=>2
[2,3,3,2,1]=>[[[]],[[],[]]]=>2
[3,1,2,2,3]=>[[[]],[[],[]]]=>2
[3,1,2,3,2]=>[[[[[],[]]]]]=>1
[3,1,3,2,2]=>[[[]],[[[]]]]=>2
[3,2,1,2,3]=>[[[],[[],[]]]]=>1
[3,2,1,3,2]=>[[[],[],[[]]]]=>1
[3,2,2,1,3]=>[[],[[],[[]]]]=>2
[3,2,2,3,1]=>[[],[[[[]]]]]=>2
[3,2,3,1,2]=>[[[[],[[]]]]]=>1
[3,2,3,2,1]=>[[[],[],[[]]]]=>1
[3,3,1,2,2]=>[[],[],[[[]]]]=>3
[3,3,2,1,2]=>[[],[[],[[]]]]=>2
[3,3,2,2,1]=>[[],[],[[],[]]]=>3
[1,2,2,3,4]=>[[],[[],[],[]]]=>2
[1,2,2,4,3]=>[[[]],[[[]]]]=>2
[1,2,3,2,4]=>[[[],[[[]]]]]=>1
[1,2,3,4,2]=>[[[],[],[[]]]]=>1
[1,2,4,2,3]=>[[[],[[[]]]]]=>1
[1,2,4,3,2]=>[[[[[],[]]]]]=>1
[1,3,2,2,4]=>[[],[[],[[]]]]=>2
[1,3,2,4,2]=>[[[],[[[]]]]]=>1
[1,3,4,2,2]=>[[],[[[[]]]]]=>2
[1,4,2,2,3]=>[[[]],[[[]]]]=>2
[1,4,2,3,2]=>[[[[[[]]]]]]=>1
[1,4,3,2,2]=>[[],[[],[[]]]]=>2
[2,1,2,3,4]=>[[[[],[],[]]]]=>1
[2,1,2,4,3]=>[[[],[[[]]]]]=>1
[2,1,3,2,4]=>[[[],[[],[]]]]=>1
[2,1,3,4,2]=>[[[[[[]]]]]]=>1
[2,1,4,2,3]=>[[[[[[]]]]]]=>1
[2,1,4,3,2]=>[[[],[],[[]]]]=>1
[2,2,1,3,4]=>[[],[[[[]]]]]=>2
[2,2,1,4,3]=>[[],[[],[[]]]]=>2
[2,2,3,1,4]=>[[],[[[[]]]]]=>2
[2,2,3,4,1]=>[[],[[],[[]]]]=>2
[2,2,4,1,3]=>[[],[[],[[]]]]=>2
[2,2,4,3,1]=>[[],[[[[]]]]]=>2
[2,3,1,2,4]=>[[[[]],[[]]]]=>1
[2,3,1,4,2]=>[[[[],[[]]]]]=>1
[2,3,2,1,4]=>[[[[],[[]]]]]=>1
[2,3,2,4,1]=>[[[[[[]]]]]]=>1
[2,3,4,1,2]=>[[[],[],[[]]]]=>1
[2,3,4,2,1]=>[[[],[[[]]]]]=>1
[2,4,1,2,3]=>[[[[[],[]]]]]=>1
[2,4,1,3,2]=>[[[[]],[[]]]]=>1
[2,4,2,1,3]=>[[[[]],[[]]]]=>1
[2,4,2,3,1]=>[[[[],[[]]]]]=>1
[2,4,3,1,2]=>[[[[[[]]]]]]=>1
[2,4,3,2,1]=>[[[[],[],[]]]]=>1
[3,1,2,2,4]=>[[[[]]],[[]]]=>2
[3,1,2,4,2]=>[[[],[[[]]]]]=>1
[3,1,4,2,2]=>[[],[[],[[]]]]=>2
[3,2,1,2,4]=>[[[],[[[]]]]]=>1
[3,2,1,4,2]=>[[[],[[[]]]]]=>1
[3,2,2,1,4]=>[[],[[],[[]]]]=>2
[3,2,2,4,1]=>[[],[[[[]]]]]=>2
[3,2,4,1,2]=>[[[[[[]]]]]]=>1
[3,2,4,2,1]=>[[[],[[[]]]]]=>1
[3,4,1,2,2]=>[[],[[],[[]]]]=>2
[3,4,2,1,2]=>[[[[]],[[]]]]=>1
[3,4,2,2,1]=>[[],[[[[]]]]]=>2
[4,1,2,2,3]=>[[],[[],[[]]]]=>2
[4,1,2,3,2]=>[[[[],[[]]]]]=>1
[4,1,3,2,2]=>[[],[[[[]]]]]=>2
[4,2,1,2,3]=>[[[[],[[]]]]]=>1
[4,2,1,3,2]=>[[[[],[[]]]]]=>1
[4,2,2,1,3]=>[[],[[[[]]]]]=>2
[4,2,2,3,1]=>[[],[[[],[]]]]=>2
[4,2,3,1,2]=>[[[],[[],[]]]]=>1
[4,2,3,2,1]=>[[[[],[[]]]]]=>1
[4,3,1,2,2]=>[[[[]]],[[]]]=>2
[4,3,2,1,2]=>[[[],[],[[]]]]=>1
[4,3,2,2,1]=>[[],[[],[],[]]]=>2
[1,2,2,3,5]=>[[],[[],[[]]]]=>2
[1,2,2,5,3]=>[[[]],[[[]]]]=>2
[1,2,3,2,5]=>[[[],[[[]]]]]=>1
[1,2,3,5,2]=>[[[],[[[]]]]]=>1
[1,2,5,2,3]=>[[[],[[],[]]]]=>1
[1,2,5,3,2]=>[[[[[[]]]]]]=>1
[1,3,2,2,5]=>[[],[[[[]]]]]=>2
[1,3,2,5,2]=>[[[[],[[]]]]]=>1
[1,3,5,2,2]=>[[],[[[],[]]]]=>2
[1,5,2,2,3]=>[[[]],[[[]]]]=>2
[1,5,2,3,2]=>[[[[[[]]]]]]=>1
[1,5,3,2,2]=>[[[]],[[],[]]]=>2
[2,1,2,3,5]=>[[[[[],[]]]]]=>1
[2,1,2,5,3]=>[[[[[[]]]]]]=>1
[2,1,3,2,5]=>[[[[]],[[]]]]=>1
[2,1,3,5,2]=>[[[[[],[]]]]]=>1
[2,1,5,2,3]=>[[[[[[]]]]]]=>1
[2,1,5,3,2]=>[[[],[[],[]]]]=>1
[2,2,1,3,5]=>[[],[[[],[]]]]=>2
[2,2,1,5,3]=>[[],[[[],[]]]]=>2
[2,2,3,1,5]=>[[],[[[],[]]]]=>2
[2,2,3,5,1]=>[[],[[[],[]]]]=>2
[2,2,5,1,3]=>[[],[[[],[]]]]=>2
[2,2,5,3,1]=>[[],[[[],[]]]]=>2
[2,3,1,2,5]=>[[[[]],[[]]]]=>1
[2,3,1,5,2]=>[[[[],[[]]]]]=>1
[2,3,2,1,5]=>[[[[],[[]]]]]=>1
[2,3,2,5,1]=>[[[[[[]]]]]]=>1
[2,3,5,1,2]=>[[[],[[],[]]]]=>1
[2,3,5,2,1]=>[[[[[[]]]]]]=>1
[2,5,1,2,3]=>[[[[[],[]]]]]=>1
[2,5,1,3,2]=>[[[[],[[]]]]]=>1
[2,5,2,1,3]=>[[[],[[[]]]]]=>1
[2,5,2,3,1]=>[[[],[[[]]]]]=>1
[2,5,3,1,2]=>[[[[],[[]]]]]=>1
[2,5,3,2,1]=>[[[[],[[]]]]]=>1
[3,1,2,2,5]=>[[[[]]],[[]]]=>2
[3,1,2,5,2]=>[[[[],[[]]]]]=>1
[3,1,5,2,2]=>[[],[[[],[]]]]=>2
[3,2,1,2,5]=>[[[],[[[]]]]]=>1
[3,2,1,5,2]=>[[[],[[[]]]]]=>1
[3,2,2,1,5]=>[[],[[],[[]]]]=>2
[3,2,2,5,1]=>[[],[[[[]]]]]=>2
[3,2,5,1,2]=>[[[[[[]]]]]]=>1
[3,2,5,2,1]=>[[[],[[],[]]]]=>1
[3,5,1,2,2]=>[[],[[[],[]]]]=>2
[3,5,2,1,2]=>[[[[[[]]]]]]=>1
[3,5,2,2,1]=>[[[[]]],[[]]]=>2
[5,1,2,2,3]=>[[],[[],[[]]]]=>2
[5,1,2,3,2]=>[[[[],[[]]]]]=>1
[5,1,3,2,2]=>[[],[[[],[]]]]=>2
[5,2,1,2,3]=>[[[[],[[]]]]]=>1
[5,2,1,3,2]=>[[[[[],[]]]]]=>1
[5,2,2,1,3]=>[[[]],[[[]]]]=>2
[5,2,2,3,1]=>[[[[]]],[[]]]=>2
[5,2,3,1,2]=>[[[[[],[]]]]]=>1
[5,2,3,2,1]=>[[[[],[[]]]]]=>1
[5,3,1,2,2]=>[[],[[[],[]]]]=>2
[5,3,2,1,2]=>[[[[[],[]]]]]=>1
[5,3,2,2,1]=>[[],[[],[[]]]]=>2
[1,2,2,4,4]=>[[],[[]],[[]]]=>3
[1,2,4,2,4]=>[[[[],[[]]]]]=>1
[1,2,4,4,2]=>[[[[]]],[[]]]=>2
[1,4,2,2,4]=>[[[]],[[[]]]]=>2
[1,4,2,4,2]=>[[[[[],[]]]]]=>1
[1,4,4,2,2]=>[[],[],[[[]]]]=>3
[2,1,2,4,4]=>[[[[]]],[[]]]=>2
[2,1,4,2,4]=>[[[[[[]]]]]]=>1
[2,1,4,4,2]=>[[[]],[[[]]]]=>2
[2,2,1,4,4]=>[[],[[]],[[]]]=>3
[2,2,4,1,4]=>[[],[[[],[]]]]=>2
[2,2,4,4,1]=>[[],[[]],[[]]]=>3
[2,4,1,2,4]=>[[[],[[[]]]]]=>1
[2,4,1,4,2]=>[[[[],[[]]]]]=>1
[2,4,2,1,4]=>[[[[[[]]]]]]=>1
[2,4,2,4,1]=>[[[[]],[[]]]]=>1
[2,4,4,1,2]=>[[[]],[[[]]]]=>2
[2,4,4,2,1]=>[[[]],[[[]]]]=>2
[4,1,2,2,4]=>[[[[]]],[[]]]=>2
[4,1,2,4,2]=>[[[[[[]]]]]]=>1
[4,1,4,2,2]=>[[],[[[],[]]]]=>2
[4,2,1,2,4]=>[[[[[[]]]]]]=>1
[4,2,1,4,2]=>[[[[]],[[]]]]=>1
[4,2,2,1,4]=>[[],[[[[]]]]]=>2
[4,2,2,4,1]=>[[[[]]],[[]]]=>2
[4,2,4,1,2]=>[[[[[[]]]]]]=>1
[4,2,4,2,1]=>[[[[]],[[]]]]=>1
[4,4,1,2,2]=>[[],[],[[[]]]]=>3
[4,4,2,1,2]=>[[],[[[[]]]]]=>2
[4,4,2,2,1]=>[[],[],[[[]]]]=>3
[1,2,2,4,5]=>[[],[[[],[]]]]=>2
[1,2,2,5,4]=>[[[]],[[[]]]]=>2
[1,2,4,2,5]=>[[[[[[]]]]]]=>1
[1,2,4,5,2]=>[[[[]],[[]]]]=>1
[1,2,5,2,4]=>[[[[],[[]]]]]=>1
[1,2,5,4,2]=>[[[[[[]]]]]]=>1
[1,4,2,2,5]=>[[[]],[[],[]]]=>2
[1,4,2,5,2]=>[[[],[],[[]]]]=>1
[1,4,5,2,2]=>[[],[[],[[]]]]=>2
[1,5,2,2,4]=>[[[]],[[[]]]]=>2
[1,5,2,4,2]=>[[[],[[[]]]]]=>1
[1,5,4,2,2]=>[[[]],[[],[]]]=>2
[2,1,2,4,5]=>[[[[],[[]]]]]=>1
[2,1,2,5,4]=>[[[],[[[]]]]]=>1
[2,1,4,2,5]=>[[[[],[[]]]]]=>1
[2,1,4,5,2]=>[[[[],[[]]]]]=>1
[2,1,5,2,4]=>[[[[[[]]]]]]=>1
[2,1,5,4,2]=>[[[],[[],[]]]]=>1
[2,2,1,4,5]=>[[],[[[[]]]]]=>2
[2,2,1,5,4]=>[[],[[],[[]]]]=>2
[2,2,4,1,5]=>[[],[[[[]]]]]=>2
[2,2,4,5,1]=>[[],[[],[[]]]]=>2
[2,2,5,1,4]=>[[],[[],[[]]]]=>2
[2,2,5,4,1]=>[[],[[],[[]]]]=>2
[2,4,1,2,5]=>[[[[],[[]]]]]=>1
[2,4,1,5,2]=>[[[[[],[]]]]]=>1
[2,4,2,1,5]=>[[[[[],[]]]]]=>1
[2,4,2,5,1]=>[[[],[[[]]]]]=>1
[2,4,5,1,2]=>[[[],[[],[]]]]=>1
[2,4,5,2,1]=>[[[[[[]]]]]]=>1
[2,5,1,2,4]=>[[[[],[[]]]]]=>1
[2,5,1,4,2]=>[[[[]],[[]]]]=>1
[2,5,2,1,4]=>[[[],[],[[]]]]=>1
[2,5,2,4,1]=>[[[],[],[[]]]]=>1
[2,5,4,1,2]=>[[[],[[[]]]]]=>1
[2,5,4,2,1]=>[[[[],[[]]]]]=>1
[4,1,2,2,5]=>[[[]],[[],[]]]=>2
[4,1,2,5,2]=>[[[],[],[[]]]]=>1
[4,1,5,2,2]=>[[],[[],[[]]]]=>2
[4,2,1,2,5]=>[[[[[[]]]]]]=>1
[4,2,1,5,2]=>[[[],[[[]]]]]=>1
[4,2,2,1,5]=>[[],[[[],[]]]]=>2
[4,2,2,5,1]=>[[[[]]],[[]]]=>2
[4,2,5,1,2]=>[[[[[[]]]]]]=>1
[4,2,5,2,1]=>[[[[[],[]]]]]=>1
[4,5,1,2,2]=>[[],[[],[[]]]]=>2
[4,5,2,1,2]=>[[[],[[[]]]]]=>1
[4,5,2,2,1]=>[[[[]]],[[]]]=>2
[5,1,2,2,4]=>[[[]],[[],[]]]=>2
[5,1,2,4,2]=>[[[[]],[[]]]]=>1
[5,1,4,2,2]=>[[],[[[[]]]]]=>2
[5,2,1,2,4]=>[[[[[[]]]]]]=>1
[5,2,1,4,2]=>[[[],[[[]]]]]=>1
[5,2,2,1,4]=>[[],[[[],[]]]]=>2
[5,2,2,4,1]=>[[],[[[],[]]]]=>2
[5,2,4,1,2]=>[[[[]],[[]]]]=>1
[5,2,4,2,1]=>[[[[[[]]]]]]=>1
[5,4,1,2,2]=>[[[[]]],[[]]]=>2
[5,4,2,1,2]=>[[[],[[[]]]]]=>1
[5,4,2,2,1]=>[[],[[],[[]]]]=>2
[1,2,3,3,3]=>[[],[],[[],[]]]=>3
[1,3,2,3,3]=>[[[]],[[[]]]]=>2
[1,3,3,2,3]=>[[[]],[[[]]]]=>2
[1,3,3,3,2]=>[[],[[]],[[]]]=>3
[2,1,3,3,3]=>[[],[[]],[[]]]=>3
[2,3,1,3,3]=>[[],[[[[]]]]]=>2
[2,3,3,1,3]=>[[[]],[[[]]]]=>2
[2,3,3,3,1]=>[[],[[]],[[]]]=>3
[3,1,2,3,3]=>[[],[[],[[]]]]=>2
[3,1,3,2,3]=>[[[[[[]]]]]]=>1
[3,1,3,3,2]=>[[[]],[[[]]]]=>2
[3,2,1,3,3]=>[[[]],[[],[]]]=>2
[3,2,3,1,3]=>[[[[[[]]]]]]=>1
[3,2,3,3,1]=>[[[]],[[[]]]]=>2
[3,3,1,2,3]=>[[],[[[],[]]]]=>2
[3,3,1,3,2]=>[[],[[[[]]]]]=>2
[3,3,2,1,3]=>[[],[[],[[]]]]=>2
[3,3,2,3,1]=>[[],[[[[]]]]]=>2
[3,3,3,1,2]=>[[],[],[[[]]]]=>3
[3,3,3,2,1]=>[[],[],[[],[]]]=>3
[1,2,3,3,4]=>[[],[[],[],[]]]=>2
[1,2,3,4,3]=>[[[],[],[[]]]]=>1
[1,2,4,3,3]=>[[],[[[[]]]]]=>2
[1,3,2,3,4]=>[[[[[],[]]]]]=>1
[1,3,2,4,3]=>[[[],[[],[]]]]=>1
[1,3,3,2,4]=>[[],[[[],[]]]]=>2
[1,3,3,4,2]=>[[[[]]],[[]]]=>2
[1,3,4,2,3]=>[[[[],[[]]]]]=>1
[1,3,4,3,2]=>[[[[[],[]]]]]=>1
[1,4,2,3,3]=>[[],[[[[]]]]]=>2
[1,4,3,2,3]=>[[[[],[[]]]]]=>1
[1,4,3,3,2]=>[[[]],[[],[]]]=>2
[2,1,3,3,4]=>[[[[]]],[[]]]=>2
[2,1,3,4,3]=>[[[],[[[]]]]]=>1
[2,1,4,3,3]=>[[],[[],[[]]]]=>2
[2,3,1,3,4]=>[[[],[[[]]]]]=>1
[2,3,1,4,3]=>[[[[[[]]]]]]=>1
[2,3,3,1,4]=>[[[]],[[[]]]]=>2
[2,3,3,4,1]=>[[],[[],[[]]]]=>2
[2,3,4,1,3]=>[[[],[[[]]]]]=>1
[2,3,4,3,1]=>[[[],[[[]]]]]=>1
[2,4,1,3,3]=>[[],[[],[[]]]]=>2
[2,4,3,1,3]=>[[[[]],[[]]]]=>1
[2,4,3,3,1]=>[[],[[[[]]]]]=>2
[3,1,2,3,4]=>[[[[],[],[]]]]=>1
[3,1,2,4,3]=>[[[[[[]]]]]]=>1
[3,1,3,2,4]=>[[[[],[[]]]]]=>1
[3,1,3,4,2]=>[[[],[[[]]]]]=>1
[3,1,4,2,3]=>[[[[]],[[]]]]=>1
[3,1,4,3,2]=>[[[[],[[]]]]]=>1
[3,2,1,3,4]=>[[[],[[[]]]]]=>1
[3,2,1,4,3]=>[[[],[],[[]]]]=>1
[3,2,3,1,4]=>[[[[[[]]]]]]=>1
[3,2,3,4,1]=>[[[[[],[]]]]]=>1
[3,2,4,1,3]=>[[[[],[[]]]]]=>1
[3,2,4,3,1]=>[[[[]],[[]]]]=>1
[3,3,1,2,4]=>[[],[[[[]]]]]=>2
[3,3,1,4,2]=>[[],[[],[[]]]]=>2
[3,3,2,1,4]=>[[],[[],[[]]]]=>2
[3,3,2,4,1]=>[[],[[[[]]]]]=>2
[3,3,4,1,2]=>[[],[[],[[]]]]=>2
[3,3,4,2,1]=>[[],[[[[]]]]]=>2
[3,4,1,2,3]=>[[[],[],[[]]]]=>1
[3,4,1,3,2]=>[[[[[[]]]]]]=>1
[3,4,2,1,3]=>[[[[[[]]]]]]=>1
[3,4,2,3,1]=>[[[],[[],[]]]]=>1
[3,4,3,1,2]=>[[[[]],[[]]]]=>1
[3,4,3,2,1]=>[[[[],[],[]]]]=>1
[4,1,2,3,3]=>[[],[[],[[]]]]=>2
[4,1,3,2,3]=>[[[[[[]]]]]]=>1
[4,1,3,3,2]=>[[[[]]],[[]]]=>2
[4,2,1,3,3]=>[[[[]]],[[]]]=>2
[4,2,3,1,3]=>[[[[]],[[]]]]=>1
[4,2,3,3,1]=>[[[]],[[],[]]]=>2
[4,3,1,2,3]=>[[[[],[[]]]]]=>1
[4,3,1,3,2]=>[[[[]],[[]]]]=>1
[4,3,2,1,3]=>[[[],[],[[]]]]=>1
[4,3,2,3,1]=>[[[],[[[]]]]]=>1
[4,3,3,1,2]=>[[],[[[[]]]]]=>2
[4,3,3,2,1]=>[[],[[],[],[]]]=>2
[1,2,3,3,5]=>[[[]],[[],[]]]=>2
[1,2,3,5,3]=>[[[],[[[]]]]]=>1
[1,2,5,3,3]=>[[],[[[[]]]]]=>2
[1,3,2,3,5]=>[[[[]],[[]]]]=>1
[1,3,2,5,3]=>[[[[[[]]]]]]=>1
[1,3,3,2,5]=>[[[]],[[[]]]]=>2
[1,3,3,5,2]=>[[],[[],[[]]]]=>2
[1,3,5,2,3]=>[[[],[[[]]]]]=>1
[1,3,5,3,2]=>[[[],[[[]]]]]=>1
[1,5,2,3,3]=>[[],[[[[]]]]]=>2
[1,5,3,2,3]=>[[[],[[[]]]]]=>1
[1,5,3,3,2]=>[[],[[[],[]]]]=>2
[2,1,3,3,5]=>[[],[[],[[]]]]=>2
[2,1,3,5,3]=>[[[[[],[]]]]]=>1
[2,1,5,3,3]=>[[[]],[[],[]]]=>2
[2,3,1,3,5]=>[[[[[],[]]]]]=>1
[2,3,1,5,3]=>[[[[],[],[]]]]=>1
[2,3,3,1,5]=>[[[]],[[],[]]]=>2
[2,3,3,5,1]=>[[[]],[[],[]]]=>2
[2,3,5,1,3]=>[[[[],[],[]]]]=>1
[2,3,5,3,1]=>[[[[[],[]]]]]=>1
[2,5,1,3,3]=>[[],[[],[[]]]]=>2
[2,5,3,1,3]=>[[[[],[[]]]]]=>1
[2,5,3,3,1]=>[[[]],[[],[]]]=>2
[3,1,2,3,5]=>[[[[],[[]]]]]=>1
[3,1,2,5,3]=>[[[],[[[]]]]]=>1
[3,1,3,2,5]=>[[[[[[]]]]]]=>1
[3,1,3,5,2]=>[[[[],[[]]]]]=>1
[3,1,5,2,3]=>[[[],[[[]]]]]=>1
[3,1,5,3,2]=>[[[],[],[[]]]]=>1
[3,2,1,3,5]=>[[[],[[],[]]]]=>1
[3,2,1,5,3]=>[[[],[[],[]]]]=>1
[3,2,3,1,5]=>[[[[],[[]]]]]=>1
[3,2,3,5,1]=>[[[[],[[]]]]]=>1
[3,2,5,1,3]=>[[[[],[[]]]]]=>1
[3,2,5,3,1]=>[[[[],[[]]]]]=>1
[3,3,1,2,5]=>[[],[[[[]]]]]=>2
[3,3,1,5,2]=>[[],[[],[[]]]]=>2
[3,3,2,1,5]=>[[],[[],[[]]]]=>2
[3,3,2,5,1]=>[[],[[[[]]]]]=>2
[3,3,5,1,2]=>[[],[[],[[]]]]=>2
[3,3,5,2,1]=>[[],[[[[]]]]]=>2
[3,5,1,2,3]=>[[[],[[],[]]]]=>1
[3,5,1,3,2]=>[[[],[],[[]]]]=>1
[3,5,2,1,3]=>[[[],[[[]]]]]=>1
[3,5,2,3,1]=>[[[[[[]]]]]]=>1
[3,5,3,1,2]=>[[[[],[[]]]]]=>1
[3,5,3,2,1]=>[[[[],[[]]]]]=>1
[5,1,2,3,3]=>[[],[[],[[]]]]=>2
[5,1,3,2,3]=>[[[],[[[]]]]]=>1
[5,1,3,3,2]=>[[[]],[[],[]]]=>2
[5,2,1,3,3]=>[[[]],[[[]]]]=>2
[5,2,3,1,3]=>[[[[[[]]]]]]=>1
[5,2,3,3,1]=>[[[[]]],[[]]]=>2
[5,3,1,2,3]=>[[[],[[],[]]]]=>1
[5,3,1,3,2]=>[[[],[[[]]]]]=>1
[5,3,2,1,3]=>[[[[[],[]]]]]=>1
[5,3,2,3,1]=>[[[[]],[[]]]]=>1
[5,3,3,1,2]=>[[],[[],[[]]]]=>2
[5,3,3,2,1]=>[[],[[],[[]]]]=>2
[1,2,3,4,4]=>[[],[[],[],[]]]=>2
[1,2,4,3,4]=>[[[],[[[]]]]]=>1
[1,2,4,4,3]=>[[[[]]],[[]]]=>2
[1,3,2,4,4]=>[[[]],[[],[]]]=>2
[1,3,4,2,4]=>[[[],[[[]]]]]=>1
[1,3,4,4,2]=>[[[[]]],[[]]]=>2
[1,4,2,3,4]=>[[[[],[[]]]]]=>1
[1,4,2,4,3]=>[[[[[[]]]]]]=>1
[1,4,3,2,4]=>[[[[],[[]]]]]=>1
[1,4,3,4,2]=>[[[[[[]]]]]]=>1
[1,4,4,2,3]=>[[[]],[[[]]]]=>2
[1,4,4,3,2]=>[[],[[],[[]]]]=>2
[2,1,3,4,4]=>[[[[]]],[[]]]=>2
[2,1,4,3,4]=>[[[[]],[[]]]]=>1
[2,1,4,4,3]=>[[[]],[[],[]]]=>2
[2,3,1,4,4]=>[[],[[[[]]]]]=>2
[2,3,4,1,4]=>[[[],[[],[]]]]=>1
[2,3,4,4,1]=>[[[]],[[],[]]]=>2
[2,4,1,3,4]=>[[[[]],[[]]]]=>1
[2,4,1,4,3]=>[[[[],[[]]]]]=>1
[2,4,3,1,4]=>[[[[[[]]]]]]=>1
[2,4,3,4,1]=>[[[[[[]]]]]]=>1
[2,4,4,1,3]=>[[],[[[],[]]]]=>2
[2,4,4,3,1]=>[[[]],[[[]]]]=>2
[3,1,2,4,4]=>[[],[[[[]]]]]=>2
[3,1,4,2,4]=>[[[[]],[[]]]]=>1
[3,1,4,4,2]=>[[[]],[[],[]]]=>2
[3,2,1,4,4]=>[[[]],[[],[]]]=>2
[3,2,4,1,4]=>[[[[],[[]]]]]=>1
[3,2,4,4,1]=>[[[]],[[[]]]]=>2
[3,4,1,2,4]=>[[[[]],[[]]]]=>1
[3,4,1,4,2]=>[[[[],[[]]]]]=>1
[3,4,2,1,4]=>[[[[[[]]]]]]=>1
[3,4,2,4,1]=>[[[[[[]]]]]]=>1
[3,4,4,1,2]=>[[],[[[],[]]]]=>2
[3,4,4,2,1]=>[[[]],[[[]]]]=>2
[4,1,2,3,4]=>[[[[],[],[]]]]=>1
[4,1,2,4,3]=>[[[[[[]]]]]]=>1
[4,1,3,2,4]=>[[[[[],[]]]]]=>1
[4,1,3,4,2]=>[[[[[[]]]]]]=>1
[4,1,4,2,3]=>[[[],[[[]]]]]=>1
[4,1,4,3,2]=>[[[],[[],[]]]]=>1
[4,2,1,3,4]=>[[[[[[]]]]]]=>1
[4,2,1,4,3]=>[[[[],[[]]]]]=>1
[4,2,3,1,4]=>[[[[]],[[]]]]=>1
[4,2,3,4,1]=>[[[[],[[]]]]]=>1
[4,2,4,1,3]=>[[[[[],[]]]]]=>1
[4,2,4,3,1]=>[[[],[[[]]]]]=>1
[4,3,1,2,4]=>[[[[[[]]]]]]=>1
[4,3,1,4,2]=>[[[[],[[]]]]]=>1
[4,3,2,1,4]=>[[[],[],[[]]]]=>1
[4,3,2,4,1]=>[[[],[[[]]]]]=>1
[4,3,4,1,2]=>[[[[],[[]]]]]=>1
[4,3,4,2,1]=>[[[],[[[]]]]]=>1
[4,4,1,2,3]=>[[],[[[],[]]]]=>2
[4,4,1,3,2]=>[[],[[[[]]]]]=>2
[4,4,2,1,3]=>[[],[[[[]]]]]=>2
[4,4,2,3,1]=>[[],[[],[[]]]]=>2
[4,4,3,1,2]=>[[],[[[[]]]]]=>2
[4,4,3,2,1]=>[[],[[],[],[]]]=>2
[1,2,3,4,5]=>[[[],[],[],[]]]=>1
[1,2,3,5,4]=>[[[],[[[]]]]]=>1
[1,2,4,3,5]=>[[[[],[[]]]]]=>1
[1,2,4,5,3]=>[[[[]],[[]]]]=>1
[1,2,5,3,4]=>[[[],[[[]]]]]=>1
[1,2,5,4,3]=>[[[[[],[]]]]]=>1
[1,3,2,4,5]=>[[[],[[[]]]]]=>1
[1,3,2,5,4]=>[[[[[],[]]]]]=>1
[1,3,4,2,5]=>[[[[[[]]]]]]=>1
[1,3,4,5,2]=>[[[[],[[]]]]]=>1
[1,3,5,2,4]=>[[[],[],[[]]]]=>1
[1,3,5,4,2]=>[[[],[[[]]]]]=>1
[1,4,2,3,5]=>[[[[[[]]]]]]=>1
[1,4,2,5,3]=>[[[],[[],[]]]]=>1
[1,4,3,2,5]=>[[[],[[],[]]]]=>1
[1,4,3,5,2]=>[[[[]],[[]]]]=>1
[1,4,5,2,3]=>[[[],[[],[]]]]=>1
[1,4,5,3,2]=>[[[[[[]]]]]]=>1
[1,5,2,3,4]=>[[[[],[[]]]]]=>1
[1,5,2,4,3]=>[[[[[[]]]]]]=>1
[1,5,3,2,4]=>[[[],[[[]]]]]=>1
[1,5,3,4,2]=>[[[],[],[[]]]]=>1
[1,5,4,2,3]=>[[[],[[[]]]]]=>1
[1,5,4,3,2]=>[[[[],[],[]]]]=>1
[2,1,3,4,5]=>[[[[],[[]]]]]=>1
[2,1,3,5,4]=>[[[],[[],[]]]]=>1
[2,1,4,3,5]=>[[[[]],[[]]]]=>1
[2,1,4,5,3]=>[[[[[[]]]]]]=>1
[2,1,5,3,4]=>[[[[[],[]]]]]=>1
[2,1,5,4,3]=>[[[],[],[[]]]]=>1
[2,3,1,4,5]=>[[[],[[[]]]]]=>1
[2,3,1,5,4]=>[[[[],[[]]]]]=>1
[2,3,4,1,5]=>[[[],[[[]]]]]=>1
[2,3,4,5,1]=>[[[],[],[[]]]]=>1
[2,3,5,1,4]=>[[[[],[[]]]]]=>1
[2,3,5,4,1]=>[[[[[[]]]]]]=>1
[2,4,1,3,5]=>[[[],[],[[]]]]=>1
[2,4,1,5,3]=>[[[[],[[]]]]]=>1
[2,4,3,1,5]=>[[[[],[[]]]]]=>1
[2,4,3,5,1]=>[[[],[],[[]]]]=>1
[2,4,5,1,3]=>[[[],[],[[]]]]=>1
[2,4,5,3,1]=>[[[[[],[]]]]]=>1
[2,5,1,3,4]=>[[[[],[[]]]]]=>1
[2,5,1,4,3]=>[[[[]],[[]]]]=>1
[2,5,3,1,4]=>[[[],[[],[]]]]=>1
[2,5,3,4,1]=>[[[],[[[]]]]]=>1
[2,5,4,1,3]=>[[[],[[[]]]]]=>1
[2,5,4,3,1]=>[[[[[],[]]]]]=>1
[3,1,2,4,5]=>[[[[[],[]]]]]=>1
[3,1,2,5,4]=>[[[[[[]]]]]]=>1
[3,1,4,2,5]=>[[[],[[],[]]]]=>1
[3,1,4,5,2]=>[[[[[],[]]]]]=>1
[3,1,5,2,4]=>[[[],[[[]]]]]=>1
[3,1,5,4,2]=>[[[],[],[[]]]]=>1
[3,2,1,4,5]=>[[[],[[[]]]]]=>1
[3,2,1,5,4]=>[[[],[],[[]]]]=>1
[3,2,4,1,5]=>[[[[[[]]]]]]=>1
[3,2,4,5,1]=>[[[[],[[]]]]]=>1
[3,2,5,1,4]=>[[[[],[[]]]]]=>1
[3,2,5,4,1]=>[[[],[[],[]]]]=>1
[3,4,1,2,5]=>[[[],[[],[]]]]=>1
[3,4,1,5,2]=>[[[[],[[]]]]]=>1
[3,4,2,1,5]=>[[[[],[[]]]]]=>1
[3,4,2,5,1]=>[[[[[[]]]]]]=>1
[3,4,5,1,2]=>[[[],[],[[]]]]=>1
[3,4,5,2,1]=>[[[],[[[]]]]]=>1
[3,5,1,2,4]=>[[[],[],[[]]]]=>1
[3,5,1,4,2]=>[[[],[[[]]]]]=>1
[3,5,2,1,4]=>[[[[[],[]]]]]=>1
[3,5,2,4,1]=>[[[],[[],[]]]]=>1
[3,5,4,1,2]=>[[[[[[]]]]]]=>1
[3,5,4,2,1]=>[[[[[],[]]]]]=>1
[4,1,2,3,5]=>[[[[],[[]]]]]=>1
[4,1,2,5,3]=>[[[[]],[[]]]]=>1
[4,1,3,2,5]=>[[[],[[[]]]]]=>1
[4,1,3,5,2]=>[[[],[[],[]]]]=>1
[4,1,5,2,3]=>[[[[]],[[]]]]=>1
[4,1,5,3,2]=>[[[[[],[]]]]]=>1
[4,2,1,3,5]=>[[[[],[[]]]]]=>1
[4,2,1,5,3]=>[[[],[],[[]]]]=>1
[4,2,3,1,5]=>[[[],[],[[]]]]=>1
[4,2,3,5,1]=>[[[[],[[]]]]]=>1
[4,2,5,1,3]=>[[[[],[[]]]]]=>1
[4,2,5,3,1]=>[[[],[],[[]]]]=>1
[4,3,1,2,5]=>[[[[[[]]]]]]=>1
[4,3,1,5,2]=>[[[[[],[]]]]]=>1
[4,3,2,1,5]=>[[[],[],[[]]]]=>1
[4,3,2,5,1]=>[[[],[[[]]]]]=>1
[4,3,5,1,2]=>[[[[[],[]]]]]=>1
[4,3,5,2,1]=>[[[],[[[]]]]]=>1
[4,5,1,2,3]=>[[[],[],[[]]]]=>1
[4,5,1,3,2]=>[[[[],[[]]]]]=>1
[4,5,2,1,3]=>[[[[[[]]]]]]=>1
[4,5,2,3,1]=>[[[[]],[[]]]]=>1
[4,5,3,1,2]=>[[[],[[],[]]]]=>1
[4,5,3,2,1]=>[[[[[],[]]]]]=>1
[5,1,2,3,4]=>[[[[],[],[]]]]=>1
[5,1,2,4,3]=>[[[[]],[[]]]]=>1
[5,1,3,2,4]=>[[[],[],[[]]]]=>1
[5,1,3,4,2]=>[[[],[[[]]]]]=>1
[5,1,4,2,3]=>[[[[[[]]]]]]=>1
[5,1,4,3,2]=>[[[[],[[]]]]]=>1
[5,2,1,3,4]=>[[[[[[]]]]]]=>1
[5,2,1,4,3]=>[[[],[[],[]]]]=>1
[5,2,3,1,4]=>[[[],[[[]]]]]=>1
[5,2,3,4,1]=>[[[],[[],[]]]]=>1
[5,2,4,1,3]=>[[[],[[],[]]]]=>1
[5,2,4,3,1]=>[[[[[[]]]]]]=>1
[5,3,1,2,4]=>[[[],[[[]]]]]=>1
[5,3,1,4,2]=>[[[],[],[[]]]]=>1
[5,3,2,1,4]=>[[[[[],[]]]]]=>1
[5,3,2,4,1]=>[[[[[[]]]]]]=>1
[5,3,4,1,2]=>[[[[[],[]]]]]=>1
[5,3,4,2,1]=>[[[[]],[[]]]]=>1
[5,4,1,2,3]=>[[[[],[[]]]]]=>1
[5,4,1,3,2]=>[[[],[[[]]]]]=>1
[5,4,2,1,3]=>[[[],[[[]]]]]=>1
[5,4,2,3,1]=>[[[[],[[]]]]]=>1
[5,4,3,1,2]=>[[[],[[[]]]]]=>1
[5,4,3,2,1]=>[[[],[],[],[]]]=>1
[1,1,1,1,1,1]=>[[],[],[],[],[],[]]=>6
[1,1,1,1,1,2]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,2,1]=>[[],[],[],[[[]]]]=>4
[1,1,1,2,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,2,1,1,1]=>[[],[],[],[[[]]]]=>4
[1,2,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[2,1,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,1,3]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,3,1]=>[[],[],[],[[[]]]]=>4
[1,1,1,3,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,3,1,1,1]=>[[],[],[],[[[]]]]=>4
[1,3,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[3,1,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,1,4]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,4,1]=>[[],[],[],[[[]]]]=>4
[1,1,1,4,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,4,1,1,1]=>[[],[],[],[[[]]]]=>4
[1,4,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,1,5]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,5,1]=>[[],[],[],[[[]]]]=>4
[1,1,1,5,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,5,1,1,1]=>[[],[],[],[[[]]]]=>4
[1,5,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,1,6]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,6,1]=>[[],[],[],[[[]]]]=>4
[1,1,1,6,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,6,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,6,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[6,1,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,2,2]=>[[],[],[],[],[[]]]=>5
[1,1,1,2,1,2]=>[[],[],[[],[[]]]]=>3
[1,1,1,2,2,1]=>[[],[],[[]],[[]]]=>4
[1,1,2,1,1,2]=>[[],[],[[],[[]]]]=>3
[1,1,2,1,2,1]=>[[],[[],[[],[]]]]=>2
[1,1,2,2,1,1]=>[[],[],[[]],[[]]]=>4
[1,2,1,1,1,2]=>[[],[],[[],[[]]]]=>3
[1,2,1,1,2,1]=>[[],[[],[[],[]]]]=>2
[1,2,1,2,1,1]=>[[],[[],[[],[]]]]=>2
[1,2,2,1,1,1]=>[[],[],[[]],[[]]]=>4
[2,1,1,1,1,2]=>[[],[],[],[[[]]]]=>4
[2,1,1,1,2,1]=>[[],[],[[[],[]]]]=>3
[2,1,1,2,1,1]=>[[],[],[[],[[]]]]=>3
[2,1,2,1,1,1]=>[[],[],[[],[[]]]]=>3
[2,2,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,2,3]=>[[],[],[],[[],[]]]=>4
[1,1,1,1,3,2]=>[[],[],[],[[[]]]]=>4
[1,1,1,2,1,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,2,3,1]=>[[],[],[[],[[]]]]=>3
[1,1,1,3,1,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,2,1]=>[[],[],[[[],[]]]]=>3
[1,1,2,1,1,3]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,2,3,1,1]=>[[],[],[[[],[]]]]=>3
[1,1,3,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,1,3,1,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,3,2,1,1]=>[[],[],[[],[[]]]]=>3
[1,2,1,1,1,3]=>[[],[],[[[[]]]]]=>3
[1,2,1,1,3,1]=>[[],[[[[[]]]]]]=>2
[1,2,1,3,1,1]=>[[[[]]],[[[]]]]=>2
[1,2,3,1,1,1]=>[[],[],[[[],[]]]]=>3
[1,3,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,3,1,1,2,1]=>[[],[[[[[]]]]]]=>2
[1,3,1,2,1,1]=>[[[[]]],[[[]]]]=>2
[1,3,2,1,1,1]=>[[],[],[[],[[]]]]=>3
[2,1,1,1,1,3]=>[[],[],[],[[[]]]]=>4
[2,1,1,1,3,1]=>[[],[],[[[[]]]]]=>3
[2,1,1,3,1,1]=>[[],[[[]]],[[]]]=>3
[2,1,3,1,1,1]=>[[],[[[]]],[[]]]=>3
[2,3,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[3,1,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,2,1]=>[[],[],[[[[]]]]]=>3
[3,1,1,2,1,1]=>[[],[[]],[[[]]]]=>3
[3,1,2,1,1,1]=>[[],[[]],[[[]]]]=>3
[3,2,1,1,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,1,1,2,4]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,4,2]=>[[],[],[],[[[]]]]=>4
[1,1,1,2,1,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,2,4,1]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,1,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,2,1]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,1,4]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,2,4,1,1]=>[[],[],[[[[]]]]]=>3
[1,1,4,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,1,4,1,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,1,1]=>[[],[[[]]],[[]]]=>3
[1,2,1,1,1,4]=>[[],[],[[[[]]]]]=>3
[1,2,1,1,4,1]=>[[],[[[[[]]]]]]=>2
[1,2,1,4,1,1]=>[[[[]]],[[[]]]]=>2
[1,2,4,1,1,1]=>[[],[],[[[[]]]]]=>3
[1,4,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,4,1,1,2,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,2,1,1]=>[[],[[[[[]]]]]]=>2
[1,4,2,1,1,1]=>[[],[[]],[[[]]]]=>3
[2,1,1,1,1,4]=>[[],[],[],[[[]]]]=>4
[2,1,1,1,4,1]=>[[],[],[[[[]]]]]=>3
[2,1,1,4,1,1]=>[[],[[[]]],[[]]]=>3
[2,1,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[2,4,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[4,1,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,2,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,2,1,1]=>[[],[],[[[[]]]]]=>3
[4,1,2,1,1,1]=>[[],[[]],[[[]]]]=>3
[4,2,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,2,5]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,5,2]=>[[],[],[],[[],[]]]=>4
[1,1,1,2,1,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,2,5,1]=>[[],[],[[[],[]]]]=>3
[1,1,1,5,1,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,2,1]=>[[],[],[[],[[]]]]=>3
[1,1,2,1,1,5]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,2,5,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,5,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,1,5,1,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,2,1,1]=>[[],[],[[[],[]]]]=>3
[1,2,1,1,1,5]=>[[],[],[[[[]]]]]=>3
[1,2,1,1,5,1]=>[[],[[[[[]]]]]]=>2
[1,2,1,5,1,1]=>[[[[]]],[[[]]]]=>2
[1,2,5,1,1,1]=>[[],[],[[],[[]]]]=>3
[1,5,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,5,1,1,2,1]=>[[[[]]],[[[]]]]=>2
[1,5,1,2,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,2,1,1,1]=>[[],[[]],[[],[]]]=>3
[2,1,1,1,1,5]=>[[],[],[],[[[]]]]=>4
[2,1,1,1,5,1]=>[[],[],[[[[]]]]]=>3
[2,1,1,5,1,1]=>[[],[[[]]],[[]]]=>3
[2,1,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[2,5,1,1,1,1]=>[[],[],[],[[],[]]]=>4
[5,1,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,2,1]=>[[],[[[]]],[[]]]=>3
[5,1,1,2,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,2,1,1,1]=>[[],[],[[[[]]]]]=>3
[5,2,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,2,6]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,6,2]=>[[],[],[],[[[]]]]=>4
[1,1,1,2,1,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,2,6,1]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,1,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,2,1]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,1,6]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,6,1]=>[[],[[[[[]]]]]]=>2
[1,1,2,6,1,1]=>[[],[],[[[[]]]]]=>3
[1,1,6,1,1,2]=>[[],[[]],[[[]]]]=>3
[1,1,6,1,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,1,1]=>[[],[[]],[[[]]]]=>3
[1,2,1,1,1,6]=>[[],[],[[[[]]]]]=>3
[1,2,1,1,6,1]=>[[],[[[[[]]]]]]=>2
[1,2,1,6,1,1]=>[[[[]]],[[[]]]]=>2
[1,2,6,1,1,1]=>[[],[],[[[[]]]]]=>3
[1,6,1,1,1,2]=>[[[]],[[]],[[]]]=>3
[1,6,1,1,2,1]=>[[[[[]]]],[[]]]=>2
[1,6,1,2,1,1]=>[[[]],[[[[]]]]]=>2
[1,6,2,1,1,1]=>[[],[[]],[[[]]]]=>3
[2,1,1,1,1,6]=>[[],[],[],[[[]]]]=>4
[2,1,1,1,6,1]=>[[],[],[[[[]]]]]=>3
[2,1,1,6,1,1]=>[[],[[[]]],[[]]]=>3
[2,1,6,1,1,1]=>[[[]],[[]],[[]]]=>3
[2,6,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[6,1,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[6,1,1,1,2,1]=>[[],[[[]]],[[]]]=>3
[6,1,1,2,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,2,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,2,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,3,3]=>[[],[],[],[],[[]]]=>5
[1,1,1,3,1,3]=>[[],[],[[],[[]]]]=>3
[1,1,1,3,3,1]=>[[],[],[[]],[[]]]=>4
[1,1,3,1,1,3]=>[[],[[]],[[],[]]]=>3
[1,1,3,1,3,1]=>[[],[[],[[],[]]]]=>2
[1,1,3,3,1,1]=>[[],[],[[]],[[]]]=>4
[1,3,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[1,3,1,1,3,1]=>[[],[[],[[],[]]]]=>2
[1,3,1,3,1,1]=>[[],[[],[[],[]]]]=>2
[1,3,3,1,1,1]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,1,3]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,3,1]=>[[],[],[[[],[]]]]=>3
[3,1,1,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,3,1,1,1]=>[[],[],[[],[[]]]]=>3
[3,3,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,3,4]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,4,3]=>[[],[],[],[[[]]]]=>4
[1,1,1,3,1,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,4,1]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,1,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,3,1]=>[[],[],[[[[]]]]]=>3
[1,1,3,1,1,4]=>[[],[[]],[[[]]]]=>3
[1,1,3,1,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,1,1]=>[[],[],[[[[]]]]]=>3
[1,1,4,1,1,3]=>[[],[[]],[[[]]]]=>3
[1,1,4,1,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,1,1]=>[[],[[]],[[[]]]]=>3
[1,3,1,1,1,4]=>[[],[[]],[[[]]]]=>3
[1,3,1,1,4,1]=>[[[[]]],[[[]]]]=>2
[1,3,1,4,1,1]=>[[],[[[[[]]]]]]=>2
[1,3,4,1,1,1]=>[[],[],[[[[]]]]]=>3
[1,4,1,1,1,3]=>[[],[[]],[[[]]]]=>3
[1,4,1,1,3,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,3,1,1]=>[[],[[[[[]]]]]]=>2
[1,4,3,1,1,1]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,1,4]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,4,1]=>[[],[[[]]],[[]]]=>3
[3,1,1,4,1,1]=>[[],[],[[[[]]]]]=>3
[3,1,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[3,4,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[4,1,1,1,1,3]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,3,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,3,1,1]=>[[],[],[[[[]]]]]=>3
[4,1,3,1,1,1]=>[[],[[]],[[[]]]]=>3
[4,3,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,3,5]=>[[],[],[],[[],[]]]=>4
[1,1,1,1,5,3]=>[[],[],[],[[[]]]]=>4
[1,1,1,3,1,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,5,1]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,1,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,3,1]=>[[],[],[[[],[]]]]=>3
[1,1,3,1,1,5]=>[[],[[]],[[[]]]]=>3
[1,1,3,1,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,3,5,1,1]=>[[],[],[[[],[]]]]=>3
[1,1,5,1,1,3]=>[[],[[]],[[[]]]]=>3
[1,1,5,1,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,1,1]=>[[],[],[[],[[]]]]=>3
[1,3,1,1,1,5]=>[[],[[]],[[[]]]]=>3
[1,3,1,1,5,1]=>[[[[]]],[[[]]]]=>2
[1,3,1,5,1,1]=>[[],[[[[[]]]]]]=>2
[1,3,5,1,1,1]=>[[],[],[[[],[]]]]=>3
[1,5,1,1,1,3]=>[[],[[]],[[[]]]]=>3
[1,5,1,1,3,1]=>[[[[]]],[[[]]]]=>2
[1,5,1,3,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,3,1,1,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,1,1,5]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,5,1]=>[[],[[[]]],[[]]]=>3
[3,1,1,5,1,1]=>[[],[],[[[[]]]]]=>3
[3,1,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[3,5,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[5,1,1,1,1,3]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,3,1]=>[[],[[[]]],[[]]]=>3
[5,1,1,3,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,3,1,1,1]=>[[],[],[[[[]]]]]=>3
[5,3,1,1,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,1,1,3,6]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,6,3]=>[[],[],[],[[[]]]]=>4
[1,1,1,3,1,6]=>[[],[],[[[],[]]]]=>3
[1,1,1,3,6,1]=>[[],[],[[],[[]]]]=>3
[1,1,1,6,1,3]=>[[],[],[[[],[]]]]=>3
[1,1,1,6,3,1]=>[[],[],[[],[[]]]]=>3
[1,1,3,1,1,6]=>[[],[],[[],[[]]]]=>3
[1,1,3,1,6,1]=>[[],[[],[[],[]]]]=>2
[1,1,3,6,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,6,1,1,3]=>[[],[[]],[[],[]]]=>3
[1,1,6,1,3,1]=>[[],[[],[[],[]]]]=>2
[1,1,6,3,1,1]=>[[],[],[[],[[]]]]=>3
[1,3,1,1,1,6]=>[[],[],[[],[[]]]]=>3
[1,3,1,1,6,1]=>[[],[[],[[],[]]]]=>2
[1,3,1,6,1,1]=>[[],[[],[[],[]]]]=>2
[1,3,6,1,1,1]=>[[],[],[[],[[]]]]=>3
[1,6,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[1,6,1,1,3,1]=>[[],[[],[[],[]]]]=>2
[1,6,1,3,1,1]=>[[],[[],[[],[]]]]=>2
[1,6,3,1,1,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,1,1,6]=>[[],[],[],[[],[]]]=>4
[3,1,1,1,6,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,6,1,1]=>[[],[],[[[],[]]]]=>3
[3,1,6,1,1,1]=>[[],[[]],[[],[]]]=>3
[3,6,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[6,1,1,1,1,3]=>[[],[],[],[[],[]]]=>4
[6,1,1,1,3,1]=>[[],[],[[],[[]]]]=>3
[6,1,1,3,1,1]=>[[],[],[[[],[]]]]=>3
[6,1,3,1,1,1]=>[[],[],[[[],[]]]]=>3
[6,3,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,4,4]=>[[],[],[],[],[[]]]=>5
[1,1,1,4,1,4]=>[[],[],[[],[[]]]]=>3
[1,1,1,4,4,1]=>[[],[],[[]],[[]]]=>4
[1,1,4,1,1,4]=>[[],[[]],[[],[]]]=>3
[1,1,4,1,4,1]=>[[],[[],[[],[]]]]=>2
[1,1,4,4,1,1]=>[[],[],[[]],[[]]]=>4
[1,4,1,1,1,4]=>[[],[[]],[[],[]]]=>3
[1,4,1,1,4,1]=>[[],[[],[[],[]]]]=>2
[1,4,1,4,1,1]=>[[],[[],[[],[]]]]=>2
[1,4,4,1,1,1]=>[[],[],[],[[[]]]]=>4
[4,1,1,1,1,4]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,4,1]=>[[],[],[[[],[]]]]=>3
[4,1,1,4,1,1]=>[[],[],[[],[[]]]]=>3
[4,1,4,1,1,1]=>[[],[],[[],[[]]]]=>3
[4,4,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,4,5]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,5,4]=>[[],[],[],[[[]]]]=>4
[1,1,1,4,1,5]=>[[],[],[[[],[]]]]=>3
[1,1,1,4,5,1]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,1,4]=>[[],[],[[[],[]]]]=>3
[1,1,1,5,4,1]=>[[],[],[[],[[]]]]=>3
[1,1,4,1,1,5]=>[[],[],[[],[[]]]]=>3
[1,1,4,1,5,1]=>[[],[[],[[],[]]]]=>2
[1,1,4,5,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,5,1,1,4]=>[[],[],[[],[[]]]]=>3
[1,1,5,1,4,1]=>[[],[[],[[],[]]]]=>2
[1,1,5,4,1,1]=>[[],[[]],[[],[]]]=>3
[1,4,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[1,4,1,1,5,1]=>[[],[[],[[],[]]]]=>2
[1,4,1,5,1,1]=>[[],[[],[[],[]]]]=>2
[1,4,5,1,1,1]=>[[],[],[[],[[]]]]=>3
[1,5,1,1,1,4]=>[[],[[]],[[],[]]]=>3
[1,5,1,1,4,1]=>[[],[[],[[],[]]]]=>2
[1,5,1,4,1,1]=>[[],[[],[[],[]]]]=>2
[1,5,4,1,1,1]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,1,5]=>[[],[],[],[[],[]]]=>4
[4,1,1,1,5,1]=>[[],[],[[],[[]]]]=>3
[4,1,1,5,1,1]=>[[],[],[[[],[]]]]=>3
[4,1,5,1,1,1]=>[[],[],[[[],[]]]]=>3
[4,5,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[5,1,1,1,1,4]=>[[],[],[],[[],[]]]=>4
[5,1,1,1,4,1]=>[[],[],[[],[[]]]]=>3
[5,1,1,4,1,1]=>[[],[],[[[],[]]]]=>3
[5,1,4,1,1,1]=>[[],[],[[[],[]]]]=>3
[5,4,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,4,6]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,6,4]=>[[],[],[],[[],[]]]=>4
[1,1,1,4,1,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,6,1]=>[[],[],[[[],[]]]]=>3
[1,1,1,6,1,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,4,1]=>[[],[],[[],[[]]]]=>3
[1,1,4,1,1,6]=>[[],[[[]]],[[]]]=>3
[1,1,4,1,6,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,6,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,6,1,1,4]=>[[],[[[]]],[[]]]=>3
[1,1,6,1,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,4,1,1]=>[[],[],[[[],[]]]]=>3
[1,4,1,1,1,6]=>[[[]],[[]],[[]]]=>3
[1,4,1,1,6,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,6,1,1]=>[[],[[[[[]]]]]]=>2
[1,4,6,1,1,1]=>[[],[],[[],[[]]]]=>3
[1,6,1,1,1,4]=>[[[]],[[]],[[]]]=>3
[1,6,1,1,4,1]=>[[[[]]],[[[]]]]=>2
[1,6,1,4,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,4,1,1,1]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,1,6]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,6,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,6,1,1]=>[[],[],[[[[]]]]]=>3
[4,1,6,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,6,1,1,1,1]=>[[],[],[],[[],[]]]=>4
[6,1,1,1,1,4]=>[[],[],[[]],[[]]]=>4
[6,1,1,1,4,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,4,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,4,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,4,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,1,5,5]=>[[],[],[],[],[[]]]=>5
[1,1,1,5,1,5]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,5,1]=>[[],[],[[]],[[]]]=>4
[1,1,5,1,1,5]=>[[],[[]],[[],[]]]=>3
[1,1,5,1,5,1]=>[[],[[],[[],[]]]]=>2
[1,1,5,5,1,1]=>[[],[],[[]],[[]]]=>4
[1,5,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[1,5,1,1,5,1]=>[[],[[],[[],[]]]]=>2
[1,5,1,5,1,1]=>[[],[[],[[],[]]]]=>2
[1,5,5,1,1,1]=>[[],[],[],[[[]]]]=>4
[5,1,1,1,1,5]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,5,1]=>[[],[],[[[],[]]]]=>3
[5,1,1,5,1,1]=>[[],[],[[],[[]]]]=>3
[5,1,5,1,1,1]=>[[],[],[[],[[]]]]=>3
[5,5,1,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,1,5,6]=>[[],[],[],[[[]]]]=>4
[1,1,1,1,6,5]=>[[],[],[],[[[]]]]=>4
[1,1,1,5,1,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,6,1]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,1,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,5,1]=>[[],[],[[[[]]]]]=>3
[1,1,5,1,1,6]=>[[],[[[]]],[[]]]=>3
[1,1,5,1,6,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,6,1,1]=>[[],[],[[[[]]]]]=>3
[1,1,6,1,1,5]=>[[],[[[]]],[[]]]=>3
[1,1,6,1,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,5,1,1]=>[[],[[[]]],[[]]]=>3
[1,5,1,1,1,6]=>[[[]],[[]],[[]]]=>3
[1,5,1,1,6,1]=>[[[[]]],[[[]]]]=>2
[1,5,1,6,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,6,1,1,1]=>[[],[],[[[[]]]]]=>3
[1,6,1,1,1,5]=>[[[]],[[]],[[]]]=>3
[1,6,1,1,5,1]=>[[[[]]],[[[]]]]=>2
[1,6,1,5,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,5,1,1,1]=>[[[]],[[]],[[]]]=>3
[5,1,1,1,1,6]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,6,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,6,1,1]=>[[],[[[]]],[[]]]=>3
[5,1,6,1,1,1]=>[[],[[]],[[[]]]]=>3
[5,6,1,1,1,1]=>[[],[],[],[[[]]]]=>4
[6,1,1,1,1,5]=>[[],[],[[]],[[]]]=>4
[6,1,1,1,5,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,5,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,5,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,5,1,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,2,2]=>[[],[],[],[],[[]]]=>5
[1,1,2,1,2,2]=>[[],[[]],[[],[]]]=>3
[1,1,2,2,1,2]=>[[],[],[[[],[]]]]=>3
[1,1,2,2,2,1]=>[[],[],[[]],[[]]]=>4
[1,2,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[1,2,1,2,1,2]=>[[[],[],[[],[]]]]=>1
[1,2,1,2,2,1]=>[[[],[]],[[],[]]]=>2
[1,2,2,1,1,2]=>[[],[],[[],[[]]]]=>3
[1,2,2,1,2,1]=>[[],[[],[[],[]]]]=>2
[1,2,2,2,1,1]=>[[],[],[[]],[[]]]=>4
[2,1,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,1,2,1,2]=>[[],[[],[[],[]]]]=>2
[2,1,1,2,2,1]=>[[],[[]],[[],[]]]=>3
[2,1,2,1,1,2]=>[[],[[],[[],[]]]]=>2
[2,1,2,1,2,1]=>[[[],[],[[],[]]]]=>1
[2,1,2,2,1,1]=>[[],[[]],[[],[]]]=>3
[2,2,1,1,1,2]=>[[],[],[],[[[]]]]=>4
[2,2,1,1,2,1]=>[[],[],[[[],[]]]]=>3
[2,2,1,2,1,1]=>[[],[],[[],[[]]]]=>3
[2,2,2,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,2,2,3]=>[[],[],[],[[],[]]]=>4
[1,1,1,2,3,2]=>[[],[],[[],[[]]]]=>3
[1,1,1,3,2,2]=>[[],[],[],[[[]]]]=>4
[1,1,2,1,2,3]=>[[],[[],[],[[]]]]=>2
[1,1,2,1,3,2]=>[[],[[[],[[]]]]]=>2
[1,1,2,2,1,3]=>[[],[[]],[[[]]]]=>3
[1,1,2,2,3,1]=>[[],[],[[],[[]]]]=>3
[1,1,2,3,1,2]=>[[],[[],[],[[]]]]=>2
[1,1,2,3,2,1]=>[[],[[],[[],[]]]]=>2
[1,1,3,1,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,3,2,1,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,1,1,2,3]=>[[],[[],[],[[]]]]=>2
[1,2,1,1,3,2]=>[[],[[[],[[]]]]]=>2
[1,2,1,2,1,3]=>[[[],[[],[[]]]]]=>1
[1,2,1,2,3,1]=>[[[],[],[[[]]]]]=>1
[1,2,1,3,1,2]=>[[[[[]]],[[]]]]=>1
[1,2,1,3,2,1]=>[[[[],[],[[]]]]]=>1
[1,2,2,1,1,3]=>[[],[[]],[[[]]]]=>3
[1,2,2,1,3,1]=>[[[]],[[[[]]]]]=>2
[1,2,2,3,1,1]=>[[],[],[[[],[]]]]=>3
[1,2,3,1,1,2]=>[[[]],[[],[],[]]]=>2
[1,2,3,1,2,1]=>[[[],[],[[[]]]]]=>1
[1,2,3,2,1,1]=>[[],[[],[[],[]]]]=>2
[1,3,1,1,2,2]=>[[],[],[[[[]]]]]=>3
[1,3,1,2,1,2]=>[[[[[],[[]]]]]]=>1
[1,3,1,2,2,1]=>[[[]],[[[[]]]]]=>2
[1,3,2,1,1,2]=>[[],[[[],[[]]]]]=>2
[1,3,2,1,2,1]=>[[[[],[],[[]]]]]=>1
[1,3,2,2,1,1]=>[[],[],[[],[[]]]]=>3
[2,1,1,1,2,3]=>[[],[],[[],[[]]]]=>3
[2,1,1,1,3,2]=>[[],[],[[[],[]]]]=>3
[2,1,1,2,1,3]=>[[],[[[],[[]]]]]=>2
[2,1,1,2,3,1]=>[[],[[],[[[]]]]]=>2
[2,1,1,3,1,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,3,2,1]=>[[],[[[],[],[]]]]=>2
[2,1,2,1,1,3]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,3,1]=>[[[[]],[[[]]]]]=>1
[2,1,2,3,1,1]=>[[[[],[]]],[[]]]=>2
[2,1,3,1,1,2]=>[[[[]]],[[[]]]]=>2
[2,1,3,1,2,1]=>[[[[]],[[[]]]]]=>1
[2,1,3,2,1,1]=>[[],[[],[],[[]]]]=>2
[2,2,1,1,1,3]=>[[],[],[],[[[]]]]=>4
[2,2,1,1,3,1]=>[[],[],[[[[]]]]]=>3
[2,2,1,3,1,1]=>[[],[[[]]],[[]]]=>3
[2,2,3,1,1,1]=>[[],[],[],[[[]]]]=>4
[2,3,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[2,3,1,1,2,1]=>[[],[[],[[[]]]]]=>2
[2,3,1,2,1,1]=>[[[]],[[[],[]]]]=>2
[2,3,2,1,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,2,2]=>[[],[],[],[[[]]]]=>4
[3,1,1,2,1,2]=>[[],[[[]],[[]]]]=>2
[3,1,1,2,2,1]=>[[],[[]],[[[]]]]=>3
[3,1,2,1,1,2]=>[[[]],[[],[[]]]]=>2
[3,1,2,1,2,1]=>[[[[],[[],[]]]]]=>1
[3,1,2,2,1,1]=>[[[]],[[]],[[]]]=>3
[3,2,1,1,1,2]=>[[],[],[[[],[]]]]=>3
[3,2,1,1,2,1]=>[[],[[[],[],[]]]]=>2
[3,2,1,2,1,1]=>[[],[[],[],[[]]]]=>2
[3,2,2,1,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,1,2,2,4]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,4,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,2,2]=>[[],[],[],[[[]]]]=>4
[1,1,2,1,2,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,1,4,2]=>[[],[[[[[]]]]]]=>2
[1,1,2,2,1,4]=>[[],[[]],[[[]]]]=>3
[1,1,2,2,4,1]=>[[],[[]],[[[]]]]=>3
[1,1,2,4,1,2]=>[[],[[],[[[]]]]]=>2
[1,1,2,4,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,4,2,1,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,2,1]=>[[],[],[[[[]]]]]=>3
[1,2,1,1,2,4]=>[[],[[],[[[]]]]]=>2
[1,2,1,1,4,2]=>[[],[[[[[]]]]]]=>2
[1,2,1,2,1,4]=>[[[],[[],[[]]]]]=>1
[1,2,1,2,4,1]=>[[[],[[[[]]]]]]=>1
[1,2,1,4,1,2]=>[[[[[]]],[[]]]]=>1
[1,2,1,4,2,1]=>[[[[],[[[]]]]]]=>1
[1,2,2,1,1,4]=>[[],[[]],[[[]]]]=>3
[1,2,2,1,4,1]=>[[[]],[[[[]]]]]=>2
[1,2,2,4,1,1]=>[[],[[]],[[[]]]]=>3
[1,2,4,1,1,2]=>[[[[]]],[[],[]]]=>2
[1,2,4,1,2,1]=>[[[[[]]],[[]]]]=>1
[1,2,4,2,1,1]=>[[[[[]]]],[[]]]=>2
[1,4,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[1,4,1,2,1,2]=>[[[[],[[[]]]]]]=>1
[1,4,1,2,2,1]=>[[[[[]]]],[[]]]=>2
[1,4,2,1,1,2]=>[[[[]]],[[[]]]]=>2
[1,4,2,1,2,1]=>[[[[[]],[[]]]]]=>1
[1,4,2,2,1,1]=>[[[]],[[]],[[]]]=>3
[2,1,1,1,2,4]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,4,2]=>[[],[],[[[[]]]]]=>3
[2,1,1,2,1,4]=>[[],[[[],[[]]]]]=>2
[2,1,1,2,4,1]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,1,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,2,1]=>[[],[[[[],[]]]]]=>2
[2,1,2,1,1,4]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,4,1]=>[[[[]],[[[]]]]]=>1
[2,1,2,4,1,1]=>[[[[[]]]],[[]]]=>2
[2,1,4,1,1,2]=>[[[[]]],[[[]]]]=>2
[2,1,4,1,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,4,2,1,1]=>[[[[]]],[[],[]]]=>2
[2,2,1,1,1,4]=>[[],[],[],[[[]]]]=>4
[2,2,1,1,4,1]=>[[],[],[[[[]]]]]=>3
[2,2,1,4,1,1]=>[[],[[[]]],[[]]]=>3
[2,2,4,1,1,1]=>[[],[],[],[[[]]]]=>4
[2,4,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[2,4,1,1,2,1]=>[[[[]]],[[[]]]]=>2
[2,4,1,2,1,1]=>[[],[[[[[]]]]]]=>2
[2,4,2,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[4,1,1,2,1,2]=>[[],[[],[[[]]]]]=>2
[4,1,1,2,2,1]=>[[],[[[]]],[[]]]=>3
[4,1,2,1,1,2]=>[[],[[],[[[]]]]]=>2
[4,1,2,1,2,1]=>[[[[],[[],[]]]]]=>1
[4,1,2,2,1,1]=>[[],[[]],[[[]]]]=>3
[4,2,1,1,1,2]=>[[],[[[]]],[[]]]=>3
[4,2,1,1,2,1]=>[[],[[[],[[]]]]]=>2
[4,2,1,2,1,1]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,2,5]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,5,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,2,2]=>[[],[],[],[[],[]]]=>4
[1,1,2,1,2,5]=>[[],[[],[[[]]]]]=>2
[1,1,2,1,5,2]=>[[],[[[[],[]]]]]=>2
[1,1,2,2,1,5]=>[[],[[]],[[[]]]]=>3
[1,1,2,2,5,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,5,1,2]=>[[],[[],[[],[]]]]=>2
[1,1,2,5,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,1,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,5,2,1,2]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,2,1]=>[[],[[]],[[],[]]]=>3
[1,2,1,1,2,5]=>[[],[[],[[[]]]]]=>2
[1,2,1,1,5,2]=>[[],[[],[[[]]]]]=>2
[1,2,1,2,1,5]=>[[[],[[],[[]]]]]=>1
[1,2,1,2,5,1]=>[[[],[[],[[]]]]]=>1
[1,2,1,5,1,2]=>[[[[[]]],[[]]]]=>1
[1,2,1,5,2,1]=>[[[[],[[],[]]]]]=>1
[1,2,2,1,1,5]=>[[],[[]],[[[]]]]=>3
[1,2,2,1,5,1]=>[[[]],[[[[]]]]]=>2
[1,2,2,5,1,1]=>[[],[[]],[[],[]]]=>3
[1,2,5,1,1,2]=>[[[],[]],[[],[]]]=>2
[1,2,5,1,2,1]=>[[[[]],[[],[]]]]=>1
[1,2,5,2,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[1,5,1,2,1,2]=>[[[[[],[[]]]]]]=>1
[1,5,1,2,2,1]=>[[[[[]]]],[[]]]=>2
[1,5,2,1,1,2]=>[[],[[[[],[]]]]]=>2
[1,5,2,1,2,1]=>[[[],[[[],[]]]]]=>1
[1,5,2,2,1,1]=>[[],[],[[[],[]]]]=>3
[2,1,1,1,2,5]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,5,2]=>[[],[],[[],[[]]]]=>3
[2,1,1,2,1,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,2,5,1]=>[[],[[[],[[]]]]]=>2
[2,1,1,5,1,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,2,1]=>[[],[[],[[],[]]]]=>2
[2,1,2,1,1,5]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,5,1]=>[[[[]],[[[]]]]]=>1
[2,1,2,5,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,5,1,1,2]=>[[[[]]],[[[]]]]=>2
[2,1,5,1,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,5,2,1,1]=>[[],[[],[[],[]]]]=>2
[2,2,1,1,1,5]=>[[],[],[],[[[]]]]=>4
[2,2,1,1,5,1]=>[[],[],[[[[]]]]]=>3
[2,2,1,5,1,1]=>[[],[[[]]],[[]]]=>3
[2,2,5,1,1,1]=>[[],[],[],[[],[]]]=>4
[2,5,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[2,5,1,1,2,1]=>[[[[]]],[[],[]]]=>2
[2,5,1,2,1,1]=>[[],[[[[],[]]]]]=>2
[2,5,2,1,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[5,1,1,2,1,2]=>[[[]],[[],[[]]]]=>2
[5,1,1,2,2,1]=>[[[]],[[]],[[]]]=>3
[5,1,2,1,1,2]=>[[],[[[]],[[]]]]=>2
[5,1,2,1,2,1]=>[[[[],[[],[]]]]]=>1
[5,1,2,2,1,1]=>[[],[[[]]],[[]]]=>3
[5,2,1,1,1,2]=>[[],[[[]]],[[]]]=>3
[5,2,1,1,2,1]=>[[[[],[]]],[[]]]=>2
[5,2,1,2,1,1]=>[[],[[],[[[]]]]]=>2
[5,2,2,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,2,6]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,6,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,2,2]=>[[],[],[],[[[]]]]=>4
[1,1,2,1,2,6]=>[[],[[],[[[]]]]]=>2
[1,1,2,1,6,2]=>[[],[[[[[]]]]]]=>2
[1,1,2,2,1,6]=>[[],[[]],[[[]]]]=>3
[1,1,2,2,6,1]=>[[],[[]],[[[]]]]=>3
[1,1,2,6,1,2]=>[[],[[],[[[]]]]]=>2
[1,1,2,6,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,6,2,1,2]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,2,1]=>[[],[[]],[[[]]]]=>3
[1,2,1,1,2,6]=>[[],[[],[[[]]]]]=>2
[1,2,1,1,6,2]=>[[],[[[[[]]]]]]=>2
[1,2,1,2,1,6]=>[[[],[[],[[]]]]]=>1
[1,2,1,2,6,1]=>[[[],[[[[]]]]]]=>1
[1,2,1,6,1,2]=>[[[[[]]],[[]]]]=>1
[1,2,1,6,2,1]=>[[[[[]],[[]]]]]=>1
[1,2,2,1,1,6]=>[[],[[]],[[[]]]]=>3
[1,2,2,1,6,1]=>[[[]],[[[[]]]]]=>2
[1,2,2,6,1,1]=>[[],[[]],[[[]]]]=>3
[1,2,6,1,1,2]=>[[[[]]],[[],[]]]=>2
[1,2,6,1,2,1]=>[[[[[]]],[[]]]]=>1
[1,2,6,2,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,1,1,2,2]=>[[],[[[]]],[[]]]=>3
[1,6,1,2,1,2]=>[[[[[]],[[]]]]]=>1
[1,6,1,2,2,1]=>[[[[]]],[[[]]]]=>2
[1,6,2,1,1,2]=>[[[[[]]]],[[]]]=>2
[1,6,2,1,2,1]=>[[[[[]],[[]]]]]=>1
[1,6,2,2,1,1]=>[[[]],[[]],[[]]]=>3
[2,1,1,1,2,6]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,6,2]=>[[],[],[[[[]]]]]=>3
[2,1,1,2,1,6]=>[[],[[[],[[]]]]]=>2
[2,1,1,2,6,1]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,1,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,2,1]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,1,6]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,6,1]=>[[[[]],[[[]]]]]=>1
[2,1,2,6,1,1]=>[[[[[]]]],[[]]]=>2
[2,1,6,1,1,2]=>[[[[]]],[[[]]]]=>2
[2,1,6,1,2,1]=>[[[[[]]],[[]]]]=>1
[2,1,6,2,1,1]=>[[[]],[[],[[]]]]=>2
[2,2,1,1,1,6]=>[[],[],[],[[[]]]]=>4
[2,2,1,1,6,1]=>[[],[],[[[[]]]]]=>3
[2,2,1,6,1,1]=>[[],[[[]]],[[]]]=>3
[2,2,6,1,1,1]=>[[],[],[],[[[]]]]=>4
[2,6,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[2,6,1,1,2,1]=>[[[[]]],[[[]]]]=>2
[2,6,1,2,1,1]=>[[],[[[[[]]]]]]=>2
[2,6,2,1,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[6,1,1,2,1,2]=>[[[]],[[],[[]]]]=>2
[6,1,1,2,2,1]=>[[[]],[[]],[[]]]=>3
[6,1,2,1,1,2]=>[[],[[[]],[[]]]]=>2
[6,1,2,1,2,1]=>[[[[],[[],[]]]]]=>1
[6,1,2,2,1,1]=>[[],[[[]]],[[]]]=>3
[6,2,1,1,1,2]=>[[],[],[[[[]]]]]=>3
[6,2,1,1,2,1]=>[[],[[[],[[]]]]]=>2
[6,2,1,2,1,1]=>[[],[[[]],[[]]]]=>2
[6,2,2,1,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,1,2,3,3]=>[[],[],[],[[],[]]]=>4
[1,1,1,3,2,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,3,2]=>[[],[],[[]],[[]]]=>4
[1,1,2,1,3,3]=>[[],[[]],[[[]]]]=>3
[1,1,2,3,1,3]=>[[],[[],[[[]]]]]=>2
[1,1,2,3,3,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,1,2,3]=>[[],[[[[],[]]]]]=>2
[1,1,3,1,3,2]=>[[],[[],[[[]]]]]=>2
[1,1,3,2,1,3]=>[[],[[],[[],[]]]]=>2
[1,1,3,2,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,3,3,1,2]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,2,1]=>[[],[[]],[[],[]]]=>3
[1,2,1,1,3,3]=>[[],[[]],[[[]]]]=>3
[1,2,1,3,1,3]=>[[[[[],[[]]]]]]=>1
[1,2,1,3,3,1]=>[[[]],[[[[]]]]]=>2
[1,2,3,1,1,3]=>[[[]],[[[],[]]]]=>2
[1,2,3,1,3,1]=>[[[],[[],[[]]]]]=>1
[1,2,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,3,1,1,2,3]=>[[],[[],[[[]]]]]=>2
[1,3,1,1,3,2]=>[[],[[],[[[]]]]]=>2
[1,3,1,2,1,3]=>[[[[]],[[[]]]]]=>1
[1,3,1,2,3,1]=>[[[[],[[],[]]]]]=>1
[1,3,1,3,1,2]=>[[[],[[],[[]]]]]=>1
[1,3,1,3,2,1]=>[[[],[[],[[]]]]]=>1
[1,3,2,1,1,3]=>[[],[[],[[],[]]]]=>2
[1,3,2,1,3,1]=>[[[],[[[],[]]]]]=>1
[1,3,2,3,1,1]=>[[[[]]],[[[]]]]=>2
[1,3,3,1,1,2]=>[[[]],[[]],[[]]]=>3
[1,3,3,1,2,1]=>[[[]],[[[[]]]]]=>2
[1,3,3,2,1,1]=>[[],[[]],[[],[]]]=>3
[2,1,1,1,3,3]=>[[],[],[[]],[[]]]=>4
[2,1,1,3,1,3]=>[[],[[[]],[[]]]]=>2
[2,1,1,3,3,1]=>[[],[[]],[[[]]]]=>3
[2,1,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,1,3,1,3,1]=>[[[[],[[],[]]]]]=>1
[2,1,3,3,1,1]=>[[[]],[[]],[[]]]=>3
[2,3,1,1,1,3]=>[[],[[]],[[[]]]]=>3
[2,3,1,1,3,1]=>[[],[[[],[[]]]]]=>2
[2,3,1,3,1,1]=>[[],[[[]],[[]]]]=>2
[2,3,3,1,1,1]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,2,3]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,3,2]=>[[],[],[[[[]]]]]=>3
[3,1,1,2,1,3]=>[[],[[[[[]]]]]]=>2
[3,1,1,2,3,1]=>[[],[[],[[],[]]]]=>2
[3,1,1,3,1,2]=>[[],[[[],[[]]]]]=>2
[3,1,1,3,2,1]=>[[],[[[],[[]]]]]=>2
[3,1,2,1,1,3]=>[[[[[]]]],[[]]]=>2
[3,1,2,1,3,1]=>[[[[]],[[[]]]]]=>1
[3,1,2,3,1,1]=>[[],[[],[[],[]]]]=>2
[3,1,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[3,1,3,1,2,1]=>[[[[]],[[[]]]]]=>1
[3,1,3,2,1,1]=>[[[]],[[],[[]]]]=>2
[3,2,1,1,1,3]=>[[],[],[[[],[]]]]=>3
[3,2,1,1,3,1]=>[[],[[[[],[]]]]]=>2
[3,2,1,3,1,1]=>[[[[]]],[[],[]]]=>2
[3,2,3,1,1,1]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[3,3,1,1,2,1]=>[[],[],[[[[]]]]]=>3
[3,3,1,2,1,1]=>[[],[[]],[[[]]]]=>3
[3,3,2,1,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,1,2,3,4]=>[[],[],[[],[],[]]]=>3
[1,1,1,2,4,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,2,4]=>[[],[],[[],[[]]]]=>3
[1,1,1,3,4,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,2,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,3,2]=>[[],[],[[[],[]]]]=>3
[1,1,2,1,3,4]=>[[],[[[]],[[]]]]=>2
[1,1,2,1,4,3]=>[[],[[[],[[]]]]]=>2
[1,1,2,3,1,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,3,4,1]=>[[],[[],[],[[]]]]=>2
[1,1,2,4,1,3]=>[[],[[[],[[]]]]]=>2
[1,1,2,4,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,3,1,2,4]=>[[],[[],[[[]]]]]=>2
[1,1,3,1,4,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,1,4]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,4,1]=>[[],[[],[[[]]]]]=>2
[1,1,3,4,1,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,4,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,2,3]=>[[],[[[[],[]]]]]=>2
[1,1,4,1,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,1,3]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,3,1]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,1,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,2,1]=>[[],[[[],[],[]]]]=>2
[1,2,1,1,3,4]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,4,3]=>[[],[[[],[[]]]]]=>2
[1,2,1,3,1,4]=>[[[[[[[]]]]]]]=>1
[1,2,1,3,4,1]=>[[[[]],[[[]]]]]=>1
[1,2,1,4,1,3]=>[[[[[[[]]]]]]]=>1
[1,2,1,4,3,1]=>[[[[[]],[[]]]]]=>1
[1,2,3,1,1,4]=>[[[]],[[[],[]]]]=>2
[1,2,3,1,4,1]=>[[[],[[[[]]]]]]=>1
[1,2,3,4,1,1]=>[[],[[[],[],[]]]]=>2
[1,2,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[1,2,4,1,3,1]=>[[[[[]],[[]]]]]=>1
[1,2,4,3,1,1]=>[[[]],[[[[]]]]]=>2
[1,3,1,1,2,4]=>[[[[],[]]],[[]]]=>2
[1,3,1,1,4,2]=>[[],[[[],[[]]]]]=>2
[1,3,1,2,1,4]=>[[[[[[[]]]]]]]=>1
[1,3,1,2,4,1]=>[[[[[]]],[[]]]]=>1
[1,3,1,4,1,2]=>[[[[[[[]]]]]]]=>1
[1,3,1,4,2,1]=>[[[[[],[[]]]]]]=>1
[1,3,2,1,1,4]=>[[],[[[],[[]]]]]=>2
[1,3,2,1,4,1]=>[[[[],[[[]]]]]]=>1
[1,3,2,4,1,1]=>[[[[],[]]],[[]]]=>2
[1,3,4,1,1,2]=>[[[]],[[],[[]]]]=>2
[1,3,4,1,2,1]=>[[[[[]],[[]]]]]=>1
[1,3,4,2,1,1]=>[[[[[]]]],[[]]]=>2
[1,4,1,1,2,3]=>[[[[]]],[[],[]]]=>2
[1,4,1,1,3,2]=>[[[[]]],[[[]]]]=>2
[1,4,1,2,1,3]=>[[[[[[[]]]]]]]=>1
[1,4,1,2,3,1]=>[[[[[]],[[]]]]]=>1
[1,4,1,3,1,2]=>[[[[[[[]]]]]]]=>1
[1,4,1,3,2,1]=>[[[[[],[[]]]]]]=>1
[1,4,2,1,1,3]=>[[[[]]],[[[]]]]=>2
[1,4,2,1,3,1]=>[[[[[],[[]]]]]]=>1
[1,4,2,3,1,1]=>[[],[[[]],[[]]]]=>2
[1,4,3,1,1,2]=>[[[[[]]]],[[]]]=>2
[1,4,3,1,2,1]=>[[[[[],[[]]]]]]=>1
[1,4,3,2,1,1]=>[[],[[],[],[[]]]]=>2
[2,1,1,1,3,4]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,4,3]=>[[],[],[[[],[]]]]=>3
[2,1,1,3,1,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,3,4,1]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,1,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,3,1]=>[[],[[[],[[]]]]]=>2
[2,1,3,1,1,4]=>[[[[]]],[[[]]]]=>2
[2,1,3,1,4,1]=>[[[[[[[]]]]]]]=>1
[2,1,3,4,1,1]=>[[[[[]]]],[[]]]=>2
[2,1,4,1,1,3]=>[[[[]]],[[[]]]]=>2
[2,1,4,1,3,1]=>[[[[[[[]]]]]]]=>1
[2,1,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,1,4]=>[[],[[]],[[[]]]]=>3
[2,3,1,1,4,1]=>[[[[]]],[[[]]]]=>2
[2,3,1,4,1,1]=>[[],[[[[[]]]]]]=>2
[2,3,4,1,1,1]=>[[],[],[[[],[]]]]=>3
[2,4,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,4,1,1,3,1]=>[[[]],[[],[[]]]]=>2
[2,4,1,3,1,1]=>[[],[[[],[[]]]]]=>2
[2,4,3,1,1,1]=>[[],[[]],[[[]]]]=>3
[3,1,1,1,2,4]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,4,2]=>[[],[],[[[],[]]]]=>3
[3,1,1,2,1,4]=>[[],[[[[[]]]]]]=>2
[3,1,1,2,4,1]=>[[[[[]]]],[[]]]=>2
[3,1,1,4,1,2]=>[[[[[]]]],[[]]]=>2
[3,1,1,4,2,1]=>[[],[[[],[[]]]]]=>2
[3,1,2,1,1,4]=>[[[[[]]]],[[]]]=>2
[3,1,2,1,4,1]=>[[[[[[[]]]]]]]=>1
[3,1,2,4,1,1]=>[[],[[[[[]]]]]]=>2
[3,1,4,1,1,2]=>[[[]],[[[[]]]]]=>2
[3,1,4,1,2,1]=>[[[[[[[]]]]]]]=>1
[3,1,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[3,2,1,1,1,4]=>[[],[],[[[],[]]]]=>3
[3,2,1,1,4,1]=>[[],[[[[],[]]]]]=>2
[3,2,1,4,1,1]=>[[[[]]],[[],[]]]=>2
[3,2,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[3,4,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[3,4,1,1,2,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,2,1,1]=>[[],[[[],[[]]]]]=>2
[3,4,2,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,2,3]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,3,2]=>[[],[[[]]],[[]]]=>3
[4,1,1,2,1,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,2,3,1]=>[[],[[[]],[[]]]]=>2
[4,1,1,3,1,2]=>[[[[[]]]],[[]]]=>2
[4,1,1,3,2,1]=>[[],[[[],[[]]]]]=>2
[4,1,2,1,1,3]=>[[],[[[[[]]]]]]=>2
[4,1,2,1,3,1]=>[[[[[[[]]]]]]]=>1
[4,1,2,3,1,1]=>[[],[[[],[[]]]]]=>2
[4,1,3,1,1,2]=>[[[]],[[[[]]]]]=>2
[4,1,3,1,2,1]=>[[[[[[[]]]]]]]=>1
[4,1,3,2,1,1]=>[[],[[[]],[[]]]]=>2
[4,2,1,1,1,3]=>[[],[[[]]],[[]]]=>3
[4,2,1,1,3,1]=>[[],[[[],[[]]]]]=>2
[4,2,1,3,1,1]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,1,1]=>[[],[],[[],[[]]]]=>3
[4,3,1,1,1,2]=>[[],[[[]]],[[]]]=>3
[4,3,1,1,2,1]=>[[],[[[],[[]]]]]=>2
[4,3,1,2,1,1]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,1,1]=>[[],[],[[],[],[]]]=>3
[1,1,1,2,3,5]=>[[],[],[[],[[]]]]=>3
[1,1,1,2,5,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,2,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,5,2]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,2,3]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,3,2]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,3,5]=>[[],[[[[],[]]]]]=>2
[1,1,2,1,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,2,3,1,5]=>[[],[[],[[[]]]]]=>2
[1,1,2,3,5,1]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,1,3]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,3,1]=>[[],[[[[],[]]]]]=>2
[1,1,3,1,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,3,1,5,2]=>[[],[[[[],[]]]]]=>2
[1,1,3,2,1,5]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,5,1]=>[[],[[[[],[]]]]]=>2
[1,1,3,5,1,2]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,2,1]=>[[],[[],[[[]]]]]=>2
[1,1,5,1,2,3]=>[[],[[[[],[]]]]]=>2
[1,1,5,1,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,5,2,1,3]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,3,1]=>[[],[[],[[[]]]]]=>2
[1,1,5,3,1,2]=>[[],[[[],[[]]]]]=>2
[1,1,5,3,2,1]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,3,5]=>[[],[[],[[[]]]]]=>2
[1,2,1,1,5,3]=>[[],[[[[[]]]]]]=>2
[1,2,1,3,1,5]=>[[[[[[[]]]]]]]=>1
[1,2,1,3,5,1]=>[[[[[[],[]]]]]]=>1
[1,2,1,5,1,3]=>[[[[[[[]]]]]]]=>1
[1,2,1,5,3,1]=>[[[[[],[[]]]]]]=>1
[1,2,3,1,1,5]=>[[[]],[[[],[]]]]=>2
[1,2,3,1,5,1]=>[[[],[[[[]]]]]]=>1
[1,2,3,5,1,1]=>[[],[[[[],[]]]]]=>2
[1,2,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[1,2,5,1,3,1]=>[[[[],[[[]]]]]]=>1
[1,2,5,3,1,1]=>[[],[[],[[[]]]]]=>2
[1,3,1,1,2,5]=>[[[[]]],[[[]]]]=>2
[1,3,1,1,5,2]=>[[],[[],[[[]]]]]=>2
[1,3,1,2,1,5]=>[[[[[[[]]]]]]]=>1
[1,3,1,2,5,1]=>[[[[[],[[]]]]]]=>1
[1,3,1,5,1,2]=>[[[[[[[]]]]]]]=>1
[1,3,1,5,2,1]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,1,5]=>[[],[[[],[[]]]]]=>2
[1,3,2,1,5,1]=>[[[[],[[[]]]]]]=>1
[1,3,2,5,1,1]=>[[[[]]],[[],[]]]=>2
[1,3,5,1,1,2]=>[[[]],[[[],[]]]]=>2
[1,3,5,1,2,1]=>[[[],[[[[]]]]]]=>1
[1,3,5,2,1,1]=>[[],[[[[],[]]]]]=>2
[1,5,1,1,2,3]=>[[[[]]],[[],[]]]=>2
[1,5,1,1,3,2]=>[[[[]]],[[[]]]]=>2
[1,5,1,2,1,3]=>[[[[[[[]]]]]]]=>1
[1,5,1,2,3,1]=>[[[[[]],[[]]]]]=>1
[1,5,1,3,1,2]=>[[[[[[[]]]]]]]=>1
[1,5,1,3,2,1]=>[[[[],[[[]]]]]]=>1
[1,5,2,1,1,3]=>[[],[[[[],[]]]]]=>2
[1,5,2,1,3,1]=>[[[],[[[[]]]]]]=>1
[1,5,2,3,1,1]=>[[],[[[[],[]]]]]=>2
[1,5,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[1,5,3,1,2,1]=>[[[[[[],[]]]]]]=>1
[1,5,3,2,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,1,3,5]=>[[],[],[[],[[]]]]=>3
[2,1,1,1,5,3]=>[[],[],[[[[]]]]]=>3
[2,1,1,3,1,5]=>[[],[[[[[]]]]]]=>2
[2,1,1,3,5,1]=>[[],[[],[[[]]]]]=>2
[2,1,1,5,1,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,3,1]=>[[],[[[],[[]]]]]=>2
[2,1,3,1,1,5]=>[[[[]]],[[[]]]]=>2
[2,1,3,1,5,1]=>[[[[[[[]]]]]]]=>1
[2,1,3,5,1,1]=>[[[[],[]]],[[]]]=>2
[2,1,5,1,1,3]=>[[[[]]],[[[]]]]=>2
[2,1,5,1,3,1]=>[[[[[[[]]]]]]]=>1
[2,1,5,3,1,1]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,1,5]=>[[],[[]],[[[]]]]=>3
[2,3,1,1,5,1]=>[[[[]]],[[[]]]]=>2
[2,3,1,5,1,1]=>[[],[[[[[]]]]]]=>2
[2,3,5,1,1,1]=>[[],[],[[[[]]]]]=>3
[2,5,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,5,1,1,3,1]=>[[[[]]],[[],[]]]=>2
[2,5,1,3,1,1]=>[[],[[[[],[]]]]]=>2
[2,5,3,1,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,2,5]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,5,2]=>[[],[],[[],[[]]]]=>3
[3,1,1,2,1,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,2,5,1]=>[[],[[[],[[]]]]]=>2
[3,1,1,5,1,2]=>[[[[[]]]],[[]]]=>2
[3,1,1,5,2,1]=>[[],[[],[[[]]]]]=>2
[3,1,2,1,1,5]=>[[[[[]]]],[[]]]=>2
[3,1,2,1,5,1]=>[[[[[[[]]]]]]]=>1
[3,1,2,5,1,1]=>[[],[[[]],[[]]]]=>2
[3,1,5,1,1,2]=>[[[]],[[[[]]]]]=>2
[3,1,5,1,2,1]=>[[[[[[[]]]]]]]=>1
[3,1,5,2,1,1]=>[[[]],[[[],[]]]]=>2
[3,2,1,1,1,5]=>[[],[],[[[],[]]]]=>3
[3,2,1,1,5,1]=>[[],[[[[],[]]]]]=>2
[3,2,1,5,1,1]=>[[[[]]],[[],[]]]=>2
[3,2,5,1,1,1]=>[[],[[]],[[],[]]]=>3
[3,5,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[3,5,1,1,2,1]=>[[[[]]],[[[]]]]=>2
[3,5,1,2,1,1]=>[[],[[[[[]]]]]]=>2
[3,5,2,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,1,1,1,2,3]=>[[],[[]],[[],[]]]=>3
[5,1,1,1,3,2]=>[[],[[[]]],[[]]]=>3
[5,1,1,2,1,3]=>[[[[[]]]],[[]]]=>2
[5,1,1,2,3,1]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,1,2]=>[[[[[]]]],[[]]]=>2
[5,1,1,3,2,1]=>[[[[],[]]],[[]]]=>2
[5,1,2,1,1,3]=>[[],[[[[[]]]]]]=>2
[5,1,2,1,3,1]=>[[[[[[[]]]]]]]=>1
[5,1,2,3,1,1]=>[[],[[[],[[]]]]]=>2
[5,1,3,1,1,2]=>[[[]],[[[[]]]]]=>2
[5,1,3,1,2,1]=>[[[[[[[]]]]]]]=>1
[5,1,3,2,1,1]=>[[],[[],[[[]]]]]=>2
[5,2,1,1,1,3]=>[[],[[[]]],[[]]]=>3
[5,2,1,1,3,1]=>[[[[[]]]],[[]]]=>2
[5,2,1,3,1,1]=>[[[[[]]]],[[]]]=>2
[5,2,3,1,1,1]=>[[],[[]],[[[]]]]=>3
[5,3,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[5,3,1,1,2,1]=>[[],[[[[],[]]]]]=>2
[5,3,1,2,1,1]=>[[[[]]],[[],[]]]=>2
[5,3,2,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,2,3,6]=>[[],[],[[],[[]]]]=>3
[1,1,1,2,6,3]=>[[],[],[[[],[]]]]=>3
[1,1,1,3,2,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,3,6,2]=>[[],[],[[[],[]]]]=>3
[1,1,1,6,2,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,3,2]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,3,6]=>[[],[[[[[]]]]]]=>2
[1,1,2,1,6,3]=>[[],[[[[[]]]]]]=>2
[1,1,2,3,1,6]=>[[],[[],[[],[]]]]=>2
[1,1,2,3,6,1]=>[[],[[],[[[]]]]]=>2
[1,1,2,6,1,3]=>[[],[[[[],[]]]]]=>2
[1,1,2,6,3,1]=>[[],[[[],[[]]]]]=>2
[1,1,3,1,2,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,1,6,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,1,6]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,6,1]=>[[],[[[]],[[]]]]=>2
[1,1,3,6,1,2]=>[[],[[[]],[[]]]]=>2
[1,1,3,6,2,1]=>[[],[[[],[[]]]]]=>2
[1,1,6,1,2,3]=>[[],[[[],[[]]]]]=>2
[1,1,6,1,3,2]=>[[],[[[[],[]]]]]=>2
[1,1,6,2,1,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,3,1]=>[[],[[],[[[]]]]]=>2
[1,1,6,3,1,2]=>[[],[[[]],[[]]]]=>2
[1,1,6,3,2,1]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,3,6]=>[[],[[[[[]]]]]]=>2
[1,2,1,1,6,3]=>[[],[[[[[]]]]]]=>2
[1,2,1,3,1,6]=>[[[[[],[[]]]]]]=>1
[1,2,1,3,6,1]=>[[[[[],[[]]]]]]=>1
[1,2,1,6,1,3]=>[[[[[],[[]]]]]]=>1
[1,2,1,6,3,1]=>[[[[[],[[]]]]]]=>1
[1,2,3,1,1,6]=>[[],[[],[[],[]]]]=>2
[1,2,3,1,6,1]=>[[[],[[],[[]]]]]=>1
[1,2,3,6,1,1]=>[[],[[[[],[]]]]]=>2
[1,2,6,1,1,3]=>[[],[[],[[[]]]]]=>2
[1,2,6,1,3,1]=>[[[[[],[[]]]]]]=>1
[1,2,6,3,1,1]=>[[],[[[],[[]]]]]=>2
[1,3,1,1,2,6]=>[[[[]]],[[[]]]]=>2
[1,3,1,1,6,2]=>[[],[[[]],[[]]]]=>2
[1,3,1,2,1,6]=>[[[[],[[[]]]]]]=>1
[1,3,1,2,6,1]=>[[[],[[[[]]]]]]=>1
[1,3,1,6,1,2]=>[[[[]],[[],[]]]]=>1
[1,3,1,6,2,1]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,1,6]=>[[],[[[],[[]]]]]=>2
[1,3,2,1,6,1]=>[[[[]],[[],[]]]]=>1
[1,3,2,6,1,1]=>[[[]],[[],[[]]]]=>2
[1,3,6,1,1,2]=>[[[]],[[],[[]]]]=>2
[1,3,6,1,2,1]=>[[[[[]]],[[]]]]=>1
[1,3,6,2,1,1]=>[[],[[[],[[]]]]]=>2
[1,6,1,1,2,3]=>[[[]],[[],[[]]]]=>2
[1,6,1,1,3,2]=>[[],[[],[[[]]]]]=>2
[1,6,1,2,1,3]=>[[[[],[[[]]]]]]=>1
[1,6,1,2,3,1]=>[[[],[[],[[]]]]]=>1
[1,6,1,3,1,2]=>[[[[]],[[],[]]]]=>1
[1,6,1,3,2,1]=>[[[[],[[],[]]]]]=>1
[1,6,2,1,1,3]=>[[[[[]]]],[[]]]=>2
[1,6,2,1,3,1]=>[[[[]],[[[]]]]]=>1
[1,6,2,3,1,1]=>[[],[[],[[[]]]]]=>2
[1,6,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[1,6,3,1,2,1]=>[[[],[[[[]]]]]]=>1
[1,6,3,2,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,1,3,6]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,6,3]=>[[],[],[[[[]]]]]=>3
[2,1,1,3,1,6]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,6,1]=>[[],[[[]],[[]]]]=>2
[2,1,1,6,1,3]=>[[],[[[],[[]]]]]=>2
[2,1,1,6,3,1]=>[[],[[[]],[[]]]]=>2
[2,1,3,1,1,6]=>[[],[[[]],[[]]]]=>2
[2,1,3,1,6,1]=>[[[[],[[],[]]]]]=>1
[2,1,3,6,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,6,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,1,6,1,3,1]=>[[[[],[[],[]]]]]=>1
[2,1,6,3,1,1]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,1,6]=>[[],[],[[],[[]]]]=>3
[2,3,1,1,6,1]=>[[],[[[]],[[]]]]=>2
[2,3,1,6,1,1]=>[[],[[[],[[]]]]]=>2
[2,3,6,1,1,1]=>[[],[],[[[[]]]]]=>3
[2,6,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,6,1,1,3,1]=>[[[]],[[],[[]]]]=>2
[2,6,1,3,1,1]=>[[],[[[],[[]]]]]=>2
[2,6,3,1,1,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,1,2,6]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,6,2]=>[[],[],[[],[[]]]]=>3
[3,1,1,2,1,6]=>[[],[[[[],[]]]]]=>2
[3,1,1,2,6,1]=>[[[[[]]]],[[]]]=>2
[3,1,1,6,1,2]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,2,1]=>[[],[[],[[[]]]]]=>2
[3,1,2,1,1,6]=>[[],[[],[[[]]]]]=>2
[3,1,2,1,6,1]=>[[[],[[[[]]]]]]=>1
[3,1,2,6,1,1]=>[[],[[[[[]]]]]]=>2
[3,1,6,1,1,2]=>[[[]],[[[],[]]]]=>2
[3,1,6,1,2,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,2,1,1]=>[[[[]]],[[],[]]]=>2
[3,2,1,1,1,6]=>[[],[],[[[],[]]]]=>3
[3,2,1,1,6,1]=>[[],[[[[],[]]]]]=>2
[3,2,1,6,1,1]=>[[[[]]],[[],[]]]=>2
[3,2,6,1,1,1]=>[[],[[[]]],[[]]]=>3
[3,6,1,1,1,2]=>[[],[[]],[[[]]]]=>3
[3,6,1,1,2,1]=>[[[[]]],[[[]]]]=>2
[3,6,1,2,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,2,1,1,1]=>[[],[],[[[],[]]]]=>3
[6,1,1,1,2,3]=>[[],[[]],[[],[]]]=>3
[6,1,1,1,3,2]=>[[],[],[[],[[]]]]=>3
[6,1,1,2,1,3]=>[[],[[[[],[]]]]]=>2
[6,1,1,2,3,1]=>[[[]],[[],[[]]]]=>2
[6,1,1,3,1,2]=>[[],[[],[[[]]]]]=>2
[6,1,1,3,2,1]=>[[],[[],[[],[]]]]=>2
[6,1,2,1,1,3]=>[[],[[],[[[]]]]]=>2
[6,1,2,1,3,1]=>[[[],[[[[]]]]]]=>1
[6,1,2,3,1,1]=>[[],[[[],[[]]]]]=>2
[6,1,3,1,1,2]=>[[[]],[[[],[]]]]=>2
[6,1,3,1,2,1]=>[[[],[[[[]]]]]]=>1
[6,1,3,2,1,1]=>[[],[[],[[],[]]]]=>2
[6,2,1,1,1,3]=>[[],[],[[[[]]]]]=>3
[6,2,1,1,3,1]=>[[],[[[[[]]]]]]=>2
[6,2,1,3,1,1]=>[[[[]]],[[[]]]]=>2
[6,2,3,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,3,1,1,1,2]=>[[[]],[[]],[[]]]=>3
[6,3,1,1,2,1]=>[[[[[]]]],[[]]]=>2
[6,3,1,2,1,1]=>[[[]],[[[[]]]]]=>2
[6,3,2,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,2,4,4]=>[[],[],[],[[[]]]]=>4
[1,1,1,4,2,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,4,2]=>[[],[],[[]],[[]]]=>4
[1,1,2,1,4,4]=>[[],[[]],[[[]]]]=>3
[1,1,2,4,1,4]=>[[],[[[[[]]]]]]=>2
[1,1,2,4,4,1]=>[[],[[[]]],[[]]]=>3
[1,1,4,1,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,4,2]=>[[],[[[]],[[]]]]=>2
[1,1,4,2,1,4]=>[[],[[[]],[[]]]]=>2
[1,1,4,2,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,4,1,2]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,2,1]=>[[],[[]],[[[]]]]=>3
[1,2,1,1,4,4]=>[[],[[]],[[[]]]]=>3
[1,2,1,4,1,4]=>[[[[[],[[]]]]]]=>1
[1,2,1,4,4,1]=>[[[]],[[[[]]]]]=>2
[1,2,4,1,1,4]=>[[[]],[[[[]]]]]=>2
[1,2,4,1,4,1]=>[[[[[],[[]]]]]]=>1
[1,2,4,4,1,1]=>[[],[[[]]],[[]]]=>3
[1,4,1,1,2,4]=>[[[[]]],[[[]]]]=>2
[1,4,1,1,4,2]=>[[[]],[[],[[]]]]=>2
[1,4,1,2,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,1,2,4,1]=>[[[[],[[[]]]]]]=>1
[1,4,1,4,1,2]=>[[[],[[],[[]]]]]=>1
[1,4,1,4,2,1]=>[[[],[[[[]]]]]]=>1
[1,4,2,1,1,4]=>[[[]],[[],[[]]]]=>2
[1,4,2,1,4,1]=>[[[[[]]],[[]]]]=>1
[1,4,2,4,1,1]=>[[],[[[[[]]]]]]=>2
[1,4,4,1,1,2]=>[[[]],[[]],[[]]]=>3
[1,4,4,1,2,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,2,1,1]=>[[],[[[]]],[[]]]=>3
[2,1,1,1,4,4]=>[[],[],[[]],[[]]]=>4
[2,1,1,4,1,4]=>[[],[[[]],[[]]]]=>2
[2,1,1,4,4,1]=>[[],[[]],[[[]]]]=>3
[2,1,4,1,1,4]=>[[[]],[[],[[]]]]=>2
[2,1,4,1,4,1]=>[[[[],[[],[]]]]]=>1
[2,1,4,4,1,1]=>[[[]],[[]],[[]]]=>3
[2,4,1,1,1,4]=>[[],[[]],[[[]]]]=>3
[2,4,1,1,4,1]=>[[],[[[],[[]]]]]=>2
[2,4,1,4,1,1]=>[[],[[[]],[[]]]]=>2
[2,4,4,1,1,1]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,2,4]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,4,2]=>[[],[[[]]],[[]]]=>3
[4,1,1,2,1,4]=>[[[[[]]]],[[]]]=>2
[4,1,1,2,4,1]=>[[],[[[[],[]]]]]=>2
[4,1,1,4,1,2]=>[[],[[[],[[]]]]]=>2
[4,1,1,4,2,1]=>[[],[[[[[]]]]]]=>2
[4,1,2,1,1,4]=>[[],[[[[[]]]]]]=>2
[4,1,2,1,4,1]=>[[[[]],[[[]]]]]=>1
[4,1,2,4,1,1]=>[[],[[],[[[]]]]]=>2
[4,1,4,1,1,2]=>[[[]],[[],[[]]]]=>2
[4,1,4,1,2,1]=>[[[[[]]],[[]]]]=>1
[4,1,4,2,1,1]=>[[[[]]],[[[]]]]=>2
[4,2,1,1,1,4]=>[[],[[[]]],[[]]]=>3
[4,2,1,1,4,1]=>[[[[[]]]],[[]]]=>2
[4,2,1,4,1,1]=>[[[[[]]]],[[]]]=>2
[4,2,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,4,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[4,4,1,1,2,1]=>[[],[[[]]],[[]]]=>3
[4,4,1,2,1,1]=>[[],[],[[[[]]]]]=>3
[4,4,2,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,4,5]=>[[],[],[[],[[]]]]=>3
[1,1,1,2,5,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,2,5]=>[[],[],[[],[[]]]]=>3
[1,1,1,4,5,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,2,4]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,4,2]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,4,5]=>[[],[[[]],[[]]]]=>2
[1,1,2,1,5,4]=>[[],[[[],[[]]]]]=>2
[1,1,2,4,1,5]=>[[],[[[[],[]]]]]=>2
[1,1,2,4,5,1]=>[[],[[[]],[[]]]]=>2
[1,1,2,5,1,4]=>[[],[[[],[],[]]]]=>2
[1,1,2,5,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,2,5]=>[[],[[],[[[]]]]]=>2
[1,1,4,1,5,2]=>[[],[[[],[],[]]]]=>2
[1,1,4,2,1,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,5,1]=>[[],[[],[],[[]]]]=>2
[1,1,4,5,1,2]=>[[],[[],[[],[]]]]=>2
[1,1,4,5,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,1,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,1,4,2]=>[[],[[[],[[]]]]]=>2
[1,1,5,2,1,4]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,4,1]=>[[],[[],[],[[]]]]=>2
[1,1,5,4,1,2]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,2,1]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,4,5]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,5,4]=>[[],[[[],[[]]]]]=>2
[1,2,1,4,1,5]=>[[[[[],[[]]]]]]=>1
[1,2,1,4,5,1]=>[[[],[[],[[]]]]]=>1
[1,2,1,5,1,4]=>[[[[[],[[]]]]]]=>1
[1,2,1,5,4,1]=>[[[[],[[],[]]]]]=>1
[1,2,4,1,1,5]=>[[],[[],[[[]]]]]=>2
[1,2,4,1,5,1]=>[[[[[],[[]]]]]]=>1
[1,2,4,5,1,1]=>[[],[[[],[[]]]]]=>2
[1,2,5,1,1,4]=>[[],[[],[],[[]]]]=>2
[1,2,5,1,4,1]=>[[[[],[],[[]]]]]=>1
[1,2,5,4,1,1]=>[[[]],[[[[]]]]]=>2
[1,4,1,1,2,5]=>[[[[],[]]],[[]]]=>2
[1,4,1,1,5,2]=>[[[]],[[],[],[]]]=>2
[1,4,1,2,1,5]=>[[[[[[],[]]]]]]=>1
[1,4,1,2,5,1]=>[[[],[],[[[]]]]]=>1
[1,4,1,5,1,2]=>[[[[]],[[],[]]]]=>1
[1,4,1,5,2,1]=>[[[[],[],[[]]]]]=>1
[1,4,2,1,1,5]=>[[[[[]]]],[[]]]=>2
[1,4,2,1,5,1]=>[[[[[]]],[[]]]]=>1
[1,4,2,5,1,1]=>[[],[[],[],[[]]]]=>2
[1,4,5,1,1,2]=>[[[],[]],[[],[]]]=>2
[1,4,5,1,2,1]=>[[[],[[],[[]]]]]=>1
[1,4,5,2,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,1,1,2,4]=>[[[[]]],[[[]]]]=>2
[1,5,1,1,4,2]=>[[[]],[[],[[]]]]=>2
[1,5,1,2,1,4]=>[[[[[[],[]]]]]]=>1
[1,5,1,2,4,1]=>[[[],[[[[]]]]]]=>1
[1,5,1,4,1,2]=>[[[[]],[[],[]]]]=>1
[1,5,1,4,2,1]=>[[[[[[],[]]]]]]=>1
[1,5,2,1,1,4]=>[[],[[[[],[]]]]]=>2
[1,5,2,1,4,1]=>[[[],[[]],[[]]]]=>1
[1,5,2,4,1,1]=>[[],[[],[],[[]]]]=>2
[1,5,4,1,1,2]=>[[[[]]],[[],[]]]=>2
[1,5,4,1,2,1]=>[[[],[[[],[]]]]]=>1
[1,5,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,1,4,5]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,5,4]=>[[],[],[[[],[]]]]=>3
[2,1,1,4,1,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,4,5,1]=>[[],[[[]],[[]]]]=>2
[2,1,1,5,1,4]=>[[],[[[],[[]]]]]=>2
[2,1,1,5,4,1]=>[[],[[],[[],[]]]]=>2
[2,1,4,1,1,5]=>[[],[[[]],[[]]]]=>2
[2,1,4,1,5,1]=>[[[[],[[],[]]]]]=>1
[2,1,4,5,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,5,1,1,4]=>[[],[[[]],[[]]]]=>2
[2,1,5,1,4,1]=>[[[[],[[],[]]]]]=>1
[2,1,5,4,1,1]=>[[[],[]],[[],[]]]=>2
[2,4,1,1,1,5]=>[[],[],[[],[[]]]]=>3
[2,4,1,1,5,1]=>[[],[[[]],[[]]]]=>2
[2,4,1,5,1,1]=>[[],[[[],[[]]]]]=>2
[2,4,5,1,1,1]=>[[],[],[[[[]]]]]=>3
[2,5,1,1,1,4]=>[[],[],[[],[],[]]]=>3
[2,5,1,1,4,1]=>[[],[[],[],[[]]]]=>2
[2,5,1,4,1,1]=>[[],[[[],[],[]]]]=>2
[2,5,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,2,5]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,5,2]=>[[],[],[[],[],[]]]=>3
[4,1,1,2,1,5]=>[[],[[[[],[]]]]]=>2
[4,1,1,2,5,1]=>[[[[],[]]],[[]]]=>2
[4,1,1,5,1,2]=>[[],[[],[[[]]]]]=>2
[4,1,1,5,2,1]=>[[],[[],[],[[]]]]=>2
[4,1,2,1,1,5]=>[[],[[],[[[]]]]]=>2
[4,1,2,1,5,1]=>[[[],[[[[]]]]]]=>1
[4,1,2,5,1,1]=>[[],[[],[[[]]]]]=>2
[4,1,5,1,1,2]=>[[[]],[[[],[]]]]=>2
[4,1,5,1,2,1]=>[[[],[[[[]]]]]]=>1
[4,1,5,2,1,1]=>[[],[[[],[],[]]]]=>2
[4,2,1,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,2,1,1,5,1]=>[[[[[]]]],[[]]]=>2
[4,2,1,5,1,1]=>[[[[[]]]],[[]]]=>2
[4,2,5,1,1,1]=>[[],[[]],[[],[]]]=>3
[4,5,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[4,5,1,1,2,1]=>[[[]],[[],[[]]]]=>2
[4,5,1,2,1,1]=>[[],[[[],[[]]]]]=>2
[4,5,2,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,1,1,1,2,4]=>[[],[[[]]],[[]]]=>3
[5,1,1,1,4,2]=>[[],[],[[],[[]]]]=>3
[5,1,1,2,1,4]=>[[],[[[[],[]]]]]=>2
[5,1,1,2,4,1]=>[[[[[]]]],[[]]]=>2
[5,1,1,4,1,2]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,2,1]=>[[],[[],[[[]]]]]=>2
[5,1,2,1,1,4]=>[[],[[],[[[]]]]]=>2
[5,1,2,1,4,1]=>[[[],[[[[]]]]]]=>1
[5,1,2,4,1,1]=>[[],[[[[[]]]]]]=>2
[5,1,4,1,1,2]=>[[[]],[[[],[]]]]=>2
[5,1,4,1,2,1]=>[[[],[[[[]]]]]]=>1
[5,1,4,2,1,1]=>[[[[],[]]],[[]]]=>2
[5,2,1,1,1,4]=>[[],[[[]]],[[]]]=>3
[5,2,1,1,4,1]=>[[],[[[],[[]]]]]=>2
[5,2,1,4,1,1]=>[[[]],[[],[[]]]]=>2
[5,2,4,1,1,1]=>[[],[],[[],[[]]]]=>3
[5,4,1,1,1,2]=>[[],[[[]]],[[]]]=>3
[5,4,1,1,2,1]=>[[[[],[]]],[[]]]=>2
[5,4,1,2,1,1]=>[[],[[],[[[]]]]]=>2
[5,4,2,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,2,4,6]=>[[],[],[[[],[]]]]=>3
[1,1,1,2,6,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,2,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,6,2]=>[[],[],[[],[[]]]]=>3
[1,1,1,6,2,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,4,2]=>[[],[],[[],[],[]]]=>3
[1,1,2,1,4,6]=>[[],[[[[[]]]]]]=>2
[1,1,2,1,6,4]=>[[],[[[[],[]]]]]=>2
[1,1,2,4,1,6]=>[[],[[[[[]]]]]]=>2
[1,1,2,4,6,1]=>[[],[[[],[],[]]]]=>2
[1,1,2,6,1,4]=>[[],[[[[[]]]]]]=>2
[1,1,2,6,4,1]=>[[],[[[],[[]]]]]=>2
[1,1,4,1,2,6]=>[[],[[[],[[]]]]]=>2
[1,1,4,1,6,2]=>[[],[[],[[[]]]]]=>2
[1,1,4,2,1,6]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,6,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,6,1,2]=>[[],[[[],[[]]]]]=>2
[1,1,4,6,2,1]=>[[],[[[]],[[]]]]=>2
[1,1,6,1,2,4]=>[[],[[[[],[]]]]]=>2
[1,1,6,1,4,2]=>[[],[[],[[[]]]]]=>2
[1,1,6,2,1,4]=>[[],[[[],[[]]]]]=>2
[1,1,6,2,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,4,1,2]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,1,1,4,6]=>[[],[[[[[]]]]]]=>2
[1,2,1,1,6,4]=>[[],[[],[[[]]]]]=>2
[1,2,1,4,1,6]=>[[[[[[[]]]]]]]=>1
[1,2,1,4,6,1]=>[[[[[],[[]]]]]]=>1
[1,2,1,6,1,4]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,4,1]=>[[[[[[],[]]]]]]=>1
[1,2,4,1,1,6]=>[[[[[]]]],[[]]]=>2
[1,2,4,1,6,1]=>[[[[],[[[]]]]]]=>1
[1,2,4,6,1,1]=>[[],[[],[],[[]]]]=>2
[1,2,6,1,1,4]=>[[[[[]]]],[[]]]=>2
[1,2,6,1,4,1]=>[[[[],[[[]]]]]]=>1
[1,2,6,4,1,1]=>[[],[[[]],[[]]]]=>2
[1,4,1,1,2,6]=>[[],[[[],[[]]]]]=>2
[1,4,1,1,6,2]=>[[[]],[[[],[]]]]=>2
[1,4,1,2,1,6]=>[[[[[[[]]]]]]]=>1
[1,4,1,2,6,1]=>[[[[[]],[[]]]]]=>1
[1,4,1,6,1,2]=>[[[[[[[]]]]]]]=>1
[1,4,1,6,2,1]=>[[[[]],[[[]]]]]=>1
[1,4,2,1,1,6]=>[[],[[],[[[]]]]]=>2
[1,4,2,1,6,1]=>[[[[[[],[]]]]]]=>1
[1,4,2,6,1,1]=>[[],[[[[[]]]]]]=>2
[1,4,6,1,1,2]=>[[[]],[[],[[]]]]=>2
[1,4,6,1,2,1]=>[[[[],[[[]]]]]]=>1
[1,4,6,2,1,1]=>[[],[[[],[[]]]]]=>2
[1,6,1,1,2,4]=>[[[[],[]]],[[]]]=>2
[1,6,1,1,4,2]=>[[[]],[[[],[]]]]=>2
[1,6,1,2,1,4]=>[[[[[[[]]]]]]]=>1
[1,6,1,2,4,1]=>[[[[[],[[]]]]]]=>1
[1,6,1,4,1,2]=>[[[[[[[]]]]]]]=>1
[1,6,1,4,2,1]=>[[[[[]]],[[]]]]=>1
[1,6,2,1,1,4]=>[[[]],[[],[[]]]]=>2
[1,6,2,1,4,1]=>[[[[],[[[]]]]]]=>1
[1,6,2,4,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,4,1,1,2]=>[[[]],[[[],[]]]]=>2
[1,6,4,1,2,1]=>[[[],[[[[]]]]]]=>1
[1,6,4,2,1,1]=>[[[]],[[],[],[]]]=>2
[2,1,1,1,4,6]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,6,4]=>[[],[],[[],[[]]]]=>3
[2,1,1,4,1,6]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,6,1]=>[[],[[[],[[]]]]]=>2
[2,1,1,6,1,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,4,1]=>[[],[[],[[[]]]]]=>2
[2,1,4,1,1,6]=>[[[[]]],[[[]]]]=>2
[2,1,4,1,6,1]=>[[[[[[[]]]]]]]=>1
[2,1,4,6,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,6,1,1,4]=>[[[[]]],[[[]]]]=>2
[2,1,6,1,4,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,4,1,1]=>[[[[],[]]],[[]]]=>2
[2,4,1,1,1,6]=>[[],[[[]]],[[]]]=>3
[2,4,1,1,6,1]=>[[[]],[[[],[]]]]=>2
[2,4,1,6,1,1]=>[[],[[],[[[]]]]]=>2
[2,4,6,1,1,1]=>[[],[],[[],[],[]]]=>3
[2,6,1,1,1,4]=>[[],[[[]]],[[]]]=>3
[2,6,1,1,4,1]=>[[[]],[[[],[]]]]=>2
[2,6,1,4,1,1]=>[[],[[],[[[]]]]]=>2
[2,6,4,1,1,1]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,2,6]=>[[],[],[[[],[]]]]=>3
[4,1,1,1,6,2]=>[[],[[]],[[[]]]]=>3
[4,1,1,2,1,6]=>[[],[[[[[]]]]]]=>2
[4,1,1,2,6,1]=>[[],[[[],[[]]]]]=>2
[4,1,1,6,1,2]=>[[[]],[[[[]]]]]=>2
[4,1,1,6,2,1]=>[[],[[[[[]]]]]]=>2
[4,1,2,1,1,6]=>[[[]],[[[[]]]]]=>2
[4,1,2,1,6,1]=>[[[[[[[]]]]]]]=>1
[4,1,2,6,1,1]=>[[],[[[],[[]]]]]=>2
[4,1,6,1,1,2]=>[[[]],[[[[]]]]]=>2
[4,1,6,1,2,1]=>[[[[[[[]]]]]]]=>1
[4,1,6,2,1,1]=>[[[]],[[[[]]]]]=>2
[4,2,1,1,1,6]=>[[],[],[[],[[]]]]=>3
[4,2,1,1,6,1]=>[[],[[],[[[]]]]]=>2
[4,2,1,6,1,1]=>[[[[],[]]],[[]]]=>2
[4,2,6,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,6,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[4,6,1,1,2,1]=>[[[[]]],[[],[]]]=>2
[4,6,1,2,1,1]=>[[],[[[[],[]]]]]=>2
[4,6,2,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,1,1,1,2,4]=>[[],[],[[[],[]]]]=>3
[6,1,1,1,4,2]=>[[],[[]],[[[]]]]=>3
[6,1,1,2,1,4]=>[[[[[]]]],[[]]]=>2
[6,1,1,2,4,1]=>[[],[[[],[[]]]]]=>2
[6,1,1,4,1,2]=>[[[]],[[[[]]]]]=>2
[6,1,1,4,2,1]=>[[[]],[[[[]]]]]=>2
[6,1,2,1,1,4]=>[[],[[[[[]]]]]]=>2
[6,1,2,1,4,1]=>[[[[[[[]]]]]]]=>1
[6,1,2,4,1,1]=>[[],[[[],[[]]]]]=>2
[6,1,4,1,1,2]=>[[[]],[[[[]]]]]=>2
[6,1,4,1,2,1]=>[[[[[[[]]]]]]]=>1
[6,1,4,2,1,1]=>[[[[[]]]],[[]]]=>2
[6,2,1,1,1,4]=>[[],[],[[],[[]]]]=>3
[6,2,1,1,4,1]=>[[],[[],[[[]]]]]=>2
[6,2,1,4,1,1]=>[[[[],[]]],[[]]]=>2
[6,2,4,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,4,1,1,1,2]=>[[[]],[[]],[[]]]=>3
[6,4,1,1,2,1]=>[[[[[]]]],[[]]]=>2
[6,4,1,2,1,1]=>[[[]],[[[[]]]]]=>2
[6,4,2,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,2,5,5]=>[[],[],[],[[[]]]]=>4
[1,1,1,5,2,5]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,5,2]=>[[],[],[],[[],[]]]=>4
[1,1,2,1,5,5]=>[[],[[]],[[[]]]]=>3
[1,1,2,5,1,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,5,1]=>[[],[],[[],[[]]]]=>3
[1,1,5,1,2,5]=>[[],[[[],[[]]]]]=>2
[1,1,5,1,5,2]=>[[],[[],[],[[]]]]=>2
[1,1,5,2,1,5]=>[[],[[],[],[[]]]]=>2
[1,1,5,2,5,1]=>[[],[[],[[],[]]]]=>2
[1,1,5,5,1,2]=>[[],[[[]]],[[]]]=>3
[1,1,5,5,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,1,1,5,5]=>[[],[[]],[[[]]]]=>3
[1,2,1,5,1,5]=>[[[[[],[[]]]]]]=>1
[1,2,1,5,5,1]=>[[[[[]]]],[[]]]=>2
[1,2,5,1,1,5]=>[[[]],[[],[[]]]]=>2
[1,2,5,1,5,1]=>[[[[],[],[[]]]]]=>1
[1,2,5,5,1,1]=>[[],[],[[],[[]]]]=>3
[1,5,1,1,2,5]=>[[],[[[],[[]]]]]=>2
[1,5,1,1,5,2]=>[[[]],[[],[],[]]]=>2
[1,5,1,2,1,5]=>[[[],[[[[]]]]]]=>1
[1,5,1,2,5,1]=>[[[[[],[],[]]]]]=>1
[1,5,1,5,1,2]=>[[[],[[],[[]]]]]=>1
[1,5,1,5,2,1]=>[[[],[[]],[[]]]]=>1
[1,5,2,1,1,5]=>[[],[[],[],[[]]]]=>2
[1,5,2,1,5,1]=>[[[],[],[[[]]]]]=>1
[1,5,2,5,1,1]=>[[],[[],[[],[]]]]=>2
[1,5,5,1,1,2]=>[[[]],[[]],[[]]]=>3
[1,5,5,1,2,1]=>[[[[[]]]],[[]]]=>2
[1,5,5,2,1,1]=>[[],[],[[[],[]]]]=>3
[2,1,1,1,5,5]=>[[],[],[[]],[[]]]=>4
[2,1,1,5,1,5]=>[[],[[[]],[[]]]]=>2
[2,1,1,5,5,1]=>[[],[[[]]],[[]]]=>3
[2,1,5,1,1,5]=>[[[]],[[],[[]]]]=>2
[2,1,5,1,5,1]=>[[[[],[[],[]]]]]=>1
[2,1,5,5,1,1]=>[[[]],[[]],[[]]]=>3
[2,5,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[2,5,1,1,5,1]=>[[],[[[],[],[]]]]=>2
[2,5,1,5,1,1]=>[[],[[],[],[[]]]]=>2
[2,5,5,1,1,1]=>[[],[],[],[[],[]]]=>4
[5,1,1,1,2,5]=>[[],[],[[[],[]]]]=>3
[5,1,1,1,5,2]=>[[],[[]],[[],[]]]=>3
[5,1,1,2,1,5]=>[[[[[]]]],[[]]]=>2
[5,1,1,2,5,1]=>[[],[[[],[],[]]]]=>2
[5,1,1,5,1,2]=>[[],[[[],[[]]]]]=>2
[5,1,1,5,2,1]=>[[],[[[]],[[]]]]=>2
[5,1,2,1,1,5]=>[[],[[[[[]]]]]]=>2
[5,1,2,1,5,1]=>[[[[]],[[[]]]]]=>1
[5,1,2,5,1,1]=>[[],[[],[],[[]]]]=>2
[5,1,5,1,1,2]=>[[[]],[[],[[]]]]=>2
[5,1,5,1,2,1]=>[[[[[]]],[[]]]]=>1
[5,1,5,2,1,1]=>[[],[[[],[[]]]]]=>2
[5,2,1,1,1,5]=>[[],[],[[],[[]]]]=>3
[5,2,1,1,5,1]=>[[],[[],[[[]]]]]=>2
[5,2,1,5,1,1]=>[[[[],[]]],[[]]]=>2
[5,2,5,1,1,1]=>[[],[],[[],[[]]]]=>3
[5,5,1,1,1,2]=>[[],[],[[]],[[]]]=>4
[5,5,1,1,2,1]=>[[],[[[]]],[[]]]=>3
[5,5,1,2,1,1]=>[[],[],[[[[]]]]]=>3
[5,5,2,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,2,5,6]=>[[],[],[[],[[]]]]=>3
[1,1,1,2,6,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,2,6]=>[[],[],[[],[],[]]]=>3
[1,1,1,5,6,2]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,2,5]=>[[],[],[[[],[]]]]=>3
[1,1,1,6,5,2]=>[[],[],[[[[]]]]]=>3
[1,1,2,1,5,6]=>[[],[[[]],[[]]]]=>2
[1,1,2,1,6,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,1,6]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,6,1]=>[[],[[[]],[[]]]]=>2
[1,1,2,6,1,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,6,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,1,2,6]=>[[],[[],[[[]]]]]=>2
[1,1,5,1,6,2]=>[[],[[[[],[]]]]]=>2
[1,1,5,2,1,6]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,6,1]=>[[],[[],[],[[]]]]=>2
[1,1,5,6,1,2]=>[[],[[[],[[]]]]]=>2
[1,1,5,6,2,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,5,2]=>[[],[[[],[[]]]]]=>2
[1,1,6,2,1,5]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,5,1]=>[[],[[[],[],[]]]]=>2
[1,1,6,5,1,2]=>[[],[[[[[]]]]]]=>2
[1,1,6,5,2,1]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,5,6]=>[[],[[[],[[]]]]]=>2
[1,2,1,1,6,5]=>[[],[[[],[[]]]]]=>2
[1,2,1,5,1,6]=>[[[[[[[]]]]]]]=>1
[1,2,1,5,6,1]=>[[[[[]]],[[]]]]=>1
[1,2,1,6,1,5]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,5,1]=>[[[[],[[[]]]]]]=>1
[1,2,5,1,1,6]=>[[[]],[[],[[]]]]=>2
[1,2,5,1,6,1]=>[[[[],[[[]]]]]]=>1
[1,2,5,6,1,1]=>[[],[[[],[[]]]]]=>2
[1,2,6,1,1,5]=>[[[]],[[],[[]]]]=>2
[1,2,6,1,5,1]=>[[[[[]],[[]]]]]=>1
[1,2,6,5,1,1]=>[[[]],[[[[]]]]]=>2
[1,5,1,1,2,6]=>[[[[],[]]],[[]]]=>2
[1,5,1,1,6,2]=>[[[]],[[[],[]]]]=>2
[1,5,1,2,1,6]=>[[[[[[[]]]]]]]=>1
[1,5,1,2,6,1]=>[[[[[]]],[[]]]]=>1
[1,5,1,6,1,2]=>[[[[[[[]]]]]]]=>1
[1,5,1,6,2,1]=>[[[[],[[[]]]]]]=>1
[1,5,2,1,1,6]=>[[[[]]],[[],[]]]=>2
[1,5,2,1,6,1]=>[[[],[[[[]]]]]]=>1
[1,5,2,6,1,1]=>[[],[[[],[],[]]]]=>2
[1,5,6,1,1,2]=>[[[]],[[],[[]]]]=>2
[1,5,6,1,2,1]=>[[[[[],[[]]]]]]=>1
[1,5,6,2,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,1,1,2,5]=>[[[[]]],[[[]]]]=>2
[1,6,1,1,5,2]=>[[[]],[[],[[]]]]=>2
[1,6,1,2,1,5]=>[[[[[[[]]]]]]]=>1
[1,6,1,2,5,1]=>[[[[],[[[]]]]]]=>1
[1,6,1,5,1,2]=>[[[[[[[]]]]]]]=>1
[1,6,1,5,2,1]=>[[[[[],[[]]]]]]=>1
[1,6,2,1,1,5]=>[[[[[]]]],[[]]]=>2
[1,6,2,1,5,1]=>[[[[[],[[]]]]]]=>1
[1,6,2,5,1,1]=>[[],[[],[],[[]]]]=>2
[1,6,5,1,1,2]=>[[[[]]],[[[]]]]=>2
[1,6,5,1,2,1]=>[[[[],[[[]]]]]]=>1
[1,6,5,2,1,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,1,5,6]=>[[],[],[[[[]]]]]=>3
[2,1,1,1,6,5]=>[[],[],[[[],[]]]]=>3
[2,1,1,5,1,6]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,6,1]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,1,5]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,5,1]=>[[],[[[[],[]]]]]=>2
[2,1,5,1,1,6]=>[[[[]]],[[[]]]]=>2
[2,1,5,1,6,1]=>[[[[[[[]]]]]]]=>1
[2,1,5,6,1,1]=>[[[[[]]]],[[]]]=>2
[2,1,6,1,1,5]=>[[[[]]],[[[]]]]=>2
[2,1,6,1,5,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,5,1,1]=>[[[[]]],[[],[]]]=>2
[2,5,1,1,1,6]=>[[],[[]],[[],[]]]=>3
[2,5,1,1,6,1]=>[[[[]]],[[],[]]]=>2
[2,5,1,6,1,1]=>[[],[[[[],[]]]]]=>2
[2,5,6,1,1,1]=>[[],[],[[[[]]]]]=>3
[2,6,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[2,6,1,1,5,1]=>[[[]],[[],[[]]]]=>2
[2,6,1,5,1,1]=>[[],[[[],[[]]]]]=>2
[2,6,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,1,1,1,2,6]=>[[],[[[]]],[[]]]=>3
[5,1,1,1,6,2]=>[[],[],[[[],[]]]]=>3
[5,1,1,2,1,6]=>[[[[[]]]],[[]]]=>2
[5,1,1,2,6,1]=>[[[[[]]]],[[]]]=>2
[5,1,1,6,1,2]=>[[[]],[[[[]]]]]=>2
[5,1,1,6,2,1]=>[[],[[[[],[]]]]]=>2
[5,1,2,1,1,6]=>[[],[[[[[]]]]]]=>2
[5,1,2,1,6,1]=>[[[[[[[]]]]]]]=>1
[5,1,2,6,1,1]=>[[],[[[[[]]]]]]=>2
[5,1,6,1,1,2]=>[[[]],[[[[]]]]]=>2
[5,1,6,1,2,1]=>[[[[[[[]]]]]]]=>1
[5,1,6,2,1,1]=>[[[]],[[[],[]]]]=>2
[5,2,1,1,1,6]=>[[],[[]],[[[]]]]=>3
[5,2,1,1,6,1]=>[[[]],[[[[]]]]]=>2
[5,2,1,6,1,1]=>[[[[[]]]],[[]]]=>2
[5,2,6,1,1,1]=>[[],[],[[[],[]]]]=>3
[5,6,1,1,1,2]=>[[],[[]],[[],[]]]=>3
[5,6,1,1,2,1]=>[[[]],[[],[[]]]]=>2
[5,6,1,2,1,1]=>[[],[[[],[[]]]]]=>2
[5,6,2,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,1,1,1,2,5]=>[[],[[[]]],[[]]]=>3
[6,1,1,1,5,2]=>[[],[[]],[[],[]]]=>3
[6,1,1,2,1,5]=>[[[[[]]]],[[]]]=>2
[6,1,1,2,5,1]=>[[[[],[]]],[[]]]=>2
[6,1,1,5,1,2]=>[[[]],[[[[]]]]]=>2
[6,1,1,5,2,1]=>[[[]],[[],[[]]]]=>2
[6,1,2,1,1,5]=>[[],[[[[[]]]]]]=>2
[6,1,2,1,5,1]=>[[[[[[[]]]]]]]=>1
[6,1,2,5,1,1]=>[[],[[],[[[]]]]]=>2
[6,1,5,1,1,2]=>[[[]],[[[[]]]]]=>2
[6,1,5,1,2,1]=>[[[[[[[]]]]]]]=>1
[6,1,5,2,1,1]=>[[],[[[],[[]]]]]=>2
[6,2,1,1,1,5]=>[[],[[]],[[[]]]]=>3
[6,2,1,1,5,1]=>[[],[[[],[[]]]]]=>2
[6,2,1,5,1,1]=>[[[]],[[],[[]]]]=>2
[6,2,5,1,1,1]=>[[],[],[[],[],[]]]=>3
[6,5,1,1,1,2]=>[[],[[[]]],[[]]]=>3
[6,5,1,1,2,1]=>[[[[],[]]],[[]]]=>2
[6,5,1,2,1,1]=>[[],[[],[[[]]]]]=>2
[6,5,2,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,3,3,3]=>[[],[],[],[],[[]]]=>5
[1,1,3,1,3,3]=>[[],[],[[],[[]]]]=>3
[1,1,3,3,1,3]=>[[],[],[[[],[]]]]=>3
[1,1,3,3,3,1]=>[[],[],[[]],[[]]]=>4
[1,3,1,1,3,3]=>[[],[],[[],[[]]]]=>3
[1,3,1,3,1,3]=>[[[],[],[[],[]]]]=>1
[1,3,1,3,3,1]=>[[[],[]],[[],[]]]=>2
[1,3,3,1,1,3]=>[[],[[]],[[],[]]]=>3
[1,3,3,1,3,1]=>[[],[[],[[],[]]]]=>2
[1,3,3,3,1,1]=>[[],[],[[]],[[]]]=>4
[3,1,1,1,3,3]=>[[],[],[],[[[]]]]=>4
[3,1,1,3,1,3]=>[[],[[],[[],[]]]]=>2
[3,1,1,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,1,3,1,1,3]=>[[[],[]],[[],[]]]=>2
[3,1,3,1,3,1]=>[[[],[],[[],[]]]]=>1
[3,1,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[3,3,1,1,1,3]=>[[],[],[[]],[[]]]=>4
[3,3,1,1,3,1]=>[[],[],[[[],[]]]]=>3
[3,3,1,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,3,3,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,3,3,4]=>[[],[],[[]],[[]]]=>4
[1,1,1,3,4,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,3,3]=>[[],[],[],[[[]]]]=>4
[1,1,3,1,3,4]=>[[],[[[]],[[]]]]=>2
[1,1,3,1,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,3,3,1,4]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,4,1]=>[[],[[[]]],[[]]]=>3
[1,1,3,4,1,3]=>[[],[[],[[[]]]]]=>2
[1,1,3,4,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,4,3,1,3]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,3,1]=>[[],[],[[[[]]]]]=>3
[1,3,1,1,3,4]=>[[[]],[[],[[]]]]=>2
[1,3,1,1,4,3]=>[[],[[[[[]]]]]]=>2
[1,3,1,3,1,4]=>[[[],[[],[[]]]]]=>1
[1,3,1,3,4,1]=>[[[[[]]],[[]]]]=>1
[1,3,1,4,1,3]=>[[[],[[[[]]]]]]=>1
[1,3,1,4,3,1]=>[[[[[[],[]]]]]]=>1
[1,3,3,1,1,4]=>[[[]],[[]],[[]]]=>3
[1,3,3,1,4,1]=>[[[]],[[[[]]]]]=>2
[1,3,3,4,1,1]=>[[],[[]],[[[]]]]=>3
[1,3,4,1,1,3]=>[[[[]]],[[],[]]]=>2
[1,3,4,1,3,1]=>[[[[[]]],[[]]]]=>1
[1,3,4,3,1,1]=>[[[]],[[[[]]]]]=>2
[1,4,1,1,3,3]=>[[],[[]],[[[]]]]=>3
[1,4,1,3,1,3]=>[[[[],[[[]]]]]]=>1
[1,4,1,3,3,1]=>[[[[[]]]],[[]]]=>2
[1,4,3,1,1,3]=>[[[[[]]]],[[]]]=>2
[1,4,3,1,3,1]=>[[[[[]],[[]]]]]=>1
[1,4,3,3,1,1]=>[[[]],[[]],[[]]]=>3
[3,1,1,1,3,4]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,4,3]=>[[],[],[[[[]]]]]=>3
[3,1,1,3,1,4]=>[[],[[[],[[]]]]]=>2
[3,1,1,3,4,1]=>[[[[[]]]],[[]]]=>2
[3,1,1,4,1,3]=>[[[[[]]]],[[]]]=>2
[3,1,1,4,3,1]=>[[],[[[[],[]]]]]=>2
[3,1,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[3,1,3,1,4,1]=>[[[[]],[[[]]]]]=>1
[3,1,3,4,1,1]=>[[],[[[[[]]]]]]=>2
[3,1,4,1,1,3]=>[[[]],[[[[]]]]]=>2
[3,1,4,1,3,1]=>[[[],[[[[]]]]]]=>1
[3,1,4,3,1,1]=>[[[[]]],[[],[]]]=>2
[3,3,1,1,1,4]=>[[],[],[[]],[[]]]=>4
[3,3,1,1,4,1]=>[[],[[[]]],[[]]]=>3
[3,3,1,4,1,1]=>[[],[],[[[[]]]]]=>3
[3,3,4,1,1,1]=>[[],[],[],[[[]]]]=>4
[3,4,1,1,1,3]=>[[],[[]],[[[]]]]=>3
[3,4,1,1,3,1]=>[[[[]]],[[[]]]]=>2
[3,4,1,3,1,1]=>[[],[[[[[]]]]]]=>2
[3,4,3,1,1,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,1,3,3]=>[[],[],[[]],[[]]]=>4
[4,1,1,3,1,3]=>[[],[[],[[[]]]]]=>2
[4,1,1,3,3,1]=>[[],[[[]]],[[]]]=>3
[4,1,3,1,1,3]=>[[[[]]],[[],[]]]=>2
[4,1,3,1,3,1]=>[[[[],[[],[]]]]]=>1
[4,1,3,3,1,1]=>[[],[[]],[[[]]]]=>3
[4,3,1,1,1,3]=>[[],[[[]]],[[]]]=>3
[4,3,1,1,3,1]=>[[],[[[],[[]]]]]=>2
[4,3,1,3,1,1]=>[[[]],[[],[[]]]]=>2
[4,3,3,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,3,3,5]=>[[],[],[],[[],[]]]=>4
[1,1,1,3,5,3]=>[[],[],[[],[[]]]]=>3
[1,1,1,5,3,3]=>[[],[],[],[[[]]]]=>4
[1,1,3,1,3,5]=>[[],[[],[],[[]]]]=>2
[1,1,3,1,5,3]=>[[],[[[],[[]]]]]=>2
[1,1,3,3,1,5]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,5,1]=>[[],[],[[],[[]]]]=>3
[1,1,3,5,1,3]=>[[],[[],[],[[]]]]=>2
[1,1,3,5,3,1]=>[[],[[],[[],[]]]]=>2
[1,1,5,1,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,5,3,1,3]=>[[],[[[],[[]]]]]=>2
[1,1,5,3,3,1]=>[[],[[]],[[],[]]]=>3
[1,3,1,1,3,5]=>[[],[[],[],[[]]]]=>2
[1,3,1,1,5,3]=>[[],[[[],[[]]]]]=>2
[1,3,1,3,1,5]=>[[[],[[],[[]]]]]=>1
[1,3,1,3,5,1]=>[[[],[[]],[[]]]]=>1
[1,3,1,5,1,3]=>[[[],[[[[]]]]]]=>1
[1,3,1,5,3,1]=>[[[[[],[],[]]]]]=>1
[1,3,3,1,1,5]=>[[[]],[[]],[[]]]=>3
[1,3,3,1,5,1]=>[[[]],[[[[]]]]]=>2
[1,3,3,5,1,1]=>[[],[],[[[],[]]]]=>3
[1,3,5,1,1,3]=>[[[]],[[],[],[]]]=>2
[1,3,5,1,3,1]=>[[[],[[]],[[]]]]=>1
[1,3,5,3,1,1]=>[[],[[],[[],[]]]]=>2
[1,5,1,1,3,3]=>[[],[[]],[[[]]]]=>3
[1,5,1,3,1,3]=>[[[[[],[[]]]]]]=>1
[1,5,1,3,3,1]=>[[[[[]]]],[[]]]=>2
[1,5,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[1,5,3,1,3,1]=>[[[[[],[],[]]]]]=>1
[1,5,3,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,3,5]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,5,3]=>[[],[],[[[],[]]]]=>3
[3,1,1,3,1,5]=>[[],[[[],[[]]]]]=>2
[3,1,1,3,5,1]=>[[],[[[]],[[]]]]=>2
[3,1,1,5,1,3]=>[[[[[]]]],[[]]]=>2
[3,1,1,5,3,1]=>[[],[[[],[],[]]]]=>2
[3,1,3,1,1,5]=>[[[]],[[],[[]]]]=>2
[3,1,3,1,5,1]=>[[[[]],[[[]]]]]=>1
[3,1,3,5,1,1]=>[[],[[[],[[]]]]]=>2
[3,1,5,1,1,3]=>[[[]],[[[[]]]]]=>2
[3,1,5,1,3,1]=>[[[],[[[[]]]]]]=>1
[3,1,5,3,1,1]=>[[],[[],[],[[]]]]=>2
[3,3,1,1,1,5]=>[[],[],[[]],[[]]]=>4
[3,3,1,1,5,1]=>[[],[[[]]],[[]]]=>3
[3,3,1,5,1,1]=>[[],[],[[[[]]]]]=>3
[3,3,5,1,1,1]=>[[],[],[],[[[]]]]=>4
[3,5,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[3,5,1,1,3,1]=>[[[]],[[],[[]]]]=>2
[3,5,1,3,1,1]=>[[],[[[],[[]]]]]=>2
[3,5,3,1,1,1]=>[[],[],[[],[[]]]]=>3
[5,1,1,1,3,3]=>[[],[],[[]],[[]]]=>4
[5,1,1,3,1,3]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,3,1]=>[[[]],[[]],[[]]]=>3
[5,1,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[5,1,3,1,3,1]=>[[[[],[[],[]]]]]=>1
[5,1,3,3,1,1]=>[[],[[[]]],[[]]]=>3
[5,3,1,1,1,3]=>[[],[[]],[[],[]]]=>3
[5,3,1,1,3,1]=>[[],[[[],[],[]]]]=>2
[5,3,1,3,1,1]=>[[],[[],[],[[]]]]=>2
[5,3,3,1,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,1,3,3,6]=>[[],[],[[]],[[]]]=>4
[1,1,1,3,6,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,3,3]=>[[],[],[],[[[]]]]=>4
[1,1,3,1,3,6]=>[[],[[[]],[[]]]]=>2
[1,1,3,1,6,3]=>[[],[[[],[[]]]]]=>2
[1,1,3,3,1,6]=>[[],[[]],[[],[]]]=>3
[1,1,3,3,6,1]=>[[],[],[[[],[]]]]=>3
[1,1,3,6,1,3]=>[[],[[],[],[[]]]]=>2
[1,1,3,6,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,3,3]=>[[],[],[[],[[]]]]=>3
[1,1,6,3,1,3]=>[[],[[[]],[[]]]]=>2
[1,1,6,3,3,1]=>[[],[[]],[[],[]]]=>3
[1,3,1,1,3,6]=>[[[]],[[],[[]]]]=>2
[1,3,1,1,6,3]=>[[],[[[]],[[]]]]=>2
[1,3,1,3,1,6]=>[[[],[[],[],[]]]]=>1
[1,3,1,3,6,1]=>[[[],[],[[[]]]]]=>1
[1,3,1,6,1,3]=>[[[],[],[[],[]]]]=>1
[1,3,1,6,3,1]=>[[[[],[],[[]]]]]=>1
[1,3,3,1,1,6]=>[[],[[]],[[],[]]]=>3
[1,3,3,1,6,1]=>[[],[[],[[],[]]]]=>2
[1,3,3,6,1,1]=>[[],[],[[],[[]]]]=>3
[1,3,6,1,1,3]=>[[],[[],[],[[]]]]=>2
[1,3,6,1,3,1]=>[[[],[[]],[[]]]]=>1
[1,3,6,3,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,1,1,3,3]=>[[],[],[[],[[]]]]=>3
[1,6,1,3,1,3]=>[[[],[[],[],[]]]]=>1
[1,6,1,3,3,1]=>[[[],[]],[[],[]]]=>2
[1,6,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[1,6,3,1,3,1]=>[[[],[],[[[]]]]]=>1
[1,6,3,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,3,6]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,6,3]=>[[],[],[[],[[]]]]=>3
[3,1,1,3,1,6]=>[[],[[[],[],[]]]]=>2
[3,1,1,3,6,1]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,1,3]=>[[],[[],[[],[]]]]=>2
[3,1,1,6,3,1]=>[[],[[],[],[[]]]]=>2
[3,1,3,1,1,6]=>[[],[[],[],[[]]]]=>2
[3,1,3,1,6,1]=>[[[],[],[[],[]]]]=>1
[3,1,3,6,1,1]=>[[],[[],[[[]]]]]=>2
[3,1,6,1,1,3]=>[[[],[]],[[],[]]]=>2
[3,1,6,1,3,1]=>[[[],[],[[],[]]]]=>1
[3,1,6,3,1,1]=>[[],[[],[],[[]]]]=>2
[3,3,1,1,1,6]=>[[],[],[],[[],[]]]=>4
[3,3,1,1,6,1]=>[[],[],[[],[[]]]]=>3
[3,3,1,6,1,1]=>[[],[],[[[],[]]]]=>3
[3,3,6,1,1,1]=>[[],[],[],[[[]]]]=>4
[3,6,1,1,1,3]=>[[],[],[[],[[]]]]=>3
[3,6,1,1,3,1]=>[[],[[[]],[[]]]]=>2
[3,6,1,3,1,1]=>[[],[[[],[[]]]]]=>2
[3,6,3,1,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,1,3,3]=>[[],[],[],[[],[]]]=>4
[6,1,1,3,1,3]=>[[],[[],[],[[]]]]=>2
[6,1,1,3,3,1]=>[[],[[]],[[],[]]]=>3
[6,1,3,1,1,3]=>[[[]],[[],[],[]]]=>2
[6,1,3,1,3,1]=>[[[],[],[[],[]]]]=>1
[6,1,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[6,3,1,1,1,3]=>[[[]],[[]],[[]]]=>3
[6,3,1,1,3,1]=>[[[[],[]]],[[]]]=>2
[6,3,1,3,1,1]=>[[],[[],[[[]]]]]=>2
[6,3,3,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,3,4,4]=>[[],[],[],[[[]]]]=>4
[1,1,1,4,3,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,4,3]=>[[],[],[[]],[[]]]=>4
[1,1,3,1,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,3,4,1,4]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,4,1]=>[[],[[[]]],[[]]]=>3
[1,1,4,1,3,4]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,4,3]=>[[],[[[]],[[]]]]=>2
[1,1,4,3,1,4]=>[[],[[[]],[[]]]]=>2
[1,1,4,3,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,4,1,3]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,3,1]=>[[],[[]],[[[]]]]=>3
[1,3,1,1,4,4]=>[[],[],[[[[]]]]]=>3
[1,3,1,4,1,4]=>[[[[],[[[]]]]]]=>1
[1,3,1,4,4,1]=>[[[[[]]]],[[]]]=>2
[1,3,4,1,1,4]=>[[[]],[[[[]]]]]=>2
[1,3,4,1,4,1]=>[[[[[],[[]]]]]]=>1
[1,3,4,4,1,1]=>[[],[[[]]],[[]]]=>3
[1,4,1,1,3,4]=>[[[[]]],[[[]]]]=>2
[1,4,1,1,4,3]=>[[[]],[[],[[]]]]=>2
[1,4,1,3,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,1,3,4,1]=>[[[[],[[[]]]]]]=>1
[1,4,1,4,1,3]=>[[[],[[],[[]]]]]=>1
[1,4,1,4,3,1]=>[[[],[[[[]]]]]]=>1
[1,4,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[1,4,3,1,4,1]=>[[[[[]]],[[]]]]=>1
[1,4,3,4,1,1]=>[[[[]]],[[[]]]]=>2
[1,4,4,1,1,3]=>[[[]],[[]],[[]]]=>3
[1,4,4,1,3,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,3,1,1]=>[[],[[]],[[[]]]]=>3
[3,1,1,1,4,4]=>[[],[],[],[[[]]]]=>4
[3,1,1,4,1,4]=>[[],[[],[[[]]]]]=>2
[3,1,1,4,4,1]=>[[],[[[]]],[[]]]=>3
[3,1,4,1,1,4]=>[[[[]]],[[],[]]]=>2
[3,1,4,1,4,1]=>[[[[],[[],[]]]]]=>1
[3,1,4,4,1,1]=>[[],[[]],[[[]]]]=>3
[3,4,1,1,1,4]=>[[],[[]],[[[]]]]=>3
[3,4,1,1,4,1]=>[[],[[[],[[]]]]]=>2
[3,4,1,4,1,1]=>[[],[[[]],[[]]]]=>2
[3,4,4,1,1,1]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,3,4]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,4,3]=>[[],[[[]]],[[]]]=>3
[4,1,1,3,1,4]=>[[[[[]]]],[[]]]=>2
[4,1,1,3,4,1]=>[[],[[[[],[]]]]]=>2
[4,1,1,4,1,3]=>[[],[[[],[[]]]]]=>2
[4,1,1,4,3,1]=>[[],[[[[[]]]]]]=>2
[4,1,3,1,1,4]=>[[[]],[[[[]]]]]=>2
[4,1,3,1,4,1]=>[[[],[[[[]]]]]]=>1
[4,1,3,4,1,1]=>[[],[[],[[[]]]]]=>2
[4,1,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,1,4,1,3,1]=>[[[[[]]],[[]]]]=>1
[4,1,4,3,1,1]=>[[[[]]],[[[]]]]=>2
[4,3,1,1,1,4]=>[[],[[[]]],[[]]]=>3
[4,3,1,1,4,1]=>[[[[[]]]],[[]]]=>2
[4,3,1,4,1,1]=>[[[[[]]]],[[]]]=>2
[4,3,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,4,1,1,1,3]=>[[],[],[[]],[[]]]=>4
[4,4,1,1,3,1]=>[[],[[[]]],[[]]]=>3
[4,4,1,3,1,1]=>[[],[],[[[[]]]]]=>3
[4,4,3,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,3,4,5]=>[[],[],[[[],[]]]]=>3
[1,1,1,3,5,4]=>[[],[],[[],[[]]]]=>3
[1,1,1,4,3,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,5,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,3,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,4,3]=>[[],[],[[[],[]]]]=>3
[1,1,3,1,4,5]=>[[],[[[[[]]]]]]=>2
[1,1,3,1,5,4]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,1,5]=>[[],[[[[],[]]]]]=>2
[1,1,3,4,5,1]=>[[],[[[],[[]]]]]=>2
[1,1,3,5,1,4]=>[[],[[],[[],[]]]]=>2
[1,1,3,5,4,1]=>[[],[[],[[[]]]]]=>2
[1,1,4,1,3,5]=>[[],[[[[],[]]]]]=>2
[1,1,4,1,5,3]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,1,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,5,1]=>[[],[[[]],[[]]]]=>2
[1,1,4,5,1,3]=>[[],[[[]],[[]]]]=>2
[1,1,4,5,3,1]=>[[],[[[[],[]]]]]=>2
[1,1,5,1,3,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,1,4,3]=>[[],[[[],[[]]]]]=>2
[1,1,5,3,1,4]=>[[],[[[],[[]]]]]=>2
[1,1,5,3,4,1]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,1,3]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,3,1]=>[[],[[[[],[]]]]]=>2
[1,3,1,1,4,5]=>[[[[]]],[[[]]]]=>2
[1,3,1,1,5,4]=>[[],[[[[[]]]]]]=>2
[1,3,1,4,1,5]=>[[[[[],[[]]]]]]=>1
[1,3,1,4,5,1]=>[[[[[[],[]]]]]]=>1
[1,3,1,5,1,4]=>[[[[[],[[]]]]]]=>1
[1,3,1,5,4,1]=>[[[[[]],[[]]]]]=>1
[1,3,4,1,1,5]=>[[],[[],[[[]]]]]=>2
[1,3,4,1,5,1]=>[[[[[],[[]]]]]]=>1
[1,3,4,5,1,1]=>[[],[[[],[[]]]]]=>2
[1,3,5,1,1,4]=>[[],[[],[[],[]]]]=>2
[1,3,5,1,4,1]=>[[[],[[],[[]]]]]=>1
[1,3,5,4,1,1]=>[[[]],[[[],[]]]]=>2
[1,4,1,1,3,5]=>[[[[]]],[[],[]]]=>2
[1,4,1,1,5,3]=>[[[]],[[],[[]]]]=>2
[1,4,1,3,1,5]=>[[[[[[],[]]]]]]=>1
[1,4,1,3,5,1]=>[[[],[[],[[]]]]]=>1
[1,4,1,5,1,3]=>[[[[]],[[],[]]]]=>1
[1,4,1,5,3,1]=>[[[[],[[],[]]]]]=>1
[1,4,3,1,1,5]=>[[[[]]],[[[]]]]=>2
[1,4,3,1,5,1]=>[[[[[]]],[[]]]]=>1
[1,4,3,5,1,1]=>[[[]],[[],[[]]]]=>2
[1,4,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[1,4,5,1,3,1]=>[[[[]],[[[]]]]]=>1
[1,4,5,3,1,1]=>[[],[[],[[[]]]]]=>2
[1,5,1,1,3,4]=>[[[[]]],[[[]]]]=>2
[1,5,1,1,4,3]=>[[[]],[[],[[]]]]=>2
[1,5,1,3,1,4]=>[[[[[[],[]]]]]]=>1
[1,5,1,3,4,1]=>[[[],[[[[]]]]]]=>1
[1,5,1,4,1,3]=>[[[[]],[[],[]]]]=>1
[1,5,1,4,3,1]=>[[[[[[],[]]]]]]=>1
[1,5,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[1,5,3,1,4,1]=>[[[],[[[],[]]]]]=>1
[1,5,3,4,1,1]=>[[],[[],[[[]]]]]=>2
[1,5,4,1,1,3]=>[[[[]]],[[],[]]]=>2
[1,5,4,1,3,1]=>[[[],[[[[]]]]]]=>1
[1,5,4,3,1,1]=>[[[[]]],[[],[]]]=>2
[3,1,1,1,4,5]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,5,4]=>[[],[],[[[[]]]]]=>3
[3,1,1,4,1,5]=>[[],[[[],[[]]]]]=>2
[3,1,1,4,5,1]=>[[],[[],[[[]]]]]=>2
[3,1,1,5,1,4]=>[[],[[[],[[]]]]]=>2
[3,1,1,5,4,1]=>[[],[[[]],[[]]]]=>2
[3,1,4,1,1,5]=>[[[]],[[],[[]]]]=>2
[3,1,4,1,5,1]=>[[[[],[[],[]]]]]=>1
[3,1,4,5,1,1]=>[[],[[],[[[]]]]]=>2
[3,1,5,1,1,4]=>[[[]],[[],[[]]]]=>2
[3,1,5,1,4,1]=>[[[[],[[],[]]]]]=>1
[3,1,5,4,1,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,1,1,5]=>[[],[],[[],[[]]]]=>3
[3,4,1,1,5,1]=>[[],[[[]],[[]]]]=>2
[3,4,1,5,1,1]=>[[],[[[],[[]]]]]=>2
[3,4,5,1,1,1]=>[[],[],[[[],[]]]]=>3
[3,5,1,1,1,4]=>[[],[],[[],[[]]]]=>3
[3,5,1,1,4,1]=>[[],[[[]],[[]]]]=>2
[3,5,1,4,1,1]=>[[],[[[],[[]]]]]=>2
[3,5,4,1,1,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,1,3,5]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,5,3]=>[[],[],[[],[[]]]]=>3
[4,1,1,3,1,5]=>[[],[[[[],[]]]]]=>2
[4,1,1,3,5,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,5,1,3]=>[[],[[],[[[]]]]]=>2
[4,1,1,5,3,1]=>[[],[[],[[],[]]]]=>2
[4,1,3,1,1,5]=>[[[[]]],[[],[]]]=>2
[4,1,3,1,5,1]=>[[[[]],[[[]]]]]=>1
[4,1,3,5,1,1]=>[[],[[[],[[]]]]]=>2
[4,1,5,1,1,3]=>[[[]],[[[],[]]]]=>2
[4,1,5,1,3,1]=>[[[],[[[[]]]]]]=>1
[4,1,5,3,1,1]=>[[],[[],[[],[]]]]=>2
[4,3,1,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,3,1,1,5,1]=>[[[[[]]]],[[]]]=>2
[4,3,1,5,1,1]=>[[[[[]]]],[[]]]=>2
[4,3,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,5,1,1,1,3]=>[[],[[]],[[[]]]]=>3
[4,5,1,1,3,1]=>[[[[]]],[[[]]]]=>2
[4,5,1,3,1,1]=>[[],[[[[[]]]]]]=>2
[4,5,3,1,1,1]=>[[],[],[[],[[]]]]=>3
[5,1,1,1,3,4]=>[[],[[[]]],[[]]]=>3
[5,1,1,1,4,3]=>[[],[],[[],[[]]]]=>3
[5,1,1,3,1,4]=>[[],[[[[],[]]]]]=>2
[5,1,1,3,4,1]=>[[[[[]]]],[[]]]=>2
[5,1,1,4,1,3]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,3,1]=>[[],[[],[[[]]]]]=>2
[5,1,3,1,1,4]=>[[[[]]],[[],[]]]=>2
[5,1,3,1,4,1]=>[[[[]],[[[]]]]]=>1
[5,1,3,4,1,1]=>[[],[[[[[]]]]]]=>2
[5,1,4,1,1,3]=>[[[]],[[[],[]]]]=>2
[5,1,4,1,3,1]=>[[[],[[[[]]]]]]=>1
[5,1,4,3,1,1]=>[[[]],[[[],[]]]]=>2
[5,3,1,1,1,4]=>[[],[[]],[[],[]]]=>3
[5,3,1,1,4,1]=>[[[[]]],[[],[]]]=>2
[5,3,1,4,1,1]=>[[],[[[[],[]]]]]=>2
[5,3,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,4,1,1,1,3]=>[[],[[[]]],[[]]]=>3
[5,4,1,1,3,1]=>[[[[[]]]],[[]]]=>2
[5,4,1,3,1,1]=>[[[[[]]]],[[]]]=>2
[5,4,3,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,3,4,6]=>[[],[],[[],[[]]]]=>3
[1,1,1,3,6,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,4,3,6]=>[[],[],[[],[[]]]]=>3
[1,1,1,4,6,3]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,3,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,4,3]=>[[],[],[[],[[]]]]=>3
[1,1,3,1,4,6]=>[[],[[],[[[]]]]]=>2
[1,1,3,1,6,4]=>[[],[[[],[],[]]]]=>2
[1,1,3,4,1,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,6,1]=>[[],[[],[],[[]]]]=>2
[1,1,3,6,1,4]=>[[],[[],[[],[]]]]=>2
[1,1,3,6,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,4,1,3,6]=>[[],[[],[[[]]]]]=>2
[1,1,4,1,6,3]=>[[],[[[[],[]]]]]=>2
[1,1,4,3,1,6]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,6,1]=>[[],[[],[[[]]]]]=>2
[1,1,4,6,1,3]=>[[],[[[],[],[]]]]=>2
[1,1,4,6,3,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,3,4]=>[[],[[[],[[]]]]]=>2
[1,1,6,1,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,1,4]=>[[],[[[]],[[]]]]=>2
[1,1,6,3,4,1]=>[[],[[[[],[]]]]]=>2
[1,1,6,4,1,3]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,3,1]=>[[],[[],[],[[]]]]=>2
[1,3,1,1,4,6]=>[[[[],[]]],[[]]]=>2
[1,3,1,1,6,4]=>[[],[[],[],[[]]]]=>2
[1,3,1,4,1,6]=>[[[[[[],[]]]]]]=>1
[1,3,1,4,6,1]=>[[[],[[]],[[]]]]=>1
[1,3,1,6,1,4]=>[[[[]],[[],[]]]]=>1
[1,3,1,6,4,1]=>[[[[],[],[[]]]]]=>1
[1,3,4,1,1,6]=>[[[[[]]]],[[]]]=>2
[1,3,4,1,6,1]=>[[[],[[[[]]]]]]=>1
[1,3,4,6,1,1]=>[[],[[],[],[[]]]]=>2
[1,3,6,1,1,4]=>[[[],[]],[[],[]]]=>2
[1,3,6,1,4,1]=>[[[],[[],[[]]]]]=>1
[1,3,6,4,1,1]=>[[],[[[[[]]]]]]=>2
[1,4,1,1,3,6]=>[[[[],[]]],[[]]]=>2
[1,4,1,1,6,3]=>[[[]],[[[],[]]]]=>2
[1,4,1,3,1,6]=>[[[[[],[[]]]]]]=>1
[1,4,1,3,6,1]=>[[[],[[],[[]]]]]=>1
[1,4,1,6,1,3]=>[[[[[],[[]]]]]]=>1
[1,4,1,6,3,1]=>[[[[],[[],[]]]]]=>1
[1,4,3,1,1,6]=>[[],[[[]],[[]]]]=>2
[1,4,3,1,6,1]=>[[[[],[[[]]]]]]=>1
[1,4,3,6,1,1]=>[[[[],[]]],[[]]]=>2
[1,4,6,1,1,3]=>[[],[[],[],[[]]]]=>2
[1,4,6,1,3,1]=>[[[[],[],[[]]]]]=>1
[1,4,6,3,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,1,1,3,4]=>[[[]],[[],[[]]]]=>2
[1,6,1,1,4,3]=>[[[]],[[[[]]]]]=>2
[1,6,1,3,1,4]=>[[[[]],[[],[]]]]=>1
[1,6,1,3,4,1]=>[[[[],[[[]]]]]]=>1
[1,6,1,4,1,3]=>[[[[[[],[]]]]]]=>1
[1,6,1,4,3,1]=>[[[],[[[[]]]]]]=>1
[1,6,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[1,6,3,1,4,1]=>[[[],[[[],[]]]]]=>1
[1,6,3,4,1,1]=>[[],[[],[[[]]]]]=>2
[1,6,4,1,1,3]=>[[[]],[[[],[]]]]=>2
[1,6,4,1,3,1]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,1,1]=>[[[]],[[],[],[]]]=>2
[3,1,1,1,4,6]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,6,4]=>[[],[],[[],[],[]]]=>3
[3,1,1,4,1,6]=>[[],[[[[],[]]]]]=>2
[3,1,1,4,6,1]=>[[],[[[],[[]]]]]=>2
[3,1,1,6,1,4]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,4,1]=>[[],[[],[],[[]]]]=>2
[3,1,4,1,1,6]=>[[[[]]],[[],[]]]=>2
[3,1,4,1,6,1]=>[[[[]],[[[]]]]]=>1
[3,1,4,6,1,1]=>[[],[[[]],[[]]]]=>2
[3,1,6,1,1,4]=>[[[[],[]]],[[]]]=>2
[3,1,6,1,4,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,4,1,1]=>[[],[[[],[],[]]]]=>2
[3,4,1,1,1,6]=>[[],[[[]]],[[]]]=>3
[3,4,1,1,6,1]=>[[[[]]],[[[]]]]=>2
[3,4,1,6,1,1]=>[[],[[[[[]]]]]]=>2
[3,4,6,1,1,1]=>[[],[],[[],[[]]]]=>3
[3,6,1,1,1,4]=>[[],[[]],[[],[]]]=>3
[3,6,1,1,4,1]=>[[[]],[[],[[]]]]=>2
[3,6,1,4,1,1]=>[[],[[[],[[]]]]]=>2
[3,6,4,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,3,6]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,6,3]=>[[],[],[[[],[]]]]=>3
[4,1,1,3,1,6]=>[[],[[[],[[]]]]]=>2
[4,1,1,3,6,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,6,1,3]=>[[],[[[],[[]]]]]=>2
[4,1,1,6,3,1]=>[[],[[],[[],[]]]]=>2
[4,1,3,1,1,6]=>[[[]],[[],[[]]]]=>2
[4,1,3,1,6,1]=>[[[[],[[],[]]]]]=>1
[4,1,3,6,1,1]=>[[],[[[]],[[]]]]=>2
[4,1,6,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,1,6,1,3,1]=>[[[[],[[],[]]]]]=>1
[4,1,6,3,1,1]=>[[],[[],[[],[]]]]=>2
[4,3,1,1,1,6]=>[[],[],[[],[[]]]]=>3
[4,3,1,1,6,1]=>[[],[[],[[[]]]]]=>2
[4,3,1,6,1,1]=>[[[[],[]]],[[]]]=>2
[4,3,6,1,1,1]=>[[],[[[]]],[[]]]=>3
[4,6,1,1,1,3]=>[[],[],[[],[],[]]]=>3
[4,6,1,1,3,1]=>[[],[[],[],[[]]]]=>2
[4,6,1,3,1,1]=>[[],[[[],[],[]]]]=>2
[4,6,3,1,1,1]=>[[],[[[]]],[[]]]=>3
[6,1,1,1,3,4]=>[[],[],[[],[[]]]]=>3
[6,1,1,1,4,3]=>[[],[[]],[[[]]]]=>3
[6,1,1,3,1,4]=>[[],[[],[[[]]]]]=>2
[6,1,1,3,4,1]=>[[],[[],[[[]]]]]=>2
[6,1,1,4,1,3]=>[[],[[[[],[]]]]]=>2
[6,1,1,4,3,1]=>[[[]],[[[[]]]]]=>2
[6,1,3,1,1,4]=>[[[]],[[[],[]]]]=>2
[6,1,3,1,4,1]=>[[[],[[[[]]]]]]=>1
[6,1,3,4,1,1]=>[[],[[[[],[]]]]]=>2
[6,1,4,1,1,3]=>[[[[]]],[[],[]]]=>2
[6,1,4,1,3,1]=>[[[[[]]],[[]]]]=>1
[6,1,4,3,1,1]=>[[[]],[[[[]]]]]=>2
[6,3,1,1,1,4]=>[[[]],[[]],[[]]]=>3
[6,3,1,1,4,1]=>[[[[],[]]],[[]]]=>2
[6,3,1,4,1,1]=>[[],[[],[[[]]]]]=>2
[6,3,4,1,1,1]=>[[],[],[[],[[]]]]=>3
[6,4,1,1,1,3]=>[[[]],[[]],[[]]]=>3
[6,4,1,1,3,1]=>[[[[],[]]],[[]]]=>2
[6,4,1,3,1,1]=>[[],[[],[[[]]]]]=>2
[6,4,3,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,3,5,5]=>[[],[],[],[[],[]]]=>4
[1,1,1,5,3,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,5,3]=>[[],[],[[]],[[]]]=>4
[1,1,3,1,5,5]=>[[],[],[[[[]]]]]=>3
[1,1,3,5,1,5]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,5,1]=>[[],[[]],[[],[]]]=>3
[1,1,5,1,3,5]=>[[],[[[[],[]]]]]=>2
[1,1,5,1,5,3]=>[[],[[[]],[[]]]]=>2
[1,1,5,3,1,5]=>[[],[[],[[],[]]]]=>2
[1,1,5,3,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,5,1,3]=>[[],[[[]]],[[]]]=>3
[1,1,5,5,3,1]=>[[],[],[[],[[]]]]=>3
[1,3,1,1,5,5]=>[[],[],[[[[]]]]]=>3
[1,3,1,5,1,5]=>[[[[],[[[]]]]]]=>1
[1,3,1,5,5,1]=>[[[]],[[[[]]]]]=>2
[1,3,5,1,1,5]=>[[[[],[]]],[[]]]=>2
[1,3,5,1,5,1]=>[[[],[[],[[]]]]]=>1
[1,3,5,5,1,1]=>[[],[[]],[[],[]]]=>3
[1,5,1,1,3,5]=>[[[[]]],[[],[]]]=>2
[1,5,1,1,5,3]=>[[[]],[[],[[]]]]=>2
[1,5,1,3,1,5]=>[[[],[[[[]]]]]]=>1
[1,5,1,3,5,1]=>[[[[],[[],[]]]]]=>1
[1,5,1,5,1,3]=>[[[],[[],[[]]]]]=>1
[1,5,1,5,3,1]=>[[[],[[],[[]]]]]=>1
[1,5,3,1,1,5]=>[[[],[]],[[],[]]]=>2
[1,5,3,1,5,1]=>[[[[]],[[],[]]]]=>1
[1,5,3,5,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,5,1,1,3]=>[[[]],[[]],[[]]]=>3
[1,5,5,1,3,1]=>[[[[[]]]],[[]]]=>2
[1,5,5,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,1,5,5]=>[[],[],[],[[[]]]]=>4
[3,1,1,5,1,5]=>[[],[[],[[[]]]]]=>2
[3,1,1,5,5,1]=>[[],[[]],[[[]]]]=>3
[3,1,5,1,1,5]=>[[[[]]],[[],[]]]=>2
[3,1,5,1,5,1]=>[[[[],[[],[]]]]]=>1
[3,1,5,5,1,1]=>[[],[[[]]],[[]]]=>3
[3,5,1,1,1,5]=>[[],[[[]]],[[]]]=>3
[3,5,1,1,5,1]=>[[],[[[],[[]]]]]=>2
[3,5,1,5,1,1]=>[[],[[[]],[[]]]]=>2
[3,5,5,1,1,1]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,3,5]=>[[],[[]],[[],[]]]=>3
[5,1,1,1,5,3]=>[[],[[]],[[[]]]]=>3
[5,1,1,3,1,5]=>[[[[[]]]],[[]]]=>2
[5,1,1,3,5,1]=>[[],[[],[[],[]]]]=>2
[5,1,1,5,1,3]=>[[],[[[],[[]]]]]=>2
[5,1,1,5,3,1]=>[[],[[[],[[]]]]]=>2
[5,1,3,1,1,5]=>[[[]],[[[[]]]]]=>2
[5,1,3,1,5,1]=>[[[],[[[[]]]]]]=>1
[5,1,3,5,1,1]=>[[],[[],[[],[]]]]=>2
[5,1,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[5,1,5,1,3,1]=>[[[[[]]],[[]]]]=>1
[5,1,5,3,1,1]=>[[],[[[]],[[]]]]=>2
[5,3,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[5,3,1,1,5,1]=>[[[[]]],[[],[]]]=>2
[5,3,1,5,1,1]=>[[],[[[[],[]]]]]=>2
[5,3,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,5,1,1,1,3]=>[[],[],[[]],[[]]]=>4
[5,5,1,1,3,1]=>[[],[[[]]],[[]]]=>3
[5,5,1,3,1,1]=>[[],[],[[[[]]]]]=>3
[5,5,3,1,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,1,3,5,6]=>[[],[],[[],[[]]]]=>3
[1,1,1,3,6,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,3,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,6,3]=>[[],[],[[],[[]]]]=>3
[1,1,1,6,3,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,5,3]=>[[],[],[[],[[]]]]=>3
[1,1,3,1,5,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,1,6,5]=>[[],[[[],[[]]]]]=>2
[1,1,3,5,1,6]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,6,1]=>[[],[[],[],[[]]]]=>2
[1,1,3,6,1,5]=>[[],[[[]],[[]]]]=>2
[1,1,3,6,5,1]=>[[],[[[],[[]]]]]=>2
[1,1,5,1,3,6]=>[[],[[[],[[]]]]]=>2
[1,1,5,1,6,3]=>[[],[[],[[[]]]]]=>2
[1,1,5,3,1,6]=>[[],[[[],[],[]]]]=>2
[1,1,5,3,6,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,6,1,3]=>[[],[[[[],[]]]]]=>2
[1,1,5,6,3,1]=>[[],[[[]],[[]]]]=>2
[1,1,6,1,3,5]=>[[],[[[],[],[]]]]=>2
[1,1,6,1,5,3]=>[[],[[],[[[]]]]]=>2
[1,1,6,3,1,5]=>[[],[[],[[],[]]]]=>2
[1,1,6,3,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,5,1,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,5,3,1]=>[[],[[],[],[[]]]]=>2
[1,3,1,1,5,6]=>[[[[]]],[[[]]]]=>2
[1,3,1,1,6,5]=>[[],[[[]],[[]]]]=>2
[1,3,1,5,1,6]=>[[[[[[],[]]]]]]=>1
[1,3,1,5,6,1]=>[[[],[[[[]]]]]]=>1
[1,3,1,6,1,5]=>[[[[]],[[],[]]]]=>1
[1,3,1,6,5,1]=>[[[[],[[[]]]]]]=>1
[1,3,5,1,1,6]=>[[[[],[]]],[[]]]=>2
[1,3,5,1,6,1]=>[[[],[],[[[]]]]]=>1
[1,3,5,6,1,1]=>[[],[[],[],[[]]]]=>2
[1,3,6,1,1,5]=>[[[]],[[],[[]]]]=>2
[1,3,6,1,5,1]=>[[[],[[[],[]]]]]=>1
[1,3,6,5,1,1]=>[[[]],[[],[[]]]]=>2
[1,5,1,1,3,6]=>[[],[[[],[[]]]]]=>2
[1,5,1,1,6,3]=>[[[]],[[[],[]]]]=>2
[1,5,1,3,1,6]=>[[[[],[[[]]]]]]=>1
[1,5,1,3,6,1]=>[[[[],[[],[]]]]]=>1
[1,5,1,6,1,3]=>[[[[],[[[]]]]]]=>1
[1,5,1,6,3,1]=>[[[[]],[[],[]]]]=>1
[1,5,3,1,1,6]=>[[[]],[[],[],[]]]=>2
[1,5,3,1,6,1]=>[[[[],[],[[]]]]]=>1
[1,5,3,6,1,1]=>[[],[[[[[]]]]]]=>2
[1,5,6,1,1,3]=>[[],[[],[[[]]]]]=>2
[1,5,6,1,3,1]=>[[[[[]],[[]]]]]=>1
[1,5,6,3,1,1]=>[[],[[[],[[]]]]]=>2
[1,6,1,1,3,5]=>[[],[[],[],[[]]]]=>2
[1,6,1,1,5,3]=>[[[]],[[[],[]]]]=>2
[1,6,1,3,1,5]=>[[[[]],[[],[]]]]=>1
[1,6,1,3,5,1]=>[[[[],[],[[]]]]]=>1
[1,6,1,5,1,3]=>[[[[[[],[]]]]]]=>1
[1,6,1,5,3,1]=>[[[],[],[[[]]]]]=>1
[1,6,3,1,1,5]=>[[[],[]],[[],[]]]=>2
[1,6,3,1,5,1]=>[[[],[[],[[]]]]]=>1
[1,6,3,5,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,5,1,1,3]=>[[[[]]],[[[]]]]=>2
[1,6,5,1,3,1]=>[[[[[]]],[[]]]]=>1
[1,6,5,3,1,1]=>[[[]],[[],[],[]]]=>2
[3,1,1,1,5,6]=>[[],[[[]]],[[]]]=>3
[3,1,1,1,6,5]=>[[],[],[[],[[]]]]=>3
[3,1,1,5,1,6]=>[[],[[[[],[]]]]]=>2
[3,1,1,5,6,1]=>[[[[[]]]],[[]]]=>2
[3,1,1,6,1,5]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,5,1]=>[[],[[],[[[]]]]]=>2
[3,1,5,1,1,6]=>[[[[]]],[[],[]]]=>2
[3,1,5,1,6,1]=>[[[[]],[[[]]]]]=>1
[3,1,5,6,1,1]=>[[],[[[[[]]]]]]=>2
[3,1,6,1,1,5]=>[[[[],[]]],[[]]]=>2
[3,1,6,1,5,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,5,1,1]=>[[[[],[]]],[[]]]=>2
[3,5,1,1,1,6]=>[[],[[[]]],[[]]]=>3
[3,5,1,1,6,1]=>[[[]],[[[],[]]]]=>2
[3,5,1,6,1,1]=>[[],[[],[[[]]]]]=>2
[3,5,6,1,1,1]=>[[],[],[[],[[]]]]=>3
[3,6,1,1,1,5]=>[[],[[[]]],[[]]]=>3
[3,6,1,1,5,1]=>[[[]],[[[],[]]]]=>2
[3,6,1,5,1,1]=>[[],[[],[[[]]]]]=>2
[3,6,5,1,1,1]=>[[],[[]],[[],[]]]=>3
[5,1,1,1,3,6]=>[[],[],[[[],[]]]]=>3
[5,1,1,1,6,3]=>[[],[[]],[[[]]]]=>3
[5,1,1,3,1,6]=>[[[[],[]]],[[]]]=>2
[5,1,1,3,6,1]=>[[],[[],[[],[]]]]=>2
[5,1,1,6,1,3]=>[[[]],[[[],[]]]]=>2
[5,1,1,6,3,1]=>[[],[[],[[[]]]]]=>2
[5,1,3,1,1,6]=>[[],[[],[[[]]]]]=>2
[5,1,3,1,6,1]=>[[[[],[[],[]]]]]=>1
[5,1,3,6,1,1]=>[[],[[],[[],[]]]]=>2
[5,1,6,1,1,3]=>[[[[]]],[[],[]]]=>2
[5,1,6,1,3,1]=>[[[[],[[],[]]]]]=>1
[5,1,6,3,1,1]=>[[],[[],[[[]]]]]=>2
[5,3,1,1,1,6]=>[[],[],[[],[],[]]]=>3
[5,3,1,1,6,1]=>[[],[[],[],[[]]]]=>2
[5,3,1,6,1,1]=>[[],[[[],[],[]]]]=>2
[5,3,6,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,6,1,1,1,3]=>[[],[],[[],[[]]]]=>3
[5,6,1,1,3,1]=>[[],[[[]],[[]]]]=>2
[5,6,1,3,1,1]=>[[],[[[],[[]]]]]=>2
[5,6,3,1,1,1]=>[[],[[[]]],[[]]]=>3
[6,1,1,1,3,5]=>[[],[],[[],[],[]]]=>3
[6,1,1,1,5,3]=>[[],[[]],[[[]]]]=>3
[6,1,1,3,1,5]=>[[],[[],[[[]]]]]=>2
[6,1,1,3,5,1]=>[[],[[],[],[[]]]]=>2
[6,1,1,5,1,3]=>[[],[[[[],[]]]]]=>2
[6,1,1,5,3,1]=>[[[]],[[[],[]]]]=>2
[6,1,3,1,1,5]=>[[[]],[[[],[]]]]=>2
[6,1,3,1,5,1]=>[[[],[[[[]]]]]]=>1
[6,1,3,5,1,1]=>[[],[[[],[],[]]]]=>2
[6,1,5,1,1,3]=>[[[[]]],[[],[]]]=>2
[6,1,5,1,3,1]=>[[[[[]]],[[]]]]=>1
[6,1,5,3,1,1]=>[[],[[],[[[]]]]]=>2
[6,3,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[6,3,1,1,5,1]=>[[[]],[[],[[]]]]=>2
[6,3,1,5,1,1]=>[[],[[[],[[]]]]]=>2
[6,3,5,1,1,1]=>[[],[],[[[[]]]]]=>3
[6,5,1,1,1,3]=>[[],[[[]]],[[]]]=>3
[6,5,1,1,3,1]=>[[[[[]]]],[[]]]=>2
[6,5,1,3,1,1]=>[[[[[]]]],[[]]]=>2
[6,5,3,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,1,4,4,4]=>[[],[],[],[],[[]]]=>5
[1,1,4,1,4,4]=>[[],[],[[],[[]]]]=>3
[1,1,4,4,1,4]=>[[],[],[[[],[]]]]=>3
[1,1,4,4,4,1]=>[[],[],[[]],[[]]]=>4
[1,4,1,1,4,4]=>[[],[[]],[[],[]]]=>3
[1,4,1,4,1,4]=>[[[],[],[[],[]]]]=>1
[1,4,1,4,4,1]=>[[[],[]],[[],[]]]=>2
[1,4,4,1,1,4]=>[[],[[]],[[],[]]]=>3
[1,4,4,1,4,1]=>[[],[[],[[],[]]]]=>2
[1,4,4,4,1,1]=>[[],[],[[]],[[]]]=>4
[4,1,1,1,4,4]=>[[],[],[[]],[[]]]=>4
[4,1,1,4,1,4]=>[[],[[],[[],[]]]]=>2
[4,1,1,4,4,1]=>[[],[[]],[[],[]]]=>3
[4,1,4,1,1,4]=>[[[],[]],[[],[]]]=>2
[4,1,4,1,4,1]=>[[[],[],[[],[]]]]=>1
[4,1,4,4,1,1]=>[[],[[]],[[],[]]]=>3
[4,4,1,1,1,4]=>[[],[],[[]],[[]]]=>4
[4,4,1,1,4,1]=>[[],[],[[[],[]]]]=>3
[4,4,1,4,1,1]=>[[],[],[[],[[]]]]=>3
[4,4,4,1,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,1,4,4,5]=>[[],[],[[]],[[]]]=>4
[1,1,1,4,5,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,4,4]=>[[],[],[],[[[]]]]=>4
[1,1,4,1,4,5]=>[[],[[[]],[[]]]]=>2
[1,1,4,1,5,4]=>[[],[[[],[[]]]]]=>2
[1,1,4,4,1,5]=>[[],[[]],[[],[]]]=>3
[1,1,4,4,5,1]=>[[],[],[[[],[]]]]=>3
[1,1,4,5,1,4]=>[[],[[],[],[[]]]]=>2
[1,1,4,5,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,1,4,4]=>[[],[],[[],[[]]]]=>3
[1,1,5,4,1,4]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,4,1]=>[[],[],[[],[[]]]]=>3
[1,4,1,1,4,5]=>[[[]],[[],[[]]]]=>2
[1,4,1,1,5,4]=>[[[]],[[],[[]]]]=>2
[1,4,1,4,1,5]=>[[[],[[],[],[]]]]=>1
[1,4,1,4,5,1]=>[[[],[[]],[[]]]]=>1
[1,4,1,5,1,4]=>[[[],[],[[],[]]]]=>1
[1,4,1,5,4,1]=>[[[[[],[],[]]]]]=>1
[1,4,4,1,1,5]=>[[],[],[[],[[]]]]=>3
[1,4,4,1,5,1]=>[[],[[],[[],[]]]]=>2
[1,4,4,5,1,1]=>[[],[],[[],[[]]]]=>3
[1,4,5,1,1,4]=>[[],[[],[],[[]]]]=>2
[1,4,5,1,4,1]=>[[[],[[]],[[]]]]=>1
[1,4,5,4,1,1]=>[[[]],[[[[]]]]]=>2
[1,5,1,1,4,4]=>[[],[[]],[[],[]]]=>3
[1,5,1,4,1,4]=>[[[],[[],[],[]]]]=>1
[1,5,1,4,4,1]=>[[[],[]],[[],[]]]=>2
[1,5,4,1,1,4]=>[[[[]]],[[],[]]]=>2
[1,5,4,1,4,1]=>[[[],[[]],[[]]]]=>1
[1,5,4,4,1,1]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,4,5]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,5,4]=>[[],[],[[],[[]]]]=>3
[4,1,1,4,1,5]=>[[],[[[],[],[]]]]=>2
[4,1,1,4,5,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,5,1,4]=>[[],[[],[[],[]]]]=>2
[4,1,1,5,4,1]=>[[],[[],[],[[]]]]=>2
[4,1,4,1,1,5]=>[[],[[],[],[[]]]]=>2
[4,1,4,1,5,1]=>[[[],[],[[],[]]]]=>1
[4,1,4,5,1,1]=>[[],[[[]],[[]]]]=>2
[4,1,5,1,1,4]=>[[],[[],[[],[]]]]=>2
[4,1,5,1,4,1]=>[[[],[],[[],[]]]]=>1
[4,1,5,4,1,1]=>[[[]],[[],[],[]]]=>2
[4,4,1,1,1,5]=>[[],[],[],[[],[]]]=>4
[4,4,1,1,5,1]=>[[],[],[[],[[]]]]=>3
[4,4,1,5,1,1]=>[[],[],[[[],[]]]]=>3
[4,4,5,1,1,1]=>[[],[],[],[[[]]]]=>4
[4,5,1,1,1,4]=>[[],[],[[],[[]]]]=>3
[4,5,1,1,4,1]=>[[],[[[]],[[]]]]=>2
[4,5,1,4,1,1]=>[[],[[[],[[]]]]]=>2
[4,5,4,1,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,1,4,4]=>[[],[],[],[[],[]]]=>4
[5,1,1,4,1,4]=>[[],[[],[],[[]]]]=>2
[5,1,1,4,4,1]=>[[],[[]],[[],[]]]=>3
[5,1,4,1,1,4]=>[[[]],[[],[],[]]]=>2
[5,1,4,1,4,1]=>[[[],[],[[],[]]]]=>1
[5,1,4,4,1,1]=>[[],[[]],[[],[]]]=>3
[5,4,1,1,1,4]=>[[],[[[]]],[[]]]=>3
[5,4,1,1,4,1]=>[[],[[[],[[]]]]]=>2
[5,4,1,4,1,1]=>[[[]],[[],[[]]]]=>2
[5,4,4,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,4,4,6]=>[[],[],[[]],[[]]]=>4
[1,1,1,4,6,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,4,4]=>[[],[],[],[[],[]]]=>4
[1,1,4,1,4,6]=>[[],[[[]],[[]]]]=>2
[1,1,4,1,6,4]=>[[],[[[],[[]]]]]=>2
[1,1,4,4,1,6]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,6,1]=>[[],[[]],[[],[]]]=>3
[1,1,4,6,1,4]=>[[],[[],[[],[]]]]=>2
[1,1,4,6,4,1]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,6,4,1,4]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,4,1]=>[[],[[]],[[],[]]]=>3
[1,4,1,1,4,6]=>[[[]],[[],[[]]]]=>2
[1,4,1,1,6,4]=>[[[]],[[],[[]]]]=>2
[1,4,1,4,1,6]=>[[[],[[],[[]]]]]=>1
[1,4,1,4,6,1]=>[[[[]],[[],[]]]]=>1
[1,4,1,6,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,1,6,4,1]=>[[[[],[[],[]]]]]=>1
[1,4,4,1,1,6]=>[[],[[[]]],[[]]]=>3
[1,4,4,1,6,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,6,1,1]=>[[],[[]],[[],[]]]=>3
[1,4,6,1,1,4]=>[[[],[]],[[],[]]]=>2
[1,4,6,1,4,1]=>[[[[]],[[],[]]]]=>1
[1,4,6,4,1,1]=>[[],[[[[[]]]]]]=>2
[1,6,1,1,4,4]=>[[],[[]],[[[]]]]=>3
[1,6,1,4,1,4]=>[[[[[],[[]]]]]]=>1
[1,6,1,4,4,1]=>[[[[[]]]],[[]]]=>2
[1,6,4,1,1,4]=>[[[]],[[[],[]]]]=>2
[1,6,4,1,4,1]=>[[[],[[[],[]]]]]=>1
[1,6,4,4,1,1]=>[[],[],[[[],[]]]]=>3
[4,1,1,1,4,6]=>[[],[[[]]],[[]]]=>3
[4,1,1,1,6,4]=>[[],[],[[],[[]]]]=>3
[4,1,1,4,1,6]=>[[],[[[],[[]]]]]=>2
[4,1,1,4,6,1]=>[[[[],[]]],[[]]]=>2
[4,1,1,6,1,4]=>[[[]],[[[[]]]]]=>2
[4,1,1,6,4,1]=>[[],[[],[[],[]]]]=>2
[4,1,4,1,1,6]=>[[[]],[[],[[]]]]=>2
[4,1,4,1,6,1]=>[[[[]],[[[]]]]]=>1
[4,1,4,6,1,1]=>[[],[[],[[[]]]]]=>2
[4,1,6,1,1,4]=>[[[[[]]]],[[]]]=>2
[4,1,6,1,4,1]=>[[[],[[[[]]]]]]=>1
[4,1,6,4,1,1]=>[[],[[],[[],[]]]]=>2
[4,4,1,1,1,6]=>[[],[],[[]],[[]]]=>4
[4,4,1,1,6,1]=>[[],[[]],[[[]]]]=>3
[4,4,1,6,1,1]=>[[],[],[[[[]]]]]=>3
[4,4,6,1,1,1]=>[[],[],[],[[],[]]]=>4
[4,6,1,1,1,4]=>[[],[[]],[[],[]]]=>3
[4,6,1,1,4,1]=>[[[[]]],[[],[]]]=>2
[4,6,1,4,1,1]=>[[],[[[[],[]]]]]=>2
[4,6,4,1,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,1,4,4]=>[[],[],[[]],[[]]]=>4
[6,1,1,4,1,4]=>[[[]],[[],[[]]]]=>2
[6,1,1,4,4,1]=>[[[]],[[]],[[]]]=>3
[6,1,4,1,1,4]=>[[[]],[[],[[]]]]=>2
[6,1,4,1,4,1]=>[[[[],[[],[]]]]]=>1
[6,1,4,4,1,1]=>[[],[[[]]],[[]]]=>3
[6,4,1,1,1,4]=>[[[]],[[]],[[]]]=>3
[6,4,1,1,4,1]=>[[[[],[]]],[[]]]=>2
[6,4,1,4,1,1]=>[[],[[],[[[]]]]]=>2
[6,4,4,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,4,5,5]=>[[],[],[],[[[]]]]=>4
[1,1,1,5,4,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,5,4]=>[[],[],[[]],[[]]]=>4
[1,1,4,1,5,5]=>[[],[],[[],[[]]]]=>3
[1,1,4,5,1,5]=>[[],[[[]],[[]]]]=>2
[1,1,4,5,5,1]=>[[],[[]],[[],[]]]=>3
[1,1,5,1,4,5]=>[[],[[[],[[]]]]]=>2
[1,1,5,1,5,4]=>[[],[[[]],[[]]]]=>2
[1,1,5,4,1,5]=>[[],[[],[],[[]]]]=>2
[1,1,5,4,5,1]=>[[],[[[[[]]]]]]=>2
[1,1,5,5,1,4]=>[[],[[]],[[],[]]]=>3
[1,1,5,5,4,1]=>[[],[],[[[],[]]]]=>3
[1,4,1,1,5,5]=>[[],[[]],[[],[]]]=>3
[1,4,1,5,1,5]=>[[[],[[],[],[]]]]=>1
[1,4,1,5,5,1]=>[[[],[]],[[],[]]]=>2
[1,4,5,1,1,5]=>[[[]],[[],[[]]]]=>2
[1,4,5,1,5,1]=>[[[],[[]],[[]]]]=>1
[1,4,5,5,1,1]=>[[],[[]],[[],[]]]=>3
[1,5,1,1,4,5]=>[[],[[[]],[[]]]]=>2
[1,5,1,1,5,4]=>[[[]],[[],[[]]]]=>2
[1,5,1,4,1,5]=>[[[],[],[[],[]]]]=>1
[1,5,1,4,5,1]=>[[[[],[],[[]]]]]=>1
[1,5,1,5,1,4]=>[[[],[[],[],[]]]]=>1
[1,5,1,5,4,1]=>[[[],[],[[[]]]]]=>1
[1,5,4,1,1,5]=>[[],[[],[],[[]]]]=>2
[1,5,4,1,5,1]=>[[[],[],[[[]]]]]=>1
[1,5,4,5,1,1]=>[[[[]]],[[[]]]]=>2
[1,5,5,1,1,4]=>[[],[],[[],[[]]]]=>3
[1,5,5,1,4,1]=>[[],[[],[[],[]]]]=>2
[1,5,5,4,1,1]=>[[],[[]],[[],[]]]=>3
[4,1,1,1,5,5]=>[[],[],[],[[],[]]]=>4
[4,1,1,5,1,5]=>[[],[[],[],[[]]]]=>2
[4,1,1,5,5,1]=>[[],[[]],[[],[]]]=>3
[4,1,5,1,1,5]=>[[[]],[[],[],[]]]=>2
[4,1,5,1,5,1]=>[[[],[],[[],[]]]]=>1
[4,1,5,5,1,1]=>[[],[[]],[[],[]]]=>3
[4,5,1,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,5,1,1,5,1]=>[[],[[[],[[]]]]]=>2
[4,5,1,5,1,1]=>[[],[[[]],[[]]]]=>2
[4,5,5,1,1,1]=>[[],[],[[]],[[]]]=>4
[5,1,1,1,4,5]=>[[],[],[[],[[]]]]=>3
[5,1,1,1,5,4]=>[[],[[]],[[[]]]]=>3
[5,1,1,4,1,5]=>[[],[[],[[],[]]]]=>2
[5,1,1,4,5,1]=>[[],[[],[],[[]]]]=>2
[5,1,1,5,1,4]=>[[],[[[],[],[]]]]=>2
[5,1,1,5,4,1]=>[[],[[],[[[]]]]]=>2
[5,1,4,1,1,5]=>[[],[[],[[],[]]]]=>2
[5,1,4,1,5,1]=>[[[],[],[[],[]]]]=>1
[5,1,4,5,1,1]=>[[],[[],[],[[]]]]=>2
[5,1,5,1,1,4]=>[[],[[],[],[[]]]]=>2
[5,1,5,1,4,1]=>[[[],[],[[],[]]]]=>1
[5,1,5,4,1,1]=>[[[[]]],[[],[]]]=>2
[5,4,1,1,1,5]=>[[],[],[[],[[]]]]=>3
[5,4,1,1,5,1]=>[[],[[],[[[]]]]]=>2
[5,4,1,5,1,1]=>[[[[],[]]],[[]]]=>2
[5,4,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[5,5,1,1,1,4]=>[[],[],[],[[],[]]]=>4
[5,5,1,1,4,1]=>[[],[],[[],[[]]]]=>3
[5,5,1,4,1,1]=>[[],[],[[[],[]]]]=>3
[5,5,4,1,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,1,4,5,6]=>[[],[],[[[],[]]]]=>3
[1,1,1,4,6,5]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,4,6]=>[[],[],[[[[]]]]]=>3
[1,1,1,5,6,4]=>[[],[],[[[[]]]]]=>3
[1,1,1,6,4,5]=>[[],[],[[],[[]]]]=>3
[1,1,1,6,5,4]=>[[],[],[[[],[]]]]=>3
[1,1,4,1,5,6]=>[[],[[[],[[]]]]]=>2
[1,1,4,1,6,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,5,1,6]=>[[],[[[]],[[]]]]=>2
[1,1,4,5,6,1]=>[[],[[[],[[]]]]]=>2
[1,1,4,6,1,5]=>[[],[[[],[[]]]]]=>2
[1,1,4,6,5,1]=>[[],[[],[[[]]]]]=>2
[1,1,5,1,4,6]=>[[],[[[],[[]]]]]=>2
[1,1,5,1,6,4]=>[[],[[[],[[]]]]]=>2
[1,1,5,4,1,6]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,6,1]=>[[],[[[],[[]]]]]=>2
[1,1,5,6,1,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,6,4,1]=>[[],[[],[[[]]]]]=>2
[1,1,6,1,4,5]=>[[],[[[[[]]]]]]=>2
[1,1,6,1,5,4]=>[[],[[[[[]]]]]]=>2
[1,1,6,4,1,5]=>[[],[[],[[],[]]]]=>2
[1,1,6,4,5,1]=>[[],[[],[[[]]]]]=>2
[1,1,6,5,1,4]=>[[],[[[],[[]]]]]=>2
[1,1,6,5,4,1]=>[[],[[[[],[]]]]]=>2
[1,4,1,1,5,6]=>[[],[[[]],[[]]]]=>2
[1,4,1,1,6,5]=>[[[]],[[[[]]]]]=>2
[1,4,1,5,1,6]=>[[[[]],[[],[]]]]=>1
[1,4,1,5,6,1]=>[[[[],[[[]]]]]]=>1
[1,4,1,6,1,5]=>[[[[[[],[]]]]]]=>1
[1,4,1,6,5,1]=>[[[[]],[[[]]]]]=>1
[1,4,5,1,1,6]=>[[[]],[[],[[]]]]=>2
[1,4,5,1,6,1]=>[[[[]],[[[]]]]]=>1
[1,4,5,6,1,1]=>[[],[[[],[[]]]]]=>2
[1,4,6,1,1,5]=>[[[]],[[],[[]]]]=>2
[1,4,6,1,5,1]=>[[[],[[[],[]]]]]=>1
[1,4,6,5,1,1]=>[[[[]]],[[],[]]]=>2
[1,5,1,1,4,6]=>[[],[[[]],[[]]]]=>2
[1,5,1,1,6,4]=>[[[]],[[],[[]]]]=>2
[1,5,1,4,1,6]=>[[[[]],[[],[]]]]=>1
[1,5,1,4,6,1]=>[[[[],[[],[]]]]]=>1
[1,5,1,6,1,4]=>[[[[[[],[]]]]]]=>1
[1,5,1,6,4,1]=>[[[],[[],[[]]]]]=>1
[1,5,4,1,1,6]=>[[[[]]],[[],[]]]=>2
[1,5,4,1,6,1]=>[[[],[[[[]]]]]]=>1
[1,5,4,6,1,1]=>[[[]],[[],[[]]]]=>2
[1,5,6,1,1,4]=>[[[[[]]]],[[]]]=>2
[1,5,6,1,4,1]=>[[[],[[[[]]]]]]=>1
[1,5,6,4,1,1]=>[[],[[],[[[]]]]]=>2
[1,6,1,1,4,5]=>[[[[]]],[[[]]]]=>2
[1,6,1,1,5,4]=>[[[]],[[[[]]]]]=>2
[1,6,1,4,1,5]=>[[[[],[[[]]]]]]=>1
[1,6,1,4,5,1]=>[[[[[],[[]]]]]]=>1
[1,6,1,5,1,4]=>[[[[],[[[]]]]]]=>1
[1,6,1,5,4,1]=>[[[[[]],[[]]]]]=>1
[1,6,4,1,1,5]=>[[[],[]],[[],[]]]=>2
[1,6,4,1,5,1]=>[[[],[[],[[]]]]]=>1
[1,6,4,5,1,1]=>[[],[[[[],[]]]]]=>2
[1,6,5,1,1,4]=>[[[]],[[],[[]]]]=>2
[1,6,5,1,4,1]=>[[[[],[[[]]]]]]=>1
[1,6,5,4,1,1]=>[[[[]]],[[],[]]]=>2
[4,1,1,1,5,6]=>[[],[],[[],[[]]]]=>3
[4,1,1,1,6,5]=>[[],[],[[[[]]]]]=>3
[4,1,1,5,1,6]=>[[],[[],[[[]]]]]=>2
[4,1,1,5,6,1]=>[[],[[],[[[]]]]]=>2
[4,1,1,6,1,5]=>[[],[[[[],[]]]]]=>2
[4,1,1,6,5,1]=>[[],[[[[[]]]]]]=>2
[4,1,5,1,1,6]=>[[[[],[]]],[[]]]=>2
[4,1,5,1,6,1]=>[[[],[[[[]]]]]]=>1
[4,1,5,6,1,1]=>[[],[[[[],[]]]]]=>2
[4,1,6,1,1,5]=>[[[[]]],[[],[]]]=>2
[4,1,6,1,5,1]=>[[[[[]]],[[]]]]=>1
[4,1,6,5,1,1]=>[[[[]]],[[[]]]]=>2
[4,5,1,1,1,6]=>[[],[[[]]],[[]]]=>3
[4,5,1,1,6,1]=>[[[[]]],[[[]]]]=>2
[4,5,1,6,1,1]=>[[],[[[[[]]]]]]=>2
[4,5,6,1,1,1]=>[[],[],[[[],[]]]]=>3
[4,6,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[4,6,1,1,5,1]=>[[[[]]],[[],[]]]=>2
[4,6,1,5,1,1]=>[[],[[[[],[]]]]]=>2
[4,6,5,1,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,1,4,6]=>[[],[],[[],[[]]]]=>3
[5,1,1,1,6,4]=>[[],[[]],[[],[]]]=>3
[5,1,1,4,1,6]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,6,1]=>[[],[[],[[],[]]]]=>2
[5,1,1,6,1,4]=>[[],[[[[],[]]]]]=>2
[5,1,1,6,4,1]=>[[],[[[]],[[]]]]=>2
[5,1,4,1,1,6]=>[[[[],[]]],[[]]]=>2
[5,1,4,1,6,1]=>[[[],[[[[]]]]]]=>1
[5,1,4,6,1,1]=>[[],[[],[[],[]]]]=>2
[5,1,6,1,1,4]=>[[[[]]],[[],[]]]=>2
[5,1,6,1,4,1]=>[[[[[]]],[[]]]]=>1
[5,1,6,4,1,1]=>[[],[[[],[[]]]]]=>2
[5,4,1,1,1,6]=>[[],[[]],[[[]]]]=>3
[5,4,1,1,6,1]=>[[[]],[[[[]]]]]=>2
[5,4,1,6,1,1]=>[[[[[]]]],[[]]]=>2
[5,4,6,1,1,1]=>[[],[[]],[[],[]]]=>3
[5,6,1,1,1,4]=>[[],[[[]]],[[]]]=>3
[5,6,1,1,4,1]=>[[[[]]],[[[]]]]=>2
[5,6,1,4,1,1]=>[[],[[[[[]]]]]]=>2
[5,6,4,1,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,1,4,5]=>[[],[[]],[[[]]]]=>3
[6,1,1,1,5,4]=>[[],[[]],[[[]]]]=>3
[6,1,1,4,1,5]=>[[[]],[[[],[]]]]=>2
[6,1,1,4,5,1]=>[[[]],[[],[[]]]]=>2
[6,1,1,5,1,4]=>[[[]],[[[],[]]]]=>2
[6,1,1,5,4,1]=>[[[]],[[],[[]]]]=>2
[6,1,4,1,1,5]=>[[],[[],[[[]]]]]=>2
[6,1,4,1,5,1]=>[[[[],[[],[]]]]]=>1
[6,1,4,5,1,1]=>[[],[[[]],[[]]]]=>2
[6,1,5,1,1,4]=>[[],[[],[[[]]]]]=>2
[6,1,5,1,4,1]=>[[[[],[[],[]]]]]=>1
[6,1,5,4,1,1]=>[[[]],[[],[[]]]]=>2
[6,4,1,1,1,5]=>[[],[[]],[[],[]]]=>3
[6,4,1,1,5,1]=>[[[]],[[],[[]]]]=>2
[6,4,1,5,1,1]=>[[],[[[],[[]]]]]=>2
[6,4,5,1,1,1]=>[[],[[[]]],[[]]]=>3
[6,5,1,1,1,4]=>[[],[],[[],[[]]]]=>3
[6,5,1,1,4,1]=>[[],[[],[[[]]]]]=>2
[6,5,1,4,1,1]=>[[[[],[]]],[[]]]=>2
[6,5,4,1,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,2,2,2]=>[[],[],[],[],[[]]]=>5
[1,2,1,2,2,2]=>[[],[[]],[[],[]]]=>3
[1,2,2,1,2,2]=>[[],[[]],[[],[]]]=>3
[1,2,2,2,1,2]=>[[],[],[[[],[]]]]=>3
[1,2,2,2,2,1]=>[[],[],[[]],[[]]]=>4
[2,1,1,2,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,2,1,2,2]=>[[[],[]],[[],[]]]=>2
[2,1,2,2,1,2]=>[[],[[],[[],[]]]]=>2
[2,1,2,2,2,1]=>[[],[[]],[[],[]]]=>3
[2,2,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[2,2,1,2,1,2]=>[[],[[],[[],[]]]]=>2
[2,2,1,2,2,1]=>[[],[[]],[[],[]]]=>3
[2,2,2,1,1,2]=>[[],[],[],[[[]]]]=>4
[2,2,2,1,2,1]=>[[],[],[[],[[]]]]=>3
[2,2,2,2,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,2,2,2,3]=>[[],[],[],[[],[]]]=>4
[1,1,2,2,3,2]=>[[],[],[[],[[]]]]=>3
[1,1,2,3,2,2]=>[[],[],[[[],[]]]]=>3
[1,1,3,2,2,2]=>[[],[],[],[[[]]]]=>4
[1,2,1,2,2,3]=>[[],[[],[],[[]]]]=>2
[1,2,1,2,3,2]=>[[[],[],[[],[]]]]=>1
[1,2,1,3,2,2]=>[[],[[[]],[[]]]]=>2
[1,2,2,1,2,3]=>[[],[[[],[],[]]]]=>2
[1,2,2,1,3,2]=>[[[]],[[],[[]]]]=>2
[1,2,2,2,1,3]=>[[],[[]],[[[]]]]=>3
[1,2,2,2,3,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,3,1,2]=>[[],[[],[],[[]]]]=>2
[1,2,2,3,2,1]=>[[],[[],[[],[]]]]=>2
[1,2,3,1,2,2]=>[[],[[],[],[[]]]]=>2
[1,2,3,2,1,2]=>[[[],[],[[],[]]]]=>1
[1,2,3,2,2,1]=>[[],[[],[[],[]]]]=>2
[1,3,1,2,2,2]=>[[],[[]],[[[]]]]=>3
[1,3,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[1,3,2,2,1,2]=>[[],[[[]],[[]]]]=>2
[1,3,2,2,2,1]=>[[],[],[[],[[]]]]=>3
[2,1,1,2,2,3]=>[[],[],[[],[[]]]]=>3
[2,1,1,2,3,2]=>[[],[[],[[],[]]]]=>2
[2,1,1,3,2,2]=>[[],[],[[],[[]]]]=>3
[2,1,2,1,2,3]=>[[[],[[],[],[]]]]=>1
[2,1,2,1,3,2]=>[[[],[[]],[[]]]]=>1
[2,1,2,2,1,3]=>[[[]],[[],[[]]]]=>2
[2,1,2,2,3,1]=>[[],[[],[[[]]]]]=>2
[2,1,2,3,1,2]=>[[[[],[],[[]]]]]=>1
[2,1,2,3,2,1]=>[[[],[],[[],[]]]]=>1
[2,1,3,1,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,3,2,1,2]=>[[[],[[]],[[]]]]=>1
[2,1,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[2,2,1,1,2,3]=>[[],[],[[],[[]]]]=>3
[2,2,1,1,3,2]=>[[],[],[[[],[]]]]=>3
[2,2,1,2,1,3]=>[[],[[[]],[[]]]]=>2
[2,2,1,2,3,1]=>[[],[[[[],[]]]]]=>2
[2,2,1,3,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,3,2,1]=>[[],[[],[],[[]]]]=>2
[2,2,2,1,1,3]=>[[],[],[],[[[]]]]=>4
[2,2,2,1,3,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,3,1,1]=>[[],[],[],[[[]]]]=>4
[2,2,3,1,1,2]=>[[],[[]],[[],[]]]=>3
[2,2,3,1,2,1]=>[[],[[],[[[]]]]]=>2
[2,2,3,2,1,1]=>[[],[],[[],[[]]]]=>3
[2,3,1,1,2,2]=>[[],[],[[],[[]]]]=>3
[2,3,1,2,1,2]=>[[[],[[]],[[]]]]=>1
[2,3,1,2,2,1]=>[[[[]]],[[],[]]]=>2
[2,3,2,1,1,2]=>[[],[[],[[],[]]]]=>2
[2,3,2,1,2,1]=>[[[],[[],[],[]]]]=>1
[2,3,2,2,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,2,2,2]=>[[],[],[[]],[[]]]=>4
[3,1,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[3,1,2,2,1,2]=>[[],[[[],[[]]]]]=>2
[3,1,2,2,2,1]=>[[],[[]],[[[]]]]=>3
[3,2,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[3,2,1,2,1,2]=>[[[],[],[[],[]]]]=>1
[3,2,1,2,2,1]=>[[[]],[[],[],[]]]=>2
[3,2,2,1,1,2]=>[[],[],[[[],[]]]]=>3
[3,2,2,1,2,1]=>[[],[[],[],[[]]]]=>2
[3,2,2,2,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,2,2,2,4]=>[[],[],[[]],[[]]]=>4
[1,1,2,2,4,2]=>[[],[[]],[[[]]]]=>3
[1,1,2,4,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,4,2,2,2]=>[[],[],[],[[[]]]]=>4
[1,2,1,2,2,4]=>[[[[]]],[[],[]]]=>2
[1,2,1,2,4,2]=>[[[],[[[[]]]]]]=>1
[1,2,1,4,2,2]=>[[[[]]],[[[]]]]=>2
[1,2,2,1,2,4]=>[[],[[[[],[]]]]]=>2
[1,2,2,1,4,2]=>[[[]],[[[[]]]]]=>2
[1,2,2,2,1,4]=>[[],[[]],[[[]]]]=>3
[1,2,2,2,4,1]=>[[],[[]],[[[]]]]=>3
[1,2,2,4,1,2]=>[[],[[[[],[]]]]]=>2
[1,2,2,4,2,1]=>[[[]],[[[[]]]]]=>2
[1,2,4,1,2,2]=>[[],[[],[[[]]]]]=>2
[1,2,4,2,1,2]=>[[[[[]]],[[]]]]=>1
[1,2,4,2,2,1]=>[[],[[[[[]]]]]]=>2
[1,4,1,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,4,2,1,2,2]=>[[[[[]]]],[[]]]=>2
[1,4,2,2,1,2]=>[[],[[[[[]]]]]]=>2
[1,4,2,2,2,1]=>[[],[[]],[[[]]]]=>3
[2,1,1,2,2,4]=>[[],[[]],[[[]]]]=>3
[2,1,1,2,4,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,2,2]=>[[],[[[]]],[[]]]=>3
[2,1,2,1,2,4]=>[[[],[[[],[]]]]]=>1
[2,1,2,1,4,2]=>[[[[]],[[[]]]]]=>1
[2,1,2,2,1,4]=>[[[]],[[],[[]]]]=>2
[2,1,2,2,4,1]=>[[[]],[[[[]]]]]=>2
[2,1,2,4,1,2]=>[[[[],[[[]]]]]]=>1
[2,1,2,4,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,4,1,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,4,2,1,2]=>[[[],[[[[]]]]]]=>1
[2,1,4,2,2,1]=>[[],[[],[[[]]]]]=>2
[2,2,1,1,2,4]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,4,2]=>[[],[],[[[[]]]]]=>3
[2,2,1,2,1,4]=>[[],[[[]],[[]]]]=>2
[2,2,1,2,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,2,1]=>[[],[[],[[[]]]]]=>2
[2,2,2,1,1,4]=>[[],[],[],[[[]]]]=>4
[2,2,2,1,4,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,4,1,1]=>[[],[],[],[[[]]]]=>4
[2,2,4,1,1,2]=>[[],[[]],[[[]]]]=>3
[2,2,4,1,2,1]=>[[],[[[[[]]]]]]=>2
[2,2,4,2,1,1]=>[[],[[[]]],[[]]]=>3
[2,4,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[2,4,1,2,1,2]=>[[[[[[],[]]]]]]=>1
[2,4,1,2,2,1]=>[[[[[]]]],[[]]]=>2
[2,4,2,1,1,2]=>[[[[]]],[[[]]]]=>2
[2,4,2,1,2,1]=>[[[[[],[[]]]]]]=>1
[2,4,2,2,1,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,2,2,2]=>[[],[],[],[[[]]]]=>4
[4,1,2,1,2,2]=>[[[[]]],[[],[]]]=>2
[4,1,2,2,1,2]=>[[[]],[[[],[]]]]=>2
[4,1,2,2,2,1]=>[[[]],[[]],[[]]]=>3
[4,2,1,1,2,2]=>[[],[[[]]],[[]]]=>3
[4,2,1,2,1,2]=>[[[[],[[],[]]]]]=>1
[4,2,1,2,2,1]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,1,2]=>[[],[[[]]],[[]]]=>3
[4,2,2,1,2,1]=>[[],[[[]],[[]]]]=>2
[4,2,2,2,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,2,2,2,5]=>[[],[],[[]],[[]]]=>4
[1,1,2,2,5,2]=>[[],[[]],[[[]]]]=>3
[1,1,2,5,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,5,2,2,2]=>[[],[],[],[[],[]]]=>4
[1,2,1,2,2,5]=>[[[[]]],[[],[]]]=>2
[1,2,1,2,5,2]=>[[[],[[[[]]]]]]=>1
[1,2,1,5,2,2]=>[[[[]]],[[],[]]]=>2
[1,2,2,1,2,5]=>[[],[[[[],[]]]]]=>2
[1,2,2,1,5,2]=>[[[]],[[[],[]]]]=>2
[1,2,2,2,1,5]=>[[],[[]],[[[]]]]=>3
[1,2,2,2,5,1]=>[[],[[]],[[],[]]]=>3
[1,2,2,5,1,2]=>[[],[[],[[],[]]]]=>2
[1,2,2,5,2,1]=>[[[]],[[[[]]]]]=>2
[1,2,5,1,2,2]=>[[],[[],[[],[]]]]=>2
[1,2,5,2,1,2]=>[[[],[[[[]]]]]]=>1
[1,2,5,2,2,1]=>[[[[[]]]],[[]]]=>2
[1,5,1,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,5,2,1,2,2]=>[[[]],[[[],[]]]]=>2
[1,5,2,2,1,2]=>[[[[]]],[[],[]]]=>2
[1,5,2,2,2,1]=>[[],[[]],[[],[]]]=>3
[2,1,1,2,2,5]=>[[],[[]],[[[]]]]=>3
[2,1,1,2,5,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,2,2]=>[[],[[]],[[],[]]]=>3
[2,1,2,1,2,5]=>[[[],[[[],[]]]]]=>1
[2,1,2,1,5,2]=>[[[[]],[[],[]]]]=>1
[2,1,2,2,1,5]=>[[[]],[[],[[]]]]=>2
[2,1,2,2,5,1]=>[[[]],[[],[[]]]]=>2
[2,1,2,5,1,2]=>[[[[],[[],[]]]]]=>1
[2,1,2,5,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,5,1,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,5,2,1,2]=>[[[[]],[[],[]]]]=>1
[2,1,5,2,2,1]=>[[[],[]],[[],[]]]=>2
[2,2,1,1,2,5]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,5,2]=>[[],[],[[],[[]]]]=>3
[2,2,1,2,1,5]=>[[],[[[]],[[]]]]=>2
[2,2,1,2,5,1]=>[[],[[[],[[]]]]]=>2
[2,2,1,5,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,2,1]=>[[],[[],[[],[]]]]=>2
[2,2,2,1,1,5]=>[[],[],[],[[[]]]]=>4
[2,2,2,1,5,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,5,1,1]=>[[],[],[],[[],[]]]=>4
[2,2,5,1,1,2]=>[[],[[]],[[],[]]]=>3
[2,2,5,1,2,1]=>[[],[[],[[[]]]]]=>2
[2,2,5,2,1,1]=>[[],[],[[[[]]]]]=>3
[2,5,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[2,5,1,2,1,2]=>[[[],[[],[[]]]]]=>1
[2,5,1,2,2,1]=>[[[[],[]]],[[]]]=>2
[2,5,2,1,1,2]=>[[],[[[[[]]]]]]=>2
[2,5,2,1,2,1]=>[[[[],[[[]]]]]]=>1
[2,5,2,2,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,2,2,2]=>[[],[],[[]],[[]]]=>4
[5,1,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[5,1,2,2,1,2]=>[[],[[[],[[]]]]]=>2
[5,1,2,2,2,1]=>[[],[[[]]],[[]]]=>3
[5,2,1,1,2,2]=>[[[]],[[]],[[]]]=>3
[5,2,1,2,1,2]=>[[[[],[[],[]]]]]=>1
[5,2,1,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,2,2,1,1,2]=>[[],[],[[[[]]]]]=>3
[5,2,2,1,2,1]=>[[],[[],[[[]]]]]=>2
[5,2,2,2,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,2,2,2,6]=>[[],[],[[]],[[]]]=>4
[1,1,2,2,6,2]=>[[],[[]],[[[]]]]=>3
[1,1,2,6,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,6,2,2,2]=>[[],[],[[]],[[]]]=>4
[1,2,1,2,2,6]=>[[[[]]],[[],[]]]=>2
[1,2,1,2,6,2]=>[[[],[[[[]]]]]]=>1
[1,2,1,6,2,2]=>[[[[]]],[[[]]]]=>2
[1,2,2,1,2,6]=>[[],[[[[],[]]]]]=>2
[1,2,2,1,6,2]=>[[[]],[[[[]]]]]=>2
[1,2,2,2,1,6]=>[[],[[]],[[[]]]]=>3
[1,2,2,2,6,1]=>[[],[[]],[[[]]]]=>3
[1,2,2,6,1,2]=>[[],[[[[],[]]]]]=>2
[1,2,2,6,2,1]=>[[[]],[[[[]]]]]=>2
[1,2,6,1,2,2]=>[[],[[],[[[]]]]]=>2
[1,2,6,2,1,2]=>[[[],[[[[]]]]]]=>1
[1,2,6,2,2,1]=>[[[[[]]]],[[]]]=>2
[1,6,1,2,2,2]=>[[],[[[]]],[[]]]=>3
[1,6,2,1,2,2]=>[[[[]]],[[[]]]]=>2
[1,6,2,2,1,2]=>[[[]],[[[[]]]]]=>2
[1,6,2,2,2,1]=>[[],[[]],[[[]]]]=>3
[2,1,1,2,2,6]=>[[],[[]],[[[]]]]=>3
[2,1,1,2,6,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,2,2]=>[[],[[[]]],[[]]]=>3
[2,1,2,1,2,6]=>[[[],[[[],[]]]]]=>1
[2,1,2,1,6,2]=>[[[[]],[[[]]]]]=>1
[2,1,2,2,1,6]=>[[[]],[[],[[]]]]=>2
[2,1,2,2,6,1]=>[[[]],[[[[]]]]]=>2
[2,1,2,6,1,2]=>[[[[],[[[]]]]]]=>1
[2,1,2,6,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,6,1,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,6,2,1,2]=>[[[[[]]],[[]]]]=>1
[2,1,6,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,2,1,1,2,6]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,6,2]=>[[],[],[[[[]]]]]=>3
[2,2,1,2,1,6]=>[[],[[[]],[[]]]]=>2
[2,2,1,2,6,1]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,2,1]=>[[],[[[]],[[]]]]=>2
[2,2,2,1,1,6]=>[[],[],[],[[[]]]]=>4
[2,2,2,1,6,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,6,1,1]=>[[],[],[],[[[]]]]=>4
[2,2,6,1,1,2]=>[[],[[]],[[[]]]]=>3
[2,2,6,1,2,1]=>[[],[[[[[]]]]]]=>2
[2,2,6,2,1,1]=>[[],[],[[[[]]]]]=>3
[2,6,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[2,6,1,2,1,2]=>[[[[[],[[]]]]]]=>1
[2,6,1,2,2,1]=>[[[[[]]]],[[]]]=>2
[2,6,2,1,1,2]=>[[],[[[[[]]]]]]=>2
[2,6,2,1,2,1]=>[[[[[],[[]]]]]]=>1
[2,6,2,2,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,2,2,2]=>[[],[],[[]],[[]]]=>4
[6,1,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[6,1,2,2,1,2]=>[[],[[[],[[]]]]]=>2
[6,1,2,2,2,1]=>[[],[[[]]],[[]]]=>3
[6,2,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[6,2,1,2,1,2]=>[[[[],[[],[]]]]]=>1
[6,2,1,2,2,1]=>[[[]],[[],[[]]]]=>2
[6,2,2,1,1,2]=>[[],[[[]]],[[]]]=>3
[6,2,2,1,2,1]=>[[[]],[[],[[]]]]=>2
[6,2,2,2,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,2,2,3,3]=>[[],[],[],[[],[]]]=>4
[1,1,2,3,2,3]=>[[],[[],[],[[]]]]=>2
[1,1,2,3,3,2]=>[[],[[]],[[],[]]]=>3
[1,1,3,2,2,3]=>[[],[],[[[[]]]]]=>3
[1,1,3,2,3,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,3,2,2]=>[[],[],[[]],[[]]]=>4
[1,2,1,2,3,3]=>[[[]],[[],[],[]]]=>2
[1,2,1,3,2,3]=>[[[],[[],[[]]]]]=>1
[1,2,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[1,2,2,1,3,3]=>[[[]],[[]],[[]]]=>3
[1,2,2,3,1,3]=>[[],[[],[[[]]]]]=>2
[1,2,2,3,3,1]=>[[],[[]],[[],[]]]=>3
[1,2,3,1,2,3]=>[[[],[],[],[[]]]]=>1
[1,2,3,1,3,2]=>[[[],[[[[]]]]]]=>1
[1,2,3,2,1,3]=>[[[],[[],[[]]]]]=>1
[1,2,3,2,3,1]=>[[[],[],[[[]]]]]=>1
[1,2,3,3,1,2]=>[[],[[[],[],[]]]]=>2
[1,2,3,3,2,1]=>[[[],[]],[[],[]]]=>2
[1,3,1,2,2,3]=>[[[[]]],[[],[]]]=>2
[1,3,1,2,3,2]=>[[[[[[],[]]]]]]=>1
[1,3,1,3,2,2]=>[[[]],[[[],[]]]]=>2
[1,3,2,1,2,3]=>[[[[],[[],[]]]]]=>1
[1,3,2,1,3,2]=>[[[],[[],[],[]]]]=>1
[1,3,2,2,1,3]=>[[],[[],[[],[]]]]=>2
[1,3,2,2,3,1]=>[[],[[[[[]]]]]]=>2
[1,3,2,3,1,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,3,2,1]=>[[[[],[],[[]]]]]=>1
[1,3,3,1,2,2]=>[[],[[[]]],[[]]]=>3
[1,3,3,2,1,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,2,1]=>[[],[[]],[[],[]]]=>3
[2,1,1,2,3,3]=>[[],[[]],[[],[]]]=>3
[2,1,1,3,2,3]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,3,2]=>[[],[[]],[[],[]]]=>3
[2,1,2,1,3,3]=>[[[]],[[],[[]]]]=>2
[2,1,2,3,1,3]=>[[[[[[],[]]]]]]=>1
[2,1,2,3,3,1]=>[[[[]]],[[],[]]]=>2
[2,1,3,1,2,3]=>[[[[],[[[]]]]]]=>1
[2,1,3,1,3,2]=>[[[[]],[[],[]]]]=>1
[2,1,3,2,1,3]=>[[[],[],[[],[]]]]=>1
[2,1,3,2,3,1]=>[[[[]],[[[]]]]]=>1
[2,1,3,3,1,2]=>[[[]],[[[[]]]]]=>2
[2,1,3,3,2,1]=>[[[]],[[],[],[]]]=>2
[2,2,1,1,3,3]=>[[],[],[[]],[[]]]=>4
[2,2,1,3,1,3]=>[[],[[[],[[]]]]]=>2
[2,2,1,3,3,1]=>[[],[[]],[[[]]]]=>3
[2,2,3,1,1,3]=>[[],[[]],[[[]]]]=>3
[2,2,3,1,3,1]=>[[],[[[],[[]]]]]=>2
[2,2,3,3,1,1]=>[[],[],[[]],[[]]]=>4
[2,3,1,1,2,3]=>[[],[[],[],[[]]]]=>2
[2,3,1,1,3,2]=>[[],[[[[[]]]]]]=>2
[2,3,1,2,1,3]=>[[[],[[[[]]]]]]=>1
[2,3,1,2,3,1]=>[[[],[],[[],[]]]]=>1
[2,3,1,3,1,2]=>[[[],[[],[[]]]]]=>1
[2,3,1,3,2,1]=>[[[[[],[[]]]]]]=>1
[2,3,2,1,1,3]=>[[],[[[],[[]]]]]=>2
[2,3,2,1,3,1]=>[[[[],[[[]]]]]]=>1
[2,3,2,3,1,1]=>[[[[],[]]],[[]]]=>2
[2,3,3,1,1,2]=>[[],[[]],[[],[]]]=>3
[2,3,3,1,2,1]=>[[],[[[[],[]]]]]=>2
[2,3,3,2,1,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,2,2,3]=>[[],[[]],[[],[]]]=>3
[3,1,1,2,3,2]=>[[],[[],[[[]]]]]=>2
[3,1,1,3,2,2]=>[[],[[]],[[[]]]]=>3
[3,1,2,1,2,3]=>[[[[],[],[[]]]]]=>1
[3,1,2,1,3,2]=>[[[[[]],[[]]]]]=>1
[3,1,2,2,1,3]=>[[[]],[[[[]]]]]=>2
[3,1,2,2,3,1]=>[[],[[],[[],[]]]]=>2
[3,1,2,3,1,2]=>[[[],[[],[],[]]]]=>1
[3,1,2,3,2,1]=>[[[[],[[],[]]]]]=>1
[3,1,3,1,2,2]=>[[],[[[],[[]]]]]=>2
[3,1,3,2,1,2]=>[[[[[],[[]]]]]]=>1
[3,1,3,2,2,1]=>[[],[[[]],[[]]]]=>2
[3,2,1,1,2,3]=>[[],[[],[[],[]]]]=>2
[3,2,1,1,3,2]=>[[],[[[],[],[]]]]=>2
[3,2,1,2,1,3]=>[[[],[[]],[[]]]]=>1
[3,2,1,2,3,1]=>[[[],[[[],[]]]]]=>1
[3,2,1,3,1,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,3,2,1]=>[[[],[],[],[[]]]]=>1
[3,2,2,1,1,3]=>[[],[],[[[],[]]]]=>3
[3,2,2,1,3,1]=>[[],[[],[[[]]]]]=>2
[3,2,2,3,1,1]=>[[],[[[]]],[[]]]=>3
[3,2,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[3,2,3,1,2,1]=>[[[[]],[[],[]]]]=>1
[3,2,3,2,1,1]=>[[],[[],[],[[]]]]=>2
[3,3,1,1,2,2]=>[[],[],[],[[[]]]]=>4
[3,3,1,2,1,2]=>[[],[[[],[[]]]]]=>2
[3,3,1,2,2,1]=>[[],[[]],[[[]]]]=>3
[3,3,2,1,1,2]=>[[],[],[[[],[]]]]=>3
[3,3,2,1,2,1]=>[[],[[],[],[[]]]]=>2
[3,3,2,2,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,2,2,3,4]=>[[],[],[[],[],[]]]=>3
[1,1,2,2,4,3]=>[[],[[]],[[[]]]]=>3
[1,1,2,3,2,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,3,4,2]=>[[],[[],[],[[]]]]=>2
[1,1,2,4,2,3]=>[[],[[],[[[]]]]]=>2
[1,1,2,4,3,2]=>[[],[[[[],[]]]]]=>2
[1,1,3,2,2,4]=>[[],[],[[],[[]]]]=>3
[1,1,3,2,4,2]=>[[],[[],[[[]]]]]=>2
[1,1,3,4,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,4,2,2,3]=>[[],[[]],[[[]]]]=>3
[1,1,4,2,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,2,2]=>[[],[],[[],[[]]]]=>3
[1,2,1,2,3,4]=>[[[],[],[],[[]]]]=>1
[1,2,1,2,4,3]=>[[[],[[[],[]]]]]=>1
[1,2,1,3,2,4]=>[[[[],[[],[]]]]]=>1
[1,2,1,3,4,2]=>[[[[]],[[[]]]]]=>1
[1,2,1,4,2,3]=>[[[[[]]],[[]]]]=>1
[1,2,1,4,3,2]=>[[[[],[],[[]]]]]=>1
[1,2,2,1,3,4]=>[[],[[[],[[]]]]]=>2
[1,2,2,1,4,3]=>[[[]],[[],[[]]]]=>2
[1,2,2,3,1,4]=>[[],[[],[[[]]]]]=>2
[1,2,2,3,4,1]=>[[],[[],[],[[]]]]=>2
[1,2,2,4,1,3]=>[[[]],[[],[[]]]]=>2
[1,2,2,4,3,1]=>[[[]],[[[[]]]]]=>2
[1,2,3,1,2,4]=>[[[],[[]],[[]]]]=>1
[1,2,3,1,4,2]=>[[[],[[],[[]]]]]=>1
[1,2,3,2,1,4]=>[[[],[[],[[]]]]]=>1
[1,2,3,2,4,1]=>[[[],[[[[]]]]]]=>1
[1,2,3,4,1,2]=>[[[],[],[],[[]]]]=>1
[1,2,3,4,2,1]=>[[[],[],[[[]]]]]=>1
[1,2,4,1,2,3]=>[[[],[],[[[]]]]]=>1
[1,2,4,1,3,2]=>[[[[[]],[[]]]]]=>1
[1,2,4,2,1,3]=>[[[[[]],[[]]]]]=>1
[1,2,4,2,3,1]=>[[[],[[],[[]]]]]=>1
[1,2,4,3,1,2]=>[[[[]],[[[]]]]]=>1
[1,2,4,3,2,1]=>[[[[[],[],[]]]]]=>1
[1,3,1,2,2,4]=>[[[[]]],[[],[]]]=>2
[1,3,1,2,4,2]=>[[[[]],[[],[]]]]=>1
[1,3,1,4,2,2]=>[[],[[[]],[[]]]]=>2
[1,3,2,1,2,4]=>[[[[]],[[],[]]]]=>1
[1,3,2,1,4,2]=>[[[[],[[[]]]]]]=>1
[1,3,2,2,1,4]=>[[],[[[]],[[]]]]=>2
[1,3,2,2,4,1]=>[[],[[],[[[]]]]]=>2
[1,3,2,4,1,2]=>[[[],[[[[]]]]]]=>1
[1,3,2,4,2,1]=>[[[],[[[],[]]]]]=>1
[1,3,4,1,2,2]=>[[],[[[]],[[]]]]=>2
[1,3,4,2,1,2]=>[[[[[]],[[]]]]]=>1
[1,3,4,2,2,1]=>[[],[[[[[]]]]]]=>2
[1,4,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[1,4,1,2,3,2]=>[[[[[]],[[]]]]]=>1
[1,4,1,3,2,2]=>[[],[[[[[]]]]]]=>2
[1,4,2,1,2,3]=>[[[[[],[[]]]]]]=>1
[1,4,2,1,3,2]=>[[[[[]],[[]]]]]=>1
[1,4,2,2,1,3]=>[[],[[[[[]]]]]]=>2
[1,4,2,2,3,1]=>[[],[[[],[[]]]]]=>2
[1,4,2,3,1,2]=>[[[[],[[],[]]]]]=>1
[1,4,2,3,2,1]=>[[[[[],[[]]]]]]=>1
[1,4,3,1,2,2]=>[[[[]]],[[[]]]]=>2
[1,4,3,2,1,2]=>[[[[],[],[[]]]]]=>1
[1,4,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[2,1,1,2,3,4]=>[[],[[],[],[[]]]]=>2
[2,1,1,2,4,3]=>[[],[[[[],[]]]]]=>2
[2,1,1,3,2,4]=>[[],[[],[[],[]]]]=>2
[2,1,1,3,4,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,2,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,3,2]=>[[],[[[],[],[]]]]=>2
[2,1,2,1,3,4]=>[[[],[[],[[]]]]]=>1
[2,1,2,1,4,3]=>[[[],[[]],[[]]]]=>1
[2,1,2,3,1,4]=>[[[[[[],[]]]]]]=>1
[2,1,2,3,4,1]=>[[[[[],[],[]]]]]=>1
[2,1,2,4,1,3]=>[[[[[]],[[]]]]]=>1
[2,1,2,4,3,1]=>[[[[[]]],[[]]]]=>1
[2,1,3,1,2,4]=>[[[[],[[[]]]]]]=>1
[2,1,3,1,4,2]=>[[[[[]],[[]]]]]=>1
[2,1,3,2,1,4]=>[[[],[[]],[[]]]]=>1
[2,1,3,2,4,1]=>[[[],[[[],[]]]]]=>1
[2,1,3,4,1,2]=>[[[[[]],[[]]]]]=>1
[2,1,3,4,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,4,1,2,3]=>[[[[],[[[]]]]]]=>1
[2,1,4,1,3,2]=>[[[],[[[[]]]]]]=>1
[2,1,4,2,1,3]=>[[[],[[[[]]]]]]=>1
[2,1,4,2,3,1]=>[[[[[]],[[]]]]]=>1
[2,1,4,3,1,2]=>[[[[[]]],[[]]]]=>1
[2,1,4,3,2,1]=>[[[],[],[],[[]]]]=>1
[2,2,1,1,3,4]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,4,3]=>[[],[],[[[],[]]]]=>3
[2,2,1,3,1,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,3,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,1,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,3,1]=>[[],[[[]],[[]]]]=>2
[2,2,3,1,1,4]=>[[],[[]],[[[]]]]=>3
[2,2,3,1,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,3,4,1,1]=>[[],[],[[[],[]]]]=>3
[2,2,4,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,2,4,1,3,1]=>[[],[[[]],[[]]]]=>2
[2,2,4,3,1,1]=>[[],[[]],[[[]]]]=>3
[2,3,1,1,2,4]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,4,2]=>[[],[[[],[[]]]]]=>2
[2,3,1,2,1,4]=>[[[],[[[[]]]]]]=>1
[2,3,1,2,4,1]=>[[[[[]]],[[]]]]=>1
[2,3,1,4,1,2]=>[[[],[[[[]]]]]]=>1
[2,3,1,4,2,1]=>[[[[[]],[[]]]]]=>1
[2,3,2,1,1,4]=>[[],[[[],[[]]]]]=>2
[2,3,2,1,4,1]=>[[[[],[[[]]]]]]=>1
[2,3,2,4,1,1]=>[[[[]]],[[[]]]]=>2
[2,3,4,1,1,2]=>[[[]],[[],[],[]]]=>2
[2,3,4,1,2,1]=>[[[],[[]],[[]]]]=>1
[2,3,4,2,1,1]=>[[[[],[]]],[[]]]=>2
[2,4,1,1,2,3]=>[[[[]]],[[],[]]]=>2
[2,4,1,1,3,2]=>[[[]],[[],[[]]]]=>2
[2,4,1,2,1,3]=>[[[],[[[[]]]]]]=>1
[2,4,1,2,3,1]=>[[[[[],[[]]]]]]=>1
[2,4,1,3,1,2]=>[[[[]],[[[]]]]]=>1
[2,4,1,3,2,1]=>[[[],[[],[[]]]]]=>1
[2,4,2,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,4,2,1,3,1]=>[[[],[[],[[]]]]]=>1
[2,4,2,3,1,1]=>[[],[[[]],[[]]]]=>2
[2,4,3,1,1,2]=>[[[[[]]]],[[]]]=>2
[2,4,3,1,2,1]=>[[[[[]],[[]]]]]=>1
[2,4,3,2,1,1]=>[[],[[],[],[[]]]]=>2
[3,1,1,2,2,4]=>[[],[[[]]],[[]]]=>3
[3,1,1,2,4,2]=>[[],[[[[],[]]]]]=>2
[3,1,1,4,2,2]=>[[],[],[[],[[]]]]=>3
[3,1,2,1,2,4]=>[[[[],[[[]]]]]]=>1
[3,1,2,1,4,2]=>[[[[]],[[[]]]]]=>1
[3,1,2,2,1,4]=>[[[]],[[[[]]]]]=>2
[3,1,2,2,4,1]=>[[[[]]],[[[]]]]=>2
[3,1,2,4,1,2]=>[[[[[[],[]]]]]]=>1
[3,1,2,4,2,1]=>[[[[[]]],[[]]]]=>1
[3,1,4,1,2,2]=>[[],[[[[[]]]]]]=>2
[3,1,4,2,1,2]=>[[[[[]]],[[]]]]=>1
[3,1,4,2,2,1]=>[[],[[[],[[]]]]]=>2
[3,2,1,1,2,4]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,4,2]=>[[],[[[[],[]]]]]=>2
[3,2,1,2,1,4]=>[[[],[[]],[[]]]]=>1
[3,2,1,2,4,1]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,1,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,2,1]=>[[[],[],[[[]]]]]=>1
[3,2,2,1,1,4]=>[[],[],[[[],[]]]]=>3
[3,2,2,1,4,1]=>[[],[[],[[[]]]]]=>2
[3,2,2,4,1,1]=>[[],[[[]]],[[]]]=>3
[3,2,4,1,1,2]=>[[[[]]],[[[]]]]=>2
[3,2,4,1,2,1]=>[[[],[[[[]]]]]]=>1
[3,2,4,2,1,1]=>[[[[]]],[[],[]]]=>2
[3,4,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[3,4,1,2,1,2]=>[[[],[],[[[]]]]]=>1
[3,4,1,2,2,1]=>[[[]],[[],[[]]]]=>2
[3,4,2,1,1,2]=>[[[]],[[],[[]]]]=>2
[3,4,2,1,2,1]=>[[[],[[],[[]]]]]=>1
[3,4,2,2,1,1]=>[[],[[[]]],[[]]]=>3
[4,1,1,2,2,3]=>[[],[],[[],[[]]]]=>3
[4,1,1,2,3,2]=>[[],[[[]],[[]]]]=>2
[4,1,1,3,2,2]=>[[],[],[[[[]]]]]=>3
[4,1,2,1,2,3]=>[[[[],[],[[]]]]]=>1
[4,1,2,1,3,2]=>[[[[[],[[]]]]]]=>1
[4,1,2,2,1,3]=>[[[[]]],[[[]]]]=>2
[4,1,2,2,3,1]=>[[[]],[[],[[]]]]=>2
[4,1,2,3,1,2]=>[[[[[],[],[]]]]]=>1
[4,1,2,3,2,1]=>[[[[],[[],[]]]]]=>1
[4,1,3,1,2,2]=>[[],[[[[[]]]]]]=>2
[4,1,3,2,1,2]=>[[[[[]],[[]]]]]=>1
[4,1,3,2,2,1]=>[[[]],[[],[[]]]]=>2
[4,2,1,1,2,3]=>[[],[[[]],[[]]]]=>2
[4,2,1,1,3,2]=>[[],[[[],[[]]]]]=>2
[4,2,1,2,1,3]=>[[[[[],[[]]]]]]=>1
[4,2,1,2,3,1]=>[[[[]],[[],[]]]]=>1
[4,2,1,3,1,2]=>[[[[[]]],[[]]]]=>1
[4,2,1,3,2,1]=>[[[[],[],[[]]]]]=>1
[4,2,2,1,1,3]=>[[],[[[]]],[[]]]=>3
[4,2,2,1,3,1]=>[[],[[[],[[]]]]]=>2
[4,2,2,3,1,1]=>[[],[],[[],[[]]]]=>3
[4,2,3,1,1,2]=>[[[],[]],[[],[]]]=>2
[4,2,3,1,2,1]=>[[[],[[[],[]]]]]=>1
[4,2,3,2,1,1]=>[[[]],[[],[[]]]]=>2
[4,3,1,1,2,2]=>[[],[[[]]],[[]]]=>3
[4,3,1,2,1,2]=>[[[],[[],[[]]]]]=>1
[4,3,1,2,2,1]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,1,2]=>[[],[[[],[],[]]]]=>2
[4,3,2,1,2,1]=>[[[],[],[],[[]]]]=>1
[4,3,2,2,1,1]=>[[],[],[[],[],[]]]=>3
[1,1,2,2,3,5]=>[[],[],[[],[[]]]]=>3
[1,1,2,2,5,3]=>[[],[[]],[[[]]]]=>3
[1,1,2,3,2,5]=>[[],[[],[[[]]]]]=>2
[1,1,2,3,5,2]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,2,3]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,3,2,2,5]=>[[],[],[[[[]]]]]=>3
[1,1,3,2,5,2]=>[[],[[[[[]]]]]]=>2
[1,1,3,5,2,2]=>[[],[],[[[],[]]]]=>3
[1,1,5,2,2,3]=>[[],[[]],[[],[]]]=>3
[1,1,5,2,3,2]=>[[],[[],[[[]]]]]=>2
[1,1,5,3,2,2]=>[[],[[]],[[[]]]]=>3
[1,2,1,2,3,5]=>[[[],[],[[[]]]]]=>1
[1,2,1,2,5,3]=>[[[],[[[[]]]]]]=>1
[1,2,1,3,2,5]=>[[[[[]],[[]]]]]=>1
[1,2,1,3,5,2]=>[[[[[[],[]]]]]]=>1
[1,2,1,5,2,3]=>[[[[]],[[],[]]]]=>1
[1,2,1,5,3,2]=>[[[[[]],[[]]]]]=>1
[1,2,2,1,3,5]=>[[[]],[[[],[]]]]=>2
[1,2,2,1,5,3]=>[[[]],[[[[]]]]]=>2
[1,2,2,3,1,5]=>[[],[[],[[[]]]]]=>2
[1,2,2,3,5,1]=>[[],[[],[[[]]]]]=>2
[1,2,2,5,1,3]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,3,1]=>[[[]],[[[],[]]]]=>2
[1,2,3,1,2,5]=>[[[],[[]],[[]]]]=>1
[1,2,3,1,5,2]=>[[[],[[[],[]]]]]=>1
[1,2,3,2,1,5]=>[[[],[[],[[]]]]]=>1
[1,2,3,2,5,1]=>[[[],[[[],[]]]]]=>1
[1,2,3,5,1,2]=>[[[],[],[[[]]]]]=>1
[1,2,3,5,2,1]=>[[[],[[[[]]]]]]=>1
[1,2,5,1,2,3]=>[[[],[],[[],[]]]]=>1
[1,2,5,1,3,2]=>[[[[],[[[]]]]]]=>1
[1,2,5,2,1,3]=>[[[[[[[]]]]]]]=>1
[1,2,5,2,3,1]=>[[[[[]]],[[]]]]=>1
[1,2,5,3,1,2]=>[[[],[[],[[]]]]]=>1
[1,2,5,3,2,1]=>[[[[[],[[]]]]]]=>1
[1,3,1,2,2,5]=>[[[[[]]]],[[]]]=>2
[1,3,1,2,5,2]=>[[[[[[[]]]]]]]=>1
[1,3,1,5,2,2]=>[[],[[],[[[]]]]]=>2
[1,3,2,1,2,5]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,5,2]=>[[[[],[[],[]]]]]=>1
[1,3,2,2,1,5]=>[[],[[[]],[[]]]]=>2
[1,3,2,2,5,1]=>[[],[[],[[[]]]]]=>2
[1,3,2,5,1,2]=>[[[[[[],[]]]]]]=>1
[1,3,2,5,2,1]=>[[[[[[],[]]]]]]=>1
[1,3,5,1,2,2]=>[[],[[[[],[]]]]]=>2
[1,3,5,2,1,2]=>[[[],[[[[]]]]]]=>1
[1,3,5,2,2,1]=>[[[[],[]]],[[]]]=>2
[1,5,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[1,5,1,2,3,2]=>[[[[[]],[[]]]]]=>1
[1,5,1,3,2,2]=>[[],[[[[[]]]]]]=>2
[1,5,2,1,2,3]=>[[[],[[],[[]]]]]=>1
[1,5,2,1,3,2]=>[[[],[[[],[]]]]]=>1
[1,5,2,2,1,3]=>[[[[]]],[[],[]]]=>2
[1,5,2,2,3,1]=>[[[[]]],[[],[]]]=>2
[1,5,2,3,1,2]=>[[[],[[[],[]]]]]=>1
[1,5,2,3,2,1]=>[[[],[[],[[]]]]]=>1
[1,5,3,1,2,2]=>[[],[[[],[[]]]]]=>2
[1,5,3,2,1,2]=>[[[[],[[[]]]]]]=>1
[1,5,3,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,2,3,5]=>[[],[[],[[[]]]]]=>2
[2,1,1,2,5,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,3,2,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,5,2]=>[[],[[],[[[]]]]]=>2
[2,1,1,5,2,3]=>[[],[[],[[[]]]]]=>2
[2,1,1,5,3,2]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,3,5]=>[[[[]],[[],[]]]]=>1
[2,1,2,1,5,3]=>[[[[]],[[[]]]]]=>1
[2,1,2,3,1,5]=>[[[[[[],[]]]]]]=>1
[2,1,2,3,5,1]=>[[[[[[],[]]]]]]=>1
[2,1,2,5,1,3]=>[[[[[],[[]]]]]]=>1
[2,1,2,5,3,1]=>[[[[],[[[]]]]]]=>1
[2,1,3,1,2,5]=>[[[[[[[]]]]]]]=>1
[2,1,3,1,5,2]=>[[[[],[[[]]]]]]=>1
[2,1,3,2,1,5]=>[[[],[[]],[[]]]]=>1
[2,1,3,2,5,1]=>[[[[]],[[],[]]]]=>1
[2,1,3,5,1,2]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,2,1]=>[[[],[[[],[]]]]]=>1
[2,1,5,1,2,3]=>[[[[],[[[]]]]]]=>1
[2,1,5,1,3,2]=>[[[],[[[[]]]]]]=>1
[2,1,5,2,1,3]=>[[[[]],[[],[]]]]=>1
[2,1,5,2,3,1]=>[[[[[[],[]]]]]]=>1
[2,1,5,3,1,2]=>[[[[[],[[]]]]]]=>1
[2,1,5,3,2,1]=>[[[],[[]],[[]]]]=>1
[2,2,1,1,3,5]=>[[],[],[[],[[]]]]=>3
[2,2,1,1,5,3]=>[[],[],[[[[]]]]]=>3
[2,2,1,3,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,1,3,5,1]=>[[],[[[[],[]]]]]=>2
[2,2,1,5,1,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,3,1]=>[[],[[[],[[]]]]]=>2
[2,2,3,1,1,5]=>[[],[[]],[[[]]]]=>3
[2,2,3,1,5,1]=>[[],[[[[[]]]]]]=>2
[2,2,3,5,1,1]=>[[],[],[[[[]]]]]=>3
[2,2,5,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,2,5,1,3,1]=>[[],[[],[[[]]]]]=>2
[2,2,5,3,1,1]=>[[],[],[[],[[]]]]=>3
[2,3,1,1,2,5]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,5,2]=>[[],[[],[[[]]]]]=>2
[2,3,1,2,1,5]=>[[[],[[[[]]]]]]=>1
[2,3,1,2,5,1]=>[[[],[[],[[]]]]]=>1
[2,3,1,5,1,2]=>[[[],[[[[]]]]]]=>1
[2,3,1,5,2,1]=>[[[[[[],[]]]]]]=>1
[2,3,2,1,1,5]=>[[],[[[],[[]]]]]=>2
[2,3,2,1,5,1]=>[[[[],[[[]]]]]]=>1
[2,3,2,5,1,1]=>[[[[]]],[[],[]]]=>2
[2,3,5,1,1,2]=>[[[[]]],[[],[]]]=>2
[2,3,5,1,2,1]=>[[[[[]]],[[]]]]=>1
[2,3,5,2,1,1]=>[[],[[[[[]]]]]]=>2
[2,5,1,1,2,3]=>[[[],[]],[[],[]]]=>2
[2,5,1,1,3,2]=>[[[[]]],[[],[]]]=>2
[2,5,1,2,1,3]=>[[[],[[[[]]]]]]=>1
[2,5,1,2,3,1]=>[[[],[[],[[]]]]]=>1
[2,5,1,3,1,2]=>[[[],[[[[]]]]]]=>1
[2,5,1,3,2,1]=>[[[],[[[],[]]]]]=>1
[2,5,2,1,1,3]=>[[],[[[[[]]]]]]=>2
[2,5,2,1,3,1]=>[[[[[[[]]]]]]]=>1
[2,5,2,3,1,1]=>[[],[[[[[]]]]]]=>2
[2,5,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[2,5,3,1,2,1]=>[[[[],[[[]]]]]]=>1
[2,5,3,2,1,1]=>[[[]],[[],[[]]]]=>2
[3,1,1,2,2,5]=>[[],[[[]]],[[]]]=>3
[3,1,1,2,5,2]=>[[[[[]]]],[[]]]=>2
[3,1,1,5,2,2]=>[[],[],[[],[[]]]]=>3
[3,1,2,1,2,5]=>[[[[],[[[]]]]]]=>1
[3,1,2,1,5,2]=>[[[[],[[[]]]]]]=>1
[3,1,2,2,1,5]=>[[[]],[[[[]]]]]=>2
[3,1,2,2,5,1]=>[[[]],[[],[[]]]]=>2
[3,1,2,5,1,2]=>[[[[],[[],[]]]]]=>1
[3,1,2,5,2,1]=>[[[[[[[]]]]]]]=>1
[3,1,5,1,2,2]=>[[],[[[[[]]]]]]=>2
[3,1,5,2,1,2]=>[[[[[[],[]]]]]]=>1
[3,1,5,2,2,1]=>[[[[]]],[[],[]]]=>2
[3,2,1,1,2,5]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,5,2]=>[[],[[],[[],[]]]]=>2
[3,2,1,2,1,5]=>[[[],[[]],[[]]]]=>1
[3,2,1,2,5,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,5,1,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,2,1]=>[[[],[],[[],[]]]]=>1
[3,2,2,1,1,5]=>[[],[],[[[],[]]]]=>3
[3,2,2,1,5,1]=>[[],[[],[[[]]]]]=>2
[3,2,2,5,1,1]=>[[],[[]],[[],[]]]=>3
[3,2,5,1,1,2]=>[[[[]]],[[],[]]]=>2
[3,2,5,1,2,1]=>[[[],[[[],[]]]]]=>1
[3,2,5,2,1,1]=>[[],[[],[[[]]]]]=>2
[3,5,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[3,5,1,2,1,2]=>[[[[[],[[]]]]]]=>1
[3,5,1,2,2,1]=>[[[[[]]]],[[]]]=>2
[3,5,2,1,1,2]=>[[],[[[[[]]]]]]=>2
[3,5,2,1,2,1]=>[[[[[[],[]]]]]]=>1
[3,5,2,2,1,1]=>[[],[],[[[[]]]]]=>3
[5,1,1,2,2,3]=>[[],[[]],[[],[]]]=>3
[5,1,1,2,3,2]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,2,2]=>[[],[[]],[[[]]]]=>3
[5,1,2,1,2,3]=>[[[[[],[],[]]]]]=>1
[5,1,2,1,3,2]=>[[[[[],[[]]]]]]=>1
[5,1,2,2,1,3]=>[[[[]]],[[[]]]]=>2
[5,1,2,2,3,1]=>[[],[[[]],[[]]]]=>2
[5,1,2,3,1,2]=>[[[[],[],[[]]]]]=>1
[5,1,2,3,2,1]=>[[[[],[[],[]]]]]=>1
[5,1,3,1,2,2]=>[[],[[[[[]]]]]]=>2
[5,1,3,2,1,2]=>[[[[[],[[]]]]]]=>1
[5,1,3,2,2,1]=>[[],[[],[[[]]]]]=>2
[5,2,1,1,2,3]=>[[[]],[[],[[]]]]=>2
[5,2,1,1,3,2]=>[[[[],[]]],[[]]]=>2
[5,2,1,2,1,3]=>[[[[[],[[]]]]]]=>1
[5,2,1,2,3,1]=>[[[[],[[[]]]]]]=>1
[5,2,1,3,1,2]=>[[[[[[[]]]]]]]=>1
[5,2,1,3,2,1]=>[[[[],[],[[]]]]]=>1
[5,2,2,1,1,3]=>[[],[],[[[[]]]]]=>3
[5,2,2,1,3,1]=>[[],[[[[[]]]]]]=>2
[5,2,2,3,1,1]=>[[],[],[[[[]]]]]=>3
[5,2,3,1,1,2]=>[[[[]]],[[],[]]]=>2
[5,2,3,1,2,1]=>[[[[],[[[]]]]]]=>1
[5,2,3,2,1,1]=>[[],[[[]],[[]]]]=>2
[5,3,1,1,2,2]=>[[],[],[[[],[]]]]=>3
[5,3,1,2,1,2]=>[[[],[[],[[]]]]]=>1
[5,3,1,2,2,1]=>[[[]],[[[],[]]]]=>2
[5,3,2,1,1,2]=>[[[[],[]]],[[]]]=>2
[5,3,2,1,2,1]=>[[[[],[],[[]]]]]=>1
[5,3,2,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,2,3,6]=>[[],[],[[],[[]]]]=>3
[1,1,2,2,6,3]=>[[],[[]],[[],[]]]=>3
[1,1,2,3,2,6]=>[[],[[],[[[]]]]]=>2
[1,1,2,3,6,2]=>[[],[[],[[],[]]]]=>2
[1,1,2,6,2,3]=>[[],[[],[[[]]]]]=>2
[1,1,2,6,3,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,2,2,6]=>[[],[],[[[[]]]]]=>3
[1,1,3,2,6,2]=>[[],[[[[[]]]]]]=>2
[1,1,3,6,2,2]=>[[],[],[[],[[]]]]=>3
[1,1,6,2,2,3]=>[[],[[]],[[[]]]]=>3
[1,1,6,2,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,2,2]=>[[],[[]],[[[]]]]=>3
[1,2,1,2,3,6]=>[[[],[],[[[]]]]]=>1
[1,2,1,2,6,3]=>[[[],[[],[[]]]]]=>1
[1,2,1,3,2,6]=>[[[[[]],[[]]]]]=>1
[1,2,1,3,6,2]=>[[[[[],[[]]]]]]=>1
[1,2,1,6,2,3]=>[[[[[]]],[[]]]]=>1
[1,2,1,6,3,2]=>[[[[[]],[[]]]]]=>1
[1,2,2,1,3,6]=>[[[]],[[[[]]]]]=>2
[1,2,2,1,6,3]=>[[[]],[[[[]]]]]=>2
[1,2,2,3,1,6]=>[[],[[],[[],[]]]]=>2
[1,2,2,3,6,1]=>[[],[[],[[[]]]]]=>2
[1,2,2,6,1,3]=>[[[]],[[[],[]]]]=>2
[1,2,2,6,3,1]=>[[[]],[[],[[]]]]=>2
[1,2,3,1,2,6]=>[[[],[[]],[[]]]]=>1
[1,2,3,1,6,2]=>[[[],[[],[[]]]]]=>1
[1,2,3,2,1,6]=>[[[],[[],[[]]]]]=>1
[1,2,3,2,6,1]=>[[[],[[[[]]]]]]=>1
[1,2,3,6,1,2]=>[[[],[],[[[]]]]]=>1
[1,2,3,6,2,1]=>[[[],[[],[[]]]]]=>1
[1,2,6,1,2,3]=>[[[],[],[[[]]]]]=>1
[1,2,6,1,3,2]=>[[[[[],[[]]]]]]=>1
[1,2,6,2,1,3]=>[[[[[[[]]]]]]]=>1
[1,2,6,2,3,1]=>[[[[[]]],[[]]]]=>1
[1,2,6,3,1,2]=>[[[],[[[],[]]]]]=>1
[1,2,6,3,2,1]=>[[[[],[[],[]]]]]=>1
[1,3,1,2,2,6]=>[[[[[]]]],[[]]]=>2
[1,3,1,2,6,2]=>[[[[[[[]]]]]]]=>1
[1,3,1,6,2,2]=>[[],[[[],[[]]]]]=>2
[1,3,2,1,2,6]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,6,2]=>[[[[],[[[]]]]]]=>1
[1,3,2,2,1,6]=>[[],[[[]],[[]]]]=>2
[1,3,2,2,6,1]=>[[],[[[],[[]]]]]=>2
[1,3,2,6,1,2]=>[[[[[]]],[[]]]]=>1
[1,3,2,6,2,1]=>[[[[[[],[]]]]]]=>1
[1,3,6,1,2,2]=>[[],[[[],[[]]]]]=>2
[1,3,6,2,1,2]=>[[[[],[[[]]]]]]=>1
[1,3,6,2,2,1]=>[[[]],[[],[[]]]]=>2
[1,6,1,2,2,3]=>[[[]],[[],[[]]]]=>2
[1,6,1,2,3,2]=>[[[[[],[[]]]]]]=>1
[1,6,1,3,2,2]=>[[[]],[[[],[]]]]=>2
[1,6,2,1,2,3]=>[[[[],[[[]]]]]]=>1
[1,6,2,1,3,2]=>[[[[[]],[[]]]]]=>1
[1,6,2,2,1,3]=>[[[]],[[[[]]]]]=>2
[1,6,2,2,3,1]=>[[[[],[]]],[[]]]=>2
[1,6,2,3,1,2]=>[[[],[[],[[]]]]]=>1
[1,6,2,3,2,1]=>[[[[],[[[]]]]]]=>1
[1,6,3,1,2,2]=>[[],[[[],[[]]]]]=>2
[1,6,3,2,1,2]=>[[[[[],[[]]]]]]=>1
[1,6,3,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,2,3,6]=>[[],[[],[[[]]]]]=>2
[2,1,1,2,6,3]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,2,6]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,6,2]=>[[],[[[],[[]]]]]=>2
[2,1,1,6,2,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,3,2]=>[[],[[[],[[]]]]]=>2
[2,1,2,1,3,6]=>[[[[]],[[[]]]]]=>1
[2,1,2,1,6,3]=>[[[[]],[[[]]]]]=>1
[2,1,2,3,1,6]=>[[[[],[[],[]]]]]=>1
[2,1,2,3,6,1]=>[[[[[[],[]]]]]]=>1
[2,1,2,6,1,3]=>[[[[],[[[]]]]]]=>1
[2,1,2,6,3,1]=>[[[[[],[[]]]]]]=>1
[2,1,3,1,2,6]=>[[[[[[[]]]]]]]=>1
[2,1,3,1,6,2]=>[[[[[],[[]]]]]]=>1
[2,1,3,2,1,6]=>[[[],[[]],[[]]]]=>1
[2,1,3,2,6,1]=>[[[],[[],[[]]]]]=>1
[2,1,3,6,1,2]=>[[[[[],[[]]]]]]=>1
[2,1,3,6,2,1]=>[[[],[[],[[]]]]]=>1
[2,1,6,1,2,3]=>[[[[[]],[[]]]]]=>1
[2,1,6,1,3,2]=>[[[[]],[[],[]]]]=>1
[2,1,6,2,1,3]=>[[[[[]]],[[]]]]=>1
[2,1,6,2,3,1]=>[[[[],[[[]]]]]]=>1
[2,1,6,3,1,2]=>[[[[[],[[]]]]]]=>1
[2,1,6,3,2,1]=>[[[],[[]],[[]]]]=>1
[2,2,1,1,3,6]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,6,3]=>[[],[],[[[[]]]]]=>3
[2,2,1,3,1,6]=>[[],[[[],[[]]]]]=>2
[2,2,1,3,6,1]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,1,3]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,3,1]=>[[],[[[],[[]]]]]=>2
[2,2,3,1,1,6]=>[[],[],[[],[[]]]]=>3
[2,2,3,1,6,1]=>[[],[[[],[[]]]]]=>2
[2,2,3,6,1,1]=>[[],[],[[[[]]]]]=>3
[2,2,6,1,1,3]=>[[],[],[[],[[]]]]=>3
[2,2,6,1,3,1]=>[[],[[[],[[]]]]]=>2
[2,2,6,3,1,1]=>[[],[],[[[],[]]]]=>3
[2,3,1,1,2,6]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,6,2]=>[[],[[[]],[[]]]]=>2
[2,3,1,2,1,6]=>[[[],[[[],[]]]]]=>1
[2,3,1,2,6,1]=>[[[[[]]],[[]]]]=>1
[2,3,1,6,1,2]=>[[[],[[[],[]]]]]=>1
[2,3,1,6,2,1]=>[[[[],[[[]]]]]]=>1
[2,3,2,1,1,6]=>[[],[[[],[[]]]]]=>2
[2,3,2,1,6,1]=>[[[[],[[[]]]]]]=>1
[2,3,2,6,1,1]=>[[[[]]],[[[]]]]=>2
[2,3,6,1,1,2]=>[[[[]]],[[],[]]]=>2
[2,3,6,1,2,1]=>[[[[[]]],[[]]]]=>1
[2,3,6,2,1,1]=>[[],[[[],[[]]]]]=>2
[2,6,1,1,2,3]=>[[[[]]],[[],[]]]=>2
[2,6,1,1,3,2]=>[[[]],[[],[[]]]]=>2
[2,6,1,2,1,3]=>[[[[[[],[]]]]]]=>1
[2,6,1,2,3,1]=>[[[[[]],[[]]]]]=>1
[2,6,1,3,1,2]=>[[[[],[[[]]]]]]=>1
[2,6,1,3,2,1]=>[[[[],[[],[]]]]]=>1
[2,6,2,1,1,3]=>[[],[[[[[]]]]]]=>2
[2,6,2,1,3,1]=>[[[[[[[]]]]]]]=>1
[2,6,2,3,1,1]=>[[],[[[[[]]]]]]=>2
[2,6,3,1,1,2]=>[[[]],[[[],[]]]]=>2
[2,6,3,1,2,1]=>[[[],[[[[]]]]]]=>1
[2,6,3,2,1,1]=>[[],[[],[[],[]]]]=>2
[3,1,1,2,2,6]=>[[],[[[]]],[[]]]=>3
[3,1,1,2,6,2]=>[[[[[]]]],[[]]]=>2
[3,1,1,6,2,2]=>[[],[],[[[],[]]]]=>3
[3,1,2,1,2,6]=>[[[[],[[[]]]]]]=>1
[3,1,2,1,6,2]=>[[[],[[[[]]]]]]=>1
[3,1,2,2,1,6]=>[[[]],[[[],[]]]]=>2
[3,1,2,2,6,1]=>[[[[]]],[[[]]]]=>2
[3,1,2,6,1,2]=>[[[[[[],[]]]]]]=>1
[3,1,2,6,2,1]=>[[[[[[[]]]]]]]=>1
[3,1,6,1,2,2]=>[[],[[[[],[]]]]]=>2
[3,1,6,2,1,2]=>[[[],[[[[]]]]]]=>1
[3,1,6,2,2,1]=>[[[]],[[[],[]]]]=>2
[3,2,1,1,2,6]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,6,2]=>[[],[[[[],[]]]]]=>2
[3,2,1,2,1,6]=>[[[],[[]],[[]]]]=>1
[3,2,1,2,6,1]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,1,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,2,1]=>[[[],[[]],[[]]]]=>1
[3,2,2,1,1,6]=>[[],[],[[[],[]]]]=>3
[3,2,2,1,6,1]=>[[],[[],[[[]]]]]=>2
[3,2,2,6,1,1]=>[[],[[[]]],[[]]]=>3
[3,2,6,1,1,2]=>[[[[]]],[[[]]]]=>2
[3,2,6,1,2,1]=>[[[],[[[[]]]]]]=>1
[3,2,6,2,1,1]=>[[],[[],[[[]]]]]=>2
[3,6,1,1,2,2]=>[[],[[]],[[[]]]]=>3
[3,6,1,2,1,2]=>[[[[[],[[]]]]]]=>1
[3,6,1,2,2,1]=>[[[[[]]]],[[]]]=>2
[3,6,2,1,1,2]=>[[],[[[[],[]]]]]=>2
[3,6,2,1,2,1]=>[[[],[[],[[]]]]]=>1
[3,6,2,2,1,1]=>[[],[[]],[[],[]]]=>3
[6,1,1,2,2,3]=>[[],[[]],[[],[]]]=>3
[6,1,1,2,3,2]=>[[[]],[[],[[]]]]=>2
[6,1,1,3,2,2]=>[[],[],[[[],[]]]]=>3
[6,1,2,1,2,3]=>[[[[],[],[[]]]]]=>1
[6,1,2,1,3,2]=>[[[],[[],[[]]]]]=>1
[6,1,2,2,1,3]=>[[[]],[[[],[]]]]=>2
[6,1,2,2,3,1]=>[[],[[[]],[[]]]]=>2
[6,1,2,3,1,2]=>[[[[],[],[[]]]]]=>1
[6,1,2,3,2,1]=>[[[[],[[],[]]]]]=>1
[6,1,3,1,2,2]=>[[],[[[[],[]]]]]=>2
[6,1,3,2,1,2]=>[[[],[[],[[]]]]]=>1
[6,1,3,2,2,1]=>[[],[[],[[],[]]]]=>2
[6,2,1,1,2,3]=>[[],[[],[[[]]]]]=>2
[6,2,1,1,3,2]=>[[],[[[],[[]]]]]=>2
[6,2,1,2,1,3]=>[[[[[]],[[]]]]]=>1
[6,2,1,2,3,1]=>[[[[],[[[]]]]]]=>1
[6,2,1,3,1,2]=>[[[[[[[]]]]]]]=>1
[6,2,1,3,2,1]=>[[[[[],[],[]]]]]=>1
[6,2,2,1,1,3]=>[[],[[[]]],[[]]]=>3
[6,2,2,1,3,1]=>[[[]],[[[[]]]]]=>2
[6,2,2,3,1,1]=>[[],[[]],[[[]]]]=>3
[6,2,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[6,2,3,1,2,1]=>[[[[[[],[]]]]]]=>1
[6,2,3,2,1,1]=>[[],[[],[[[]]]]]=>2
[6,3,1,1,2,2]=>[[],[[[]]],[[]]]=>3
[6,3,1,2,1,2]=>[[[[[],[[]]]]]]=>1
[6,3,1,2,2,1]=>[[[[]]],[[[]]]]=>2
[6,3,2,1,1,2]=>[[],[[[],[[]]]]]=>2
[6,3,2,1,2,1]=>[[[[[],[],[]]]]]=>1
[6,3,2,2,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,2,2,4,4]=>[[],[],[[]],[[]]]=>4
[1,1,2,4,2,4]=>[[],[[[],[[]]]]]=>2
[1,1,2,4,4,2]=>[[],[[[]]],[[]]]=>3
[1,1,4,2,2,4]=>[[],[[]],[[[]]]]=>3
[1,1,4,2,4,2]=>[[],[[[],[[]]]]]=>2
[1,1,4,4,2,2]=>[[],[],[[]],[[]]]=>4
[1,2,1,2,4,4]=>[[[[],[]]],[[]]]=>2
[1,2,1,4,2,4]=>[[[[[[[]]]]]]]=>1
[1,2,1,4,4,2]=>[[[]],[[[[]]]]]=>2
[1,2,2,1,4,4]=>[[[]],[[]],[[]]]=>3
[1,2,2,4,1,4]=>[[[]],[[[[]]]]]=>2
[1,2,2,4,4,1]=>[[[]],[[]],[[]]]=>3
[1,2,4,1,2,4]=>[[[[]],[[],[]]]]=>1
[1,2,4,1,4,2]=>[[[[[[[]]]]]]]=>1
[1,2,4,2,1,4]=>[[[[[[[]]]]]]]=>1
[1,2,4,2,4,1]=>[[[[[]],[[]]]]]=>1
[1,2,4,4,1,2]=>[[[]],[[[],[]]]]=>2
[1,2,4,4,2,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,2,2,4]=>[[[[[]]]],[[]]]=>2
[1,4,1,2,4,2]=>[[[[[[[]]]]]]]=>1
[1,4,1,4,2,2]=>[[],[[[],[[]]]]]=>2
[1,4,2,1,2,4]=>[[[[[[[]]]]]]]=>1
[1,4,2,1,4,2]=>[[[],[[],[[]]]]]=>1
[1,4,2,2,1,4]=>[[],[[[],[[]]]]]=>2
[1,4,2,2,4,1]=>[[[[]]],[[[]]]]=>2
[1,4,2,4,1,2]=>[[[[[[[]]]]]]]=>1
[1,4,2,4,2,1]=>[[[[[],[[]]]]]]=>1
[1,4,4,1,2,2]=>[[],[[[]]],[[]]]=>3
[1,4,4,2,1,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,2,2,1]=>[[],[],[[[[]]]]]=>3
[2,1,1,2,4,4]=>[[],[[[]]],[[]]]=>3
[2,1,1,4,2,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,4,2]=>[[],[[]],[[[]]]]=>3
[2,1,2,1,4,4]=>[[[]],[[],[[]]]]=>2
[2,1,2,4,1,4]=>[[[[[[[]]]]]]]=>1
[2,1,2,4,4,1]=>[[[[]]],[[[]]]]=>2
[2,1,4,1,2,4]=>[[[[[[[]]]]]]]=>1
[2,1,4,1,4,2]=>[[[[[],[[]]]]]]=>1
[2,1,4,2,1,4]=>[[[],[[],[[]]]]]=>1
[2,1,4,2,4,1]=>[[[[[[[]]]]]]]=>1
[2,1,4,4,1,2]=>[[[]],[[[[]]]]]=>2
[2,1,4,4,2,1]=>[[[]],[[[],[]]]]=>2
[2,2,1,1,4,4]=>[[],[],[[]],[[]]]=>4
[2,2,1,4,1,4]=>[[],[[[],[[]]]]]=>2
[2,2,1,4,4,1]=>[[],[[]],[[[]]]]=>3
[2,2,4,1,1,4]=>[[],[[]],[[[]]]]=>3
[2,2,4,1,4,1]=>[[],[[[],[[]]]]]=>2
[2,2,4,4,1,1]=>[[],[],[[]],[[]]]=>4
[2,4,1,1,2,4]=>[[[[],[]]],[[]]]=>2
[2,4,1,1,4,2]=>[[[[]]],[[[]]]]=>2
[2,4,1,2,1,4]=>[[[[[[[]]]]]]]=>1
[2,4,1,2,4,1]=>[[[[]],[[],[]]]]=>1
[2,4,1,4,1,2]=>[[[[[]],[[]]]]]=>1
[2,4,1,4,2,1]=>[[[[[[[]]]]]]]=>1
[2,4,2,1,1,4]=>[[[[]]],[[[]]]]=>2
[2,4,2,1,4,1]=>[[[[[[[]]]]]]]=>1
[2,4,2,4,1,1]=>[[],[[[],[[]]]]]=>2
[2,4,4,1,1,2]=>[[[]],[[]],[[]]]=>3
[2,4,4,1,2,1]=>[[[]],[[[[]]]]]=>2
[2,4,4,2,1,1]=>[[[]],[[]],[[]]]=>3
[4,1,1,2,2,4]=>[[[]],[[]],[[]]]=>3
[4,1,1,2,4,2]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,2,2]=>[[],[],[[[[]]]]]=>3
[4,1,2,1,2,4]=>[[[[[[],[]]]]]]=>1
[4,1,2,1,4,2]=>[[[[[[[]]]]]]]=>1
[4,1,2,2,1,4]=>[[[[]]],[[[]]]]=>2
[4,1,2,2,4,1]=>[[[]],[[[],[]]]]=>2
[4,1,2,4,1,2]=>[[[[]],[[],[]]]]=>1
[4,1,2,4,2,1]=>[[[[[[[]]]]]]]=>1
[4,1,4,1,2,2]=>[[],[[[],[[]]]]]=>2
[4,1,4,2,1,2]=>[[[[[[[]]]]]]]=>1
[4,1,4,2,2,1]=>[[[]],[[[[]]]]]=>2
[4,2,1,1,2,4]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,4,2]=>[[],[[[],[[]]]]]=>2
[4,2,1,2,1,4]=>[[[[[],[[]]]]]]=>1
[4,2,1,2,4,1]=>[[[[[[[]]]]]]]=>1
[4,2,1,4,1,2]=>[[[[[[[]]]]]]]=>1
[4,2,1,4,2,1]=>[[[[]],[[],[]]]]=>1
[4,2,2,1,1,4]=>[[],[[[]]],[[]]]=>3
[4,2,2,1,4,1]=>[[],[[[[[]]]]]]=>2
[4,2,2,4,1,1]=>[[],[],[[[[]]]]]=>3
[4,2,4,1,1,2]=>[[[]],[[[[]]]]]=>2
[4,2,4,1,2,1]=>[[[[[[[]]]]]]]=>1
[4,2,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[4,4,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[4,4,1,2,1,2]=>[[],[[[[],[]]]]]=>2
[4,4,1,2,2,1]=>[[],[[[]]],[[]]]=>3
[4,4,2,1,1,2]=>[[],[[[]]],[[]]]=>3
[4,4,2,1,2,1]=>[[],[[[],[[]]]]]=>2
[4,4,2,2,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,2,2,4,5]=>[[],[],[[[],[]]]]=>3
[1,1,2,2,5,4]=>[[],[[]],[[[]]]]=>3
[1,1,2,4,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,2,4,5,2]=>[[],[[[]],[[]]]]=>2
[1,1,2,5,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,2,5,4,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,1,4,2,5,2]=>[[],[[[]],[[]]]]=>2
[1,1,4,5,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,5,2,2,4]=>[[],[[]],[[],[]]]=>3
[1,1,5,2,4,2]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,2,2]=>[[],[[[]]],[[]]]=>3
[1,2,1,2,4,5]=>[[[],[[]],[[]]]]=>1
[1,2,1,2,5,4]=>[[[],[[[],[]]]]]=>1
[1,2,1,4,2,5]=>[[[[[],[[]]]]]]=>1
[1,2,1,4,5,2]=>[[[[]],[[[]]]]]=>1
[1,2,1,5,2,4]=>[[[[[[],[]]]]]]=>1
[1,2,1,5,4,2]=>[[[[],[[[]]]]]]=>1
[1,2,2,1,4,5]=>[[],[[[],[[]]]]]=>2
[1,2,2,1,5,4]=>[[[]],[[],[[]]]]=>2
[1,2,2,4,1,5]=>[[[]],[[[],[]]]]=>2
[1,2,2,4,5,1]=>[[],[[[],[[]]]]]=>2
[1,2,2,5,1,4]=>[[[]],[[],[],[]]]=>2
[1,2,2,5,4,1]=>[[[]],[[[[]]]]]=>2
[1,2,4,1,2,5]=>[[[[]],[[[]]]]]=>1
[1,2,4,1,5,2]=>[[[[[],[],[]]]]]=>1
[1,2,4,2,1,5]=>[[[[[[[]]]]]]]=>1
[1,2,4,2,5,1]=>[[[[[[],[]]]]]]=>1
[1,2,4,5,1,2]=>[[[],[[]],[[]]]]=>1
[1,2,4,5,2,1]=>[[[[]],[[[]]]]]=>1
[1,2,5,1,2,4]=>[[[[]],[[],[]]]]=>1
[1,2,5,1,4,2]=>[[[[],[],[[]]]]]=>1
[1,2,5,2,1,4]=>[[[[],[[[]]]]]]=>1
[1,2,5,2,4,1]=>[[[[[],[[]]]]]]=>1
[1,2,5,4,1,2]=>[[[[]],[[[]]]]]=>1
[1,2,5,4,2,1]=>[[[[[[],[]]]]]]=>1
[1,4,1,2,2,5]=>[[[[]]],[[],[]]]=>2
[1,4,1,2,5,2]=>[[[[]],[[],[]]]]=>1
[1,4,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[1,4,2,1,2,5]=>[[[[[]]],[[]]]]=>1
[1,4,2,1,5,2]=>[[[[[]],[[]]]]]=>1
[1,4,2,2,1,5]=>[[[]],[[[[]]]]]=>2
[1,4,2,2,5,1]=>[[],[[],[],[[]]]]=>2
[1,4,2,5,1,2]=>[[[],[[]],[[]]]]=>1
[1,4,2,5,2,1]=>[[[],[[[[]]]]]]=>1
[1,4,5,1,2,2]=>[[],[[],[[],[]]]]=>2
[1,4,5,2,1,2]=>[[[[[[],[]]]]]]=>1
[1,4,5,2,2,1]=>[[[[[]]]],[[]]]=>2
[1,5,1,2,2,4]=>[[[[[]]]],[[]]]=>2
[1,5,1,2,4,2]=>[[[[[[[]]]]]]]=>1
[1,5,1,4,2,2]=>[[],[[[],[[]]]]]=>2
[1,5,2,1,2,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,4,2]=>[[[],[[[[]]]]]]=>1
[1,5,2,2,1,4]=>[[[[]]],[[],[]]]=>2
[1,5,2,2,4,1]=>[[],[[[],[],[]]]]=>2
[1,5,2,4,1,2]=>[[[],[[]],[[]]]]=>1
[1,5,2,4,2,1]=>[[[],[[[[]]]]]]=>1
[1,5,4,1,2,2]=>[[[[],[]]],[[]]]=>2
[1,5,4,2,1,2]=>[[[[],[[[]]]]]]=>1
[1,5,4,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,2,4,5]=>[[],[[[]],[[]]]]=>2
[2,1,1,2,5,4]=>[[],[[[[],[]]]]]=>2
[2,1,1,4,2,5]=>[[],[[[]],[[]]]]=>2
[2,1,1,4,5,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,2,4]=>[[],[[],[[[]]]]]=>2
[2,1,1,5,4,2]=>[[],[[[[],[]]]]]=>2
[2,1,2,1,4,5]=>[[[],[[],[[]]]]]=>1
[2,1,2,1,5,4]=>[[[],[[]],[[]]]]=>1
[2,1,2,4,1,5]=>[[[[],[[[]]]]]]=>1
[2,1,2,4,5,1]=>[[[[[],[[]]]]]]=>1
[2,1,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[2,1,2,5,4,1]=>[[[[[]]],[[]]]]=>1
[2,1,4,1,2,5]=>[[[[],[[[]]]]]]=>1
[2,1,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[2,1,4,2,1,5]=>[[[[]],[[[]]]]]=>1
[2,1,4,2,5,1]=>[[[[],[],[[]]]]]=>1
[2,1,4,5,1,2]=>[[[[],[[],[]]]]]=>1
[2,1,4,5,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,5,1,2,4]=>[[[[[[[]]]]]]]=>1
[2,1,5,1,4,2]=>[[[[[],[[]]]]]]=>1
[2,1,5,2,1,4]=>[[[[]],[[],[]]]]=>1
[2,1,5,2,4,1]=>[[[[],[],[[]]]]]=>1
[2,1,5,4,1,2]=>[[[],[[[],[]]]]]=>1
[2,1,5,4,2,1]=>[[[],[[]],[[]]]]=>1
[2,2,1,1,4,5]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,5,4]=>[[],[],[[[],[]]]]=>3
[2,2,1,4,1,5]=>[[],[[[],[[]]]]]=>2
[2,2,1,4,5,1]=>[[],[[[],[[]]]]]=>2
[2,2,1,5,1,4]=>[[],[[[],[[]]]]]=>2
[2,2,1,5,4,1]=>[[],[[],[[],[]]]]=>2
[2,2,4,1,1,5]=>[[],[],[[],[[]]]]=>3
[2,2,4,1,5,1]=>[[],[[[],[[]]]]]=>2
[2,2,4,5,1,1]=>[[],[],[[[[]]]]]=>3
[2,2,5,1,1,4]=>[[],[],[[],[],[]]]=>3
[2,2,5,1,4,1]=>[[],[[],[],[[]]]]=>2
[2,2,5,4,1,1]=>[[],[[]],[[[]]]]=>3
[2,4,1,1,2,5]=>[[[[]]],[[[]]]]=>2
[2,4,1,1,5,2]=>[[],[[],[],[[]]]]=>2
[2,4,1,2,1,5]=>[[[[],[[[]]]]]]=>1
[2,4,1,2,5,1]=>[[[[[[],[]]]]]]=>1
[2,4,1,5,1,2]=>[[[[],[[[]]]]]]=>1
[2,4,1,5,2,1]=>[[[[],[],[[]]]]]=>1
[2,4,2,1,1,5]=>[[[[]]],[[[]]]]=>2
[2,4,2,1,5,1]=>[[[[[[[]]]]]]]=>1
[2,4,2,5,1,1]=>[[],[[],[[[]]]]]=>2
[2,4,5,1,1,2]=>[[[]],[[],[[]]]]=>2
[2,4,5,1,2,1]=>[[[[[]],[[]]]]]=>1
[2,4,5,2,1,1]=>[[],[[[[[]]]]]]=>2
[2,5,1,1,2,4]=>[[[[]]],[[],[]]]=>2
[2,5,1,1,4,2]=>[[],[[],[],[[]]]]=>2
[2,5,1,2,1,4]=>[[[],[],[[[]]]]]=>1
[2,5,1,2,4,1]=>[[[],[[[[]]]]]]=>1
[2,5,1,4,1,2]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,2,1]=>[[[],[],[[[]]]]]=>1
[2,5,2,1,1,4]=>[[],[[],[[[]]]]]=>2
[2,5,2,1,4,1]=>[[[],[[],[[]]]]]=>1
[2,5,2,4,1,1]=>[[],[[[]],[[]]]]=>2
[2,5,4,1,1,2]=>[[[[[]]]],[[]]]=>2
[2,5,4,1,2,1]=>[[[[[[],[]]]]]]=>1
[2,5,4,2,1,1]=>[[[[]]],[[],[]]]=>2
[4,1,1,2,2,5]=>[[[]],[[]],[[]]]=>3
[4,1,1,2,5,2]=>[[],[[[[],[]]]]]=>2
[4,1,1,5,2,2]=>[[],[],[[],[],[]]]=>3
[4,1,2,1,2,5]=>[[[[[[],[]]]]]]=>1
[4,1,2,1,5,2]=>[[[],[],[[[]]]]]=>1
[4,1,2,2,1,5]=>[[[]],[[[],[]]]]=>2
[4,1,2,2,5,1]=>[[[[]]],[[],[]]]=>2
[4,1,2,5,1,2]=>[[[[],[[],[]]]]]=>1
[4,1,2,5,2,1]=>[[[[[]]],[[]]]]=>1
[4,1,5,1,2,2]=>[[],[[[[],[]]]]]=>2
[4,1,5,2,1,2]=>[[[],[],[[[]]]]]=>1
[4,1,5,2,2,1]=>[[[]],[[],[],[]]]=>2
[4,2,1,1,2,5]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,5,2]=>[[],[[[]],[[]]]]=>2
[4,2,1,2,1,5]=>[[[[[],[[]]]]]]=>1
[4,2,1,2,5,1]=>[[[[[]],[[]]]]]=>1
[4,2,1,5,1,2]=>[[[[[[[]]]]]]]=>1
[4,2,1,5,2,1]=>[[[[],[[],[]]]]]=>1
[4,2,2,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,2,2,1,5,1]=>[[],[[[[[]]]]]]=>2
[4,2,2,5,1,1]=>[[],[],[[],[[]]]]=>3
[4,2,5,1,1,2]=>[[[]],[[],[[]]]]=>2
[4,2,5,1,2,1]=>[[[[[[],[]]]]]]=>1
[4,2,5,2,1,1]=>[[[]],[[[[]]]]]=>2
[4,5,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[4,5,1,2,1,2]=>[[[],[[]],[[]]]]=>1
[4,5,1,2,2,1]=>[[[]],[[],[[]]]]=>2
[4,5,2,1,1,2]=>[[],[[],[[[]]]]]=>2
[4,5,2,1,2,1]=>[[[[]],[[],[]]]]=>1
[4,5,2,2,1,1]=>[[],[],[[[[]]]]]=>3
[5,1,1,2,2,4]=>[[[]],[[]],[[]]]=>3
[5,1,1,2,4,2]=>[[[[[]]]],[[]]]=>2
[5,1,1,4,2,2]=>[[],[],[[[],[]]]]=>3
[5,1,2,1,2,4]=>[[[[],[[[]]]]]]=>1
[5,1,2,1,4,2]=>[[[],[[[[]]]]]]=>1
[5,1,2,2,1,4]=>[[[]],[[[],[]]]]=>2
[5,1,2,2,4,1]=>[[[[]]],[[[]]]]=>2
[5,1,2,4,1,2]=>[[[[],[[[]]]]]]=>1
[5,1,2,4,2,1]=>[[[[[[[]]]]]]]=>1
[5,1,4,1,2,2]=>[[],[[[[],[]]]]]=>2
[5,1,4,2,1,2]=>[[[],[[[[]]]]]]=>1
[5,1,4,2,2,1]=>[[],[[[[],[]]]]]=>2
[5,2,1,1,2,4]=>[[],[[[[[]]]]]]=>2
[5,2,1,1,4,2]=>[[[[[]]]],[[]]]=>2
[5,2,1,2,1,4]=>[[[[[],[[]]]]]]=>1
[5,2,1,2,4,1]=>[[[[[]]],[[]]]]=>1
[5,2,1,4,1,2]=>[[[[[]]],[[]]]]=>1
[5,2,1,4,2,1]=>[[[[],[[[]]]]]]=>1
[5,2,2,1,1,4]=>[[],[],[[[[]]]]]=>3
[5,2,2,1,4,1]=>[[],[[[],[[]]]]]=>2
[5,2,2,4,1,1]=>[[],[],[[],[[]]]]=>3
[5,2,4,1,1,2]=>[[[]],[[],[[]]]]=>2
[5,2,4,1,2,1]=>[[[[[]]],[[]]]]=>1
[5,2,4,2,1,1]=>[[[[]]],[[[]]]]=>2
[5,4,1,1,2,2]=>[[[]],[[]],[[]]]=>3
[5,4,1,2,1,2]=>[[[[]],[[],[]]]]=>1
[5,4,1,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,4,2,1,1,2]=>[[[[],[]]],[[]]]=>2
[5,4,2,1,2,1]=>[[[],[[]],[[]]]]=>1
[5,4,2,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,2,4,6]=>[[],[[]],[[],[]]]=>3
[1,1,2,2,6,4]=>[[],[[]],[[[]]]]=>3
[1,1,2,4,2,6]=>[[],[[[[[]]]]]]=>2
[1,1,2,4,6,2]=>[[],[[[],[[]]]]]=>2
[1,1,2,6,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,2,6,4,2]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,2,6]=>[[],[[]],[[[]]]]=>3
[1,1,4,2,6,2]=>[[],[[],[[[]]]]]=>2
[1,1,4,6,2,2]=>[[],[],[[],[[]]]]=>3
[1,1,6,2,2,4]=>[[],[[]],[[[]]]]=>3
[1,1,6,2,4,2]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,2,2]=>[[],[],[[],[],[]]]=>3
[1,2,1,2,4,6]=>[[[],[[],[[]]]]]=>1
[1,2,1,2,6,4]=>[[[],[[[[]]]]]]=>1
[1,2,1,4,2,6]=>[[[[[[[]]]]]]]=>1
[1,2,1,4,6,2]=>[[[[[],[[]]]]]]=>1
[1,2,1,6,2,4]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,4,2]=>[[[[[],[],[]]]]]=>1
[1,2,2,1,4,6]=>[[[]],[[[[]]]]]=>2
[1,2,2,1,6,4]=>[[[]],[[[],[]]]]=>2
[1,2,2,4,1,6]=>[[[]],[[[[]]]]]=>2
[1,2,2,4,6,1]=>[[[]],[[],[],[]]]=>2
[1,2,2,6,1,4]=>[[[]],[[[[]]]]]=>2
[1,2,2,6,4,1]=>[[[]],[[],[[]]]]=>2
[1,2,4,1,2,6]=>[[[],[[],[[]]]]]=>1
[1,2,4,1,6,2]=>[[[[[[[]]]]]]]=>1
[1,2,4,2,1,6]=>[[[[[],[[]]]]]]=>1
[1,2,4,2,6,1]=>[[[[],[[[]]]]]]=>1
[1,2,4,6,1,2]=>[[[],[[],[],[]]]]=>1
[1,2,4,6,2,1]=>[[[[],[[[]]]]]]=>1
[1,2,6,1,2,4]=>[[[],[[],[[]]]]]=>1
[1,2,6,1,4,2]=>[[[[[[[]]]]]]]=>1
[1,2,6,2,1,4]=>[[[[[[],[]]]]]]=>1
[1,2,6,2,4,1]=>[[[[],[[[]]]]]]=>1
[1,2,6,4,1,2]=>[[[],[[],[[]]]]]=>1
[1,2,6,4,2,1]=>[[[[[[],[]]]]]]=>1
[1,4,1,2,2,6]=>[[[]],[[],[[]]]]=>2
[1,4,1,2,6,2]=>[[[],[[],[[]]]]]=>1
[1,4,1,6,2,2]=>[[],[[],[[[]]]]]=>2
[1,4,2,1,2,6]=>[[[[[[[]]]]]]]=>1
[1,4,2,1,6,2]=>[[[[]],[[],[]]]]=>1
[1,4,2,2,1,6]=>[[[]],[[[],[]]]]=>2
[1,4,2,2,6,1]=>[[[[]]],[[[]]]]=>2
[1,4,2,6,1,2]=>[[[[[[[]]]]]]]=>1
[1,4,2,6,2,1]=>[[[[]],[[[]]]]]=>1
[1,4,6,1,2,2]=>[[],[[[],[[]]]]]=>2
[1,4,6,2,1,2]=>[[[[]],[[[]]]]]=>1
[1,4,6,2,2,1]=>[[[]],[[],[[]]]]=>2
[1,6,1,2,2,4]=>[[[[]]],[[],[]]]=>2
[1,6,1,2,4,2]=>[[[],[[],[[]]]]]=>1
[1,6,1,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,6,2,1,2,4]=>[[[[[[[]]]]]]]=>1
[1,6,2,1,4,2]=>[[[[]],[[],[]]]]=>1
[1,6,2,2,1,4]=>[[],[[[],[[]]]]]=>2
[1,6,2,2,4,1]=>[[[[]]],[[[]]]]=>2
[1,6,2,4,1,2]=>[[[[[[[]]]]]]]=>1
[1,6,2,4,2,1]=>[[[[[]]],[[]]]]=>1
[1,6,4,1,2,2]=>[[],[[[[],[]]]]]=>2
[1,6,4,2,1,2]=>[[[],[],[[[]]]]]=>1
[1,6,4,2,2,1]=>[[],[[[],[],[]]]]=>2
[2,1,1,2,4,6]=>[[],[[[],[[]]]]]=>2
[2,1,1,2,6,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,2,6]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,6,2]=>[[],[[[]],[[]]]]=>2
[2,1,1,6,2,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,4,2]=>[[],[[],[],[[]]]]=>2
[2,1,2,1,4,6]=>[[[[]],[[[]]]]]=>1
[2,1,2,1,6,4]=>[[[[]],[[],[]]]]=>1
[2,1,2,4,1,6]=>[[[[[[[]]]]]]]=>1
[2,1,2,4,6,1]=>[[[[],[],[[]]]]]=>1
[2,1,2,6,1,4]=>[[[[[[[]]]]]]]=>1
[2,1,2,6,4,1]=>[[[[[]],[[]]]]]=>1
[2,1,4,1,2,6]=>[[[[[]],[[]]]]]=>1
[2,1,4,1,6,2]=>[[[[],[[[]]]]]]=>1
[2,1,4,2,1,6]=>[[[[]],[[],[]]]]=>1
[2,1,4,2,6,1]=>[[[[[[[]]]]]]]=>1
[2,1,4,6,1,2]=>[[[[[],[[]]]]]]=>1
[2,1,4,6,2,1]=>[[[],[[],[[]]]]]=>1
[2,1,6,1,2,4]=>[[[[],[[[]]]]]]=>1
[2,1,6,1,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,6,2,1,4]=>[[[],[[],[[]]]]]=>1
[2,1,6,2,4,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,4,1,2]=>[[[[[[],[]]]]]]=>1
[2,1,6,4,2,1]=>[[[],[[],[],[]]]]=>1
[2,2,1,1,4,6]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,6,4]=>[[],[],[[],[[]]]]=>3
[2,2,1,4,1,6]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,6,1]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,1,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,4,1]=>[[],[[[[],[]]]]]=>2
[2,2,4,1,1,6]=>[[],[[[]]],[[]]]=>3
[2,2,4,1,6,1]=>[[],[[],[[[]]]]]=>2
[2,2,4,6,1,1]=>[[],[],[[],[],[]]]=>3
[2,2,6,1,1,4]=>[[],[[[]]],[[]]]=>3
[2,2,6,1,4,1]=>[[],[[],[[[]]]]]=>2
[2,2,6,4,1,1]=>[[],[],[[],[[]]]]=>3
[2,4,1,1,2,6]=>[[],[[[],[[]]]]]=>2
[2,4,1,1,6,2]=>[[[[]]],[[[]]]]=>2
[2,4,1,2,1,6]=>[[[[[[[]]]]]]]=>1
[2,4,1,2,6,1]=>[[[],[[],[[]]]]]=>1
[2,4,1,6,1,2]=>[[[[]],[[[]]]]]=>1
[2,4,1,6,2,1]=>[[[[[[[]]]]]]]=>1
[2,4,2,1,1,6]=>[[],[[[]],[[]]]]=>2
[2,4,2,1,6,1]=>[[[[]],[[],[]]]]=>1
[2,4,2,6,1,1]=>[[],[[],[[[]]]]]=>2
[2,4,6,1,1,2]=>[[[]],[[],[],[]]]=>2
[2,4,6,1,2,1]=>[[[],[],[[[]]]]]=>1
[2,4,6,2,1,1]=>[[],[[[[],[]]]]]=>2
[2,6,1,1,2,4]=>[[],[[[],[[]]]]]=>2
[2,6,1,1,4,2]=>[[[[]]],[[[]]]]=>2
[2,6,1,2,1,4]=>[[[[[[[]]]]]]]=>1
[2,6,1,2,4,1]=>[[[],[[],[[]]]]]=>1
[2,6,1,4,1,2]=>[[[[]],[[[]]]]]=>1
[2,6,1,4,2,1]=>[[[[[[[]]]]]]]=>1
[2,6,2,1,1,4]=>[[],[[],[[[]]]]]=>2
[2,6,2,1,4,1]=>[[[[]],[[],[]]]]=>1
[2,6,2,4,1,1]=>[[],[[],[[[]]]]]=>2
[2,6,4,1,1,2]=>[[[]],[[],[[]]]]=>2
[2,6,4,1,2,1]=>[[[],[[[[]]]]]]=>1
[2,6,4,2,1,1]=>[[[[]]],[[],[]]]=>2
[4,1,1,2,2,6]=>[[],[[]],[[],[]]]=>3
[4,1,1,2,6,2]=>[[],[[[],[[]]]]]=>2
[4,1,1,6,2,2]=>[[],[],[[[[]]]]]=>3
[4,1,2,1,2,6]=>[[[[]],[[],[]]]]=>1
[4,1,2,1,6,2]=>[[[[[[[]]]]]]]=>1
[4,1,2,2,1,6]=>[[[]],[[[[]]]]]=>2
[4,1,2,2,6,1]=>[[[]],[[],[[]]]]=>2
[4,1,2,6,1,2]=>[[[],[[[],[]]]]]=>1
[4,1,2,6,2,1]=>[[[[]],[[[]]]]]=>1
[4,1,6,1,2,2]=>[[],[[[[[]]]]]]=>2
[4,1,6,2,1,2]=>[[[[[[[]]]]]]]=>1
[4,1,6,2,2,1]=>[[[[]]],[[[]]]]=>2
[4,2,1,1,2,6]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,6,2]=>[[],[[],[[[]]]]]=>2
[4,2,1,2,1,6]=>[[[],[[],[[]]]]]=>1
[4,2,1,2,6,1]=>[[[[[[[]]]]]]]=>1
[4,2,1,6,1,2]=>[[[],[[[[]]]]]]=>1
[4,2,1,6,2,1]=>[[[],[[],[[]]]]]=>1
[4,2,2,1,1,6]=>[[],[],[[],[[]]]]=>3
[4,2,2,1,6,1]=>[[],[[[[],[]]]]]=>2
[4,2,2,6,1,1]=>[[],[],[[[[]]]]]=>3
[4,2,6,1,1,2]=>[[[]],[[[[]]]]]=>2
[4,2,6,1,2,1]=>[[[[[[[]]]]]]]=>1
[4,2,6,2,1,1]=>[[[]],[[[[]]]]]=>2
[4,6,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[4,6,1,2,1,2]=>[[[],[[],[[]]]]]=>1
[4,6,1,2,2,1]=>[[[[],[]]],[[]]]=>2
[4,6,2,1,1,2]=>[[],[[[[[]]]]]]=>2
[4,6,2,1,2,1]=>[[[[[],[[]]]]]]=>1
[4,6,2,2,1,1]=>[[],[[[]]],[[]]]=>3
[6,1,1,2,2,4]=>[[],[[]],[[],[]]]=>3
[6,1,1,2,4,2]=>[[],[[[],[[]]]]]=>2
[6,1,1,4,2,2]=>[[],[[]],[[[]]]]=>3
[6,1,2,1,2,4]=>[[[[]],[[],[]]]]=>1
[6,1,2,1,4,2]=>[[[[[[[]]]]]]]=>1
[6,1,2,2,1,4]=>[[[[]]],[[[]]]]=>2
[6,1,2,2,4,1]=>[[[]],[[],[[]]]]=>2
[6,1,2,4,1,2]=>[[[],[[[],[]]]]]=>1
[6,1,2,4,2,1]=>[[[[]],[[[]]]]]=>1
[6,1,4,1,2,2]=>[[],[[[[[]]]]]]=>2
[6,1,4,2,1,2]=>[[[[[[[]]]]]]]=>1
[6,1,4,2,2,1]=>[[],[[[[[]]]]]]=>2
[6,2,1,1,2,4]=>[[],[[[[[]]]]]]=>2
[6,2,1,1,4,2]=>[[],[[],[[[]]]]]=>2
[6,2,1,2,1,4]=>[[[],[[],[[]]]]]=>1
[6,2,1,2,4,1]=>[[[[[[[]]]]]]]=>1
[6,2,1,4,1,2]=>[[[],[[[[]]]]]]=>1
[6,2,1,4,2,1]=>[[[],[[[],[]]]]]=>1
[6,2,2,1,1,4]=>[[],[],[[],[[]]]]=>3
[6,2,2,1,4,1]=>[[],[[[[],[]]]]]=>2
[6,2,2,4,1,1]=>[[],[[]],[[[]]]]=>3
[6,2,4,1,1,2]=>[[[]],[[[[]]]]]=>2
[6,2,4,1,2,1]=>[[[[[[[]]]]]]]=>1
[6,2,4,2,1,1]=>[[[[[]]]],[[]]]=>2
[6,4,1,1,2,2]=>[[],[[[]]],[[]]]=>3
[6,4,1,2,1,2]=>[[[[],[[[]]]]]]=>1
[6,4,1,2,2,1]=>[[[[]]],[[[]]]]=>2
[6,4,2,1,1,2]=>[[[[]]],[[],[]]]=>2
[6,4,2,1,2,1]=>[[[],[[],[[]]]]]=>1
[6,4,2,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,2,5,5]=>[[],[],[[]],[[]]]=>4
[1,1,2,5,2,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,5,2]=>[[],[[[]]],[[]]]=>3
[1,1,5,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,1,5,2,5,2]=>[[],[[],[],[[]]]]=>2
[1,1,5,5,2,2]=>[[],[],[],[[],[]]]=>4
[1,2,1,2,5,5]=>[[[[],[]]],[[]]]=>2
[1,2,1,5,2,5]=>[[[[[[],[]]]]]]=>1
[1,2,1,5,5,2]=>[[],[[],[[[]]]]]=>2
[1,2,2,1,5,5]=>[[[]],[[]],[[]]]=>3
[1,2,2,5,1,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,5,1]=>[[],[[]],[[],[]]]=>3
[1,2,5,1,2,5]=>[[[],[[],[],[]]]]=>1
[1,2,5,1,5,2]=>[[[[],[[],[]]]]]=>1
[1,2,5,2,1,5]=>[[[[[[],[]]]]]]=>1
[1,2,5,2,5,1]=>[[[[],[],[[]]]]]=>1
[1,2,5,5,1,2]=>[[],[[],[[],[]]]]=>2
[1,2,5,5,2,1]=>[[[[]]],[[[]]]]=>2
[1,5,1,2,2,5]=>[[[]],[[],[[]]]]=>2
[1,5,1,2,5,2]=>[[[],[[],[[]]]]]=>1
[1,5,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[1,5,2,1,2,5]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,5,2]=>[[[],[],[],[[]]]]=>1
[1,5,2,2,1,5]=>[[],[[[],[],[]]]]=>2
[1,5,2,2,5,1]=>[[[],[]],[[],[]]]=>2
[1,5,2,5,1,2]=>[[[],[[],[[]]]]]=>1
[1,5,2,5,2,1]=>[[[],[[]],[[]]]]=>1
[1,5,5,1,2,2]=>[[],[[[]]],[[]]]=>3
[1,5,5,2,1,2]=>[[],[[],[[[]]]]]=>2
[1,5,5,2,2,1]=>[[],[[]],[[],[]]]=>3
[2,1,1,2,5,5]=>[[],[[[]]],[[]]]=>3
[2,1,1,5,2,5]=>[[],[[],[[[]]]]]=>2
[2,1,1,5,5,2]=>[[],[],[[],[[]]]]=>3
[2,1,2,1,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,2,5,1,5]=>[[[[[],[[]]]]]]=>1
[2,1,2,5,5,1]=>[[],[[[]],[[]]]]=>2
[2,1,5,1,2,5]=>[[[[[]],[[]]]]]=>1
[2,1,5,1,5,2]=>[[[[],[],[[]]]]]=>1
[2,1,5,2,1,5]=>[[[],[[],[],[]]]]=>1
[2,1,5,2,5,1]=>[[[[],[[],[]]]]]=>1
[2,1,5,5,1,2]=>[[[[[]]]],[[]]]=>2
[2,1,5,5,2,1]=>[[],[[],[[],[]]]]=>2
[2,2,1,1,5,5]=>[[],[],[[]],[[]]]=>4
[2,2,1,5,1,5]=>[[],[[[],[[]]]]]=>2
[2,2,1,5,5,1]=>[[],[[[]]],[[]]]=>3
[2,2,5,1,1,5]=>[[],[[]],[[],[]]]=>3
[2,2,5,1,5,1]=>[[],[[],[],[[]]]]=>2
[2,2,5,5,1,1]=>[[],[],[],[[],[]]]=>4
[2,5,1,1,2,5]=>[[],[[[],[],[]]]]=>2
[2,5,1,1,5,2]=>[[[],[]],[[],[]]]=>2
[2,5,1,2,1,5]=>[[[],[[[[]]]]]]=>1
[2,5,1,2,5,1]=>[[[],[],[],[[]]]]=>1
[2,5,1,5,1,2]=>[[[],[[]],[[]]]]=>1
[2,5,1,5,2,1]=>[[[],[[],[[]]]]]=>1
[2,5,2,1,1,5]=>[[],[[],[[[]]]]]=>2
[2,5,2,1,5,1]=>[[[[]],[[],[]]]]=>1
[2,5,2,5,1,1]=>[[],[[],[],[[]]]]=>2
[2,5,5,1,1,2]=>[[],[[]],[[],[]]]=>3
[2,5,5,1,2,1]=>[[],[[],[[[]]]]]=>2
[2,5,5,2,1,1]=>[[],[],[[[[]]]]]=>3
[5,1,1,2,2,5]=>[[],[[]],[[],[]]]=>3
[5,1,1,2,5,2]=>[[],[[[],[[]]]]]=>2
[5,1,1,5,2,2]=>[[],[],[[],[[]]]]=>3
[5,1,2,1,2,5]=>[[[[]],[[],[]]]]=>1
[5,1,2,1,5,2]=>[[[[],[[[]]]]]]=>1
[5,1,2,2,1,5]=>[[[[]]],[[[]]]]=>2
[5,1,2,2,5,1]=>[[[]],[[],[],[]]]=>2
[5,1,2,5,1,2]=>[[[],[],[[],[]]]]=>1
[5,1,2,5,2,1]=>[[[[]],[[[]]]]]=>1
[5,1,5,1,2,2]=>[[],[[[],[[]]]]]=>2
[5,1,5,2,1,2]=>[[[[],[[[]]]]]]=>1
[5,1,5,2,2,1]=>[[[]],[[],[[]]]]=>2
[5,2,1,1,2,5]=>[[],[[[[[]]]]]]=>2
[5,2,1,1,5,2]=>[[],[[],[],[[]]]]=>2
[5,2,1,2,1,5]=>[[[],[[],[[]]]]]=>1
[5,2,1,2,5,1]=>[[[[[],[[]]]]]]=>1
[5,2,1,5,1,2]=>[[[],[[[[]]]]]]=>1
[5,2,1,5,2,1]=>[[[],[],[[],[]]]]=>1
[5,2,2,1,1,5]=>[[],[],[[],[[]]]]=>3
[5,2,2,1,5,1]=>[[],[[[[],[]]]]]=>2
[5,2,2,5,1,1]=>[[],[],[[],[[]]]]=>3
[5,2,5,1,1,2]=>[[[]],[[],[[]]]]=>2
[5,2,5,1,2,1]=>[[[[],[[[]]]]]]=>1
[5,2,5,2,1,1]=>[[],[[[],[[]]]]]=>2
[5,5,1,1,2,2]=>[[],[],[[]],[[]]]=>4
[5,5,1,2,1,2]=>[[],[[[],[[]]]]]=>2
[5,5,1,2,2,1]=>[[],[[[]]],[[]]]=>3
[5,5,2,1,1,2]=>[[],[],[[[[]]]]]=>3
[5,5,2,1,2,1]=>[[],[[[[],[]]]]]=>2
[5,5,2,2,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,2,2,5,6]=>[[],[],[[[],[]]]]=>3
[1,1,2,2,6,5]=>[[],[[]],[[[]]]]=>3
[1,1,2,5,2,6]=>[[],[[[[],[]]]]]=>2
[1,1,2,5,6,2]=>[[],[[],[[],[]]]]=>2
[1,1,2,6,2,5]=>[[],[[[[],[]]]]]=>2
[1,1,2,6,5,2]=>[[],[[[],[[]]]]]=>2
[1,1,5,2,2,6]=>[[],[],[[],[],[]]]=>3
[1,1,5,2,6,2]=>[[],[[],[],[[]]]]=>2
[1,1,5,6,2,2]=>[[],[],[[[[]]]]]=>3
[1,1,6,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,1,6,2,5,2]=>[[],[[[],[[]]]]]=>2
[1,1,6,5,2,2]=>[[],[[[]]],[[]]]=>3
[1,2,1,2,5,6]=>[[[],[[]],[[]]]]=>1
[1,2,1,2,6,5]=>[[[],[[[],[]]]]]=>1
[1,2,1,5,2,6]=>[[[[[],[],[]]]]]=>1
[1,2,1,5,6,2]=>[[[[[]]],[[]]]]=>1
[1,2,1,6,2,5]=>[[[[[],[[]]]]]]=>1
[1,2,1,6,5,2]=>[[[[],[[[]]]]]]=>1
[1,2,2,1,5,6]=>[[],[[[],[[]]]]]=>2
[1,2,2,1,6,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,1,6]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,6,1]=>[[],[[[],[[]]]]]=>2
[1,2,2,6,1,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,6,5,1]=>[[[]],[[[[]]]]]=>2
[1,2,5,1,2,6]=>[[[[]],[[],[]]]]=>1
[1,2,5,1,6,2]=>[[[[],[],[[]]]]]=>1
[1,2,5,2,1,6]=>[[[[[[[]]]]]]]=>1
[1,2,5,2,6,1]=>[[[[[],[[]]]]]]=>1
[1,2,5,6,1,2]=>[[[],[[]],[[]]]]=>1
[1,2,5,6,2,1]=>[[[],[[],[[]]]]]=>1
[1,2,6,1,2,5]=>[[[[[]]],[[]]]]=>1
[1,2,6,1,5,2]=>[[[[],[],[[]]]]]=>1
[1,2,6,2,1,5]=>[[[[],[[[]]]]]]=>1
[1,2,6,2,5,1]=>[[[[[],[],[]]]]]=>1
[1,2,6,5,1,2]=>[[[[]],[[[]]]]]=>1
[1,2,6,5,2,1]=>[[[[],[[],[]]]]]=>1
[1,5,1,2,2,6]=>[[[[]]],[[],[]]]=>2
[1,5,1,2,6,2]=>[[[[]],[[],[]]]]=>1
[1,5,1,6,2,2]=>[[],[[],[[[]]]]]=>2
[1,5,2,1,2,6]=>[[[],[[]],[[]]]]=>1
[1,5,2,1,6,2]=>[[[],[[[[]]]]]]=>1
[1,5,2,2,1,6]=>[[],[[[[],[]]]]]=>2
[1,5,2,2,6,1]=>[[],[[],[],[[]]]]=>2
[1,5,2,6,1,2]=>[[[],[],[[[]]]]]=>1
[1,5,2,6,2,1]=>[[[],[],[[[]]]]]=>1
[1,5,6,1,2,2]=>[[],[[[]],[[]]]]=>2
[1,5,6,2,1,2]=>[[[[[[],[]]]]]]=>1
[1,5,6,2,2,1]=>[[[[[]]]],[[]]]=>2
[1,6,1,2,2,5]=>[[[[[]]]],[[]]]=>2
[1,6,1,2,5,2]=>[[[[[[[]]]]]]]=>1
[1,6,1,5,2,2]=>[[],[[[]],[[]]]]=>2
[1,6,2,1,2,5]=>[[[[[],[[]]]]]]=>1
[1,6,2,1,5,2]=>[[[[[]],[[]]]]]=>1
[1,6,2,2,1,5]=>[[[]],[[[[]]]]]=>2
[1,6,2,2,5,1]=>[[],[[],[],[[]]]]=>2
[1,6,2,5,1,2]=>[[[[],[],[[]]]]]=>1
[1,6,2,5,2,1]=>[[[[[[],[]]]]]]=>1
[1,6,5,1,2,2]=>[[[[[]]]],[[]]]=>2
[1,6,5,2,1,2]=>[[[[[],[[]]]]]]=>1
[1,6,5,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,1,1,2,5,6]=>[[],[[[]],[[]]]]=>2
[2,1,1,2,6,5]=>[[],[[[[],[]]]]]=>2
[2,1,1,5,2,6]=>[[],[[],[],[[]]]]=>2
[2,1,1,5,6,2]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,2,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,6,5,2]=>[[],[[[[],[]]]]]=>2
[2,1,2,1,5,6]=>[[[],[[],[[]]]]]=>1
[2,1,2,1,6,5]=>[[[],[[]],[[]]]]=>1
[2,1,2,5,1,6]=>[[[[[],[[]]]]]]=>1
[2,1,2,5,6,1]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,1,5]=>[[[[[]],[[]]]]]=>1
[2,1,2,6,5,1]=>[[[[]],[[[]]]]]=>1
[2,1,5,1,2,6]=>[[[[],[[[]]]]]]=>1
[2,1,5,1,6,2]=>[[[[],[[[]]]]]]=>1
[2,1,5,2,1,6]=>[[[],[[[],[]]]]]=>1
[2,1,5,2,6,1]=>[[[[[],[],[]]]]]=>1
[2,1,5,6,1,2]=>[[[[[]],[[]]]]]=>1
[2,1,5,6,2,1]=>[[[],[[[[]]]]]]=>1
[2,1,6,1,2,5]=>[[[[[[[]]]]]]]=>1
[2,1,6,1,5,2]=>[[[[[]],[[]]]]]=>1
[2,1,6,2,1,5]=>[[[[]],[[[]]]]]=>1
[2,1,6,2,5,1]=>[[[[],[],[[]]]]]=>1
[2,1,6,5,1,2]=>[[[],[[[[]]]]]]=>1
[2,1,6,5,2,1]=>[[[],[[]],[[]]]]=>1
[2,2,1,1,5,6]=>[[],[],[[[[]]]]]=>3
[2,2,1,1,6,5]=>[[],[],[[[],[]]]]=>3
[2,2,1,5,1,6]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,6,1]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,5,1]=>[[],[[],[[[]]]]]=>2
[2,2,5,1,1,6]=>[[],[[]],[[],[]]]=>3
[2,2,5,1,6,1]=>[[],[[],[[[]]]]]=>2
[2,2,5,6,1,1]=>[[],[],[[[[]]]]]=>3
[2,2,6,1,1,5]=>[[],[[]],[[],[]]]=>3
[2,2,6,1,5,1]=>[[],[[[]],[[]]]]=>2
[2,2,6,5,1,1]=>[[],[[]],[[[]]]]=>3
[2,5,1,1,2,6]=>[[[[]]],[[],[]]]=>2
[2,5,1,1,6,2]=>[[],[[[],[],[]]]]=>2
[2,5,1,2,1,6]=>[[[],[[[[]]]]]]=>1
[2,5,1,2,6,1]=>[[[],[[[[]]]]]]=>1
[2,5,1,6,1,2]=>[[[],[[[[]]]]]]=>1
[2,5,1,6,2,1]=>[[[],[],[[[]]]]]=>1
[2,5,2,1,1,6]=>[[[]],[[[[]]]]]=>2
[2,5,2,1,6,1]=>[[[[[[[]]]]]]]=>1
[2,5,2,6,1,1]=>[[],[[[],[[]]]]]=>2
[2,5,6,1,1,2]=>[[[]],[[],[[]]]]=>2
[2,5,6,1,2,1]=>[[[[[]],[[]]]]]=>1
[2,5,6,2,1,1]=>[[],[[[],[[]]]]]=>2
[2,6,1,1,2,5]=>[[[[]]],[[[]]]]=>2
[2,6,1,1,5,2]=>[[[]],[[],[],[]]]=>2
[2,6,1,2,1,5]=>[[[],[[[[]]]]]]=>1
[2,6,1,2,5,1]=>[[[[[[],[]]]]]]=>1
[2,6,1,5,1,2]=>[[[[]],[[[]]]]]=>1
[2,6,1,5,2,1]=>[[[],[[]],[[]]]]=>1
[2,6,2,1,1,5]=>[[],[[],[[[]]]]]=>2
[2,6,2,1,5,1]=>[[[],[[],[[]]]]]=>1
[2,6,2,5,1,1]=>[[],[[],[],[[]]]]=>2
[2,6,5,1,1,2]=>[[[[[]]]],[[]]]=>2
[2,6,5,1,2,1]=>[[[[[[],[]]]]]]=>1
[2,6,5,2,1,1]=>[[],[[],[[],[]]]]=>2
[5,1,1,2,2,6]=>[[[]],[[]],[[]]]=>3
[5,1,1,2,6,2]=>[[],[[[[],[]]]]]=>2
[5,1,1,6,2,2]=>[[],[],[[],[[]]]]=>3
[5,1,2,1,2,6]=>[[[[[[],[]]]]]]=>1
[5,1,2,1,6,2]=>[[[[]],[[[]]]]]=>1
[5,1,2,2,1,6]=>[[[[]]],[[[]]]]=>2
[5,1,2,2,6,1]=>[[[[]]],[[[]]]]=>2
[5,1,2,6,1,2]=>[[[[],[[[]]]]]]=>1
[5,1,2,6,2,1]=>[[[[[]]],[[]]]]=>1
[5,1,6,1,2,2]=>[[],[[[[[]]]]]]=>2
[5,1,6,2,1,2]=>[[[],[[[[]]]]]]=>1
[5,1,6,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,2,1,1,2,6]=>[[],[[[],[[]]]]]=>2
[5,2,1,1,6,2]=>[[[]],[[[[]]]]]=>2
[5,2,1,2,1,6]=>[[[[[],[[]]]]]]=>1
[5,2,1,2,6,1]=>[[[[]],[[[]]]]]=>1
[5,2,1,6,1,2]=>[[[[[[[]]]]]]]=>1
[5,2,1,6,2,1]=>[[[[[],[[]]]]]]=>1
[5,2,2,1,1,6]=>[[],[[]],[[[]]]]=>3
[5,2,2,1,6,1]=>[[],[[[[[]]]]]]=>2
[5,2,2,6,1,1]=>[[],[],[[[],[]]]]=>3
[5,2,6,1,1,2]=>[[[]],[[[],[]]]]=>2
[5,2,6,1,2,1]=>[[[],[[[[]]]]]]=>1
[5,2,6,2,1,1]=>[[],[[[[],[]]]]]=>2
[5,6,1,1,2,2]=>[[],[[]],[[],[]]]=>3
[5,6,1,2,1,2]=>[[[],[[]],[[]]]]=>1
[5,6,1,2,2,1]=>[[[]],[[],[[]]]]=>2
[5,6,2,1,1,2]=>[[],[[],[[[]]]]]=>2
[5,6,2,1,2,1]=>[[[],[[],[[]]]]]=>1
[5,6,2,2,1,1]=>[[],[[[]]],[[]]]=>3
[6,1,1,2,2,5]=>[[[]],[[]],[[]]]=>3
[6,1,1,2,5,2]=>[[[[[]]]],[[]]]=>2
[6,1,1,5,2,2]=>[[],[[]],[[],[]]]=>3
[6,1,2,1,2,5]=>[[[[],[[[]]]]]]=>1
[6,1,2,1,5,2]=>[[[[[[],[]]]]]]=>1
[6,1,2,2,1,5]=>[[[[]]],[[[]]]]=>2
[6,1,2,2,5,1]=>[[[[]]],[[],[]]]=>2
[6,1,2,5,1,2]=>[[[[],[[],[]]]]]=>1
[6,1,2,5,2,1]=>[[[[[[[]]]]]]]=>1
[6,1,5,1,2,2]=>[[],[[[[[]]]]]]=>2
[6,1,5,2,1,2]=>[[[[],[[[]]]]]]=>1
[6,1,5,2,2,1]=>[[[]],[[],[[]]]]=>2
[6,2,1,1,2,5]=>[[],[[[],[[]]]]]=>2
[6,2,1,1,5,2]=>[[[]],[[],[[]]]]=>2
[6,2,1,2,1,5]=>[[[[[],[[]]]]]]=>1
[6,2,1,2,5,1]=>[[[],[[]],[[]]]]=>1
[6,2,1,5,1,2]=>[[[[[]]],[[]]]]=>1
[6,2,1,5,2,1]=>[[[[],[[],[]]]]]=>1
[6,2,2,1,1,5]=>[[],[],[[[[]]]]]=>3
[6,2,2,1,5,1]=>[[],[[[],[[]]]]]=>2
[6,2,2,5,1,1]=>[[],[],[[],[],[]]]=>3
[6,2,5,1,1,2]=>[[[]],[[],[],[]]]=>2
[6,2,5,1,2,1]=>[[[],[],[[[]]]]]=>1
[6,2,5,2,1,1]=>[[],[[[[],[]]]]]=>2
[6,5,1,1,2,2]=>[[[]],[[]],[[]]]=>3
[6,5,1,2,1,2]=>[[[],[[],[[]]]]]=>1
[6,5,1,2,2,1]=>[[[[]]],[[],[]]]=>2
[6,5,2,1,1,2]=>[[],[[[],[[]]]]]=>2
[6,5,2,1,2,1]=>[[[],[],[[[]]]]]=>1
[6,5,2,2,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,2,3,3,3]=>[[],[],[],[[],[]]]=>4
[1,1,3,2,3,3]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,2,3]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,3,2]=>[[],[],[[]],[[]]]=>4
[1,2,1,3,3,3]=>[[],[[]],[[[]]]]=>3
[1,2,3,1,3,3]=>[[],[[[[],[]]]]]=>2
[1,2,3,3,1,3]=>[[[[]]],[[],[]]]=>2
[1,2,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[1,3,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[1,3,1,3,2,3]=>[[[],[[[[]]]]]]=>1
[1,3,1,3,3,2]=>[[[[]]],[[],[]]]=>2
[1,3,2,1,3,3]=>[[[],[]],[[],[]]]=>2
[1,3,2,3,1,3]=>[[[[[]]],[[]]]]=>1
[1,3,2,3,3,1]=>[[[]],[[[[]]]]]=>2
[1,3,3,1,2,3]=>[[[]],[[[],[]]]]=>2
[1,3,3,1,3,2]=>[[],[[[[],[]]]]]=>2
[1,3,3,2,1,3]=>[[],[[],[[],[]]]]=>2
[1,3,3,2,3,1]=>[[[]],[[[[]]]]]=>2
[1,3,3,3,1,2]=>[[],[[]],[[[]]]]=>3
[1,3,3,3,2,1]=>[[],[[]],[[],[]]]=>3
[2,1,1,3,3,3]=>[[],[],[[]],[[]]]=>4
[2,1,3,1,3,3]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,1,3]=>[[],[[[],[[]]]]]=>2
[2,1,3,3,3,1]=>[[],[[]],[[[]]]]=>3
[2,3,1,1,3,3]=>[[],[],[[[[]]]]]=>3
[2,3,1,3,1,3]=>[[[[],[[],[]]]]]=>1
[2,3,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[2,3,3,1,1,3]=>[[[]],[[]],[[]]]=>3
[2,3,3,1,3,1]=>[[[]],[[],[[]]]]=>2
[2,3,3,3,1,1]=>[[],[],[[]],[[]]]=>4
[3,1,1,2,3,3]=>[[],[],[[],[[]]]]=>3
[3,1,1,3,2,3]=>[[],[[[[[]]]]]]=>2
[3,1,1,3,3,2]=>[[],[[]],[[[]]]]=>3
[3,1,2,1,3,3]=>[[[[]]],[[[]]]]=>2
[3,1,2,3,1,3]=>[[[[]],[[],[]]]]=>1
[3,1,2,3,3,1]=>[[[],[]],[[],[]]]=>2
[3,1,3,1,2,3]=>[[[[]],[[],[]]]]=>1
[3,1,3,1,3,2]=>[[[],[[[],[]]]]]=>1
[3,1,3,2,1,3]=>[[[[],[[],[]]]]]=>1
[3,1,3,2,3,1]=>[[[[]],[[[]]]]]=>1
[3,1,3,3,1,2]=>[[[]],[[],[[]]]]=>2
[3,1,3,3,2,1]=>[[[]],[[],[[]]]]=>2
[3,2,1,1,3,3]=>[[],[[]],[[],[]]]=>3
[3,2,1,3,1,3]=>[[[],[[],[[]]]]]=>1
[3,2,1,3,3,1]=>[[[]],[[[],[]]]]=>2
[3,2,3,1,1,3]=>[[[[]]],[[[]]]]=>2
[3,2,3,1,3,1]=>[[[[[]],[[]]]]]=>1
[3,2,3,3,1,1]=>[[[]],[[]],[[]]]=>3
[3,3,1,1,2,3]=>[[],[],[[],[[]]]]=>3
[3,3,1,1,3,2]=>[[],[],[[[[]]]]]=>3
[3,3,1,2,1,3]=>[[],[[[[[]]]]]]=>2
[3,3,1,2,3,1]=>[[],[[],[[],[]]]]=>2
[3,3,1,3,1,2]=>[[],[[[]],[[]]]]=>2
[3,3,1,3,2,1]=>[[],[[[],[[]]]]]=>2
[3,3,2,1,1,3]=>[[],[],[[[],[]]]]=>3
[3,3,2,1,3,1]=>[[],[[],[[[]]]]]=>2
[3,3,2,3,1,1]=>[[],[[[]]],[[]]]=>3
[3,3,3,1,1,2]=>[[],[],[[]],[[]]]=>4
[3,3,3,1,2,1]=>[[],[],[[[[]]]]]=>3
[3,3,3,2,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,2,3,3,4]=>[[],[],[[],[],[]]]=>3
[1,1,2,3,4,3]=>[[],[[],[],[[]]]]=>2
[1,1,2,4,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,3,2,3,4]=>[[],[[[[],[]]]]]=>2
[1,1,3,2,4,3]=>[[],[[],[[],[]]]]=>2
[1,1,3,3,2,4]=>[[],[],[[[],[]]]]=>3
[1,1,3,3,4,2]=>[[],[[[]]],[[]]]=>3
[1,1,3,4,2,3]=>[[],[[[],[[]]]]]=>2
[1,1,3,4,3,2]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,4,3,2,3]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,3,2]=>[[],[],[[],[[]]]]=>3
[1,2,1,3,3,4]=>[[[]],[[],[[]]]]=>2
[1,2,1,3,4,3]=>[[[[]],[[],[]]]]=>1
[1,2,1,4,3,3]=>[[],[[[]],[[]]]]=>2
[1,2,3,1,3,4]=>[[[],[],[[[]]]]]=>1
[1,2,3,1,4,3]=>[[[],[[[[]]]]]]=>1
[1,2,3,3,1,4]=>[[[[]]],[[],[]]]=>2
[1,2,3,3,4,1]=>[[],[[],[],[[]]]]=>2
[1,2,3,4,1,3]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,3,1]=>[[[],[],[[[]]]]]=>1
[1,2,4,1,3,3]=>[[],[[[]],[[]]]]=>2
[1,2,4,3,1,3]=>[[[[[]],[[]]]]]=>1
[1,2,4,3,3,1]=>[[],[[[[[]]]]]]=>2
[1,3,1,2,3,4]=>[[[[[],[],[]]]]]=>1
[1,3,1,2,4,3]=>[[[[]],[[[]]]]]=>1
[1,3,1,3,2,4]=>[[[],[[]],[[]]]]=>1
[1,3,1,3,4,2]=>[[[],[[[],[]]]]]=>1
[1,3,1,4,2,3]=>[[[[[]],[[]]]]]=>1
[1,3,1,4,3,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,1,3,4]=>[[[],[[[],[]]]]]=>1
[1,3,2,1,4,3]=>[[[[],[],[[]]]]]=>1
[1,3,2,3,1,4]=>[[[[[[[]]]]]]]=>1
[1,3,2,3,4,1]=>[[[[[[],[]]]]]]=>1
[1,3,2,4,1,3]=>[[[],[[]],[[]]]]=>1
[1,3,2,4,3,1]=>[[[],[[],[[]]]]]=>1
[1,3,3,1,2,4]=>[[],[[[[],[]]]]]=>2
[1,3,3,1,4,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,1,4]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,4,1]=>[[],[[[[],[]]]]]=>2
[1,3,3,4,1,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,4,2,1]=>[[[[[]]]],[[]]]=>2
[1,3,4,1,2,3]=>[[[[],[],[[]]]]]=>1
[1,3,4,1,3,2]=>[[[[[]]],[[]]]]=>1
[1,3,4,2,1,3]=>[[[[[]]],[[]]]]=>1
[1,3,4,2,3,1]=>[[[[],[[],[]]]]]=>1
[1,3,4,3,1,2]=>[[[[[]],[[]]]]]=>1
[1,3,4,3,2,1]=>[[[[[],[],[]]]]]=>1
[1,4,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[1,4,1,3,2,3]=>[[[[[[[]]]]]]]=>1
[1,4,1,3,3,2]=>[[[[[]]]],[[]]]=>2
[1,4,2,1,3,3]=>[[[[[]]]],[[]]]=>2
[1,4,2,3,1,3]=>[[[[[]],[[]]]]]=>1
[1,4,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[1,4,3,1,2,3]=>[[[[[],[[]]]]]]=>1
[1,4,3,1,3,2]=>[[[[[],[[]]]]]]=>1
[1,4,3,2,1,3]=>[[[[],[],[[]]]]]=>1
[1,4,3,2,3,1]=>[[[[],[[[]]]]]]=>1
[1,4,3,3,1,2]=>[[],[[[[[]]]]]]=>2
[1,4,3,3,2,1]=>[[[]],[[],[],[]]]=>2
[2,1,1,3,3,4]=>[[],[[[]]],[[]]]=>3
[2,1,1,3,4,3]=>[[],[[[[],[]]]]]=>2
[2,1,1,4,3,3]=>[[],[],[[],[[]]]]=>3
[2,1,3,1,3,4]=>[[[[[],[[]]]]]]=>1
[2,1,3,1,4,3]=>[[[[]],[[[]]]]]=>1
[2,1,3,3,1,4]=>[[[]],[[[[]]]]]=>2
[2,1,3,3,4,1]=>[[[[[]]]],[[]]]=>2
[2,1,3,4,1,3]=>[[[[],[[[]]]]]]=>1
[2,1,3,4,3,1]=>[[[[[]]],[[]]]]=>1
[2,1,4,1,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,4,3,1,3]=>[[[[[]]],[[]]]]=>1
[2,1,4,3,3,1]=>[[],[[[],[[]]]]]=>2
[2,3,1,1,3,4]=>[[[[],[]]],[[]]]=>2
[2,3,1,1,4,3]=>[[],[[[[[]]]]]]=>2
[2,3,1,3,1,4]=>[[[[[]],[[]]]]]=>1
[2,3,1,3,4,1]=>[[[[[]]],[[]]]]=>1
[2,3,1,4,1,3]=>[[[[[[[]]]]]]]=>1
[2,3,1,4,3,1]=>[[[[],[[[]]]]]]=>1
[2,3,3,1,1,4]=>[[[]],[[]],[[]]]=>3
[2,3,3,1,4,1]=>[[[]],[[[[]]]]]=>2
[2,3,3,4,1,1]=>[[],[],[[[],[]]]]=>3
[2,3,4,1,1,3]=>[[[]],[[[],[]]]]=>2
[2,3,4,1,3,1]=>[[[],[[[[]]]]]]=>1
[2,3,4,3,1,1]=>[[[]],[[[],[]]]]=>2
[2,4,1,1,3,3]=>[[],[[]],[[],[]]]=>3
[2,4,1,3,1,3]=>[[[],[],[[[]]]]]=>1
[2,4,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[2,4,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,4,3,1,3,1]=>[[[],[[],[[]]]]]=>1
[2,4,3,3,1,1]=>[[],[[]],[[[]]]]=>3
[3,1,1,2,3,4]=>[[],[[],[],[[]]]]=>2
[3,1,1,2,4,3]=>[[],[[[[[]]]]]]=>2
[3,1,1,3,2,4]=>[[],[[[]],[[]]]]=>2
[3,1,1,3,4,2]=>[[],[[[[],[]]]]]=>2
[3,1,1,4,2,3]=>[[],[[[],[[]]]]]=>2
[3,1,1,4,3,2]=>[[],[[[],[[]]]]]=>2
[3,1,2,1,3,4]=>[[[[[],[[]]]]]]=>1
[3,1,2,1,4,3]=>[[[[[]],[[]]]]]=>1
[3,1,2,3,1,4]=>[[[[]],[[],[]]]]=>1
[3,1,2,3,4,1]=>[[[[],[],[[]]]]]=>1
[3,1,2,4,1,3]=>[[[[[],[[]]]]]]=>1
[3,1,2,4,3,1]=>[[[],[[[[]]]]]]=>1
[3,1,3,1,2,4]=>[[[],[[[],[]]]]]=>1
[3,1,3,1,4,2]=>[[[],[[]],[[]]]]=>1
[3,1,3,2,1,4]=>[[[[[],[[]]]]]]=>1
[3,1,3,2,4,1]=>[[[[],[[[]]]]]]=>1
[3,1,3,4,1,2]=>[[[[[],[[]]]]]]=>1
[3,1,3,4,2,1]=>[[[[[]]],[[]]]]=>1
[3,1,4,1,2,3]=>[[[[],[[[]]]]]]=>1
[3,1,4,1,3,2]=>[[[[[[[]]]]]]]=>1
[3,1,4,2,1,3]=>[[[[[]]],[[]]]]=>1
[3,1,4,2,3,1]=>[[[],[[]],[[]]]]=>1
[3,1,4,3,1,2]=>[[[],[[[[]]]]]]=>1
[3,1,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[3,2,1,1,3,4]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,4,3]=>[[],[[[],[],[]]]]=>2
[3,2,1,3,1,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,3,4,1]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,1,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,3,1]=>[[[],[[]],[[]]]]=>1
[3,2,3,1,1,4]=>[[[[]]],[[[]]]]=>2
[3,2,3,1,4,1]=>[[[[[[[]]]]]]]=>1
[3,2,3,4,1,1]=>[[[[],[]]],[[]]]=>2
[3,2,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[3,2,4,1,3,1]=>[[[[[],[[]]]]]]=>1
[3,2,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[3,3,1,1,2,4]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,4,2]=>[[],[],[[[],[]]]]=>3
[3,3,1,2,1,4]=>[[],[[[[[]]]]]]=>2
[3,3,1,2,4,1]=>[[],[[[[[]]]]]]=>2
[3,3,1,4,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,1,4,2,1]=>[[],[[[]],[[]]]]=>2
[3,3,2,1,1,4]=>[[],[],[[[],[]]]]=>3
[3,3,2,1,4,1]=>[[],[[],[[[]]]]]=>2
[3,3,2,4,1,1]=>[[],[[[]]],[[]]]=>3
[3,3,4,1,1,2]=>[[],[[]],[[],[]]]=>3
[3,3,4,1,2,1]=>[[],[[[]],[[]]]]=>2
[3,3,4,2,1,1]=>[[],[[[]]],[[]]]=>3
[3,4,1,1,2,3]=>[[[]],[[],[],[]]]=>2
[3,4,1,1,3,2]=>[[[[]]],[[[]]]]=>2
[3,4,1,2,1,3]=>[[[[]],[[[]]]]]=>1
[3,4,1,2,3,1]=>[[[],[[]],[[]]]]=>1
[3,4,1,3,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,1,3,2,1]=>[[[[[],[[]]]]]]=>1
[3,4,2,1,1,3]=>[[[[]]],[[[]]]]=>2
[3,4,2,1,3,1]=>[[[[[]],[[]]]]]=>1
[3,4,2,3,1,1]=>[[],[[],[[],[]]]]=>2
[3,4,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[3,4,3,1,2,1]=>[[[],[[],[[]]]]]=>1
[3,4,3,2,1,1]=>[[],[[],[],[[]]]]=>2
[4,1,1,2,3,3]=>[[],[],[[],[[]]]]=>3
[4,1,1,3,2,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,3,3,2]=>[[],[[[]]],[[]]]=>3
[4,1,2,1,3,3]=>[[[]],[[[[]]]]]=>2
[4,1,2,3,1,3]=>[[[[],[[[]]]]]]=>1
[4,1,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[4,1,3,1,2,3]=>[[[[],[[[]]]]]]=>1
[4,1,3,1,3,2]=>[[[[],[[[]]]]]]=>1
[4,1,3,2,1,3]=>[[[[],[[],[]]]]]=>1
[4,1,3,2,3,1]=>[[[[[[[]]]]]]]=>1
[4,1,3,3,1,2]=>[[[[]]],[[[]]]]=>2
[4,1,3,3,2,1]=>[[[]],[[],[[]]]]=>2
[4,2,1,1,3,3]=>[[],[[[]]],[[]]]=>3
[4,2,1,3,1,3]=>[[[],[[],[[]]]]]=>1
[4,2,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,3,1]=>[[[],[[]],[[]]]]=>1
[4,2,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[4,3,1,1,2,3]=>[[],[[[]],[[]]]]=>2
[4,3,1,1,3,2]=>[[],[[[],[[]]]]]=>2
[4,3,1,2,1,3]=>[[[[]],[[[]]]]]=>1
[4,3,1,2,3,1]=>[[[[],[[],[]]]]]=>1
[4,3,1,3,1,2]=>[[[[[],[[]]]]]]=>1
[4,3,1,3,2,1]=>[[[],[[]],[[]]]]=>1
[4,3,2,1,1,3]=>[[],[[[],[],[]]]]=>2
[4,3,2,1,3,1]=>[[[],[],[[[]]]]]=>1
[4,3,2,3,1,1]=>[[[[]]],[[],[]]]=>2
[4,3,3,1,1,2]=>[[],[[[]]],[[]]]=>3
[4,3,3,1,2,1]=>[[],[[[],[[]]]]]=>2
[4,3,3,2,1,1]=>[[],[],[[],[],[]]]=>3
[1,1,2,3,3,5]=>[[],[[]],[[],[]]]=>3
[1,1,2,3,5,3]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,3,2,3,5]=>[[],[[[]],[[]]]]=>2
[1,1,3,2,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,3,3,2,5]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,5,2]=>[[],[],[[],[[]]]]=>3
[1,1,3,5,2,3]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,3,2]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,3,3]=>[[],[],[[[],[]]]]=>3
[1,1,5,3,2,3]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,3,2]=>[[],[[]],[[[]]]]=>3
[1,2,1,3,3,5]=>[[],[[],[[[]]]]]=>2
[1,2,1,3,5,3]=>[[[[[[],[]]]]]]=>1
[1,2,1,5,3,3]=>[[[[]]],[[[]]]]=>2
[1,2,3,1,3,5]=>[[[],[[[],[]]]]]=>1
[1,2,3,1,5,3]=>[[[],[[],[[]]]]]=>1
[1,2,3,3,1,5]=>[[[[]]],[[],[]]]=>2
[1,2,3,3,5,1]=>[[[[]]],[[],[]]]=>2
[1,2,3,5,1,3]=>[[[],[[],[[]]]]]=>1
[1,2,3,5,3,1]=>[[[],[[[],[]]]]]=>1
[1,2,5,1,3,3]=>[[],[[[],[[]]]]]=>2
[1,2,5,3,1,3]=>[[[[[],[[]]]]]]=>1
[1,2,5,3,3,1]=>[[],[[],[[[]]]]]=>2
[1,3,1,2,3,5]=>[[[],[[],[[]]]]]=>1
[1,3,1,2,5,3]=>[[[[],[[[]]]]]]=>1
[1,3,1,3,2,5]=>[[[],[[[[]]]]]]=>1
[1,3,1,3,5,2]=>[[[],[[]],[[]]]]=>1
[1,3,1,5,2,3]=>[[[[[],[[]]]]]]=>1
[1,3,1,5,3,2]=>[[[[[[],[]]]]]]=>1
[1,3,2,1,3,5]=>[[[],[],[[],[]]]]=>1
[1,3,2,1,5,3]=>[[[[],[[[]]]]]]=>1
[1,3,2,3,1,5]=>[[[[[[[]]]]]]]=>1
[1,3,2,3,5,1]=>[[[[]],[[[]]]]]=>1
[1,3,2,5,1,3]=>[[[[]],[[],[]]]]=>1
[1,3,2,5,3,1]=>[[[[[],[[]]]]]]=>1
[1,3,3,1,2,5]=>[[[]],[[[[]]]]]=>2
[1,3,3,1,5,2]=>[[[]],[[[],[]]]]=>2
[1,3,3,2,1,5]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,5,1]=>[[[]],[[[],[]]]]=>2
[1,3,3,5,1,2]=>[[],[[],[[[]]]]]=>2
[1,3,3,5,2,1]=>[[],[[],[[[]]]]]=>2
[1,3,5,1,2,3]=>[[[],[[[],[]]]]]=>1
[1,3,5,1,3,2]=>[[[],[[]],[[]]]]=>1
[1,3,5,2,1,3]=>[[[],[],[[[]]]]]=>1
[1,3,5,2,3,1]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,1,2]=>[[[],[[],[[]]]]]=>1
[1,3,5,3,2,1]=>[[[],[[[],[]]]]]=>1
[1,5,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[1,5,1,3,2,3]=>[[[[[[[]]]]]]]=>1
[1,5,1,3,3,2]=>[[[[[]]]],[[]]]=>2
[1,5,2,1,3,3]=>[[[]],[[[],[]]]]=>2
[1,5,2,3,1,3]=>[[[],[[[[]]]]]]=>1
[1,5,2,3,3,1]=>[[[[],[]]],[[]]]=>2
[1,5,3,1,2,3]=>[[[[],[[],[]]]]]=>1
[1,5,3,1,3,2]=>[[[[[[],[]]]]]]=>1
[1,5,3,2,1,3]=>[[[[],[[[]]]]]]=>1
[1,5,3,2,3,1]=>[[[[[],[[]]]]]]=>1
[1,5,3,3,1,2]=>[[[]],[[],[[]]]]=>2
[1,5,3,3,2,1]=>[[],[[[]],[[]]]]=>2
[2,1,1,3,3,5]=>[[],[],[[],[[]]]]=>3
[2,1,1,3,5,3]=>[[],[[],[[[]]]]]=>2
[2,1,1,5,3,3]=>[[],[[[]]],[[]]]=>3
[2,1,3,1,3,5]=>[[[[],[],[[]]]]]=>1
[2,1,3,1,5,3]=>[[[[[]],[[]]]]]=>1
[2,1,3,3,1,5]=>[[[]],[[[[]]]]]=>2
[2,1,3,3,5,1]=>[[],[[],[[[]]]]]=>2
[2,1,3,5,1,3]=>[[[[],[],[[]]]]]=>1
[2,1,3,5,3,1]=>[[[[],[[],[]]]]]=>1
[2,1,5,1,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,5,3,1,3]=>[[[[[],[[]]]]]]=>1
[2,1,5,3,3,1]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,3,5]=>[[],[[],[[[]]]]]=>2
[2,3,1,1,5,3]=>[[],[[[],[[]]]]]=>2
[2,3,1,3,1,5]=>[[[[[]],[[]]]]]=>1
[2,3,1,3,5,1]=>[[[[[],[[]]]]]]=>1
[2,3,1,5,1,3]=>[[[[[[[]]]]]]]=>1
[2,3,1,5,3,1]=>[[[[],[],[[]]]]]=>1
[2,3,3,1,1,5]=>[[[]],[[]],[[]]]=>3
[2,3,3,1,5,1]=>[[[]],[[[[]]]]]=>2
[2,3,3,5,1,1]=>[[],[[]],[[[]]]]=>3
[2,3,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,3,5,1,3,1]=>[[[[[]],[[]]]]]=>1
[2,3,5,3,1,1]=>[[],[[],[[[]]]]]=>2
[2,5,1,1,3,3]=>[[],[[]],[[],[]]]=>3
[2,5,1,3,1,3]=>[[[],[[],[[]]]]]=>1
[2,5,1,3,3,1]=>[[[[],[]]],[[]]]=>2
[2,5,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,5,3,1,3,1]=>[[[[],[],[[]]]]]=>1
[2,5,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,2,3,5]=>[[],[[[]],[[]]]]=>2
[3,1,1,2,5,3]=>[[],[[[[],[]]]]]=>2
[3,1,1,3,2,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,3,5,2]=>[[],[[[]],[[]]]]=>2
[3,1,1,5,2,3]=>[[],[[[]],[[]]]]=>2
[3,1,1,5,3,2]=>[[],[[[[],[]]]]]=>2
[3,1,2,1,3,5]=>[[[[],[[[]]]]]]=>1
[3,1,2,1,5,3]=>[[[[]],[[[]]]]]=>1
[3,1,2,3,1,5]=>[[[[]],[[],[]]]]=>1
[3,1,2,3,5,1]=>[[[[],[[[]]]]]]=>1
[3,1,2,5,1,3]=>[[[[[]],[[]]]]]=>1
[3,1,2,5,3,1]=>[[[],[],[[[]]]]]=>1
[3,1,3,1,2,5]=>[[[[[]]],[[]]]]=>1
[3,1,3,1,5,2]=>[[[[]],[[],[]]]]=>1
[3,1,3,2,1,5]=>[[[[[],[[]]]]]]=>1
[3,1,3,2,5,1]=>[[[[],[[[]]]]]]=>1
[3,1,3,5,1,2]=>[[[[],[[[]]]]]]=>1
[3,1,3,5,2,1]=>[[[[[[],[]]]]]]=>1
[3,1,5,1,2,3]=>[[[[],[[[]]]]]]=>1
[3,1,5,1,3,2]=>[[[[[[[]]]]]]]=>1
[3,1,5,2,1,3]=>[[[[[[],[]]]]]]=>1
[3,1,5,2,3,1]=>[[[],[[[],[]]]]]=>1
[3,1,5,3,1,2]=>[[[],[[]],[[]]]]=>1
[3,1,5,3,2,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,1,3,5]=>[[],[[],[[],[]]]]=>2
[3,2,1,1,5,3]=>[[],[[[[],[]]]]]=>2
[3,2,1,3,1,5]=>[[[],[[[[]]]]]]=>1
[3,2,1,3,5,1]=>[[[],[[[],[]]]]]=>1
[3,2,1,5,1,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,3,1]=>[[[],[[],[[]]]]]=>1
[3,2,3,1,1,5]=>[[[[]]],[[[]]]]=>2
[3,2,3,1,5,1]=>[[[[[[[]]]]]]]=>1
[3,2,3,5,1,1]=>[[[[[]]]],[[]]]=>2
[3,2,5,1,1,3]=>[[[[]]],[[],[]]]=>2
[3,2,5,1,3,1]=>[[[[[[],[]]]]]]=>1
[3,2,5,3,1,1]=>[[[]],[[],[[]]]]=>2
[3,3,1,1,2,5]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,5,2]=>[[],[],[[],[[]]]]=>3
[3,3,1,2,1,5]=>[[],[[[[[]]]]]]=>2
[3,3,1,2,5,1]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,1,5,2,1]=>[[],[[[[],[]]]]]=>2
[3,3,2,1,1,5]=>[[],[],[[[],[]]]]=>3
[3,3,2,1,5,1]=>[[],[[],[[[]]]]]=>2
[3,3,2,5,1,1]=>[[],[[]],[[],[]]]=>3
[3,3,5,1,1,2]=>[[],[[]],[[[]]]]=>3
[3,3,5,1,2,1]=>[[],[[[[[]]]]]]=>2
[3,3,5,2,1,1]=>[[],[],[[[[]]]]]=>3
[3,5,1,1,2,3]=>[[[[]]],[[],[]]]=>2
[3,5,1,1,3,2]=>[[[]],[[],[[]]]]=>2
[3,5,1,2,1,3]=>[[[],[[[[]]]]]]=>1
[3,5,1,2,3,1]=>[[[[[],[[]]]]]]=>1
[3,5,1,3,1,2]=>[[[[]],[[[]]]]]=>1
[3,5,1,3,2,1]=>[[[[]],[[],[]]]]=>1
[3,5,2,1,1,3]=>[[],[[],[[[]]]]]=>2
[3,5,2,1,3,1]=>[[[[]],[[[]]]]]=>1
[3,5,2,3,1,1]=>[[],[[[[[]]]]]]=>2
[3,5,3,1,1,2]=>[[[]],[[],[[]]]]=>2
[3,5,3,1,2,1]=>[[[[],[[[]]]]]]=>1
[3,5,3,2,1,1]=>[[[[]]],[[],[]]]=>2
[5,1,1,2,3,3]=>[[],[[]],[[],[]]]=>3
[5,1,1,3,2,3]=>[[[[[]]]],[[]]]=>2
[5,1,1,3,3,2]=>[[[]],[[]],[[]]]=>3
[5,1,2,1,3,3]=>[[[]],[[[[]]]]]=>2
[5,1,2,3,1,3]=>[[[[],[[[]]]]]]=>1
[5,1,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,1,3,1,2,3]=>[[[[[[],[]]]]]]=>1
[5,1,3,1,3,2]=>[[[[[[],[]]]]]]=>1
[5,1,3,2,1,3]=>[[[[],[[],[]]]]]=>1
[5,1,3,2,3,1]=>[[[[[[[]]]]]]]=>1
[5,1,3,3,1,2]=>[[[[]]],[[[]]]]=>2
[5,1,3,3,2,1]=>[[[[]]],[[],[]]]=>2
[5,2,1,1,3,3]=>[[[]],[[]],[[]]]=>3
[5,2,1,3,1,3]=>[[[[[],[[]]]]]]=>1
[5,2,1,3,3,1]=>[[[[]]],[[[]]]]=>2
[5,2,3,1,1,3]=>[[[]],[[[[]]]]]=>2
[5,2,3,1,3,1]=>[[[[[],[[]]]]]]=>1
[5,2,3,3,1,1]=>[[],[[]],[[[]]]]=>3
[5,3,1,1,2,3]=>[[],[[],[[],[]]]]=>2
[5,3,1,1,3,2]=>[[],[[[[],[]]]]]=>2
[5,3,1,2,1,3]=>[[[],[[[[]]]]]]=>1
[5,3,1,2,3,1]=>[[[],[],[[],[]]]]=>1
[5,3,1,3,1,2]=>[[[],[[]],[[]]]]=>1
[5,3,1,3,2,1]=>[[[],[[],[[]]]]]=>1
[5,3,2,1,1,3]=>[[[[],[]]],[[]]]=>2
[5,3,2,1,3,1]=>[[[[]],[[],[]]]]=>1
[5,3,2,3,1,1]=>[[[]],[[],[[]]]]=>2
[5,3,3,1,1,2]=>[[],[[]],[[],[]]]=>3
[5,3,3,1,2,1]=>[[],[[],[[[]]]]]=>2
[5,3,3,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,3,3,6]=>[[],[[]],[[],[]]]=>3
[1,1,2,3,6,3]=>[[],[[],[[[]]]]]=>2
[1,1,2,6,3,3]=>[[],[],[[],[[]]]]=>3
[1,1,3,2,3,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,2,6,3]=>[[],[[[[],[]]]]]=>2
[1,1,3,3,2,6]=>[[],[[]],[[[]]]]=>3
[1,1,3,3,6,2]=>[[],[[]],[[],[]]]=>3
[1,1,3,6,2,3]=>[[],[[[],[[]]]]]=>2
[1,1,3,6,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,6,3,2,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,3,2]=>[[],[[]],[[[]]]]=>3
[1,2,1,3,3,6]=>[[[]],[[[[]]]]]=>2
[1,2,1,3,6,3]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,3,3]=>[[[[]]],[[[]]]]=>2
[1,2,3,1,3,6]=>[[[],[[[[]]]]]]=>1
[1,2,3,1,6,3]=>[[[],[[],[[]]]]]=>1
[1,2,3,3,1,6]=>[[[],[]],[[],[]]]=>2
[1,2,3,3,6,1]=>[[[[]]],[[],[]]]=>2
[1,2,3,6,1,3]=>[[[],[[[],[]]]]]=>1
[1,2,3,6,3,1]=>[[[],[[[[]]]]]]=>1
[1,2,6,1,3,3]=>[[],[[],[[[]]]]]=>2
[1,2,6,3,1,3]=>[[[[],[[[]]]]]]=>1
[1,2,6,3,3,1]=>[[[]],[[],[[]]]]=>2
[1,3,1,2,3,6]=>[[[[[],[[]]]]]]=>1
[1,3,1,2,6,3]=>[[[[[],[[]]]]]]=>1
[1,3,1,3,2,6]=>[[[],[[[[]]]]]]=>1
[1,3,1,3,6,2]=>[[[],[[],[[]]]]]=>1
[1,3,1,6,2,3]=>[[[[],[[[]]]]]]=>1
[1,3,1,6,3,2]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,3,6]=>[[[],[[[],[]]]]]=>1
[1,3,2,1,6,3]=>[[[[],[[[]]]]]]=>1
[1,3,2,3,1,6]=>[[[[[],[[]]]]]]=>1
[1,3,2,3,6,1]=>[[[[[]]],[[]]]]=>1
[1,3,2,6,1,3]=>[[[],[[]],[[]]]]=>1
[1,3,2,6,3,1]=>[[[[],[[[]]]]]]=>1
[1,3,3,1,2,6]=>[[[]],[[[[]]]]]=>2
[1,3,3,1,6,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,1,6]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,6,1]=>[[],[[[],[[]]]]]=>2
[1,3,3,6,1,2]=>[[],[[[],[[]]]]]=>2
[1,3,3,6,2,1]=>[[[]],[[],[[]]]]=>2
[1,3,6,1,2,3]=>[[[[]],[[],[]]]]=>1
[1,3,6,1,3,2]=>[[[],[[]],[[]]]]=>1
[1,3,6,2,1,3]=>[[[],[[[],[]]]]]=>1
[1,3,6,2,3,1]=>[[[[],[[[]]]]]]=>1
[1,3,6,3,1,2]=>[[[[[[[]]]]]]]=>1
[1,3,6,3,2,1]=>[[[[[],[[]]]]]]=>1
[1,6,1,2,3,3]=>[[],[[[]],[[]]]]=>2
[1,6,1,3,2,3]=>[[[[[[],[]]]]]]=>1
[1,6,1,3,3,2]=>[[[[]]],[[],[]]]=>2
[1,6,2,1,3,3]=>[[[[]]],[[[]]]]=>2
[1,6,2,3,1,3]=>[[[[[]]],[[]]]]=>1
[1,6,2,3,3,1]=>[[[[]]],[[],[]]]=>2
[1,6,3,1,2,3]=>[[[],[[],[[]]]]]=>1
[1,6,3,1,3,2]=>[[[],[[[[]]]]]]=>1
[1,6,3,2,1,3]=>[[[[[],[[]]]]]]=>1
[1,6,3,2,3,1]=>[[[[[]]],[[]]]]=>1
[1,6,3,3,1,2]=>[[[]],[[],[[]]]]=>2
[1,6,3,3,2,1]=>[[],[[[]],[[]]]]=>2
[2,1,1,3,3,6]=>[[],[[]],[[[]]]]=>3
[2,1,1,3,6,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,3,3]=>[[],[[[]]],[[]]]=>3
[2,1,3,1,3,6]=>[[[[[],[[]]]]]]=>1
[2,1,3,1,6,3]=>[[[[[],[[]]]]]]=>1
[2,1,3,3,1,6]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,6,1]=>[[],[[[],[[]]]]]=>2
[2,1,3,6,1,3]=>[[[[],[],[[]]]]]=>1
[2,1,3,6,3,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,1,3,3]=>[[[]],[[],[[]]]]=>2
[2,1,6,3,1,3]=>[[[[[],[[]]]]]]=>1
[2,1,6,3,3,1]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,3,6]=>[[[[]]],[[[]]]]=>2
[2,3,1,1,6,3]=>[[],[[[]],[[]]]]=>2
[2,3,1,3,1,6]=>[[[[],[],[[]]]]]=>1
[2,3,1,3,6,1]=>[[[[[[],[]]]]]]=>1
[2,3,1,6,1,3]=>[[[[],[[],[]]]]]=>1
[2,3,1,6,3,1]=>[[[[],[],[[]]]]]=>1
[2,3,3,1,1,6]=>[[],[[]],[[],[]]]=>3
[2,3,3,1,6,1]=>[[[]],[[],[[]]]]=>2
[2,3,3,6,1,1]=>[[],[[]],[[[]]]]=>3
[2,3,6,1,1,3]=>[[],[[],[[[]]]]]=>2
[2,3,6,1,3,1]=>[[[[[],[[]]]]]]=>1
[2,3,6,3,1,1]=>[[],[[[[[]]]]]]=>2
[2,6,1,1,3,3]=>[[],[[]],[[],[]]]=>3
[2,6,1,3,1,3]=>[[[[[],[],[]]]]]=>1
[2,6,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[2,6,3,1,1,3]=>[[[]],[[[],[]]]]=>2
[2,6,3,1,3,1]=>[[[],[[[],[]]]]]=>1
[2,6,3,3,1,1]=>[[],[],[[[],[]]]]=>3
[3,1,1,2,3,6]=>[[],[[[]],[[]]]]=>2
[3,1,1,2,6,3]=>[[],[[[],[[]]]]]=>2
[3,1,1,3,2,6]=>[[],[[[[[]]]]]]=>2
[3,1,1,3,6,2]=>[[],[[[],[[]]]]]=>2
[3,1,1,6,2,3]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,3,2]=>[[],[[],[[[]]]]]=>2
[3,1,2,1,3,6]=>[[[[[[[]]]]]]]=>1
[3,1,2,1,6,3]=>[[[],[[[[]]]]]]=>1
[3,1,2,3,1,6]=>[[[],[],[[],[]]]]=>1
[3,1,2,3,6,1]=>[[[[],[[[]]]]]]=>1
[3,1,2,6,1,3]=>[[[[],[[[]]]]]]=>1
[3,1,2,6,3,1]=>[[[],[[],[[]]]]]=>1
[3,1,3,1,2,6]=>[[[[[]]],[[]]]]=>1
[3,1,3,1,6,2]=>[[[],[[]],[[]]]]=>1
[3,1,3,2,1,6]=>[[[],[[],[[]]]]]=>1
[3,1,3,2,6,1]=>[[[[[],[[]]]]]]=>1
[3,1,3,6,1,2]=>[[[[[],[[]]]]]]=>1
[3,1,3,6,2,1]=>[[[[[],[[]]]]]]=>1
[3,1,6,1,2,3]=>[[[],[[],[[]]]]]=>1
[3,1,6,1,3,2]=>[[[],[[[],[]]]]]=>1
[3,1,6,2,1,3]=>[[[],[[[[]]]]]]=>1
[3,1,6,2,3,1]=>[[[],[],[[[]]]]]=>1
[3,1,6,3,1,2]=>[[[],[[]],[[]]]]=>1
[3,1,6,3,2,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,1,3,6]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,6,3]=>[[],[[[[],[]]]]]=>2
[3,2,1,3,1,6]=>[[[],[[],[[]]]]]=>1
[3,2,1,3,6,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,1,3]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,3,1]=>[[[],[[],[[]]]]]=>1
[3,2,3,1,1,6]=>[[],[[[]],[[]]]]=>2
[3,2,3,1,6,1]=>[[[[[],[[]]]]]]=>1
[3,2,3,6,1,1]=>[[[[[]]]],[[]]]=>2
[3,2,6,1,1,3]=>[[],[[[]],[[]]]]=>2
[3,2,6,1,3,1]=>[[[[[],[[]]]]]]=>1
[3,2,6,3,1,1]=>[[[[],[]]],[[]]]=>2
[3,3,1,1,2,6]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,6,2]=>[[],[],[[],[[]]]]=>3
[3,3,1,2,1,6]=>[[],[[],[[[]]]]]=>2
[3,3,1,2,6,1]=>[[],[[[[[]]]]]]=>2
[3,3,1,6,1,2]=>[[],[[],[[[]]]]]=>2
[3,3,1,6,2,1]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,1,6]=>[[],[],[[[],[]]]]=>3
[3,3,2,1,6,1]=>[[],[[],[[[]]]]]=>2
[3,3,2,6,1,1]=>[[],[[[]]],[[]]]=>3
[3,3,6,1,1,2]=>[[],[[]],[[[]]]]=>3
[3,3,6,1,2,1]=>[[],[[[[[]]]]]]=>2
[3,3,6,2,1,1]=>[[],[],[[[],[]]]]=>3
[3,6,1,1,2,3]=>[[[[]]],[[],[]]]=>2
[3,6,1,1,3,2]=>[[],[[[]],[[]]]]=>2
[3,6,1,2,1,3]=>[[[[],[[[]]]]]]=>1
[3,6,1,2,3,1]=>[[[[[],[[]]]]]]=>1
[3,6,1,3,1,2]=>[[[[],[[[]]]]]]=>1
[3,6,1,3,2,1]=>[[[[],[[],[]]]]]=>1
[3,6,2,1,1,3]=>[[],[[[[],[]]]]]=>2
[3,6,2,1,3,1]=>[[[],[[[[]]]]]]=>1
[3,6,2,3,1,1]=>[[],[[[[],[]]]]]=>2
[3,6,3,1,1,2]=>[[[]],[[[[]]]]]=>2
[3,6,3,1,2,1]=>[[[[[[[]]]]]]]=>1
[3,6,3,2,1,1]=>[[],[[[]],[[]]]]=>2
[6,1,1,2,3,3]=>[[],[[]],[[],[]]]=>3
[6,1,1,3,2,3]=>[[],[[],[[[]]]]]=>2
[6,1,1,3,3,2]=>[[],[[]],[[],[]]]=>3
[6,1,2,1,3,3]=>[[[[]]],[[],[]]]=>2
[6,1,2,3,1,3]=>[[[],[[[],[]]]]]=>1
[6,1,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[6,1,3,1,2,3]=>[[[],[[[],[]]]]]=>1
[6,1,3,1,3,2]=>[[[],[],[[[]]]]]=>1
[6,1,3,2,1,3]=>[[[],[],[[],[]]]]=>1
[6,1,3,2,3,1]=>[[[],[[[[]]]]]]=>1
[6,1,3,3,1,2]=>[[[[]]],[[],[]]]=>2
[6,1,3,3,2,1]=>[[[],[]],[[],[]]]=>2
[6,2,1,1,3,3]=>[[],[[]],[[[]]]]=>3
[6,2,1,3,1,3]=>[[[[[]],[[]]]]]=>1
[6,2,1,3,3,1]=>[[[]],[[[[]]]]]=>2
[6,2,3,1,1,3]=>[[[]],[[[[]]]]]=>2
[6,2,3,1,3,1]=>[[[[[],[[]]]]]]=>1
[6,2,3,3,1,1]=>[[],[[[]]],[[]]]=>3
[6,3,1,1,2,3]=>[[[]],[[],[[]]]]=>2
[6,3,1,1,3,2]=>[[[[[]]]],[[]]]=>2
[6,3,1,2,1,3]=>[[[[[[[]]]]]]]=>1
[6,3,1,2,3,1]=>[[[[],[[],[]]]]]=>1
[6,3,1,3,1,2]=>[[[[[],[[]]]]]]=>1
[6,3,1,3,2,1]=>[[[[[]],[[]]]]]=>1
[6,3,2,1,1,3]=>[[],[[[],[[]]]]]=>2
[6,3,2,1,3,1]=>[[[[[[],[]]]]]]=>1
[6,3,2,3,1,1]=>[[[[[]]]],[[]]]=>2
[6,3,3,1,1,2]=>[[],[[]],[[[]]]]=>3
[6,3,3,1,2,1]=>[[],[[[[[]]]]]]=>2
[6,3,3,2,1,1]=>[[],[],[[],[[]]]]=>3
[1,1,2,3,4,4]=>[[],[],[[],[],[]]]=>3
[1,1,2,4,3,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,4,4,3]=>[[],[[[]]],[[]]]=>3
[1,1,3,2,4,4]=>[[],[[]],[[],[]]]=>3
[1,1,3,4,2,4]=>[[],[[],[[[]]]]]=>2
[1,1,3,4,4,2]=>[[],[[[]]],[[]]]=>3
[1,1,4,2,3,4]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,2,4]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,4,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,4,2,3]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,3,2]=>[[],[[]],[[],[]]]=>3
[1,2,1,3,4,4]=>[[[]],[[],[[]]]]=>2
[1,2,1,4,3,4]=>[[[],[[],[[]]]]]=>1
[1,2,1,4,4,3]=>[[[]],[[],[[]]]]=>2
[1,2,3,1,4,4]=>[[],[[[[],[]]]]]=>2
[1,2,3,4,1,4]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,4,1]=>[[[]],[[],[],[]]]=>2
[1,2,4,1,3,4]=>[[[],[[],[[]]]]]=>1
[1,2,4,1,4,3]=>[[[[[[[]]]]]]]=>1
[1,2,4,3,1,4]=>[[[[[[[]]]]]]]=>1
[1,2,4,3,4,1]=>[[[],[[[[]]]]]]=>1
[1,2,4,4,1,3]=>[[],[[[],[[]]]]]=>2
[1,2,4,4,3,1]=>[[[[]]],[[[]]]]=>2
[1,3,1,2,4,4]=>[[],[[],[[[]]]]]=>2
[1,3,1,4,2,4]=>[[[],[[],[[]]]]]=>1
[1,3,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[1,3,2,1,4,4]=>[[[]],[[],[[]]]]=>2
[1,3,2,4,1,4]=>[[[],[[[[]]]]]]=>1
[1,3,2,4,4,1]=>[[[[]]],[[],[]]]=>2
[1,3,4,1,2,4]=>[[[],[[],[[]]]]]=>1
[1,3,4,1,4,2]=>[[[[[[[]]]]]]]=>1
[1,3,4,2,1,4]=>[[[[[[[]]]]]]]=>1
[1,3,4,2,4,1]=>[[[[]],[[[]]]]]=>1
[1,3,4,4,1,2]=>[[],[[[],[[]]]]]=>2
[1,3,4,4,2,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[1,4,1,2,4,3]=>[[[[[[[]]]]]]]=>1
[1,4,1,3,2,4]=>[[[[],[[[]]]]]]=>1
[1,4,1,3,4,2]=>[[[[[[[]]]]]]]=>1
[1,4,1,4,2,3]=>[[[[]],[[[]]]]]=>1
[1,4,1,4,3,2]=>[[[],[[],[[]]]]]=>1
[1,4,2,1,3,4]=>[[[[[[[]]]]]]]=>1
[1,4,2,1,4,3]=>[[[],[[],[[]]]]]=>1
[1,4,2,3,1,4]=>[[[],[[],[[]]]]]=>1
[1,4,2,3,4,1]=>[[[[[]],[[]]]]]=>1
[1,4,2,4,1,3]=>[[[[],[[[]]]]]]=>1
[1,4,2,4,3,1]=>[[[[[[],[]]]]]]=>1
[1,4,3,1,2,4]=>[[[[[[[]]]]]]]=>1
[1,4,3,1,4,2]=>[[[],[[],[[]]]]]=>1
[1,4,3,2,1,4]=>[[[],[[],[],[]]]]=>1
[1,4,3,2,4,1]=>[[[[],[[[]]]]]]=>1
[1,4,3,4,1,2]=>[[[[[]],[[]]]]]=>1
[1,4,3,4,2,1]=>[[[[[[],[]]]]]]=>1
[1,4,4,1,2,3]=>[[[]],[[[],[]]]]=>2
[1,4,4,1,3,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,2,1,3]=>[[[]],[[[[]]]]]=>2
[1,4,4,2,3,1]=>[[[]],[[],[[]]]]=>2
[1,4,4,3,1,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,3,2,1]=>[[],[[],[],[[]]]]=>2
[2,1,1,3,4,4]=>[[],[[[]]],[[]]]=>3
[2,1,1,4,3,4]=>[[],[[[],[[]]]]]=>2
[2,1,1,4,4,3]=>[[],[[]],[[],[]]]=>3
[2,1,3,1,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,3,4,1,4]=>[[[[[[[]]]]]]]=>1
[2,1,3,4,4,1]=>[[[[]]],[[[]]]]=>2
[2,1,4,1,3,4]=>[[[[[[[]]]]]]]=>1
[2,1,4,1,4,3]=>[[[],[[],[[]]]]]=>1
[2,1,4,3,1,4]=>[[[],[[],[[]]]]]=>1
[2,1,4,3,4,1]=>[[[[]],[[[]]]]]=>1
[2,1,4,4,1,3]=>[[[]],[[[[]]]]]=>2
[2,1,4,4,3,1]=>[[[]],[[],[[]]]]=>2
[2,3,1,1,4,4]=>[[],[],[[[[]]]]]=>3
[2,3,1,4,1,4]=>[[[[[[],[]]]]]]=>1
[2,3,1,4,4,1]=>[[[[[]]]],[[]]]=>2
[2,3,4,1,1,4]=>[[[]],[[[],[]]]]=>2
[2,3,4,1,4,1]=>[[[],[[],[[]]]]]=>1
[2,3,4,4,1,1]=>[[],[[]],[[],[]]]=>3
[2,4,1,1,3,4]=>[[[]],[[],[[]]]]=>2
[2,4,1,1,4,3]=>[[[[]]],[[[]]]]=>2
[2,4,1,3,1,4]=>[[[[]],[[[]]]]]=>1
[2,4,1,3,4,1]=>[[[],[[[],[]]]]]=>1
[2,4,1,4,1,3]=>[[[],[[],[[]]]]]=>1
[2,4,1,4,3,1]=>[[[[[[[]]]]]]]=>1
[2,4,3,1,1,4]=>[[[[[]]]],[[]]]=>2
[2,4,3,1,4,1]=>[[[[[[[]]]]]]]=>1
[2,4,3,4,1,1]=>[[[[]]],[[[]]]]=>2
[2,4,4,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,4,4,1,3,1]=>[[],[[[],[[]]]]]=>2
[2,4,4,3,1,1]=>[[[]],[[]],[[]]]=>3
[3,1,1,2,4,4]=>[[],[],[[[[]]]]]=>3
[3,1,1,4,2,4]=>[[],[[[],[[]]]]]=>2
[3,1,1,4,4,2]=>[[],[[]],[[],[]]]=>3
[3,1,2,1,4,4]=>[[[[]]],[[[]]]]=>2
[3,1,2,4,1,4]=>[[[[[[[]]]]]]]=>1
[3,1,2,4,4,1]=>[[[[[]]]],[[]]]=>2
[3,1,4,1,2,4]=>[[[[[[[]]]]]]]=>1
[3,1,4,1,4,2]=>[[[],[[],[[]]]]]=>1
[3,1,4,2,1,4]=>[[[],[[],[[]]]]]=>1
[3,1,4,2,4,1]=>[[[[[]]],[[]]]]=>1
[3,1,4,4,1,2]=>[[[[]]],[[[]]]]=>2
[3,1,4,4,2,1]=>[[[]],[[],[[]]]]=>2
[3,2,1,1,4,4]=>[[],[[]],[[],[]]]=>3
[3,2,1,4,1,4]=>[[[],[[],[[]]]]]=>1
[3,2,1,4,4,1]=>[[[]],[[[],[]]]]=>2
[3,2,4,1,1,4]=>[[[[]]],[[[]]]]=>2
[3,2,4,1,4,1]=>[[[[[]],[[]]]]]=>1
[3,2,4,4,1,1]=>[[[]],[[]],[[]]]=>3
[3,4,1,1,2,4]=>[[[]],[[],[[]]]]=>2
[3,4,1,1,4,2]=>[[[[]]],[[[]]]]=>2
[3,4,1,2,1,4]=>[[[[]],[[[]]]]]=>1
[3,4,1,2,4,1]=>[[[],[[[],[]]]]]=>1
[3,4,1,4,1,2]=>[[[],[[],[[]]]]]=>1
[3,4,1,4,2,1]=>[[[[[[[]]]]]]]=>1
[3,4,2,1,1,4]=>[[[[]]],[[[]]]]=>2
[3,4,2,1,4,1]=>[[[[[[[]]]]]]]=>1
[3,4,2,4,1,1]=>[[],[[[[[]]]]]]=>2
[3,4,4,1,1,2]=>[[],[[]],[[],[]]]=>3
[3,4,4,1,2,1]=>[[],[[[],[[]]]]]=>2
[3,4,4,2,1,1]=>[[[]],[[]],[[]]]=>3
[4,1,1,2,3,4]=>[[],[[],[],[[]]]]=>2
[4,1,1,2,4,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,3,2,4]=>[[],[[],[[[]]]]]=>2
[4,1,1,3,4,2]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,2,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,3,2]=>[[],[[[],[[]]]]]=>2
[4,1,2,1,3,4]=>[[[[[],[[]]]]]]=>1
[4,1,2,1,4,3]=>[[[[[],[[]]]]]]=>1
[4,1,2,3,1,4]=>[[[[],[[[]]]]]]=>1
[4,1,2,3,4,1]=>[[[],[[],[],[]]]]=>1
[4,1,2,4,1,3]=>[[[],[[],[[]]]]]=>1
[4,1,2,4,3,1]=>[[[[[[[]]]]]]]=>1
[4,1,3,1,2,4]=>[[[[[[],[]]]]]]=>1
[4,1,3,1,4,2]=>[[[[[],[[]]]]]]=>1
[4,1,3,2,1,4]=>[[[[[]],[[]]]]]=>1
[4,1,3,2,4,1]=>[[[[]],[[],[]]]]=>1
[4,1,3,4,1,2]=>[[[],[[],[[]]]]]=>1
[4,1,3,4,2,1]=>[[[[[[[]]]]]]]=>1
[4,1,4,1,2,3]=>[[[[]],[[],[]]]]=>1
[4,1,4,1,3,2]=>[[[[[]]],[[]]]]=>1
[4,1,4,2,1,3]=>[[[[[[[]]]]]]]=>1
[4,1,4,2,3,1]=>[[[[[],[[]]]]]]=>1
[4,1,4,3,1,2]=>[[[[[[[]]]]]]]=>1
[4,1,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[4,2,1,1,3,4]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,4,3]=>[[],[[[],[[]]]]]=>2
[4,2,1,3,1,4]=>[[[[]],[[[]]]]]=>1
[4,2,1,3,4,1]=>[[[[[[[]]]]]]]=>1
[4,2,1,4,1,3]=>[[[[[[[]]]]]]]=>1
[4,2,1,4,3,1]=>[[[],[[],[[]]]]]=>1
[4,2,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,4,1]=>[[[[]],[[[]]]]]=>1
[4,2,3,4,1,1]=>[[],[[[],[[]]]]]=>2
[4,2,4,1,1,3]=>[[[[]]],[[],[]]]=>2
[4,2,4,1,3,1]=>[[[],[[],[[]]]]]=>1
[4,2,4,3,1,1]=>[[[[]]],[[],[]]]=>2
[4,3,1,1,2,4]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,4,2]=>[[],[[[],[[]]]]]=>2
[4,3,1,2,1,4]=>[[[[]],[[[]]]]]=>1
[4,3,1,2,4,1]=>[[[[[[[]]]]]]]=>1
[4,3,1,4,1,2]=>[[[[[[[]]]]]]]=>1
[4,3,1,4,2,1]=>[[[],[[],[[]]]]]=>1
[4,3,2,1,1,4]=>[[],[[[],[],[]]]]=>2
[4,3,2,1,4,1]=>[[[],[],[[[]]]]]=>1
[4,3,2,4,1,1]=>[[[[]]],[[],[]]]=>2
[4,3,4,1,1,2]=>[[[]],[[],[[]]]]=>2
[4,3,4,1,2,1]=>[[[],[[],[[]]]]]=>1
[4,3,4,2,1,1]=>[[[[]]],[[],[]]]=>2
[4,4,1,1,2,3]=>[[],[[]],[[],[]]]=>3
[4,4,1,1,3,2]=>[[],[[[]]],[[]]]=>3
[4,4,1,2,1,3]=>[[],[[[[[]]]]]]=>2
[4,4,1,2,3,1]=>[[],[[[],[[]]]]]=>2
[4,4,1,3,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,1,3,2,1]=>[[],[[[],[[]]]]]=>2
[4,4,2,1,1,3]=>[[],[[[]]],[[]]]=>3
[4,4,2,1,3,1]=>[[],[[[]],[[]]]]=>2
[4,4,2,3,1,1]=>[[],[],[[],[[]]]]=>3
[4,4,3,1,1,2]=>[[],[[[]]],[[]]]=>3
[4,4,3,1,2,1]=>[[],[[[]],[[]]]]=>2
[4,4,3,2,1,1]=>[[],[],[[],[],[]]]=>3
[1,1,2,3,4,5]=>[[],[[],[],[],[]]]=>2
[1,1,2,3,5,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,4,3,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,4,5,3]=>[[],[[[]],[[]]]]=>2
[1,1,2,5,3,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,4,3]=>[[],[[[[],[]]]]]=>2
[1,1,3,2,4,5]=>[[],[[],[[[]]]]]=>2
[1,1,3,2,5,4]=>[[],[[[],[[]]]]]=>2
[1,1,3,4,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,5,2]=>[[],[[[],[[]]]]]=>2
[1,1,3,5,2,4]=>[[],[[],[],[[]]]]=>2
[1,1,3,5,4,2]=>[[],[[],[[[]]]]]=>2
[1,1,4,2,3,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,5,3]=>[[],[[],[[],[]]]]=>2
[1,1,4,3,2,5]=>[[],[[],[[],[]]]]=>2
[1,1,4,3,5,2]=>[[],[[[[[]]]]]]=>2
[1,1,4,5,2,3]=>[[],[[[],[[]]]]]=>2
[1,1,4,5,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,5,2,3,4]=>[[],[[],[[],[]]]]=>2
[1,1,5,2,4,3]=>[[],[[],[[[]]]]]=>2
[1,1,5,3,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,4,2]=>[[],[[[[],[]]]]]=>2
[1,1,5,4,2,3]=>[[],[[[[[]]]]]]=>2
[1,1,5,4,3,2]=>[[],[[[],[],[]]]]=>2
[1,2,1,3,4,5]=>[[[],[[]],[[]]]]=>1
[1,2,1,3,5,4]=>[[[[],[[],[]]]]]=>1
[1,2,1,4,3,5]=>[[[[[]],[[]]]]]=>1
[1,2,1,4,5,3]=>[[[[]],[[[]]]]]=>1
[1,2,1,5,3,4]=>[[[[[]]],[[]]]]=>1
[1,2,1,5,4,3]=>[[[[],[],[[]]]]]=>1
[1,2,3,1,4,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,1,5,4]=>[[[],[[[[]]]]]]=>1
[1,2,3,4,1,5]=>[[[],[],[[],[]]]]=>1
[1,2,3,4,5,1]=>[[[],[],[],[[]]]]=>1
[1,2,3,5,1,4]=>[[[],[[[],[]]]]]=>1
[1,2,3,5,4,1]=>[[[],[[[[]]]]]]=>1
[1,2,4,1,3,5]=>[[[[],[],[[]]]]]=>1
[1,2,4,1,5,3]=>[[[[[],[[]]]]]]=>1
[1,2,4,3,1,5]=>[[[[[[[]]]]]]]=>1
[1,2,4,3,5,1]=>[[[[],[[[]]]]]]=>1
[1,2,4,5,1,3]=>[[[],[[[],[]]]]]=>1
[1,2,4,5,3,1]=>[[[[]],[[],[]]]]=>1
[1,2,5,1,3,4]=>[[[],[[[],[]]]]]=>1
[1,2,5,1,4,3]=>[[[[],[],[[]]]]]=>1
[1,2,5,3,1,4]=>[[[[],[[],[]]]]]=>1
[1,2,5,3,4,1]=>[[[[]],[[[]]]]]=>1
[1,2,5,4,1,3]=>[[[[[[[]]]]]]]=>1
[1,2,5,4,3,1]=>[[[[[],[[]]]]]]=>1
[1,3,1,2,4,5]=>[[[[]],[[],[]]]]=>1
[1,3,1,2,5,4]=>[[[[[[[]]]]]]]=>1
[1,3,1,4,2,5]=>[[[[],[[],[]]]]]=>1
[1,3,1,4,5,2]=>[[[[[[[]]]]]]]=>1
[1,3,1,5,2,4]=>[[[],[[],[[]]]]]=>1
[1,3,1,5,4,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,1,4,5]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,5,4]=>[[[[],[],[[]]]]]=>1
[1,3,2,4,1,5]=>[[[],[[],[[]]]]]=>1
[1,3,2,4,5,1]=>[[[],[[[[]]]]]]=>1
[1,3,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[1,3,2,5,4,1]=>[[[[[],[[]]]]]]=>1
[1,3,4,1,2,5]=>[[[[[]],[[]]]]]=>1
[1,3,4,1,5,2]=>[[[[[],[],[]]]]]=>1
[1,3,4,2,1,5]=>[[[[[[[]]]]]]]=>1
[1,3,4,2,5,1]=>[[[[[[],[]]]]]]=>1
[1,3,4,5,1,2]=>[[[[],[],[[]]]]]=>1
[1,3,4,5,2,1]=>[[[[],[[[]]]]]]=>1
[1,3,5,1,2,4]=>[[[],[],[[[]]]]]=>1
[1,3,5,1,4,2]=>[[[],[[],[[]]]]]=>1
[1,3,5,2,1,4]=>[[[],[[[[]]]]]]=>1
[1,3,5,2,4,1]=>[[[],[],[[],[]]]]=>1
[1,3,5,4,1,2]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,2,1]=>[[[],[[],[[]]]]]=>1
[1,4,1,2,3,5]=>[[[[[],[[]]]]]]=>1
[1,4,1,2,5,3]=>[[[[[]]],[[]]]]=>1
[1,4,1,3,2,5]=>[[[],[[[[]]]]]]=>1
[1,4,1,3,5,2]=>[[[[],[[],[]]]]]=>1
[1,4,1,5,2,3]=>[[[[],[],[[]]]]]=>1
[1,4,1,5,3,2]=>[[[[[[],[]]]]]]=>1
[1,4,2,1,3,5]=>[[[[[],[[]]]]]]=>1
[1,4,2,1,5,3]=>[[[[[],[[]]]]]]=>1
[1,4,2,3,1,5]=>[[[[[],[[]]]]]]=>1
[1,4,2,3,5,1]=>[[[],[[[[]]]]]]=>1
[1,4,2,5,1,3]=>[[[],[[]],[[]]]]=>1
[1,4,2,5,3,1]=>[[[],[[],[],[]]]]=>1
[1,4,3,1,2,5]=>[[[[[]]],[[]]]]=>1
[1,4,3,1,5,2]=>[[[[[]],[[]]]]]=>1
[1,4,3,2,1,5]=>[[[[],[],[[]]]]]=>1
[1,4,3,2,5,1]=>[[[],[],[[],[]]]]=>1
[1,4,3,5,1,2]=>[[[[[]]],[[]]]]=>1
[1,4,3,5,2,1]=>[[[[[[],[]]]]]]=>1
[1,4,5,1,2,3]=>[[[],[[],[],[]]]]=>1
[1,4,5,1,3,2]=>[[[[]],[[[]]]]]=>1
[1,4,5,2,1,3]=>[[[[[[[]]]]]]]=>1
[1,4,5,2,3,1]=>[[[[[],[[]]]]]]=>1
[1,4,5,3,1,2]=>[[[[],[[],[]]]]]=>1
[1,4,5,3,2,1]=>[[[[],[[[]]]]]]=>1
[1,5,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[1,5,1,2,4,3]=>[[[[[[[]]]]]]]=>1
[1,5,1,3,2,4]=>[[[[[],[[]]]]]]=>1
[1,5,1,3,4,2]=>[[[[[[[]]]]]]]=>1
[1,5,1,4,2,3]=>[[[[],[[[]]]]]]=>1
[1,5,1,4,3,2]=>[[[[],[[],[]]]]]=>1
[1,5,2,1,3,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,4,3]=>[[[],[[[],[]]]]]=>1
[1,5,2,3,1,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,3,4,1]=>[[[],[],[[],[]]]]=>1
[1,5,2,4,1,3]=>[[[],[],[[],[]]]]=>1
[1,5,2,4,3,1]=>[[[],[[[[]]]]]]=>1
[1,5,3,1,2,4]=>[[[[],[[[]]]]]]=>1
[1,5,3,1,4,2]=>[[[[[],[],[]]]]]=>1
[1,5,3,2,1,4]=>[[[[],[[[]]]]]]=>1
[1,5,3,2,4,1]=>[[[[[]]],[[]]]]=>1
[1,5,3,4,1,2]=>[[[[]],[[],[]]]]=>1
[1,5,3,4,2,1]=>[[[[[],[[]]]]]]=>1
[1,5,4,1,2,3]=>[[[],[[],[[]]]]]=>1
[1,5,4,1,3,2]=>[[[],[[[],[]]]]]=>1
[1,5,4,2,1,3]=>[[[[],[[[]]]]]]=>1
[1,5,4,2,3,1]=>[[[[[],[[]]]]]]=>1
[1,5,4,3,1,2]=>[[[[[[],[]]]]]]=>1
[1,5,4,3,2,1]=>[[[[],[],[],[]]]]=>1
[2,1,1,3,4,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,5,4]=>[[],[[],[[],[]]]]=>2
[2,1,1,4,3,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,4,5,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,3,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,4,3]=>[[],[[[],[],[]]]]=>2
[2,1,3,1,4,5]=>[[[[[[[]]]]]]]=>1
[2,1,3,1,5,4]=>[[[[]],[[[]]]]]=>1
[2,1,3,4,1,5]=>[[[[],[[[]]]]]]=>1
[2,1,3,4,5,1]=>[[[[[],[[]]]]]]=>1
[2,1,3,5,1,4]=>[[[[],[[],[]]]]]=>1
[2,1,3,5,4,1]=>[[[[]],[[],[]]]]=>1
[2,1,4,1,3,5]=>[[[[],[[[]]]]]]=>1
[2,1,4,1,5,3]=>[[[[[],[[]]]]]]=>1
[2,1,4,3,1,5]=>[[[],[[[[]]]]]]=>1
[2,1,4,3,5,1]=>[[[],[[],[[]]]]]=>1
[2,1,4,5,1,3]=>[[[[[],[[]]]]]]=>1
[2,1,4,5,3,1]=>[[[[],[[[]]]]]]=>1
[2,1,5,1,3,4]=>[[[[[[[]]]]]]]=>1
[2,1,5,1,4,3]=>[[[],[[],[[]]]]]=>1
[2,1,5,3,1,4]=>[[[[[],[[]]]]]]=>1
[2,1,5,3,4,1]=>[[[[],[[[]]]]]]=>1
[2,1,5,4,1,3]=>[[[],[[[],[]]]]]=>1
[2,1,5,4,3,1]=>[[[],[],[[[]]]]]=>1
[2,3,1,1,4,5]=>[[[[],[]]],[[]]]=>2
[2,3,1,1,5,4]=>[[],[[[[[]]]]]]=>2
[2,3,1,4,1,5]=>[[[[[],[[]]]]]]=>1
[2,3,1,4,5,1]=>[[[[]],[[],[]]]]=>1
[2,3,1,5,1,4]=>[[[[[],[[]]]]]]=>1
[2,3,1,5,4,1]=>[[[[[],[[]]]]]]=>1
[2,3,4,1,1,5]=>[[],[[],[[],[]]]]=>2
[2,3,4,1,5,1]=>[[[],[[],[[]]]]]=>1
[2,3,4,5,1,1]=>[[],[[[],[],[]]]]=>2
[2,3,5,1,1,4]=>[[],[[],[[[]]]]]=>2
[2,3,5,1,4,1]=>[[[[[],[[]]]]]]=>1
[2,3,5,4,1,1]=>[[[]],[[[[]]]]]=>2
[2,4,1,1,3,5]=>[[[]],[[],[],[]]]=>2
[2,4,1,1,5,3]=>[[],[[[]],[[]]]]=>2
[2,4,1,3,1,5]=>[[[],[[[],[]]]]]=>1
[2,4,1,3,5,1]=>[[[],[[]],[[]]]]=>1
[2,4,1,5,1,3]=>[[[],[[[],[]]]]]=>1
[2,4,1,5,3,1]=>[[[[],[[],[]]]]]=>1
[2,4,3,1,1,5]=>[[[[[]]]],[[]]]=>2
[2,4,3,1,5,1]=>[[[[[[[]]]]]]]=>1
[2,4,3,5,1,1]=>[[[[],[]]],[[]]]=>2
[2,4,5,1,1,3]=>[[[[]]],[[],[]]]=>2
[2,4,5,1,3,1]=>[[[[[]]],[[]]]]=>1
[2,4,5,3,1,1]=>[[],[[],[[[]]]]]=>2
[2,5,1,1,3,4]=>[[[[]]],[[],[]]]=>2
[2,5,1,1,4,3]=>[[],[[],[],[[]]]]=>2
[2,5,1,3,1,4]=>[[[],[],[[[]]]]]=>1
[2,5,1,3,4,1]=>[[[],[[[[]]]]]]=>1
[2,5,1,4,1,3]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,3,1]=>[[[],[],[[[]]]]]=>1
[2,5,3,1,1,4]=>[[[],[]],[[],[]]]=>2
[2,5,3,1,4,1]=>[[[[]],[[],[]]]]=>1
[2,5,3,4,1,1]=>[[],[[[[[]]]]]]=>2
[2,5,4,1,1,3]=>[[[[[]]]],[[]]]=>2
[2,5,4,1,3,1]=>[[[[[[[]]]]]]]=>1
[2,5,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[3,1,1,2,4,5]=>[[],[[],[[[]]]]]=>2
[3,1,1,2,5,4]=>[[],[[[[[]]]]]]=>2
[3,1,1,4,2,5]=>[[],[[],[[],[]]]]=>2
[3,1,1,4,5,2]=>[[[[[]]]],[[]]]=>2
[3,1,1,5,2,4]=>[[],[[[]],[[]]]]=>2
[3,1,1,5,4,2]=>[[],[[[],[[]]]]]=>2
[3,1,2,1,4,5]=>[[[[[],[[]]]]]]=>1
[3,1,2,1,5,4]=>[[[[[]],[[]]]]]=>1
[3,1,2,4,1,5]=>[[[[],[[[]]]]]]=>1
[3,1,2,4,5,1]=>[[[[[],[[]]]]]]=>1
[3,1,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[3,1,2,5,4,1]=>[[[[[[[]]]]]]]=>1
[3,1,4,1,2,5]=>[[[[[[],[]]]]]]=>1
[3,1,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[3,1,4,2,1,5]=>[[[],[[[[]]]]]]=>1
[3,1,4,2,5,1]=>[[[],[[],[],[]]]]=>1
[3,1,4,5,1,2]=>[[[[],[[],[]]]]]=>1
[3,1,4,5,2,1]=>[[[[[[[]]]]]]]=>1
[3,1,5,1,2,4]=>[[[[[[[]]]]]]]=>1
[3,1,5,1,4,2]=>[[[],[[],[[]]]]]=>1
[3,1,5,2,1,4]=>[[[[[[],[]]]]]]=>1
[3,1,5,2,4,1]=>[[[[[],[],[]]]]]=>1
[3,1,5,4,1,2]=>[[[[],[[[]]]]]]=>1
[3,1,5,4,2,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,1,4,5]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,5,4]=>[[],[[[],[],[]]]]=>2
[3,2,1,4,1,5]=>[[[],[[],[[]]]]]=>1
[3,2,1,4,5,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,5,1,4]=>[[[],[[],[[]]]]]=>1
[3,2,1,5,4,1]=>[[[],[],[[],[]]]]=>1
[3,2,4,1,1,5]=>[[],[[[]],[[]]]]=>2
[3,2,4,1,5,1]=>[[[[[],[[]]]]]]=>1
[3,2,4,5,1,1]=>[[[[[]]]],[[]]]=>2
[3,2,5,1,1,4]=>[[],[[],[],[[]]]]=>2
[3,2,5,1,4,1]=>[[[[[],[],[]]]]]=>1
[3,2,5,4,1,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,1,2,5]=>[[[]],[[],[[]]]]=>2
[3,4,1,1,5,2]=>[[],[[],[],[[]]]]=>2
[3,4,1,2,1,5]=>[[[],[[[],[]]]]]=>1
[3,4,1,2,5,1]=>[[[[]],[[],[]]]]=>1
[3,4,1,5,1,2]=>[[[],[[[],[]]]]]=>1
[3,4,1,5,2,1]=>[[[[],[],[[]]]]]=>1
[3,4,2,1,1,5]=>[[[[]]],[[[]]]]=>2
[3,4,2,1,5,1]=>[[[[[[[]]]]]]]=>1
[3,4,2,5,1,1]=>[[],[[],[[[]]]]]=>2
[3,4,5,1,1,2]=>[[[]],[[],[],[]]]=>2
[3,4,5,1,2,1]=>[[[],[[]],[[]]]]=>1
[3,4,5,2,1,1]=>[[],[[[[],[]]]]]=>2
[3,5,1,1,2,4]=>[[[[],[]]],[[]]]=>2
[3,5,1,1,4,2]=>[[],[[[]],[[]]]]=>2
[3,5,1,2,1,4]=>[[[[],[[[]]]]]]=>1
[3,5,1,2,4,1]=>[[[[[]]],[[]]]]=>1
[3,5,1,4,1,2]=>[[[[],[[[]]]]]]=>1
[3,5,1,4,2,1]=>[[[[],[[[]]]]]]=>1
[3,5,2,1,1,4]=>[[],[[[[[]]]]]]=>2
[3,5,2,1,4,1]=>[[[[[],[[]]]]]]=>1
[3,5,2,4,1,1]=>[[],[[],[[],[]]]]=>2
[3,5,4,1,1,2]=>[[[[[]]]],[[]]]=>2
[3,5,4,1,2,1]=>[[[[],[[[]]]]]]=>1
[3,5,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,2,3,5]=>[[[]],[[],[[]]]]=>2
[4,1,1,2,5,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,3,2,5]=>[[[[[]]]],[[]]]=>2
[4,1,1,3,5,2]=>[[],[[],[[],[]]]]=>2
[4,1,1,5,2,3]=>[[],[[],[],[[]]]]=>2
[4,1,1,5,3,2]=>[[],[[],[[[]]]]]=>2
[4,1,2,1,3,5]=>[[[[],[[[]]]]]]=>1
[4,1,2,1,5,3]=>[[[],[[[[]]]]]]=>1
[4,1,2,3,1,5]=>[[[],[[[],[]]]]]=>1
[4,1,2,3,5,1]=>[[[[],[[[]]]]]]=>1
[4,1,2,5,1,3]=>[[[[[],[[]]]]]]=>1
[4,1,2,5,3,1]=>[[[[],[[[]]]]]]=>1
[4,1,3,1,2,5]=>[[[[[[[]]]]]]]=>1
[4,1,3,1,5,2]=>[[[],[],[[[]]]]]=>1
[4,1,3,2,1,5]=>[[[],[[],[[]]]]]=>1
[4,1,3,2,5,1]=>[[[[],[[[]]]]]]=>1
[4,1,3,5,1,2]=>[[[[],[[[]]]]]]=>1
[4,1,3,5,2,1]=>[[[[]],[[],[]]]]=>1
[4,1,5,1,2,3]=>[[[],[[[],[]]]]]=>1
[4,1,5,1,3,2]=>[[[],[[[[]]]]]]=>1
[4,1,5,2,1,3]=>[[[],[],[[[]]]]]=>1
[4,1,5,2,3,1]=>[[[],[],[[[]]]]]=>1
[4,1,5,3,1,2]=>[[[],[[],[[]]]]]=>1
[4,1,5,3,2,1]=>[[[],[[],[[]]]]]=>1
[4,2,1,1,3,5]=>[[],[[[]],[[]]]]=>2
[4,2,1,1,5,3]=>[[],[[[],[[]]]]]=>2
[4,2,1,3,1,5]=>[[[[]],[[[]]]]]=>1
[4,2,1,3,5,1]=>[[[[],[[[]]]]]]=>1
[4,2,1,5,1,3]=>[[[[[[[]]]]]]]=>1
[4,2,1,5,3,1]=>[[[],[[]],[[]]]]=>1
[4,2,3,1,1,5]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,5,1]=>[[[[]],[[[]]]]]=>1
[4,2,3,5,1,1]=>[[],[[[[[]]]]]]=>2
[4,2,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,2,5,1,3,1]=>[[[],[[[],[]]]]]=>1
[4,2,5,3,1,1]=>[[],[[],[],[[]]]]=>2
[4,3,1,1,2,5]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,5,2]=>[[],[[[]],[[]]]]=>2
[4,3,1,2,1,5]=>[[[[]],[[[]]]]]=>1
[4,3,1,2,5,1]=>[[[[[]],[[]]]]]=>1
[4,3,1,5,1,2]=>[[[[[[[]]]]]]]=>1
[4,3,1,5,2,1]=>[[[[]],[[],[]]]]=>1
[4,3,2,1,1,5]=>[[],[[[],[],[]]]]=>2
[4,3,2,1,5,1]=>[[[],[],[[[]]]]]=>1
[4,3,2,5,1,1]=>[[[],[]],[[],[]]]=>2
[4,3,5,1,1,2]=>[[[[]]],[[[]]]]=>2
[4,3,5,1,2,1]=>[[[],[[[[]]]]]]=>1
[4,3,5,2,1,1]=>[[],[[],[[[]]]]]=>2
[4,5,1,1,2,3]=>[[[]],[[],[],[]]]=>2
[4,5,1,1,3,2]=>[[[[]]],[[[]]]]=>2
[4,5,1,2,1,3]=>[[[[]],[[[]]]]]=>1
[4,5,1,2,3,1]=>[[[],[[]],[[]]]]=>1
[4,5,1,3,1,2]=>[[[],[[[[]]]]]]=>1
[4,5,1,3,2,1]=>[[[[[[],[]]]]]]=>1
[4,5,2,1,1,3]=>[[],[[[[[]]]]]]=>2
[4,5,2,1,3,1]=>[[[[[[[]]]]]]]=>1
[4,5,2,3,1,1]=>[[],[[[],[[]]]]]=>2
[4,5,3,1,1,2]=>[[[],[]],[[],[]]]=>2
[4,5,3,1,2,1]=>[[[],[[[],[]]]]]=>1
[4,5,3,2,1,1]=>[[[[]]],[[],[]]]=>2
[5,1,1,2,3,4]=>[[[]],[[],[],[]]]=>2
[5,1,1,2,4,3]=>[[[[[]]]],[[]]]=>2
[5,1,1,3,2,4]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,4,2]=>[[[[[]]]],[[]]]=>2
[5,1,1,4,2,3]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,3,2]=>[[],[[],[[],[]]]]=>2
[5,1,2,1,3,4]=>[[[[[]],[[]]]]]=>1
[5,1,2,1,4,3]=>[[[],[[],[[]]]]]=>1
[5,1,2,3,1,4]=>[[[],[[[],[]]]]]=>1
[5,1,2,3,4,1]=>[[[[],[],[[]]]]]=>1
[5,1,2,4,1,3]=>[[[[[],[[]]]]]]=>1
[5,1,2,4,3,1]=>[[[[[[[]]]]]]]=>1
[5,1,3,1,2,4]=>[[[[],[[[]]]]]]=>1
[5,1,3,1,4,2]=>[[[],[[],[[]]]]]=>1
[5,1,3,2,1,4]=>[[[],[[],[[]]]]]=>1
[5,1,3,2,4,1]=>[[[[[[],[]]]]]]=>1
[5,1,3,4,1,2]=>[[[[[],[[]]]]]]=>1
[5,1,3,4,2,1]=>[[[[[[[]]]]]]]=>1
[5,1,4,1,2,3]=>[[[],[[[],[]]]]]=>1
[5,1,4,1,3,2]=>[[[],[[[[]]]]]]=>1
[5,1,4,2,1,3]=>[[[],[[[[]]]]]]=>1
[5,1,4,2,3,1]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,1,2]=>[[[],[[[[]]]]]]=>1
[5,1,4,3,2,1]=>[[[],[[],[],[]]]]=>1
[5,2,1,1,3,4]=>[[],[[[[[]]]]]]=>2
[5,2,1,1,4,3]=>[[[[],[]]],[[]]]=>2
[5,2,1,3,1,4]=>[[[[[[[]]]]]]]=>1
[5,2,1,3,4,1]=>[[[[[]]],[[]]]]=>1
[5,2,1,4,1,3]=>[[[[[]]],[[]]]]=>1
[5,2,1,4,3,1]=>[[[[[],[[]]]]]]=>1
[5,2,3,1,1,4]=>[[[]],[[[[]]]]]=>2
[5,2,3,1,4,1]=>[[[],[[[[]]]]]]=>1
[5,2,3,4,1,1]=>[[],[[],[[],[]]]]=>2
[5,2,4,1,1,3]=>[[[],[]],[[],[]]]=>2
[5,2,4,1,3,1]=>[[[],[[],[[]]]]]=>1
[5,2,4,3,1,1]=>[[[[]]],[[[]]]]=>2
[5,3,1,1,2,4]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,4,2]=>[[],[[[],[],[]]]]=>2
[5,3,1,2,1,4]=>[[[],[[[[]]]]]]=>1
[5,3,1,2,4,1]=>[[[],[[[[]]]]]]=>1
[5,3,1,4,1,2]=>[[[],[[[[]]]]]]=>1
[5,3,1,4,2,1]=>[[[],[[]],[[]]]]=>1
[5,3,2,1,1,4]=>[[[[],[]]],[[]]]=>2
[5,3,2,1,4,1]=>[[[[[[],[]]]]]]=>1
[5,3,2,4,1,1]=>[[[[[]]]],[[]]]=>2
[5,3,4,1,1,2]=>[[[[]]],[[],[]]]=>2
[5,3,4,1,2,1]=>[[[[[],[[]]]]]]=>1
[5,3,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[5,4,1,1,2,3]=>[[[]],[[],[[]]]]=>2
[5,4,1,1,3,2]=>[[[[],[]]],[[]]]=>2
[5,4,1,2,1,3]=>[[[[[]]],[[]]]]=>1
[5,4,1,2,3,1]=>[[[[[],[[]]]]]]=>1
[5,4,1,3,1,2]=>[[[[[[[]]]]]]]=>1
[5,4,1,3,2,1]=>[[[],[[]],[[]]]]=>1
[5,4,2,1,1,3]=>[[[[],[]]],[[]]]=>2
[5,4,2,1,3,1]=>[[[],[[],[[]]]]]=>1
[5,4,2,3,1,1]=>[[[]],[[],[[]]]]=>2
[5,4,3,1,1,2]=>[[[[],[]]],[[]]]=>2
[5,4,3,1,2,1]=>[[[],[[]],[[]]]]=>1
[5,4,3,2,1,1]=>[[],[[],[],[],[]]]=>2
[1,1,2,3,4,6]=>[[],[[],[],[[]]]]=>2
[1,1,2,3,6,4]=>[[],[[],[[[]]]]]=>2
[1,1,2,4,3,6]=>[[],[[[[[]]]]]]=>2
[1,1,2,4,6,3]=>[[],[[[],[[]]]]]=>2
[1,1,2,6,3,4]=>[[],[[],[[],[]]]]=>2
[1,1,2,6,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,3,2,4,6]=>[[],[[],[],[[]]]]=>2
[1,1,3,2,6,4]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,2,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,6,2]=>[[],[[[]],[[]]]]=>2
[1,1,3,6,2,4]=>[[],[[],[[],[]]]]=>2
[1,1,3,6,4,2]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,3,6]=>[[],[[],[[[]]]]]=>2
[1,1,4,2,6,3]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,2,6]=>[[],[[[],[[]]]]]=>2
[1,1,4,3,6,2]=>[[],[[],[],[[]]]]=>2
[1,1,4,6,2,3]=>[[],[[[]],[[]]]]=>2
[1,1,4,6,3,2]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,3,4]=>[[],[[[],[[]]]]]=>2
[1,1,6,2,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,4,2]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,2,3]=>[[],[[],[],[[]]]]=>2
[1,1,6,4,3,2]=>[[],[[],[[],[]]]]=>2
[1,2,1,3,4,6]=>[[[],[[],[[]]]]]=>1
[1,2,1,3,6,4]=>[[[[[[[]]]]]]]=>1
[1,2,1,4,3,6]=>[[[[],[[],[]]]]]=>1
[1,2,1,4,6,3]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,3,4]=>[[[[[]]],[[]]]]=>1
[1,2,1,6,4,3]=>[[[[],[[],[]]]]]=>1
[1,2,3,1,4,6]=>[[[],[[[[]]]]]]=>1
[1,2,3,1,6,4]=>[[[],[[],[],[]]]]=>1
[1,2,3,4,1,6]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,6,1]=>[[[],[],[[],[]]]]=>1
[1,2,3,6,1,4]=>[[[],[[],[[]]]]]=>1
[1,2,3,6,4,1]=>[[[],[[[[]]]]]]=>1
[1,2,4,1,3,6]=>[[[[[]],[[]]]]]=>1
[1,2,4,1,6,3]=>[[[[[],[[]]]]]]=>1
[1,2,4,3,1,6]=>[[[[[[],[]]]]]]=>1
[1,2,4,3,6,1]=>[[[[[]],[[]]]]]=>1
[1,2,4,6,1,3]=>[[[[],[],[],[]]]]=>1
[1,2,4,6,3,1]=>[[[[],[[[]]]]]]=>1
[1,2,6,1,3,4]=>[[[],[[],[[]]]]]=>1
[1,2,6,1,4,3]=>[[[[[[[]]]]]]]=>1
[1,2,6,3,1,4]=>[[[[],[[[]]]]]]=>1
[1,2,6,3,4,1]=>[[[],[[],[],[]]]]=>1
[1,2,6,4,1,3]=>[[[[[]],[[]]]]]=>1
[1,2,6,4,3,1]=>[[[[[],[[]]]]]]=>1
[1,3,1,2,4,6]=>[[[],[[]],[[]]]]=>1
[1,3,1,2,6,4]=>[[[[],[[[]]]]]]=>1
[1,3,1,4,2,6]=>[[[[[],[[]]]]]]=>1
[1,3,1,4,6,2]=>[[[[]],[[],[]]]]=>1
[1,3,1,6,2,4]=>[[[],[[[],[]]]]]=>1
[1,3,1,6,4,2]=>[[[[],[],[],[]]]]=>1
[1,3,2,1,4,6]=>[[[[]],[[],[]]]]=>1
[1,3,2,1,6,4]=>[[[[],[[],[]]]]]=>1
[1,3,2,4,1,6]=>[[[],[[[[]]]]]]=>1
[1,3,2,4,6,1]=>[[[],[],[],[[]]]]=>1
[1,3,2,6,1,4]=>[[[[[]]],[[]]]]=>1
[1,3,2,6,4,1]=>[[[[[]],[[]]]]]=>1
[1,3,4,1,2,6]=>[[[[],[[],[]]]]]=>1
[1,3,4,1,6,2]=>[[[[[[[]]]]]]]=>1
[1,3,4,2,1,6]=>[[[[[],[[]]]]]]=>1
[1,3,4,2,6,1]=>[[[],[[[[]]]]]]=>1
[1,3,4,6,1,2]=>[[[],[],[[],[]]]]=>1
[1,3,4,6,2,1]=>[[[[]],[[[]]]]]=>1
[1,3,6,1,2,4]=>[[[],[[]],[[]]]]=>1
[1,3,6,1,4,2]=>[[[],[[],[[]]]]]=>1
[1,3,6,2,1,4]=>[[[[],[],[[]]]]]=>1
[1,3,6,2,4,1]=>[[[[]],[[],[]]]]=>1
[1,3,6,4,1,2]=>[[[[[[[]]]]]]]=>1
[1,3,6,4,2,1]=>[[[[[]],[[]]]]]=>1
[1,4,1,2,3,6]=>[[[],[[],[[]]]]]=>1
[1,4,1,2,6,3]=>[[[[[],[],[]]]]]=>1
[1,4,1,3,2,6]=>[[[[[[],[]]]]]]=>1
[1,4,1,3,6,2]=>[[[],[],[[[]]]]]=>1
[1,4,1,6,2,3]=>[[[[]],[[[]]]]]=>1
[1,4,1,6,3,2]=>[[[[],[[[]]]]]]=>1
[1,4,2,1,3,6]=>[[[[[]]],[[]]]]=>1
[1,4,2,1,6,3]=>[[[[],[[[]]]]]]=>1
[1,4,2,3,1,6]=>[[[[[],[],[]]]]]=>1
[1,4,2,3,6,1]=>[[[[[]]],[[]]]]=>1
[1,4,2,6,1,3]=>[[[[[],[[]]]]]]=>1
[1,4,2,6,3,1]=>[[[[],[[],[]]]]]=>1
[1,4,3,1,2,6]=>[[[[[[[]]]]]]]=>1
[1,4,3,1,6,2]=>[[[[]],[[],[]]]]=>1
[1,4,3,2,1,6]=>[[[[],[],[[]]]]]=>1
[1,4,3,2,6,1]=>[[[[],[[[]]]]]]=>1
[1,4,3,6,1,2]=>[[[],[[[[]]]]]]=>1
[1,4,3,6,2,1]=>[[[],[],[[],[]]]]=>1
[1,4,6,1,2,3]=>[[[[],[[],[]]]]]=>1
[1,4,6,1,3,2]=>[[[[],[],[[]]]]]=>1
[1,4,6,2,1,3]=>[[[],[[[],[]]]]]=>1
[1,4,6,2,3,1]=>[[[[[]]],[[]]]]=>1
[1,4,6,3,1,2]=>[[[[[[[]]]]]]]=>1
[1,4,6,3,2,1]=>[[[[],[[[]]]]]]=>1
[1,6,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[1,6,1,2,4,3]=>[[[[[],[[]]]]]]=>1
[1,6,1,3,2,4]=>[[[[],[],[[]]]]]=>1
[1,6,1,3,4,2]=>[[[],[[[],[]]]]]=>1
[1,6,1,4,2,3]=>[[[[]],[[[]]]]]=>1
[1,6,1,4,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,2,1,3,4]=>[[[[[[[]]]]]]]=>1
[1,6,2,1,4,3]=>[[[[],[[],[]]]]]=>1
[1,6,2,3,1,4]=>[[[[]],[[],[]]]]=>1
[1,6,2,3,4,1]=>[[[[[]],[[]]]]]=>1
[1,6,2,4,1,3]=>[[[[[],[[]]]]]]=>1
[1,6,2,4,3,1]=>[[[],[[[[]]]]]]=>1
[1,6,3,1,2,4]=>[[[[[]]],[[]]]]=>1
[1,6,3,1,4,2]=>[[[],[],[[[]]]]]=>1
[1,6,3,2,1,4]=>[[[[[],[[]]]]]]=>1
[1,6,3,2,4,1]=>[[[[[],[[]]]]]]=>1
[1,6,3,4,1,2]=>[[[[],[[],[]]]]]=>1
[1,6,3,4,2,1]=>[[[[]],[[[]]]]]=>1
[1,6,4,1,2,3]=>[[[],[[],[[]]]]]=>1
[1,6,4,1,3,2]=>[[[],[[[[]]]]]]=>1
[1,6,4,2,1,3]=>[[[],[],[[[]]]]]=>1
[1,6,4,2,3,1]=>[[[],[],[],[[]]]]=>1
[1,6,4,3,1,2]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,2,1]=>[[[],[[],[],[]]]]=>1
[2,1,1,3,4,6]=>[[],[[[]],[[]]]]=>2
[2,1,1,3,6,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,4,3,6]=>[[],[[],[[],[]]]]=>2
[2,1,1,4,6,3]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,3,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,4,3]=>[[],[[],[[],[]]]]=>2
[2,1,3,1,4,6]=>[[[[],[[[]]]]]]=>1
[2,1,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[2,1,3,4,1,6]=>[[[[[[[]]]]]]]=>1
[2,1,3,4,6,1]=>[[[[],[],[[]]]]]=>1
[2,1,3,6,1,4]=>[[[[],[[],[]]]]]=>1
[2,1,3,6,4,1]=>[[[[[[[]]]]]]]=>1
[2,1,4,1,3,6]=>[[[[],[[[]]]]]]=>1
[2,1,4,1,6,3]=>[[[[],[[[]]]]]]=>1
[2,1,4,3,1,6]=>[[[],[[],[[]]]]]=>1
[2,1,4,3,6,1]=>[[[],[[[],[]]]]]=>1
[2,1,4,6,1,3]=>[[[[],[],[[]]]]]=>1
[2,1,4,6,3,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,1,3,4]=>[[[[[],[[]]]]]]=>1
[2,1,6,1,4,3]=>[[[[[]]],[[]]]]=>1
[2,1,6,3,1,4]=>[[[[[],[[]]]]]]=>1
[2,1,6,3,4,1]=>[[[[],[[[]]]]]]=>1
[2,1,6,4,1,3]=>[[[[[[],[]]]]]]=>1
[2,1,6,4,3,1]=>[[[],[[],[],[]]]]=>1
[2,3,1,1,4,6]=>[[[[]]],[[[]]]]=>2
[2,3,1,1,6,4]=>[[],[[],[],[[]]]]=>2
[2,3,1,4,1,6]=>[[[[],[[[]]]]]]=>1
[2,3,1,4,6,1]=>[[[[[],[[]]]]]]=>1
[2,3,1,6,1,4]=>[[[[],[[[]]]]]]=>1
[2,3,1,6,4,1]=>[[[[],[],[[]]]]]=>1
[2,3,4,1,1,6]=>[[[[],[]]],[[]]]=>2
[2,3,4,1,6,1]=>[[[],[[[[]]]]]]=>1
[2,3,4,6,1,1]=>[[],[[],[[],[]]]]=>2
[2,3,6,1,1,4]=>[[[]],[[],[[]]]]=>2
[2,3,6,1,4,1]=>[[[[[]],[[]]]]]=>1
[2,3,6,4,1,1]=>[[],[[[[[]]]]]]=>2
[2,4,1,1,3,6]=>[[[]],[[],[[]]]]=>2
[2,4,1,1,6,3]=>[[],[[[],[[]]]]]=>2
[2,4,1,3,1,6]=>[[[],[[],[[]]]]]=>1
[2,4,1,3,6,1]=>[[[],[[]],[[]]]]=>1
[2,4,1,6,1,3]=>[[[],[[]],[[]]]]=>1
[2,4,1,6,3,1]=>[[[[],[[],[]]]]]=>1
[2,4,3,1,1,6]=>[[],[[],[[[]]]]]=>2
[2,4,3,1,6,1]=>[[[[]],[[],[]]]]=>1
[2,4,3,6,1,1]=>[[[]],[[],[[]]]]=>2
[2,4,6,1,1,3]=>[[],[[],[],[],[]]]=>2
[2,4,6,1,3,1]=>[[[],[],[],[[]]]]=>1
[2,4,6,3,1,1]=>[[],[[[[],[]]]]]=>2
[2,6,1,1,3,4]=>[[],[[[]],[[]]]]=>2
[2,6,1,1,4,3]=>[[[[]]],[[[]]]]=>2
[2,6,1,3,1,4]=>[[[[],[[[]]]]]]=>1
[2,6,1,3,4,1]=>[[[],[[[],[]]]]]=>1
[2,6,1,4,1,3]=>[[[[]],[[],[]]]]=>1
[2,6,1,4,3,1]=>[[[[[[[]]]]]]]=>1
[2,6,3,1,1,4]=>[[[]],[[[],[]]]]=>2
[2,6,3,1,4,1]=>[[[],[],[[[]]]]]=>1
[2,6,3,4,1,1]=>[[],[[],[],[[]]]]=>2
[2,6,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[2,6,4,1,3,1]=>[[[],[[[],[]]]]]=>1
[2,6,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[3,1,1,2,4,6]=>[[],[[[],[[]]]]]=>2
[3,1,1,2,6,4]=>[[],[[[[],[]]]]]=>2
[3,1,1,4,2,6]=>[[],[[[],[[]]]]]=>2
[3,1,1,4,6,2]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,2,4]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,4,2]=>[[],[[],[],[],[]]]=>2
[3,1,2,1,4,6]=>[[[[[[[]]]]]]]=>1
[3,1,2,1,6,4]=>[[[],[],[[[]]]]]=>1
[3,1,2,4,1,6]=>[[[],[[[[]]]]]]=>1
[3,1,2,4,6,1]=>[[[[],[],[[]]]]]=>1
[3,1,2,6,1,4]=>[[[[[[[]]]]]]]=>1
[3,1,2,6,4,1]=>[[[],[[],[[]]]]]=>1
[3,1,4,1,2,6]=>[[[[[],[[]]]]]]=>1
[3,1,4,1,6,2]=>[[[[]],[[],[]]]]=>1
[3,1,4,2,1,6]=>[[[],[],[[[]]]]]=>1
[3,1,4,2,6,1]=>[[[[]],[[[]]]]]=>1
[3,1,4,6,1,2]=>[[[[[]],[[]]]]]=>1
[3,1,4,6,2,1]=>[[[[[],[[]]]]]]=>1
[3,1,6,1,2,4]=>[[[],[[[],[]]]]]=>1
[3,1,6,1,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,6,2,1,4]=>[[[],[[],[[]]]]]=>1
[3,1,6,2,4,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,4,1,2]=>[[[],[],[[[]]]]]=>1
[3,1,6,4,2,1]=>[[[],[],[],[[]]]]=>1
[3,2,1,1,4,6]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,6,4]=>[[],[[],[[],[]]]]=>2
[3,2,1,4,1,6]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,6,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,1,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,4,1]=>[[[],[[[],[]]]]]=>1
[3,2,4,1,1,6]=>[[[[]]],[[[]]]]=>2
[3,2,4,1,6,1]=>[[[[],[[[]]]]]]=>1
[3,2,4,6,1,1]=>[[[]],[[],[],[]]]=>2
[3,2,6,1,1,4]=>[[[[]]],[[[]]]]=>2
[3,2,6,1,4,1]=>[[[[],[[[]]]]]]=>1
[3,2,6,4,1,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,1,2,6]=>[[],[[],[[],[]]]]=>2
[3,4,1,1,6,2]=>[[[[]]],[[[]]]]=>2
[3,4,1,2,1,6]=>[[[],[[[[]]]]]]=>1
[3,4,1,2,6,1]=>[[[],[[],[[]]]]]=>1
[3,4,1,6,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,1,6,2,1]=>[[[[[[[]]]]]]]=>1
[3,4,2,1,1,6]=>[[],[[[]],[[]]]]=>2
[3,4,2,1,6,1]=>[[[[],[[[]]]]]]=>1
[3,4,2,6,1,1]=>[[],[[[[[]]]]]]=>2
[3,4,6,1,1,2]=>[[[],[]],[[],[]]]=>2
[3,4,6,1,2,1]=>[[[[]],[[],[]]]]=>1
[3,4,6,2,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,1,1,2,4]=>[[],[[[],[[]]]]]=>2
[3,6,1,1,4,2]=>[[[]],[[],[[]]]]=>2
[3,6,1,2,1,4]=>[[[],[[[[]]]]]]=>1
[3,6,1,2,4,1]=>[[[[[]],[[]]]]]=>1
[3,6,1,4,1,2]=>[[[[]],[[[]]]]]=>1
[3,6,1,4,2,1]=>[[[[]],[[[]]]]]=>1
[3,6,2,1,1,4]=>[[],[[],[],[[]]]]=>2
[3,6,2,1,4,1]=>[[[],[],[[[]]]]]=>1
[3,6,2,4,1,1]=>[[],[[[[],[]]]]]=>2
[3,6,4,1,1,2]=>[[[]],[[[[]]]]]=>2
[3,6,4,1,2,1]=>[[[[[[[]]]]]]]=>1
[3,6,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,2,3,6]=>[[[]],[[],[[]]]]=>2
[4,1,1,2,6,3]=>[[],[[[],[],[]]]]=>2
[4,1,1,3,2,6]=>[[],[[[[],[]]]]]=>2
[4,1,1,3,6,2]=>[[[[],[]]],[[]]]=>2
[4,1,1,6,2,3]=>[[[]],[[[[]]]]]=>2
[4,1,1,6,3,2]=>[[],[[[[],[]]]]]=>2
[4,1,2,1,3,6]=>[[[[[[[]]]]]]]=>1
[4,1,2,1,6,3]=>[[[[]],[[[]]]]]=>1
[4,1,2,3,1,6]=>[[[[],[[],[]]]]]=>1
[4,1,2,3,6,1]=>[[[[],[[[]]]]]]=>1
[4,1,2,6,1,3]=>[[[[]],[[],[]]]]=>1
[4,1,2,6,3,1]=>[[[],[[]],[[]]]]=>1
[4,1,3,1,2,6]=>[[[],[[[[]]]]]]=>1
[4,1,3,1,6,2]=>[[[[[]],[[]]]]]=>1
[4,1,3,2,1,6]=>[[[[[],[[]]]]]]=>1
[4,1,3,2,6,1]=>[[[],[[],[[]]]]]=>1
[4,1,3,6,1,2]=>[[[[[]],[[]]]]]=>1
[4,1,3,6,2,1]=>[[[[[]],[[]]]]]=>1
[4,1,6,1,2,3]=>[[[[[],[[]]]]]]=>1
[4,1,6,1,3,2]=>[[[[],[[[]]]]]]=>1
[4,1,6,2,1,3]=>[[[[[[[]]]]]]]=>1
[4,1,6,2,3,1]=>[[[[[[],[]]]]]]=>1
[4,1,6,3,1,2]=>[[[],[[],[[]]]]]=>1
[4,1,6,3,2,1]=>[[[],[[],[[]]]]]=>1
[4,2,1,1,3,6]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,6,3]=>[[],[[],[[[]]]]]=>2
[4,2,1,3,1,6]=>[[[],[[]],[[]]]]=>1
[4,2,1,3,6,1]=>[[[[[],[[]]]]]]=>1
[4,2,1,6,1,3]=>[[[],[[],[[]]]]]=>1
[4,2,1,6,3,1]=>[[[],[[]],[[]]]]=>1
[4,2,3,1,1,6]=>[[],[[],[],[[]]]]=>2
[4,2,3,1,6,1]=>[[[],[[]],[[]]]]=>1
[4,2,3,6,1,1]=>[[],[[[[[]]]]]]=>2
[4,2,6,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,2,6,1,3,1]=>[[[],[[],[[]]]]]=>1
[4,2,6,3,1,1]=>[[],[[],[[],[]]]]=>2
[4,3,1,1,2,6]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,6,2]=>[[],[[],[[[]]]]]=>2
[4,3,1,2,1,6]=>[[[[]],[[],[]]]]=>1
[4,3,1,2,6,1]=>[[[[[[[]]]]]]]=>1
[4,3,1,6,1,2]=>[[[[[[],[]]]]]]=>1
[4,3,1,6,2,1]=>[[[[]],[[],[]]]]=>1
[4,3,2,1,1,6]=>[[],[[[],[],[]]]]=>2
[4,3,2,1,6,1]=>[[[],[],[[[]]]]]=>1
[4,3,2,6,1,1]=>[[[[]]],[[],[]]]=>2
[4,3,6,1,1,2]=>[[[[]]],[[[]]]]=>2
[4,3,6,1,2,1]=>[[[],[[[[]]]]]]=>1
[4,3,6,2,1,1]=>[[],[[],[[],[]]]]=>2
[4,6,1,1,2,3]=>[[[],[]],[[],[]]]=>2
[4,6,1,1,3,2]=>[[],[[],[],[[]]]]=>2
[4,6,1,2,1,3]=>[[[],[],[[[]]]]]=>1
[4,6,1,2,3,1]=>[[[],[[],[[]]]]]=>1
[4,6,1,3,1,2]=>[[[],[],[[[]]]]]=>1
[4,6,1,3,2,1]=>[[[],[],[[],[]]]]=>1
[4,6,2,1,1,3]=>[[],[[],[[[]]]]]=>2
[4,6,2,1,3,1]=>[[[],[[[[]]]]]]=>1
[4,6,2,3,1,1]=>[[],[[[[[]]]]]]=>2
[4,6,3,1,1,2]=>[[[]],[[[[]]]]]=>2
[4,6,3,1,2,1]=>[[[[[[[]]]]]]]=>1
[4,6,3,2,1,1]=>[[],[[],[[[]]]]]=>2
[6,1,1,2,3,4]=>[[[]],[[],[],[]]]=>2
[6,1,1,2,4,3]=>[[],[[[],[[]]]]]=>2
[6,1,1,3,2,4]=>[[],[[],[],[[]]]]=>2
[6,1,1,3,4,2]=>[[],[[],[[[]]]]]=>2
[6,1,1,4,2,3]=>[[[]],[[[[]]]]]=>2
[6,1,1,4,3,2]=>[[[]],[[[],[]]]]=>2
[6,1,2,1,3,4]=>[[[],[[],[[]]]]]=>1
[6,1,2,1,4,3]=>[[[[[],[[]]]]]]=>1
[6,1,2,3,1,4]=>[[[[],[[[]]]]]]=>1
[6,1,2,3,4,1]=>[[[[],[],[[]]]]]=>1
[6,1,2,4,1,3]=>[[[],[[]],[[]]]]=>1
[6,1,2,4,3,1]=>[[[[]],[[[]]]]]=>1
[6,1,3,1,2,4]=>[[[],[],[[[]]]]]=>1
[6,1,3,1,4,2]=>[[[],[[],[[]]]]]=>1
[6,1,3,2,1,4]=>[[[],[[],[[]]]]]=>1
[6,1,3,2,4,1]=>[[[],[],[[[]]]]]=>1
[6,1,3,4,1,2]=>[[[],[[],[[]]]]]=>1
[6,1,3,4,2,1]=>[[[],[[[[]]]]]]=>1
[6,1,4,1,2,3]=>[[[[[[],[]]]]]]=>1
[6,1,4,1,3,2]=>[[[[[]]],[[]]]]=>1
[6,1,4,2,1,3]=>[[[[[]]],[[]]]]=>1
[6,1,4,2,3,1]=>[[[[[],[[]]]]]]=>1
[6,1,4,3,1,2]=>[[[[[[[]]]]]]]=>1
[6,1,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[6,2,1,1,3,4]=>[[],[[[[[]]]]]]=>2
[6,2,1,1,4,3]=>[[],[[],[[],[]]]]=>2
[6,2,1,3,1,4]=>[[[[[]]],[[]]]]=>1
[6,2,1,3,4,1]=>[[[[[[[]]]]]]]=>1
[6,2,1,4,1,3]=>[[[],[[[[]]]]]]=>1
[6,2,1,4,3,1]=>[[[],[[],[[]]]]]=>1
[6,2,3,1,1,4]=>[[[[]]],[[],[]]]=>2
[6,2,3,1,4,1]=>[[[[]],[[[]]]]]=>1
[6,2,3,4,1,1]=>[[],[[[],[[]]]]]=>2
[6,2,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[6,2,4,1,3,1]=>[[[[[],[[]]]]]]=>1
[6,2,4,3,1,1]=>[[[]],[[[[]]]]]=>2
[6,3,1,1,2,4]=>[[[[]]],[[[]]]]=>2
[6,3,1,1,4,2]=>[[[[],[]]],[[]]]=>2
[6,3,1,2,1,4]=>[[[[[[[]]]]]]]=>1
[6,3,1,2,4,1]=>[[[],[[[[]]]]]]=>1
[6,3,1,4,1,2]=>[[[[]],[[[]]]]]=>1
[6,3,1,4,2,1]=>[[[[[],[[]]]]]]=>1
[6,3,2,1,1,4]=>[[],[[[],[[]]]]]=>2
[6,3,2,1,4,1]=>[[[[]],[[],[]]]]=>1
[6,3,2,4,1,1]=>[[[]],[[],[[]]]]=>2
[6,3,4,1,1,2]=>[[[],[]],[[],[]]]=>2
[6,3,4,1,2,1]=>[[[],[[],[[]]]]]=>1
[6,3,4,2,1,1]=>[[[[]]],[[[]]]]=>2
[6,4,1,1,2,3]=>[[[]],[[],[[]]]]=>2
[6,4,1,1,3,2]=>[[[[[]]]],[[]]]=>2
[6,4,1,2,1,3]=>[[[[[[[]]]]]]]=>1
[6,4,1,2,3,1]=>[[[],[[],[[]]]]]=>1
[6,4,1,3,1,2]=>[[[[]],[[[]]]]]=>1
[6,4,1,3,2,1]=>[[[[[]],[[]]]]]=>1
[6,4,2,1,1,3]=>[[[[]]],[[],[]]]=>2
[6,4,2,1,3,1]=>[[[],[[]],[[]]]]=>1
[6,4,2,3,1,1]=>[[],[[],[],[[]]]]=>2
[6,4,3,1,1,2]=>[[[[]]],[[],[]]]=>2
[6,4,3,1,2,1]=>[[[],[[],[[]]]]]=>1
[6,4,3,2,1,1]=>[[[]],[[],[],[]]]=>2
[1,1,2,3,5,5]=>[[],[],[[[],[]]]]=>3
[1,1,2,5,3,5]=>[[],[[[[[]]]]]]=>2
[1,1,2,5,5,3]=>[[],[[[]]],[[]]]=>3
[1,1,3,2,5,5]=>[[],[[]],[[[]]]]=>3
[1,1,3,5,2,5]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,5,2]=>[[],[[]],[[],[]]]=>3
[1,1,5,2,3,5]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,5,3]=>[[],[[],[[[]]]]]=>2
[1,1,5,3,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,5,2]=>[[],[[],[[[]]]]]=>2
[1,1,5,5,2,3]=>[[],[],[[],[[]]]]=>3
[1,1,5,5,3,2]=>[[],[],[[[[]]]]]=>3
[1,2,1,3,5,5]=>[[[[]]],[[],[]]]=>2
[1,2,1,5,3,5]=>[[[[[[[]]]]]]]=>1
[1,2,1,5,5,3]=>[[[]],[[[[]]]]]=>2
[1,2,3,1,5,5]=>[[],[[[[],[]]]]]=>2
[1,2,3,5,1,5]=>[[[],[[[[]]]]]]=>1
[1,2,3,5,5,1]=>[[[[],[]]],[[]]]=>2
[1,2,5,1,3,5]=>[[[[],[[],[]]]]]=>1
[1,2,5,1,5,3]=>[[[[],[[[]]]]]]=>1
[1,2,5,3,1,5]=>[[[[[],[[]]]]]]=>1
[1,2,5,3,5,1]=>[[[[],[[[]]]]]]=>1
[1,2,5,5,1,3]=>[[],[[[]],[[]]]]=>2
[1,2,5,5,3,1]=>[[[[]]],[[],[]]]=>2
[1,3,1,2,5,5]=>[[],[[[[[]]]]]]=>2
[1,3,1,5,2,5]=>[[[[[]],[[]]]]]=>1
[1,3,1,5,5,2]=>[[[[]]],[[],[]]]=>2
[1,3,2,1,5,5]=>[[[]],[[],[[]]]]=>2
[1,3,2,5,1,5]=>[[[[],[[[]]]]]]=>1
[1,3,2,5,5,1]=>[[],[[],[[[]]]]]=>2
[1,3,5,1,2,5]=>[[[],[[],[[]]]]]=>1
[1,3,5,1,5,2]=>[[[],[[[],[]]]]]=>1
[1,3,5,2,1,5]=>[[[],[[],[[]]]]]=>1
[1,3,5,2,5,1]=>[[[],[[[],[]]]]]=>1
[1,3,5,5,1,2]=>[[[[]]],[[],[]]]=>2
[1,3,5,5,2,1]=>[[[[]]],[[],[]]]=>2
[1,5,1,2,3,5]=>[[[[[],[[]]]]]]=>1
[1,5,1,2,5,3]=>[[[[[],[[]]]]]]=>1
[1,5,1,3,2,5]=>[[[[[[],[]]]]]]=>1
[1,5,1,3,5,2]=>[[[],[[],[[]]]]]=>1
[1,5,1,5,2,3]=>[[[],[[]],[[]]]]=>1
[1,5,1,5,3,2]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,3,5]=>[[[],[[],[[]]]]]=>1
[1,5,2,1,5,3]=>[[[],[],[[[]]]]]=>1
[1,5,2,3,1,5]=>[[[],[],[[[]]]]]=>1
[1,5,2,3,5,1]=>[[[],[[[[]]]]]]=>1
[1,5,2,5,1,3]=>[[[],[[],[[]]]]]=>1
[1,5,2,5,3,1]=>[[[],[[],[[]]]]]=>1
[1,5,3,1,2,5]=>[[[[],[[[]]]]]]=>1
[1,5,3,1,5,2]=>[[[],[],[[],[]]]]=>1
[1,5,3,2,1,5]=>[[[[]],[[],[]]]]=>1
[1,5,3,2,5,1]=>[[[[[]],[[]]]]]=>1
[1,5,3,5,1,2]=>[[[[[[[]]]]]]]=>1
[1,5,3,5,2,1]=>[[[[]],[[[]]]]]=>1
[1,5,5,1,2,3]=>[[[[],[]]],[[]]]=>2
[1,5,5,1,3,2]=>[[[[[]]]],[[]]]=>2
[1,5,5,2,1,3]=>[[],[[],[[[]]]]]=>2
[1,5,5,2,3,1]=>[[],[[],[[[]]]]]=>2
[1,5,5,3,1,2]=>[[],[[[]],[[]]]]=>2
[1,5,5,3,2,1]=>[[],[[[],[[]]]]]=>2
[2,1,1,3,5,5]=>[[],[[]],[[],[]]]=>3
[2,1,1,5,3,5]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,5,3]=>[[],[[]],[[[]]]]=>3
[2,1,3,1,5,5]=>[[[[[]]]],[[]]]=>2
[2,1,3,5,1,5]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,5,1]=>[[[[]]],[[],[]]]=>2
[2,1,5,1,3,5]=>[[[[],[[[]]]]]]=>1
[2,1,5,1,5,3]=>[[[[[],[[]]]]]]=>1
[2,1,5,3,1,5]=>[[[[],[[],[]]]]]=>1
[2,1,5,3,5,1]=>[[[[[[[]]]]]]]=>1
[2,1,5,5,1,3]=>[[[[[]]]],[[]]]=>2
[2,1,5,5,3,1]=>[[],[[[]],[[]]]]=>2
[2,3,1,1,5,5]=>[[],[],[[[[]]]]]=>3
[2,3,1,5,1,5]=>[[[[[[],[]]]]]]=>1
[2,3,1,5,5,1]=>[[[]],[[[[]]]]]=>2
[2,3,5,1,1,5]=>[[[[[]]]],[[]]]=>2
[2,3,5,1,5,1]=>[[[[[],[[]]]]]]=>1
[2,3,5,5,1,1]=>[[],[[[]]],[[]]]=>3
[2,5,1,1,3,5]=>[[[],[]],[[],[]]]=>2
[2,5,1,1,5,3]=>[[[[]]],[[],[]]]=>2
[2,5,1,3,1,5]=>[[[],[[[[]]]]]]=>1
[2,5,1,3,5,1]=>[[[],[],[[],[]]]]=>1
[2,5,1,5,1,3]=>[[[],[[]],[[]]]]=>1
[2,5,1,5,3,1]=>[[[],[[],[[]]]]]=>1
[2,5,3,1,1,5]=>[[[]],[[],[[]]]]=>2
[2,5,3,1,5,1]=>[[[],[[[],[]]]]]=>1
[2,5,3,5,1,1]=>[[],[[],[[[]]]]]=>2
[2,5,5,1,1,3]=>[[],[[]],[[],[]]]=>3
[2,5,5,1,3,1]=>[[],[[],[[[]]]]]=>2
[2,5,5,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,1,1,2,5,5]=>[[],[],[[[[]]]]]=>3
[3,1,1,5,2,5]=>[[],[[[]],[[]]]]=>2
[3,1,1,5,5,2]=>[[],[[]],[[],[]]]=>3
[3,1,2,1,5,5]=>[[[[]]],[[[]]]]=>2
[3,1,2,5,1,5]=>[[[[[]],[[]]]]]=>1
[3,1,2,5,5,1]=>[[[]],[[],[[]]]]=>2
[3,1,5,1,2,5]=>[[[[[],[[]]]]]]=>1
[3,1,5,1,5,2]=>[[[[],[],[[]]]]]=>1
[3,1,5,2,1,5]=>[[[[],[],[[]]]]]=>1
[3,1,5,2,5,1]=>[[[[],[[],[]]]]]=>1
[3,1,5,5,1,2]=>[[[[]]],[[[]]]]=>2
[3,1,5,5,2,1]=>[[],[[],[[[]]]]]=>2
[3,2,1,1,5,5]=>[[],[[]],[[],[]]]=>3
[3,2,1,5,1,5]=>[[[],[[],[[]]]]]=>1
[3,2,1,5,5,1]=>[[[[],[]]],[[]]]=>2
[3,2,5,1,1,5]=>[[[[]]],[[],[]]]=>2
[3,2,5,1,5,1]=>[[[[],[],[[]]]]]=>1
[3,2,5,5,1,1]=>[[],[[]],[[],[]]]=>3
[3,5,1,1,2,5]=>[[],[[[],[[]]]]]=>2
[3,5,1,1,5,2]=>[[[[]]],[[],[]]]=>2
[3,5,1,2,1,5]=>[[[[[[[]]]]]]]=>1
[3,5,1,2,5,1]=>[[[[],[],[[]]]]]=>1
[3,5,1,5,1,2]=>[[[[[]],[[]]]]]=>1
[3,5,1,5,2,1]=>[[[[[]],[[]]]]]=>1
[3,5,2,1,1,5]=>[[],[[[]],[[]]]]=>2
[3,5,2,1,5,1]=>[[[[[[],[]]]]]]=>1
[3,5,2,5,1,1]=>[[],[[],[[[]]]]]=>2
[3,5,5,1,1,2]=>[[[]],[[]],[[]]]=>3
[3,5,5,1,2,1]=>[[[]],[[[[]]]]]=>2
[3,5,5,2,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,2,3,5]=>[[[]],[[],[[]]]]=>2
[5,1,1,2,5,3]=>[[],[[[],[[]]]]]=>2
[5,1,1,3,2,5]=>[[],[[[[],[]]]]]=>2
[5,1,1,3,5,2]=>[[[]],[[],[[]]]]=>2
[5,1,1,5,2,3]=>[[[]],[[],[[]]]]=>2
[5,1,1,5,3,2]=>[[],[[[[[]]]]]]=>2
[5,1,2,1,3,5]=>[[[[[[],[]]]]]]=>1
[5,1,2,1,5,3]=>[[[[[[[]]]]]]]=>1
[5,1,2,3,1,5]=>[[[[],[[[]]]]]]=>1
[5,1,2,3,5,1]=>[[[],[[[],[]]]]]=>1
[5,1,2,5,1,3]=>[[[],[[]],[[]]]]=>1
[5,1,2,5,3,1]=>[[[[]],[[],[]]]]=>1
[5,1,3,1,2,5]=>[[[],[[[[]]]]]]=>1
[5,1,3,1,5,2]=>[[[[],[[[]]]]]]=>1
[5,1,3,2,1,5]=>[[[[[]],[[]]]]]=>1
[5,1,3,2,5,1]=>[[[],[],[[[]]]]]=>1
[5,1,3,5,1,2]=>[[[[]],[[],[]]]]=>1
[5,1,3,5,2,1]=>[[[[],[[[]]]]]]=>1
[5,1,5,1,2,3]=>[[[[]],[[],[]]]]=>1
[5,1,5,1,3,2]=>[[[[[]]],[[]]]]=>1
[5,1,5,2,1,3]=>[[[[],[[[]]]]]]=>1
[5,1,5,2,3,1]=>[[[[],[[[]]]]]]=>1
[5,1,5,3,1,2]=>[[[[[]],[[]]]]]=>1
[5,1,5,3,2,1]=>[[[[[]],[[]]]]]=>1
[5,2,1,1,3,5]=>[[[]],[[],[[]]]]=>2
[5,2,1,1,5,3]=>[[],[[],[[[]]]]]=>2
[5,2,1,3,1,5]=>[[[[[]]],[[]]]]=>1
[5,2,1,3,5,1]=>[[[[],[[[]]]]]]=>1
[5,2,1,5,1,3]=>[[[],[[[[]]]]]]=>1
[5,2,1,5,3,1]=>[[[],[[],[[]]]]]=>1
[5,2,3,1,1,5]=>[[[[]]],[[],[]]]=>2
[5,2,3,1,5,1]=>[[[[]],[[[]]]]]=>1
[5,2,3,5,1,1]=>[[],[[[[[]]]]]]=>2
[5,2,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[5,2,5,1,3,1]=>[[[[],[[[]]]]]]=>1
[5,2,5,3,1,1]=>[[],[[[]],[[]]]]=>2
[5,3,1,1,2,5]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,5,2]=>[[],[[],[[],[]]]]=>2
[5,3,1,2,1,5]=>[[[],[[[[]]]]]]=>1
[5,3,1,2,5,1]=>[[[],[[],[[]]]]]=>1
[5,3,1,5,1,2]=>[[[],[[[[]]]]]]=>1
[5,3,1,5,2,1]=>[[[],[[[],[]]]]]=>1
[5,3,2,1,1,5]=>[[[[],[]]],[[]]]=>2
[5,3,2,1,5,1]=>[[[[[[],[]]]]]]=>1
[5,3,2,5,1,1]=>[[[]],[[],[[]]]]=>2
[5,3,5,1,1,2]=>[[[]],[[[[]]]]]=>2
[5,3,5,1,2,1]=>[[[[[[[]]]]]]]=>1
[5,3,5,2,1,1]=>[[[]],[[[[]]]]]=>2
[5,5,1,1,2,3]=>[[],[[]],[[],[]]]=>3
[5,5,1,1,3,2]=>[[],[[[]]],[[]]]=>3
[5,5,1,2,1,3]=>[[],[[[[[]]]]]]=>2
[5,5,1,2,3,1]=>[[],[[[],[[]]]]]=>2
[5,5,1,3,1,2]=>[[],[[[[[]]]]]]=>2
[5,5,1,3,2,1]=>[[],[[[[],[]]]]]=>2
[5,5,2,1,1,3]=>[[],[],[[[[]]]]]=>3
[5,5,2,1,3,1]=>[[],[[[[[]]]]]]=>2
[5,5,2,3,1,1]=>[[],[],[[[[]]]]]=>3
[5,5,3,1,1,2]=>[[],[[]],[[],[]]]=>3
[5,5,3,1,2,1]=>[[],[[],[[[]]]]]=>2
[5,5,3,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,3,5,6]=>[[],[[],[],[[]]]]=>2
[1,1,2,3,6,5]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,3,6]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,6,3]=>[[],[[[]],[[]]]]=>2
[1,1,2,6,3,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,6,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,3,2,5,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,2,6,5]=>[[],[[[],[[]]]]]=>2
[1,1,3,5,2,6]=>[[],[[],[[],[]]]]=>2
[1,1,3,5,6,2]=>[[],[[],[[[]]]]]=>2
[1,1,3,6,2,5]=>[[],[[[],[],[]]]]=>2
[1,1,3,6,5,2]=>[[],[[[[[]]]]]]=>2
[1,1,5,2,3,6]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,6,3]=>[[],[[],[],[],[]]]=>2
[1,1,5,3,2,6]=>[[],[[[]],[[]]]]=>2
[1,1,5,3,6,2]=>[[],[[[],[[]]]]]=>2
[1,1,5,6,2,3]=>[[],[[[],[[]]]]]=>2
[1,1,5,6,3,2]=>[[],[[[]],[[]]]]=>2
[1,1,6,2,3,5]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,5,3]=>[[],[[],[[],[]]]]=>2
[1,1,6,3,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,5,2]=>[[],[[[[],[]]]]]=>2
[1,1,6,5,2,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,5,3,2]=>[[],[[],[[],[]]]]=>2
[1,2,1,3,5,6]=>[[[[]],[[],[]]]]=>1
[1,2,1,3,6,5]=>[[[[],[[[]]]]]]=>1
[1,2,1,5,3,6]=>[[[[[[[]]]]]]]=>1
[1,2,1,5,6,3]=>[[[],[[],[[]]]]]=>1
[1,2,1,6,3,5]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,5,3]=>[[[[],[[],[]]]]]=>1
[1,2,3,1,5,6]=>[[[],[],[[[]]]]]=>1
[1,2,3,1,6,5]=>[[[],[[],[[]]]]]=>1
[1,2,3,5,1,6]=>[[[],[[[[]]]]]]=>1
[1,2,3,5,6,1]=>[[[],[],[[],[]]]]=>1
[1,2,3,6,1,5]=>[[[],[[[[]]]]]]=>1
[1,2,3,6,5,1]=>[[[],[[],[[]]]]]=>1
[1,2,5,1,3,6]=>[[[[],[],[[]]]]]=>1
[1,2,5,1,6,3]=>[[[[],[[[]]]]]]=>1
[1,2,5,3,1,6]=>[[[[[],[],[]]]]]=>1
[1,2,5,3,6,1]=>[[[[[]],[[]]]]]=>1
[1,2,5,6,1,3]=>[[[[]],[[],[]]]]=>1
[1,2,5,6,3,1]=>[[[[]],[[[]]]]]=>1
[1,2,6,1,3,5]=>[[[[[],[],[]]]]]=>1
[1,2,6,1,5,3]=>[[[[[]],[[]]]]]=>1
[1,2,6,3,1,5]=>[[[[],[],[[]]]]]=>1
[1,2,6,3,5,1]=>[[[[],[[[]]]]]]=>1
[1,2,6,5,1,3]=>[[[[[[[]]]]]]]=>1
[1,2,6,5,3,1]=>[[[[[],[[]]]]]]=>1
[1,3,1,2,5,6]=>[[[[[[],[]]]]]]=>1
[1,3,1,2,6,5]=>[[[[[[[]]]]]]]=>1
[1,3,1,5,2,6]=>[[[[],[],[[]]]]]=>1
[1,3,1,5,6,2]=>[[[[[[[]]]]]]]=>1
[1,3,1,6,2,5]=>[[[[],[[],[]]]]]=>1
[1,3,1,6,5,2]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,5,6]=>[[[[],[[[]]]]]]=>1
[1,3,2,1,6,5]=>[[[[],[],[[]]]]]=>1
[1,3,2,5,1,6]=>[[[[],[[[]]]]]]=>1
[1,3,2,5,6,1]=>[[[[[]]],[[]]]]=>1
[1,3,2,6,1,5]=>[[[],[[],[[]]]]]=>1
[1,3,2,6,5,1]=>[[[[[],[[]]]]]]=>1
[1,3,5,1,2,6]=>[[[],[[[[]]]]]]=>1
[1,3,5,1,6,2]=>[[[],[[],[[]]]]]=>1
[1,3,5,2,1,6]=>[[[],[[[[]]]]]]=>1
[1,3,5,2,6,1]=>[[[],[],[[],[]]]]=>1
[1,3,5,6,1,2]=>[[[],[],[[],[]]]]=>1
[1,3,5,6,2,1]=>[[[],[[[[]]]]]]=>1
[1,3,6,1,2,5]=>[[[],[[[],[]]]]]=>1
[1,3,6,1,5,2]=>[[[[]],[[],[]]]]=>1
[1,3,6,2,1,5]=>[[[[],[[[]]]]]]=>1
[1,3,6,2,5,1]=>[[[[],[],[],[]]]]=>1
[1,3,6,5,1,2]=>[[[[],[[[]]]]]]=>1
[1,3,6,5,2,1]=>[[[[],[[[]]]]]]=>1
[1,5,1,2,3,6]=>[[[[],[[],[]]]]]=>1
[1,5,1,2,6,3]=>[[[],[],[[[]]]]]=>1
[1,5,1,3,2,6]=>[[[],[[[[]]]]]]=>1
[1,5,1,3,6,2]=>[[[[[],[],[]]]]]=>1
[1,5,1,6,2,3]=>[[[[[],[[]]]]]]=>1
[1,5,1,6,3,2]=>[[[[]],[[[]]]]]=>1
[1,5,2,1,3,6]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,6,3]=>[[[],[[]],[[]]]]=>1
[1,5,2,3,1,6]=>[[[],[[],[[]]]]]=>1
[1,5,2,3,6,1]=>[[[],[[[[]]]]]]=>1
[1,5,2,6,1,3]=>[[[],[],[[],[]]]]=>1
[1,5,2,6,3,1]=>[[[],[],[],[[]]]]=>1
[1,5,3,1,2,6]=>[[[],[[[],[]]]]]=>1
[1,5,3,1,6,2]=>[[[[],[],[[]]]]]=>1
[1,5,3,2,1,6]=>[[[[],[[],[]]]]]=>1
[1,5,3,2,6,1]=>[[[[[]]],[[]]]]=>1
[1,5,3,6,1,2]=>[[[[[[[]]]]]]]=>1
[1,5,3,6,2,1]=>[[[[],[[[]]]]]]=>1
[1,5,6,1,2,3]=>[[[[[],[],[]]]]]=>1
[1,5,6,1,3,2]=>[[[[[]],[[]]]]]=>1
[1,5,6,2,1,3]=>[[[[[[[]]]]]]]=>1
[1,5,6,2,3,1]=>[[[[[],[[]]]]]]=>1
[1,5,6,3,1,2]=>[[[],[[[],[]]]]]=>1
[1,5,6,3,2,1]=>[[[[]],[[],[]]]]=>1
[1,6,1,2,3,5]=>[[[[],[[],[]]]]]=>1
[1,6,1,2,5,3]=>[[[],[[[[]]]]]]=>1
[1,6,1,3,2,5]=>[[[[[[],[]]]]]]=>1
[1,6,1,3,5,2]=>[[[[],[],[[]]]]]=>1
[1,6,1,5,2,3]=>[[[[[]],[[]]]]]=>1
[1,6,1,5,3,2]=>[[[],[[[[]]]]]]=>1
[1,6,2,1,3,5]=>[[[[],[[[]]]]]]=>1
[1,6,2,1,5,3]=>[[[[[]]],[[]]]]=>1
[1,6,2,3,1,5]=>[[[[[]]],[[]]]]=>1
[1,6,2,3,5,1]=>[[[[[[],[]]]]]]=>1
[1,6,2,5,1,3]=>[[[[],[],[[]]]]]=>1
[1,6,2,5,3,1]=>[[[],[],[[],[]]]]=>1
[1,6,3,1,2,5]=>[[[[[]]],[[]]]]=>1
[1,6,3,1,5,2]=>[[[],[[],[],[]]]]=>1
[1,6,3,2,1,5]=>[[[[],[[],[]]]]]=>1
[1,6,3,2,5,1]=>[[[[[]],[[]]]]]=>1
[1,6,3,5,1,2]=>[[[[[[[]]]]]]]=>1
[1,6,3,5,2,1]=>[[[[[],[[]]]]]]=>1
[1,6,5,1,2,3]=>[[[[[]],[[]]]]]=>1
[1,6,5,1,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,5,2,1,3]=>[[[[[],[[]]]]]]=>1
[1,6,5,2,3,1]=>[[[[[]]],[[]]]]=>1
[1,6,5,3,1,2]=>[[[],[],[[[]]]]]=>1
[1,6,5,3,2,1]=>[[[],[[],[],[]]]]=>1
[2,1,1,3,5,6]=>[[],[[],[[[]]]]]=>2
[2,1,1,3,6,5]=>[[],[[[[],[]]]]]=>2
[2,1,1,5,3,6]=>[[],[[[[[]]]]]]=>2
[2,1,1,5,6,3]=>[[],[[[]],[[]]]]=>2
[2,1,1,6,3,5]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,5,3]=>[[],[[],[[],[]]]]=>2
[2,1,3,1,5,6]=>[[[[[[[]]]]]]]=>1
[2,1,3,1,6,5]=>[[[],[[],[[]]]]]=>1
[2,1,3,5,1,6]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,6,1]=>[[[[],[],[[]]]]]=>1
[2,1,3,6,1,5]=>[[[[[],[[]]]]]]=>1
[2,1,3,6,5,1]=>[[[],[[],[[]]]]]=>1
[2,1,5,1,3,6]=>[[[[[]],[[]]]]]=>1
[2,1,5,1,6,3]=>[[[[],[[[]]]]]]=>1
[2,1,5,3,1,6]=>[[[[],[],[[]]]]]=>1
[2,1,5,3,6,1]=>[[[[[[[]]]]]]]=>1
[2,1,5,6,1,3]=>[[[[],[[[]]]]]]=>1
[2,1,5,6,3,1]=>[[[[[],[[]]]]]]=>1
[2,1,6,1,3,5]=>[[[[],[],[[]]]]]=>1
[2,1,6,1,5,3]=>[[[[],[[[]]]]]]=>1
[2,1,6,3,1,5]=>[[[[],[[],[]]]]]=>1
[2,1,6,3,5,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,5,1,3]=>[[[],[[[[]]]]]]=>1
[2,1,6,5,3,1]=>[[[],[[],[],[]]]]=>1
[2,3,1,1,5,6]=>[[[[],[]]],[[]]]=>2
[2,3,1,1,6,5]=>[[],[[[]],[[]]]]=>2
[2,3,1,5,1,6]=>[[[[],[[[]]]]]]=>1
[2,3,1,5,6,1]=>[[[[]],[[[]]]]]=>1
[2,3,1,6,1,5]=>[[[[],[[[]]]]]]=>1
[2,3,1,6,5,1]=>[[[[],[[[]]]]]]=>1
[2,3,5,1,1,6]=>[[[[[]]]],[[]]]=>2
[2,3,5,1,6,1]=>[[[[],[[[]]]]]]=>1
[2,3,5,6,1,1]=>[[],[[],[[],[]]]]=>2
[2,3,6,1,1,5]=>[[[[[]]]],[[]]]=>2
[2,3,6,1,5,1]=>[[[[],[[[]]]]]]=>1
[2,3,6,5,1,1]=>[[[]],[[],[[]]]]=>2
[2,5,1,1,3,6]=>[[],[[[],[],[]]]]=>2
[2,5,1,1,6,3]=>[[[[]]],[[],[]]]=>2
[2,5,1,3,1,6]=>[[[],[[[],[]]]]]=>1
[2,5,1,3,6,1]=>[[[],[],[[],[]]]]=>1
[2,5,1,6,1,3]=>[[[],[[[],[]]]]]=>1
[2,5,1,6,3,1]=>[[[],[[[],[]]]]]=>1
[2,5,3,1,1,6]=>[[],[[],[],[[]]]]=>2
[2,5,3,1,6,1]=>[[[[],[],[[]]]]]=>1
[2,5,3,6,1,1]=>[[],[[[],[[]]]]]=>2
[2,5,6,1,1,3]=>[[],[[],[[[]]]]]=>2
[2,5,6,1,3,1]=>[[[[[],[[]]]]]]=>1
[2,5,6,3,1,1]=>[[],[[[[[]]]]]]=>2
[2,6,1,1,3,5]=>[[[]],[[],[],[]]]=>2
[2,6,1,1,5,3]=>[[[]],[[],[[]]]]=>2
[2,6,1,3,1,5]=>[[[],[[[],[]]]]]=>1
[2,6,1,3,5,1]=>[[[[],[],[[]]]]]=>1
[2,6,1,5,1,3]=>[[[],[[[],[]]]]]=>1
[2,6,1,5,3,1]=>[[[[]],[[],[]]]]=>1
[2,6,3,1,1,5]=>[[[]],[[],[],[]]]=>2
[2,6,3,1,5,1]=>[[[],[[]],[[]]]]=>1
[2,6,3,5,1,1]=>[[],[[[[],[]]]]]=>2
[2,6,5,1,1,3]=>[[[[[]]]],[[]]]=>2
[2,6,5,1,3,1]=>[[[[[[[]]]]]]]=>1
[2,6,5,3,1,1]=>[[[]],[[],[[]]]]=>2
[3,1,1,2,5,6]=>[[],[[],[[[]]]]]=>2
[3,1,1,2,6,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,5,2,6]=>[[],[[],[],[[]]]]=>2
[3,1,1,5,6,2]=>[[[[[]]]],[[]]]=>2
[3,1,1,6,2,5]=>[[],[[],[[],[]]]]=>2
[3,1,1,6,5,2]=>[[],[[],[[[]]]]]=>2
[3,1,2,1,5,6]=>[[[[[],[[]]]]]]=>1
[3,1,2,1,6,5]=>[[[],[[],[[]]]]]=>1
[3,1,2,5,1,6]=>[[[],[[],[[]]]]]=>1
[3,1,2,5,6,1]=>[[[[[],[[]]]]]]=>1
[3,1,2,6,1,5]=>[[[[[],[[]]]]]]=>1
[3,1,2,6,5,1]=>[[[[[[[]]]]]]]=>1
[3,1,5,1,2,6]=>[[[[[[],[]]]]]]=>1
[3,1,5,1,6,2]=>[[[[]],[[],[]]]]=>1
[3,1,5,2,1,6]=>[[[[]],[[],[]]]]=>1
[3,1,5,2,6,1]=>[[[[],[],[[]]]]]=>1
[3,1,5,6,1,2]=>[[[[[],[[]]]]]]=>1
[3,1,5,6,2,1]=>[[[[[[[]]]]]]]=>1
[3,1,6,1,2,5]=>[[[],[[[[]]]]]]=>1
[3,1,6,1,5,2]=>[[[],[[],[[]]]]]=>1
[3,1,6,2,1,5]=>[[[],[[[[]]]]]]=>1
[3,1,6,2,5,1]=>[[[],[[],[],[]]]]=>1
[3,1,6,5,1,2]=>[[[],[[[[]]]]]]=>1
[3,1,6,5,2,1]=>[[[],[[],[[]]]]]=>1
[3,2,1,1,5,6]=>[[],[[[[],[]]]]]=>2
[3,2,1,1,6,5]=>[[],[[[],[],[]]]]=>2
[3,2,1,5,1,6]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,6,1]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,1,5]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,5,1]=>[[[],[],[[[]]]]]=>1
[3,2,5,1,1,6]=>[[[[]]],[[],[]]]=>2
[3,2,5,1,6,1]=>[[[[[[],[]]]]]]=>1
[3,2,5,6,1,1]=>[[[[[]]]],[[]]]=>2
[3,2,6,1,1,5]=>[[[]],[[],[[]]]]=>2
[3,2,6,1,5,1]=>[[[[[],[[]]]]]]=>1
[3,2,6,5,1,1]=>[[[]],[[],[[]]]]=>2
[3,5,1,1,2,6]=>[[[[]]],[[[]]]]=>2
[3,5,1,1,6,2]=>[[],[[[],[[]]]]]=>2
[3,5,1,2,1,6]=>[[[[[[[]]]]]]]=>1
[3,5,1,2,6,1]=>[[[],[[[[]]]]]]=>1
[3,5,1,6,1,2]=>[[[[]],[[[]]]]]=>1
[3,5,1,6,2,1]=>[[[[[[],[]]]]]]=>1
[3,5,2,1,1,6]=>[[[[]]],[[[]]]]=>2
[3,5,2,1,6,1]=>[[[[[]]],[[]]]]=>1
[3,5,2,6,1,1]=>[[],[[],[[],[]]]]=>2
[3,5,6,1,1,2]=>[[[],[]],[[],[]]]=>2
[3,5,6,1,2,1]=>[[[],[[],[[]]]]]=>1
[3,5,6,2,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,1,1,2,5]=>[[[[],[]]],[[]]]=>2
[3,6,1,1,5,2]=>[[[[]]],[[],[]]]=>2
[3,6,1,2,1,5]=>[[[[[[[]]]]]]]=>1
[3,6,1,2,5,1]=>[[[],[],[[[]]]]]=>1
[3,6,1,5,1,2]=>[[[[]],[[[]]]]]=>1
[3,6,1,5,2,1]=>[[[[[]],[[]]]]]=>1
[3,6,2,1,1,5]=>[[],[[[[],[]]]]]=>2
[3,6,2,1,5,1]=>[[[],[[]],[[]]]]=>1
[3,6,2,5,1,1]=>[[],[[],[],[],[]]]=>2
[3,6,5,1,1,2]=>[[[[]]],[[],[]]]=>2
[3,6,5,1,2,1]=>[[[],[[[],[]]]]]=>1
[3,6,5,2,1,1]=>[[],[[],[[[]]]]]=>2
[5,1,1,2,3,6]=>[[],[[],[[],[]]]]=>2
[5,1,1,2,6,3]=>[[[[],[]]],[[]]]=>2
[5,1,1,3,2,6]=>[[[[[]]]],[[]]]=>2
[5,1,1,3,6,2]=>[[],[[[],[],[]]]]=>2
[5,1,1,6,2,3]=>[[],[[[],[[]]]]]=>2
[5,1,1,6,3,2]=>[[],[[[[[]]]]]]=>2
[5,1,2,1,3,6]=>[[[[]],[[[]]]]]=>1
[5,1,2,1,6,3]=>[[[[[[[]]]]]]]=>1
[5,1,2,3,1,6]=>[[[[],[[],[]]]]]=>1
[5,1,2,3,6,1]=>[[[[]],[[],[]]]]=>1
[5,1,2,6,1,3]=>[[[[[[],[]]]]]]=>1
[5,1,2,6,3,1]=>[[[[[]],[[]]]]]=>1
[5,1,3,1,2,6]=>[[[[[[[]]]]]]]=>1
[5,1,3,1,6,2]=>[[[],[[],[[]]]]]=>1
[5,1,3,2,1,6]=>[[[[[]],[[]]]]]=>1
[5,1,3,2,6,1]=>[[[[[],[[]]]]]]=>1
[5,1,3,6,1,2]=>[[[],[[],[[]]]]]=>1
[5,1,3,6,2,1]=>[[[],[[]],[[]]]]=>1
[5,1,6,1,2,3]=>[[[[[],[[]]]]]]=>1
[5,1,6,1,3,2]=>[[[[],[[[]]]]]]=>1
[5,1,6,2,1,3]=>[[[],[[[[]]]]]]=>1
[5,1,6,2,3,1]=>[[[],[[[],[]]]]]=>1
[5,1,6,3,1,2]=>[[[[[],[[]]]]]]=>1
[5,1,6,3,2,1]=>[[[[[]],[[]]]]]=>1
[5,2,1,1,3,6]=>[[],[[[[[]]]]]]=>2
[5,2,1,1,6,3]=>[[],[[[],[[]]]]]=>2
[5,2,1,3,1,6]=>[[[[[]],[[]]]]]=>1
[5,2,1,3,6,1]=>[[[[[]],[[]]]]]=>1
[5,2,1,6,1,3]=>[[[[[]],[[]]]]]=>1
[5,2,1,6,3,1]=>[[[],[[],[[]]]]]=>1
[5,2,3,1,1,6]=>[[[]],[[],[[]]]]=>2
[5,2,3,1,6,1]=>[[[[[]],[[]]]]]=>1
[5,2,3,6,1,1]=>[[],[[[[[]]]]]]=>2
[5,2,6,1,1,3]=>[[],[[],[[],[]]]]=>2
[5,2,6,1,3,1]=>[[[],[[],[[]]]]]=>1
[5,2,6,3,1,1]=>[[],[[[],[],[]]]]=>2
[5,3,1,1,2,6]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,6,2]=>[[],[[],[],[[]]]]=>2
[5,3,1,2,1,6]=>[[[],[],[[[]]]]]=>1
[5,3,1,2,6,1]=>[[[],[[[[]]]]]]=>1
[5,3,1,6,1,2]=>[[[],[],[[[]]]]]=>1
[5,3,1,6,2,1]=>[[[],[],[[[]]]]]=>1
[5,3,2,1,1,6]=>[[],[[],[[],[]]]]=>2
[5,3,2,1,6,1]=>[[[],[[[],[]]]]]=>1
[5,3,2,6,1,1]=>[[[[[]]]],[[]]]=>2
[5,3,6,1,1,2]=>[[[]],[[[[]]]]]=>2
[5,3,6,1,2,1]=>[[[[[[[]]]]]]]=>1
[5,3,6,2,1,1]=>[[[]],[[[],[]]]]=>2
[5,6,1,1,2,3]=>[[[]],[[],[],[]]]=>2
[5,6,1,1,3,2]=>[[],[[[]],[[]]]]=>2
[5,6,1,2,1,3]=>[[[],[[[],[]]]]]=>1
[5,6,1,2,3,1]=>[[[],[[]],[[]]]]=>1
[5,6,1,3,1,2]=>[[[],[[[],[]]]]]=>1
[5,6,1,3,2,1]=>[[[[],[[],[]]]]]=>1
[5,6,2,1,1,3]=>[[],[[[[[]]]]]]=>2
[5,6,2,1,3,1]=>[[[[[[[]]]]]]]=>1
[5,6,2,3,1,1]=>[[],[[[],[[]]]]]=>2
[5,6,3,1,1,2]=>[[[[]]],[[],[]]]=>2
[5,6,3,1,2,1]=>[[[[]],[[[]]]]]=>1
[5,6,3,2,1,1]=>[[],[[],[[[]]]]]=>2
[6,1,1,2,3,5]=>[[],[[],[[],[]]]]=>2
[6,1,1,2,5,3]=>[[[[[]]]],[[]]]=>2
[6,1,1,3,2,5]=>[[],[[],[[[]]]]]=>2
[6,1,1,3,5,2]=>[[],[[],[],[[]]]]=>2
[6,1,1,5,2,3]=>[[[]],[[],[[]]]]=>2
[6,1,1,5,3,2]=>[[[]],[[[[]]]]]=>2
[6,1,2,1,3,5]=>[[[],[],[[[]]]]]=>1
[6,1,2,1,5,3]=>[[[[[[[]]]]]]]=>1
[6,1,2,3,1,5]=>[[[[],[[[]]]]]]=>1
[6,1,2,3,5,1]=>[[[[]],[[],[]]]]=>1
[6,1,2,5,1,3]=>[[[],[[],[[]]]]]=>1
[6,1,2,5,3,1]=>[[[[[[],[]]]]]]=>1
[6,1,3,1,2,5]=>[[[],[[[[]]]]]]=>1
[6,1,3,1,5,2]=>[[[],[[[],[]]]]]=>1
[6,1,3,2,1,5]=>[[[],[[],[[]]]]]=>1
[6,1,3,2,5,1]=>[[[],[[[],[]]]]]=>1
[6,1,3,5,1,2]=>[[[],[],[[[]]]]]=>1
[6,1,3,5,2,1]=>[[[],[],[[[]]]]]=>1
[6,1,5,1,2,3]=>[[[[[[],[]]]]]]=>1
[6,1,5,1,3,2]=>[[[[[]]],[[]]]]=>1
[6,1,5,2,1,3]=>[[[],[[[],[]]]]]=>1
[6,1,5,2,3,1]=>[[[[],[[[]]]]]]=>1
[6,1,5,3,1,2]=>[[[[[],[[]]]]]]=>1
[6,1,5,3,2,1]=>[[[[[],[[]]]]]]=>1
[6,2,1,1,3,5]=>[[],[[],[[[]]]]]=>2
[6,2,1,1,5,3]=>[[[]],[[[[]]]]]=>2
[6,2,1,3,1,5]=>[[[[[[[]]]]]]]=>1
[6,2,1,3,5,1]=>[[[[]],[[],[]]]]=>1
[6,2,1,5,1,3]=>[[[[[]]],[[]]]]=>1
[6,2,1,5,3,1]=>[[[[[]],[[]]]]]=>1
[6,2,3,1,1,5]=>[[[]],[[[[]]]]]=>2
[6,2,3,1,5,1]=>[[[],[[[[]]]]]]=>1
[6,2,3,5,1,1]=>[[],[[],[[[]]]]]=>2
[6,2,5,1,1,3]=>[[[]],[[],[],[]]]=>2
[6,2,5,1,3,1]=>[[[],[],[[[]]]]]=>1
[6,2,5,3,1,1]=>[[],[[],[[],[]]]]=>2
[6,3,1,1,2,5]=>[[[[]]],[[[]]]]=>2
[6,3,1,1,5,2]=>[[],[[],[],[[]]]]=>2
[6,3,1,2,1,5]=>[[[[]],[[[]]]]]=>1
[6,3,1,2,5,1]=>[[[[[],[[]]]]]]=>1
[6,3,1,5,1,2]=>[[[[[]]],[[]]]]=>1
[6,3,1,5,2,1]=>[[[],[],[[[]]]]]=>1
[6,3,2,1,1,5]=>[[],[[],[[],[]]]]=>2
[6,3,2,1,5,1]=>[[[],[[[],[]]]]]=>1
[6,3,2,5,1,1]=>[[[]],[[],[[]]]]=>2
[6,3,5,1,1,2]=>[[[]],[[[[]]]]]=>2
[6,3,5,1,2,1]=>[[[[[[[]]]]]]]=>1
[6,3,5,2,1,1]=>[[],[[[],[[]]]]]=>2
[6,5,1,1,2,3]=>[[[]],[[],[[]]]]=>2
[6,5,1,1,3,2]=>[[[[],[]]],[[]]]=>2
[6,5,1,2,1,3]=>[[[[[]]],[[]]]]=>1
[6,5,1,2,3,1]=>[[[[[],[[]]]]]]=>1
[6,5,1,3,1,2]=>[[[[[[[]]]]]]]=>1
[6,5,1,3,2,1]=>[[[],[],[[[]]]]]=>1
[6,5,2,1,1,3]=>[[],[[[],[[]]]]]=>2
[6,5,2,1,3,1]=>[[[],[[[[]]]]]]=>1
[6,5,2,3,1,1]=>[[[[[]]]],[[]]]=>2
[6,5,3,1,1,2]=>[[[[]]],[[],[]]]=>2
[6,5,3,1,2,1]=>[[[[]],[[],[]]]]=>1
[6,5,3,2,1,1]=>[[[]],[[],[],[]]]=>2
[1,1,2,4,4,4]=>[[],[],[],[[[]]]]=>4
[1,1,4,2,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,4,4,2,4]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,4,2]=>[[],[],[[]],[[]]]=>4
[1,2,1,4,4,4]=>[[],[[]],[[[]]]]=>3
[1,2,4,1,4,4]=>[[],[[[[[]]]]]]=>2
[1,2,4,4,1,4]=>[[[[]]],[[[]]]]=>2
[1,2,4,4,4,1]=>[[],[[[]]],[[]]]=>3
[1,4,1,2,4,4]=>[[],[[[[[]]]]]]=>2
[1,4,1,4,2,4]=>[[[[]],[[[]]]]]=>1
[1,4,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[1,4,2,1,4,4]=>[[[]],[[],[[]]]]=>2
[1,4,2,4,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,2,4,4,1]=>[[[[[]]]],[[]]]=>2
[1,4,4,1,2,4]=>[[[]],[[[[]]]]]=>2
[1,4,4,1,4,2]=>[[],[[[],[[]]]]]=>2
[1,4,4,2,1,4]=>[[],[[[],[[]]]]]=>2
[1,4,4,2,4,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,4,1,2]=>[[],[[]],[[[]]]]=>3
[1,4,4,4,2,1]=>[[],[[]],[[[]]]]=>3
[2,1,1,4,4,4]=>[[],[],[[]],[[]]]=>4
[2,1,4,1,4,4]=>[[[]],[[],[[]]]]=>2
[2,1,4,4,1,4]=>[[],[[[],[[]]]]]=>2
[2,1,4,4,4,1]=>[[],[[]],[[[]]]]=>3
[2,4,1,1,4,4]=>[[],[[]],[[[]]]]=>3
[2,4,1,4,1,4]=>[[[[],[[],[]]]]]=>1
[2,4,1,4,4,1]=>[[[]],[[],[[]]]]=>2
[2,4,4,1,1,4]=>[[[]],[[]],[[]]]=>3
[2,4,4,1,4,1]=>[[[]],[[],[[]]]]=>2
[2,4,4,4,1,1]=>[[],[],[[]],[[]]]=>4
[4,1,1,2,4,4]=>[[],[[[]]],[[]]]=>3
[4,1,1,4,2,4]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,4,2]=>[[],[[[]]],[[]]]=>3
[4,1,2,1,4,4]=>[[[]],[[[[]]]]]=>2
[4,1,2,4,1,4]=>[[[[[]]],[[]]]]=>1
[4,1,2,4,4,1]=>[[[[]]],[[],[]]]=>2
[4,1,4,1,2,4]=>[[[[[]]],[[]]]]=>1
[4,1,4,1,4,2]=>[[[],[[],[[]]]]]=>1
[4,1,4,2,1,4]=>[[[[[],[[]]]]]]=>1
[4,1,4,2,4,1]=>[[[],[[[[]]]]]]=>1
[4,1,4,4,1,2]=>[[[]],[[],[[]]]]=>2
[4,1,4,4,2,1]=>[[[]],[[[[]]]]]=>2
[4,2,1,1,4,4]=>[[],[[[]]],[[]]]=>3
[4,2,1,4,1,4]=>[[[[[],[[]]]]]]=>1
[4,2,1,4,4,1]=>[[[[]]],[[[]]]]=>2
[4,2,4,1,1,4]=>[[[]],[[[[]]]]]=>2
[4,2,4,1,4,1]=>[[[[[],[[]]]]]]=>1
[4,2,4,4,1,1]=>[[],[[]],[[[]]]]=>3
[4,4,1,1,2,4]=>[[],[[[]]],[[]]]=>3
[4,4,1,1,4,2]=>[[],[[[]]],[[]]]=>3
[4,4,1,2,1,4]=>[[],[[[[[]]]]]]=>2
[4,4,1,2,4,1]=>[[],[[],[[[]]]]]=>2
[4,4,1,4,1,2]=>[[],[[[]],[[]]]]=>2
[4,4,1,4,2,1]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,1,4]=>[[],[[[]]],[[]]]=>3
[4,4,2,1,4,1]=>[[],[[[[[]]]]]]=>2
[4,4,2,4,1,1]=>[[],[],[[[[]]]]]=>3
[4,4,4,1,1,2]=>[[],[],[[]],[[]]]=>4
[4,4,4,1,2,1]=>[[],[],[[[[]]]]]=>3
[4,4,4,2,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,2,4,4,5]=>[[],[[]],[[],[]]]=>3
[1,1,2,4,5,4]=>[[],[[[]],[[]]]]=>2
[1,1,2,5,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,4,2,4,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,2,5,4]=>[[],[[],[[[]]]]]=>2
[1,1,4,4,2,5]=>[[],[],[[[],[]]]]=>3
[1,1,4,4,5,2]=>[[],[[[]]],[[]]]=>3
[1,1,4,5,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,4,5,4,2]=>[[],[[[[[]]]]]]=>2
[1,1,5,2,4,4]=>[[],[],[[[],[]]]]=>3
[1,1,5,4,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,4,4,2]=>[[],[[]],[[[]]]]=>3
[1,2,1,4,4,5]=>[[[]],[[],[[]]]]=>2
[1,2,1,4,5,4]=>[[[[]],[[],[]]]]=>1
[1,2,1,5,4,4]=>[[],[[[]],[[]]]]=>2
[1,2,4,1,4,5]=>[[[],[[[[]]]]]]=>1
[1,2,4,1,5,4]=>[[[[[],[[]]]]]]=>1
[1,2,4,4,1,5]=>[[[[]]],[[],[]]]=>2
[1,2,4,4,5,1]=>[[[]],[[],[[]]]]=>2
[1,2,4,5,1,4]=>[[[[]],[[],[]]]]=>1
[1,2,4,5,4,1]=>[[[[]],[[[]]]]]=>1
[1,2,5,1,4,4]=>[[],[[],[],[[]]]]=>2
[1,2,5,4,1,4]=>[[[[[]],[[]]]]]=>1
[1,2,5,4,4,1]=>[[],[[[[[]]]]]]=>2
[1,4,1,2,4,5]=>[[[[[],[[]]]]]]=>1
[1,4,1,2,5,4]=>[[[[[]]],[[]]]]=>1
[1,4,1,4,2,5]=>[[[],[],[[[]]]]]=>1
[1,4,1,4,5,2]=>[[[],[[[],[]]]]]=>1
[1,4,1,5,2,4]=>[[[[],[],[[]]]]]=>1
[1,4,1,5,4,2]=>[[[[[[],[]]]]]]=>1
[1,4,2,1,4,5]=>[[[[[]]],[[]]]]=>1
[1,4,2,1,5,4]=>[[[[[],[[]]]]]]=>1
[1,4,2,4,1,5]=>[[[[[],[[]]]]]]=>1
[1,4,2,4,5,1]=>[[[],[[[[]]]]]]=>1
[1,4,2,5,1,4]=>[[[],[],[],[[]]]]=>1
[1,4,2,5,4,1]=>[[[],[[[[]]]]]]=>1
[1,4,4,1,2,5]=>[[],[[[[],[]]]]]=>2
[1,4,4,1,5,2]=>[[],[[],[],[[]]]]=>2
[1,4,4,2,1,5]=>[[],[[[[[]]]]]]=>2
[1,4,4,2,5,1]=>[[],[[[],[],[]]]]=>2
[1,4,4,5,1,2]=>[[],[[],[[],[]]]]=>2
[1,4,4,5,2,1]=>[[[[[]]]],[[]]]=>2
[1,4,5,1,2,4]=>[[[],[[],[[]]]]]=>1
[1,4,5,1,4,2]=>[[[],[[]],[[]]]]=>1
[1,4,5,2,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,5,2,4,1]=>[[[[[],[[]]]]]]=>1
[1,4,5,4,1,2]=>[[[[[],[[]]]]]]=>1
[1,4,5,4,2,1]=>[[[[[],[[]]]]]]=>1
[1,5,1,2,4,4]=>[[],[[[[[]]]]]]=>2
[1,5,1,4,2,4]=>[[[[],[[[]]]]]]=>1
[1,5,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[1,5,2,1,4,4]=>[[[]],[[[],[]]]]=>2
[1,5,2,4,1,4]=>[[[],[[]],[[]]]]=>1
[1,5,2,4,4,1]=>[[[]],[[],[],[]]]=>2
[1,5,4,1,2,4]=>[[[],[[[[]]]]]]=>1
[1,5,4,1,4,2]=>[[[],[[[[]]]]]]=>1
[1,5,4,2,1,4]=>[[[[],[[[]]]]]]=>1
[1,5,4,2,4,1]=>[[[[[]]],[[]]]]=>1
[1,5,4,4,1,2]=>[[],[[],[[[]]]]]=>2
[1,5,4,4,2,1]=>[[],[[[],[[]]]]]=>2
[2,1,1,4,4,5]=>[[],[[[]]],[[]]]=>3
[2,1,1,4,5,4]=>[[],[[[[],[]]]]]=>2
[2,1,1,5,4,4]=>[[],[],[[],[[]]]]=>3
[2,1,4,1,4,5]=>[[[[[],[[]]]]]]=>1
[2,1,4,1,5,4]=>[[[],[[],[[]]]]]=>1
[2,1,4,4,1,5]=>[[[]],[[],[[]]]]=>2
[2,1,4,4,5,1]=>[[],[[[],[[]]]]]=>2
[2,1,4,5,1,4]=>[[[[],[],[[]]]]]=>1
[2,1,4,5,4,1]=>[[[[[]]],[[]]]]=>1
[2,1,5,1,4,4]=>[[[]],[[],[[]]]]=>2
[2,1,5,4,1,4]=>[[[],[[[],[]]]]]=>1
[2,1,5,4,4,1]=>[[],[[],[[],[]]]]=>2
[2,4,1,1,4,5]=>[[[[]]],[[[]]]]=>2
[2,4,1,1,5,4]=>[[],[[[]],[[]]]]=>2
[2,4,1,4,1,5]=>[[[[[],[],[]]]]]=>1
[2,4,1,4,5,1]=>[[[[[],[[]]]]]]=>1
[2,4,1,5,1,4]=>[[[[],[[],[]]]]]=>1
[2,4,1,5,4,1]=>[[[[],[],[[]]]]]=>1
[2,4,4,1,1,5]=>[[],[[]],[[],[]]]=>3
[2,4,4,1,5,1]=>[[[]],[[],[[]]]]=>2
[2,4,4,5,1,1]=>[[],[[]],[[[]]]]=>3
[2,4,5,1,1,4]=>[[],[[],[[[]]]]]=>2
[2,4,5,1,4,1]=>[[[[[],[[]]]]]]=>1
[2,4,5,4,1,1]=>[[[]],[[[[]]]]]=>2
[2,5,1,1,4,4]=>[[],[],[[],[],[]]]=>3
[2,5,1,4,1,4]=>[[[],[],[],[[]]]]=>1
[2,5,1,4,4,1]=>[[[]],[[],[],[]]]=>2
[2,5,4,1,1,4]=>[[[]],[[],[[]]]]=>2
[2,5,4,1,4,1]=>[[[],[[],[[]]]]]=>1
[2,5,4,4,1,1]=>[[[]],[[]],[[]]]=>3
[4,1,1,2,4,5]=>[[[]],[[],[[]]]]=>2
[4,1,1,2,5,4]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,2,5]=>[[],[[],[[[]]]]]=>2
[4,1,1,4,5,2]=>[[],[[[[],[]]]]]=>2
[4,1,1,5,2,4]=>[[],[[],[],[[]]]]=>2
[4,1,1,5,4,2]=>[[],[[],[[[]]]]]=>2
[4,1,2,1,4,5]=>[[[[[],[[]]]]]]=>1
[4,1,2,1,5,4]=>[[[],[[],[[]]]]]=>1
[4,1,2,4,1,5]=>[[[],[],[[[]]]]]=>1
[4,1,2,4,5,1]=>[[[[[]],[[]]]]]=>1
[4,1,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[4,1,2,5,4,1]=>[[[],[[[[]]]]]]=>1
[4,1,4,1,2,5]=>[[[],[[[],[]]]]]=>1
[4,1,4,1,5,2]=>[[[],[],[],[[]]]]=>1
[4,1,4,2,1,5]=>[[[[]],[[[]]]]]=>1
[4,1,4,2,5,1]=>[[[[],[],[[]]]]]=>1
[4,1,4,5,1,2]=>[[[[],[[],[]]]]]=>1
[4,1,4,5,2,1]=>[[[[[]]],[[]]]]=>1
[4,1,5,1,2,4]=>[[[],[[[[]]]]]]=>1
[4,1,5,1,4,2]=>[[[],[[],[[]]]]]=>1
[4,1,5,2,1,4]=>[[[],[],[[[]]]]]=>1
[4,1,5,2,4,1]=>[[[],[],[],[[]]]]=>1
[4,1,5,4,1,2]=>[[[],[],[[[]]]]]=>1
[4,1,5,4,2,1]=>[[[],[[],[[]]]]]=>1
[4,2,1,1,4,5]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,5,4]=>[[],[[[],[[]]]]]=>2
[4,2,1,4,1,5]=>[[[[[]],[[]]]]]=>1
[4,2,1,4,5,1]=>[[[[[],[[]]]]]]=>1
[4,2,1,5,1,4]=>[[[[[]],[[]]]]]=>1
[4,2,1,5,4,1]=>[[[[],[[],[]]]]]=>1
[4,2,4,1,1,5]=>[[[]],[[],[[]]]]=>2
[4,2,4,1,5,1]=>[[[[[]],[[]]]]]=>1
[4,2,4,5,1,1]=>[[],[[[[[]]]]]]=>2
[4,2,5,1,1,4]=>[[[]],[[],[],[]]]=>2
[4,2,5,1,4,1]=>[[[[],[],[[]]]]]=>1
[4,2,5,4,1,1]=>[[[[]]],[[[]]]]=>2
[4,4,1,1,2,5]=>[[],[[[]]],[[]]]=>3
[4,4,1,1,5,2]=>[[],[],[[],[],[]]]=>3
[4,4,1,2,1,5]=>[[],[[],[[[]]]]]=>2
[4,4,1,2,5,1]=>[[],[[[[],[]]]]]=>2
[4,4,1,5,1,2]=>[[],[[],[[[]]]]]=>2
[4,4,1,5,2,1]=>[[],[[],[],[[]]]]=>2
[4,4,2,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,4,2,1,5,1]=>[[],[[[[[]]]]]]=>2
[4,4,2,5,1,1]=>[[],[],[[],[[]]]]=>3
[4,4,5,1,1,2]=>[[],[[]],[[],[]]]=>3
[4,4,5,1,2,1]=>[[],[[[]],[[]]]]=>2
[4,4,5,2,1,1]=>[[],[],[[[[]]]]]=>3
[4,5,1,1,2,4]=>[[[]],[[],[[]]]]=>2
[4,5,1,1,4,2]=>[[],[[[]],[[]]]]=>2
[4,5,1,2,1,4]=>[[[],[[[],[]]]]]=>1
[4,5,1,2,4,1]=>[[[[[]]],[[]]]]=>1
[4,5,1,4,1,2]=>[[[],[[[],[]]]]]=>1
[4,5,1,4,2,1]=>[[[[],[[[]]]]]]=>1
[4,5,2,1,1,4]=>[[],[[[[[]]]]]]=>2
[4,5,2,1,4,1]=>[[[[[]],[[]]]]]=>1
[4,5,2,4,1,1]=>[[],[[[]],[[]]]]=>2
[4,5,4,1,1,2]=>[[[]],[[],[[]]]]=>2
[4,5,4,1,2,1]=>[[[[]],[[],[]]]]=>1
[4,5,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[5,1,1,2,4,4]=>[[],[[[]]],[[]]]=>3
[5,1,1,4,2,4]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,4,2]=>[[],[[]],[[],[]]]=>3
[5,1,2,1,4,4]=>[[[[]]],[[],[]]]=>2
[5,1,2,4,1,4]=>[[[],[[[[]]]]]]=>1
[5,1,2,4,4,1]=>[[[[[]]]],[[]]]=>2
[5,1,4,1,2,4]=>[[[],[[[[]]]]]]=>1
[5,1,4,1,4,2]=>[[[],[[]],[[]]]]=>1
[5,1,4,2,1,4]=>[[[],[[]],[[]]]]=>1
[5,1,4,2,4,1]=>[[[],[[[[]]]]]]=>1
[5,1,4,4,1,2]=>[[[[]]],[[],[]]]=>2
[5,1,4,4,2,1]=>[[[[]]],[[],[]]]=>2
[5,2,1,1,4,4]=>[[[]],[[]],[[]]]=>3
[5,2,1,4,1,4]=>[[[],[[],[[]]]]]=>1
[5,2,1,4,4,1]=>[[[]],[[],[[]]]]=>2
[5,2,4,1,1,4]=>[[[]],[[],[[]]]]=>2
[5,2,4,1,4,1]=>[[[],[[]],[[]]]]=>1
[5,2,4,4,1,1]=>[[],[[]],[[],[]]]=>3
[5,4,1,1,2,4]=>[[[[[]]]],[[]]]=>2
[5,4,1,1,4,2]=>[[[[[]]]],[[]]]=>2
[5,4,1,2,1,4]=>[[[[[]]],[[]]]]=>1
[5,4,1,2,4,1]=>[[[[],[[[]]]]]]=>1
[5,4,1,4,1,2]=>[[[[[],[[]]]]]]=>1
[5,4,1,4,2,1]=>[[[[]],[[[]]]]]=>1
[5,4,2,1,1,4]=>[[[[],[]]],[[]]]=>2
[5,4,2,1,4,1]=>[[[],[[[[]]]]]]=>1
[5,4,2,4,1,1]=>[[[[[]]]],[[]]]=>2
[5,4,4,1,1,2]=>[[],[[[]]],[[]]]=>3
[5,4,4,1,2,1]=>[[],[[[[],[]]]]]=>2
[5,4,4,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,4,4,6]=>[[],[],[[],[[]]]]=>3
[1,1,2,4,6,4]=>[[],[[[],[[]]]]]=>2
[1,1,2,6,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,4,2,4,6]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,6,4]=>[[],[[[[],[]]]]]=>2
[1,1,4,4,2,6]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,6,2]=>[[],[],[[[],[]]]]=>3
[1,1,4,6,2,4]=>[[],[[],[[],[]]]]=>2
[1,1,4,6,4,2]=>[[],[[[[],[]]]]]=>2
[1,1,6,2,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,6,4,2,4]=>[[],[[],[],[[]]]]=>2
[1,1,6,4,4,2]=>[[],[],[[],[],[]]]=>3
[1,2,1,4,4,6]=>[[[[[]]]],[[]]]=>2
[1,2,1,4,6,4]=>[[[[[[[]]]]]]]=>1
[1,2,1,6,4,4]=>[[[[]]],[[],[]]]=>2
[1,2,4,1,4,6]=>[[[[],[[[]]]]]]=>1
[1,2,4,1,6,4]=>[[[[[[],[]]]]]]=>1
[1,2,4,4,1,6]=>[[[[]]],[[[]]]]=>2
[1,2,4,4,6,1]=>[[],[[],[],[[]]]]=>2
[1,2,4,6,1,4]=>[[[[],[],[[]]]]]=>1
[1,2,4,6,4,1]=>[[[[],[[[]]]]]]=>1
[1,2,6,1,4,4]=>[[],[[[[[]]]]]]=>2
[1,2,6,4,1,4]=>[[[[[]],[[]]]]]=>1
[1,2,6,4,4,1]=>[[[]],[[],[[]]]]=>2
[1,4,1,2,4,6]=>[[[[[[],[]]]]]]=>1
[1,4,1,2,6,4]=>[[[[[],[[]]]]]]=>1
[1,4,1,4,2,6]=>[[[],[[[],[]]]]]=>1
[1,4,1,4,6,2]=>[[[],[[]],[[]]]]=>1
[1,4,1,6,2,4]=>[[[[]],[[[]]]]]=>1
[1,4,1,6,4,2]=>[[[[],[],[[]]]]]=>1
[1,4,2,1,4,6]=>[[[[[]]],[[]]]]=>1
[1,4,2,1,6,4]=>[[[[],[],[[]]]]]=>1
[1,4,2,4,1,6]=>[[[[[[],[]]]]]]=>1
[1,4,2,4,6,1]=>[[[[],[],[[]]]]]=>1
[1,4,2,6,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,2,6,4,1]=>[[[[],[[],[]]]]]=>1
[1,4,4,1,2,6]=>[[[]],[[],[[]]]]=>2
[1,4,4,1,6,2]=>[[],[[[[],[]]]]]=>2
[1,4,4,2,1,6]=>[[],[[],[[[]]]]]=>2
[1,4,4,2,6,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,6,1,2]=>[[[]],[[],[[]]]]=>2
[1,4,4,6,2,1]=>[[],[[[],[[]]]]]=>2
[1,4,6,1,2,4]=>[[[[],[],[[]]]]]=>1
[1,4,6,1,4,2]=>[[[[]],[[],[]]]]=>1
[1,4,6,2,1,4]=>[[[],[[]],[[]]]]=>1
[1,4,6,2,4,1]=>[[[],[[],[[]]]]]=>1
[1,4,6,4,1,2]=>[[[[[[[]]]]]]]=>1
[1,4,6,4,2,1]=>[[[[[]],[[]]]]]=>1
[1,6,1,2,4,4]=>[[],[[],[[[]]]]]=>2
[1,6,1,4,2,4]=>[[[[]],[[],[]]]]=>1
[1,6,1,4,4,2]=>[[[[]]],[[],[]]]=>2
[1,6,2,1,4,4]=>[[[]],[[],[[]]]]=>2
[1,6,2,4,1,4]=>[[[[[[],[]]]]]]=>1
[1,6,2,4,4,1]=>[[[[[]]]],[[]]]=>2
[1,6,4,1,2,4]=>[[[],[[[[]]]]]]=>1
[1,6,4,1,4,2]=>[[[],[],[[[]]]]]=>1
[1,6,4,2,1,4]=>[[[],[],[[[]]]]]=>1
[1,6,4,2,4,1]=>[[[],[],[[[]]]]]=>1
[1,6,4,4,1,2]=>[[[[]]],[[],[]]]=>2
[1,6,4,4,2,1]=>[[],[[],[],[[]]]]=>2
[2,1,1,4,4,6]=>[[],[[[]]],[[]]]=>3
[2,1,1,4,6,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,4,4]=>[[],[[]],[[],[]]]=>3
[2,1,4,1,4,6]=>[[[[[],[[]]]]]]=>1
[2,1,4,1,6,4]=>[[[[[]],[[]]]]]=>1
[2,1,4,4,1,6]=>[[[]],[[[[]]]]]=>2
[2,1,4,4,6,1]=>[[[]],[[],[[]]]]=>2
[2,1,4,6,1,4]=>[[[[],[[],[]]]]]=>1
[2,1,4,6,4,1]=>[[[[[[[]]]]]]]=>1
[2,1,6,1,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,6,4,1,4]=>[[[[[[],[]]]]]]=>1
[2,1,6,4,4,1]=>[[[[]]],[[],[]]]=>2
[2,4,1,1,4,6]=>[[[[],[]]],[[]]]=>2
[2,4,1,1,6,4]=>[[],[[],[[[]]]]]=>2
[2,4,1,4,1,6]=>[[[[[],[[]]]]]]=>1
[2,4,1,4,6,1]=>[[[],[],[[[]]]]]=>1
[2,4,1,6,1,4]=>[[[[]],[[[]]]]]=>1
[2,4,1,6,4,1]=>[[[[],[[],[]]]]]=>1
[2,4,4,1,1,6]=>[[[]],[[]],[[]]]=>3
[2,4,4,1,6,1]=>[[],[[[[],[]]]]]=>2
[2,4,4,6,1,1]=>[[],[],[[],[],[]]]=>3
[2,4,6,1,1,4]=>[[[]],[[],[],[]]]=>2
[2,4,6,1,4,1]=>[[[],[],[[[]]]]]=>1
[2,4,6,4,1,1]=>[[],[[[[],[]]]]]=>2
[2,6,1,1,4,4]=>[[],[[[]]],[[]]]=>3
[2,6,1,4,1,4]=>[[[],[[],[[]]]]]=>1
[2,6,1,4,4,1]=>[[[[]]],[[],[]]]=>2
[2,6,4,1,1,4]=>[[[]],[[],[[]]]]=>2
[2,6,4,1,4,1]=>[[[],[],[[[]]]]]=>1
[2,6,4,4,1,1]=>[[],[],[[],[[]]]]=>3
[4,1,1,2,4,6]=>[[[[],[]]],[[]]]=>2
[4,1,1,2,6,4]=>[[],[[[],[[]]]]]=>2
[4,1,1,4,2,6]=>[[],[[[[],[]]]]]=>2
[4,1,1,4,6,2]=>[[[]],[[],[[]]]]=>2
[4,1,1,6,2,4]=>[[[]],[[[[]]]]]=>2
[4,1,1,6,4,2]=>[[],[[],[],[[]]]]=>2
[4,1,2,1,4,6]=>[[[[[[[]]]]]]]=>1
[4,1,2,1,6,4]=>[[[[],[[[]]]]]]=>1
[4,1,2,4,1,6]=>[[[[[]]],[[]]]]=>1
[4,1,2,4,6,1]=>[[[[],[],[[]]]]]=>1
[4,1,2,6,1,4]=>[[[[]],[[[]]]]]=>1
[4,1,2,6,4,1]=>[[[],[[]],[[]]]]=>1
[4,1,4,1,2,6]=>[[[],[[]],[[]]]]=>1
[4,1,4,1,6,2]=>[[[],[[[],[]]]]]=>1
[4,1,4,2,1,6]=>[[[[],[[[]]]]]]=>1
[4,1,4,2,6,1]=>[[[[]],[[[]]]]]=>1
[4,1,4,6,1,2]=>[[[[[],[[]]]]]]=>1
[4,1,4,6,2,1]=>[[[[[],[[]]]]]]=>1
[4,1,6,1,2,4]=>[[[[],[[[]]]]]]=>1
[4,1,6,1,4,2]=>[[[[[[],[]]]]]]=>1
[4,1,6,2,1,4]=>[[[[[],[[]]]]]]=>1
[4,1,6,2,4,1]=>[[[],[[[[]]]]]]=>1
[4,1,6,4,1,2]=>[[[[]],[[],[]]]]=>1
[4,1,6,4,2,1]=>[[[[[],[],[]]]]]=>1
[4,2,1,1,4,6]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,6,4]=>[[],[[],[],[[]]]]=>2
[4,2,1,4,1,6]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,6,1]=>[[[[[]],[[]]]]]=>1
[4,2,1,6,1,4]=>[[[],[[[[]]]]]]=>1
[4,2,1,6,4,1]=>[[[],[],[[[]]]]]=>1
[4,2,4,1,1,6]=>[[[[]]],[[],[]]]=>2
[4,2,4,1,6,1]=>[[[[]],[[],[]]]]=>1
[4,2,4,6,1,1]=>[[],[[],[],[[]]]]=>2
[4,2,6,1,1,4]=>[[[[[]]]],[[]]]=>2
[4,2,6,1,4,1]=>[[[[[[],[]]]]]]=>1
[4,2,6,4,1,1]=>[[],[[],[[],[]]]]=>2
[4,4,1,1,2,6]=>[[],[],[[[],[]]]]=>3
[4,4,1,1,6,2]=>[[],[[]],[[[]]]]=>3
[4,4,1,2,1,6]=>[[],[[[[[]]]]]]=>2
[4,4,1,2,6,1]=>[[],[[[]],[[]]]]=>2
[4,4,1,6,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,1,6,2,1]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,1,6]=>[[],[],[[],[[]]]]=>3
[4,4,2,1,6,1]=>[[],[[],[[[]]]]]=>2
[4,4,2,6,1,1]=>[[],[],[[[[]]]]]=>3
[4,4,6,1,1,2]=>[[],[[]],[[],[]]]=>3
[4,4,6,1,2,1]=>[[],[[],[[[]]]]]=>2
[4,4,6,2,1,1]=>[[],[],[[[[]]]]]=>3
[4,6,1,1,2,4]=>[[],[[[],[],[]]]]=>2
[4,6,1,1,4,2]=>[[[[]]],[[],[]]]=>2
[4,6,1,2,1,4]=>[[[],[[[[]]]]]]=>1
[4,6,1,2,4,1]=>[[[],[[]],[[]]]]=>1
[4,6,1,4,1,2]=>[[[],[[[[]]]]]]=>1
[4,6,1,4,2,1]=>[[[],[[[[]]]]]]=>1
[4,6,2,1,1,4]=>[[],[[[]],[[]]]]=>2
[4,6,2,1,4,1]=>[[[[[[],[]]]]]]=>1
[4,6,2,4,1,1]=>[[],[[[],[[]]]]]=>2
[4,6,4,1,1,2]=>[[[]],[[[[]]]]]=>2
[4,6,4,1,2,1]=>[[[[[[[]]]]]]]=>1
[4,6,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[6,1,1,2,4,4]=>[[],[],[[],[[]]]]=>3
[6,1,1,4,2,4]=>[[],[[[[],[]]]]]=>2
[6,1,1,4,4,2]=>[[[]],[[]],[[]]]=>3
[6,1,2,1,4,4]=>[[[]],[[[[]]]]]=>2
[6,1,2,4,1,4]=>[[[[]],[[[]]]]]=>1
[6,1,2,4,4,1]=>[[[]],[[],[[]]]]=>2
[6,1,4,1,2,4]=>[[[],[[[[]]]]]]=>1
[6,1,4,1,4,2]=>[[[[[],[[]]]]]]=>1
[6,1,4,2,1,4]=>[[[[[],[[]]]]]]=>1
[6,1,4,2,4,1]=>[[[[]],[[[]]]]]=>1
[6,1,4,4,1,2]=>[[[[]]],[[[]]]]=>2
[6,1,4,4,2,1]=>[[[[]]],[[[]]]]=>2
[6,2,1,1,4,4]=>[[],[[]],[[],[]]]=>3
[6,2,1,4,1,4]=>[[[],[[]],[[]]]]=>1
[6,2,1,4,4,1]=>[[[[]]],[[],[]]]=>2
[6,2,4,1,1,4]=>[[[[]]],[[],[]]]=>2
[6,2,4,1,4,1]=>[[[],[[],[[]]]]]=>1
[6,2,4,4,1,1]=>[[],[[[]]],[[]]]=>3
[6,4,1,1,2,4]=>[[[[]]],[[[]]]]=>2
[6,4,1,1,4,2]=>[[[[],[]]],[[]]]=>2
[6,4,1,2,1,4]=>[[[[[[[]]]]]]]=>1
[6,4,1,2,4,1]=>[[[[[[],[]]]]]]=>1
[6,4,1,4,1,2]=>[[[[[],[[]]]]]]=>1
[6,4,1,4,2,1]=>[[[[]],[[[]]]]]=>1
[6,4,2,1,1,4]=>[[[[]]],[[],[]]]=>2
[6,4,2,1,4,1]=>[[[],[[[[]]]]]]=>1
[6,4,2,4,1,1]=>[[],[[[[],[]]]]]=>2
[6,4,4,1,1,2]=>[[],[[]],[[[]]]]=>3
[6,4,4,1,2,1]=>[[],[[[[[]]]]]]=>2
[6,4,4,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,4,5,5]=>[[],[],[[],[[]]]]=>3
[1,1,2,5,4,5]=>[[],[[],[[[]]]]]=>2
[1,1,2,5,5,4]=>[[],[[[]]],[[]]]=>3
[1,1,4,2,5,5]=>[[],[],[[],[[]]]]=>3
[1,1,4,5,2,5]=>[[],[[],[[[]]]]]=>2
[1,1,4,5,5,2]=>[[],[[[]]],[[]]]=>3
[1,1,5,2,4,5]=>[[],[[],[[[]]]]]=>2
[1,1,5,2,5,4]=>[[],[[],[[[]]]]]=>2
[1,1,5,4,2,5]=>[[],[[[[[]]]]]]=>2
[1,1,5,4,5,2]=>[[],[[[]],[[]]]]=>2
[1,1,5,5,2,4]=>[[],[],[[],[[]]]]=>3
[1,1,5,5,4,2]=>[[],[],[[[[]]]]]=>3
[1,2,1,4,5,5]=>[[[]],[[],[[]]]]=>2
[1,2,1,5,4,5]=>[[[],[[],[[]]]]]=>1
[1,2,1,5,5,4]=>[[[]],[[],[[]]]]=>2
[1,2,4,1,5,5]=>[[],[[],[[[]]]]]=>2
[1,2,4,5,1,5]=>[[[[]],[[[]]]]]=>1
[1,2,4,5,5,1]=>[[[]],[[],[[]]]]=>2
[1,2,5,1,4,5]=>[[[],[[],[],[]]]]=>1
[1,2,5,1,5,4]=>[[[[],[[[]]]]]]=>1
[1,2,5,4,1,5]=>[[[[[],[[]]]]]]=>1
[1,2,5,4,5,1]=>[[[],[[],[[]]]]]=>1
[1,2,5,5,1,4]=>[[],[[],[],[[]]]]=>2
[1,2,5,5,4,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,2,5,5]=>[[],[[],[[[]]]]]=>2
[1,4,1,5,2,5]=>[[[],[[],[],[]]]]=>1
[1,4,1,5,5,2]=>[[],[[],[],[[]]]]=>2
[1,4,2,1,5,5]=>[[[[]]],[[[]]]]=>2
[1,4,2,5,1,5]=>[[[],[[]],[[]]]]=>1
[1,4,2,5,5,1]=>[[[]],[[],[],[]]]=>2
[1,4,5,1,2,5]=>[[[],[],[[],[]]]]=>1
[1,4,5,1,5,2]=>[[[[]],[[],[]]]]=>1
[1,4,5,2,1,5]=>[[[[[],[[]]]]]]=>1
[1,4,5,2,5,1]=>[[[],[],[[[]]]]]=>1
[1,4,5,5,1,2]=>[[],[[],[[],[]]]]=>2
[1,4,5,5,2,1]=>[[[[]]],[[[]]]]=>2
[1,5,1,2,4,5]=>[[[[[],[[]]]]]]=>1
[1,5,1,2,5,4]=>[[[[[],[[]]]]]]=>1
[1,5,1,4,2,5]=>[[[[[],[],[]]]]]=>1
[1,5,1,4,5,2]=>[[[],[[[],[]]]]]=>1
[1,5,1,5,2,4]=>[[[],[[]],[[]]]]=>1
[1,5,1,5,4,2]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,4,5]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,5,4]=>[[[],[],[[],[]]]]=>1
[1,5,2,4,1,5]=>[[[],[],[],[[]]]]=>1
[1,5,2,4,5,1]=>[[[],[[[[]]]]]]=>1
[1,5,2,5,1,4]=>[[[],[[],[],[]]]]=>1
[1,5,2,5,4,1]=>[[[],[],[[[]]]]]=>1
[1,5,4,1,2,5]=>[[[],[[[[]]]]]]=>1
[1,5,4,1,5,2]=>[[[],[],[],[[]]]]=>1
[1,5,4,2,1,5]=>[[[[]],[[],[]]]]=>1
[1,5,4,2,5,1]=>[[[[[]],[[]]]]]=>1
[1,5,4,5,1,2]=>[[[[[]],[[]]]]]=>1
[1,5,4,5,2,1]=>[[[[]],[[],[]]]]=>1
[1,5,5,1,2,4]=>[[[[[]]]],[[]]]=>2
[1,5,5,1,4,2]=>[[],[[[]],[[]]]]=>2
[1,5,5,2,1,4]=>[[],[[],[[[]]]]]=>2
[1,5,5,2,4,1]=>[[],[[],[],[[]]]]=>2
[1,5,5,4,1,2]=>[[],[[[[],[]]]]]=>2
[1,5,5,4,2,1]=>[[],[[[]],[[]]]]=>2
[2,1,1,4,5,5]=>[[],[[[]]],[[]]]=>3
[2,1,1,5,4,5]=>[[],[[[],[[]]]]]=>2
[2,1,1,5,5,4]=>[[],[[]],[[],[]]]=>3
[2,1,4,1,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,4,5,1,5]=>[[[[[],[[]]]]]]=>1
[2,1,4,5,5,1]=>[[[]],[[],[[]]]]=>2
[2,1,5,1,4,5]=>[[[[[],[[]]]]]]=>1
[2,1,5,1,5,4]=>[[[],[[],[[]]]]]=>1
[2,1,5,4,1,5]=>[[[],[[],[],[]]]]=>1
[2,1,5,4,5,1]=>[[[[[]]],[[]]]]=>1
[2,1,5,5,1,4]=>[[[]],[[],[[]]]]=>2
[2,1,5,5,4,1]=>[[],[[],[[],[]]]]=>2
[2,4,1,1,5,5]=>[[],[],[[],[[]]]]=>3
[2,4,1,5,1,5]=>[[[[],[],[[]]]]]=>1
[2,4,1,5,5,1]=>[[[]],[[],[[]]]]=>2
[2,4,5,1,1,5]=>[[[[[]]]],[[]]]=>2
[2,4,5,1,5,1]=>[[[[[],[[]]]]]]=>1
[2,4,5,5,1,1]=>[[],[[[]]],[[]]]=>3
[2,5,1,1,4,5]=>[[],[[],[],[[]]]]=>2
[2,5,1,1,5,4]=>[[[[]]],[[],[]]]=>2
[2,5,1,4,1,5]=>[[[],[],[[],[]]]]=>1
[2,5,1,4,5,1]=>[[[],[],[],[[]]]]=>1
[2,5,1,5,1,4]=>[[[],[],[],[[]]]]=>1
[2,5,1,5,4,1]=>[[[],[[[],[]]]]]=>1
[2,5,4,1,1,5]=>[[],[[[]],[[]]]]=>2
[2,5,4,1,5,1]=>[[[[]],[[],[]]]]=>1
[2,5,4,5,1,1]=>[[[]],[[],[[]]]]=>2
[2,5,5,1,1,4]=>[[],[],[[],[],[]]]=>3
[2,5,5,1,4,1]=>[[],[[],[],[[]]]]=>2
[2,5,5,4,1,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,2,5,5]=>[[],[[[]]],[[]]]=>3
[4,1,1,5,2,5]=>[[],[[],[],[[]]]]=>2
[4,1,1,5,5,2]=>[[],[],[[],[],[]]]=>3
[4,1,2,1,5,5]=>[[[[]]],[[],[]]]=>2
[4,1,2,5,1,5]=>[[[],[[],[[]]]]]=>1
[4,1,2,5,5,1]=>[[],[[],[[[]]]]]=>2
[4,1,5,1,2,5]=>[[[],[[],[[]]]]]=>1
[4,1,5,1,5,2]=>[[[],[],[],[[]]]]=>1
[4,1,5,2,1,5]=>[[[],[],[],[[]]]]=>1
[4,1,5,2,5,1]=>[[[],[],[[],[]]]]=>1
[4,1,5,5,1,2]=>[[[[]]],[[],[]]]=>2
[4,1,5,5,2,1]=>[[],[[],[],[[]]]]=>2
[4,2,1,1,5,5]=>[[],[[[]]],[[]]]=>3
[4,2,1,5,1,5]=>[[[[[],[[]]]]]]=>1
[4,2,1,5,5,1]=>[[[[]]],[[[]]]]=>2
[4,2,5,1,1,5]=>[[[]],[[],[[]]]]=>2
[4,2,5,1,5,1]=>[[[[[],[],[]]]]]=>1
[4,2,5,5,1,1]=>[[],[],[[],[[]]]]=>3
[4,5,1,1,2,5]=>[[],[[],[[],[]]]]=>2
[4,5,1,1,5,2]=>[[[[]]],[[],[]]]=>2
[4,5,1,2,1,5]=>[[[[]],[[[]]]]]=>1
[4,5,1,2,5,1]=>[[[],[[],[],[]]]]=>1
[4,5,1,5,1,2]=>[[[],[[],[[]]]]]=>1
[4,5,1,5,2,1]=>[[[[[],[[]]]]]]=>1
[4,5,2,1,1,5]=>[[],[[[]],[[]]]]=>2
[4,5,2,1,5,1]=>[[[[],[[[]]]]]]=>1
[4,5,2,5,1,1]=>[[],[[],[[[]]]]]=>2
[4,5,5,1,1,2]=>[[],[[]],[[],[]]]=>3
[4,5,5,1,2,1]=>[[],[[[],[[]]]]]=>2
[4,5,5,2,1,1]=>[[],[[]],[[[]]]]=>3
[5,1,1,2,4,5]=>[[[]],[[],[[]]]]=>2
[5,1,1,2,5,4]=>[[],[[[],[[]]]]]=>2
[5,1,1,4,2,5]=>[[],[[],[],[[]]]]=>2
[5,1,1,4,5,2]=>[[],[[],[[[]]]]]=>2
[5,1,1,5,2,4]=>[[[]],[[],[[]]]]=>2
[5,1,1,5,4,2]=>[[],[[[[[]]]]]]=>2
[5,1,2,1,4,5]=>[[[],[[],[[]]]]]=>1
[5,1,2,1,5,4]=>[[[[[],[[]]]]]]=>1
[5,1,2,4,1,5]=>[[[[[[],[]]]]]]=>1
[5,1,2,4,5,1]=>[[[],[[],[[]]]]]=>1
[5,1,2,5,1,4]=>[[[],[],[],[[]]]]=>1
[5,1,2,5,4,1]=>[[[[]],[[[]]]]]=>1
[5,1,4,1,2,5]=>[[[],[],[[[]]]]]=>1
[5,1,4,1,5,2]=>[[[],[[],[],[]]]]=>1
[5,1,4,2,1,5]=>[[[],[[[[]]]]]]=>1
[5,1,4,2,5,1]=>[[[],[],[],[[]]]]=>1
[5,1,4,5,1,2]=>[[[],[],[[],[]]]]=>1
[5,1,4,5,2,1]=>[[[],[[[[]]]]]]=>1
[5,1,5,1,2,4]=>[[[[[]]],[[]]]]=>1
[5,1,5,1,4,2]=>[[[],[[]],[[]]]]=>1
[5,1,5,2,1,4]=>[[[],[[[],[]]]]]=>1
[5,1,5,2,4,1]=>[[[[],[],[[]]]]]=>1
[5,1,5,4,1,2]=>[[[[[[],[]]]]]]=>1
[5,1,5,4,2,1]=>[[[[[],[[]]]]]]=>1
[5,2,1,1,4,5]=>[[],[[[[[]]]]]]=>2
[5,2,1,1,5,4]=>[[],[[],[[],[]]]]=>2
[5,2,1,4,1,5]=>[[[],[[]],[[]]]]=>1
[5,2,1,4,5,1]=>[[[[[]],[[]]]]]=>1
[5,2,1,5,1,4]=>[[[],[[],[[]]]]]=>1
[5,2,1,5,4,1]=>[[[],[],[[],[]]]]=>1
[5,2,4,1,1,5]=>[[],[[],[],[[]]]]=>2
[5,2,4,1,5,1]=>[[[],[[]],[[]]]]=>1
[5,2,4,5,1,1]=>[[],[[[[[]]]]]]=>2
[5,2,5,1,1,4]=>[[],[[],[],[[]]]]=>2
[5,2,5,1,4,1]=>[[[],[[],[],[]]]]=>1
[5,2,5,4,1,1]=>[[[[]]],[[],[]]]=>2
[5,4,1,1,2,5]=>[[[[[]]]],[[]]]=>2
[5,4,1,1,5,2]=>[[],[[],[],[[]]]]=>2
[5,4,1,2,1,5]=>[[[[]],[[],[]]]]=>1
[5,4,1,2,5,1]=>[[[[],[[[]]]]]]=>1
[5,4,1,5,1,2]=>[[[[[[],[]]]]]]=>1
[5,4,1,5,2,1]=>[[[],[[],[],[]]]]=>1
[5,4,2,1,1,5]=>[[[[],[]]],[[]]]=>2
[5,4,2,1,5,1]=>[[[],[[[[]]]]]]=>1
[5,4,2,5,1,1]=>[[[]],[[],[[]]]]=>2
[5,4,5,1,1,2]=>[[[]],[[],[[]]]]=>2
[5,4,5,1,2,1]=>[[[],[[],[[]]]]]=>1
[5,4,5,2,1,1]=>[[],[[],[[[]]]]]=>2
[5,5,1,1,2,4]=>[[],[[[]]],[[]]]=>3
[5,5,1,1,4,2]=>[[],[],[[],[[]]]]=>3
[5,5,1,2,1,4]=>[[],[[],[[[]]]]]=>2
[5,5,1,2,4,1]=>[[],[[[[[]]]]]]=>2
[5,5,1,4,1,2]=>[[],[[],[[[]]]]]=>2
[5,5,1,4,2,1]=>[[],[[],[[[]]]]]=>2
[5,5,2,1,1,4]=>[[],[],[[[[]]]]]=>3
[5,5,2,1,4,1]=>[[],[[[]],[[]]]]=>2
[5,5,2,4,1,1]=>[[],[],[[],[[]]]]=>3
[5,5,4,1,1,2]=>[[],[[[]]],[[]]]=>3
[5,5,4,1,2,1]=>[[],[[],[[[]]]]]=>2
[5,5,4,2,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,2,4,5,6]=>[[],[[],[],[[]]]]=>2
[1,1,2,4,6,5]=>[[],[[[],[[]]]]]=>2
[1,1,2,5,4,6]=>[[],[[[[[]]]]]]=>2
[1,1,2,5,6,4]=>[[],[[[]],[[]]]]=>2
[1,1,2,6,4,5]=>[[],[[],[[[]]]]]=>2
[1,1,2,6,5,4]=>[[],[[[[],[]]]]]=>2
[1,1,4,2,5,6]=>[[],[[[]],[[]]]]=>2
[1,1,4,2,6,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,5,2,6]=>[[],[[[[],[]]]]]=>2
[1,1,4,5,6,2]=>[[],[[],[[],[]]]]=>2
[1,1,4,6,2,5]=>[[],[[],[],[[]]]]=>2
[1,1,4,6,5,2]=>[[],[[[[[]]]]]]=>2
[1,1,5,2,4,6]=>[[],[[],[[],[]]]]=>2
[1,1,5,2,6,4]=>[[],[[],[],[[]]]]=>2
[1,1,5,4,2,6]=>[[],[[[]],[[]]]]=>2
[1,1,5,4,6,2]=>[[],[[[[[]]]]]]=>2
[1,1,5,6,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,6,4,2]=>[[],[[[],[[]]]]]=>2
[1,1,6,2,4,5]=>[[],[[[[[]]]]]]=>2
[1,1,6,2,5,4]=>[[],[[[[],[]]]]]=>2
[1,1,6,4,2,5]=>[[],[[],[],[[]]]]=>2
[1,1,6,4,5,2]=>[[],[[],[[[]]]]]=>2
[1,1,6,5,2,4]=>[[],[[[[[]]]]]]=>2
[1,1,6,5,4,2]=>[[],[[],[[],[]]]]=>2
[1,2,1,4,5,6]=>[[[],[[]],[[]]]]=>1
[1,2,1,4,6,5]=>[[[[],[[[]]]]]]=>1
[1,2,1,5,4,6]=>[[[[[]],[[]]]]]=>1
[1,2,1,5,6,4]=>[[[[]],[[[]]]]]=>1
[1,2,1,6,4,5]=>[[[[]],[[],[]]]]=>1
[1,2,1,6,5,4]=>[[[[],[],[[]]]]]=>1
[1,2,4,1,5,6]=>[[[],[[],[[]]]]]=>1
[1,2,4,1,6,5]=>[[[[[[[]]]]]]]=>1
[1,2,4,5,1,6]=>[[[[]],[[[]]]]]=>1
[1,2,4,5,6,1]=>[[[],[],[[],[]]]]=>1
[1,2,4,6,1,5]=>[[[[],[],[[]]]]]=>1
[1,2,4,6,5,1]=>[[[[],[[[]]]]]]=>1
[1,2,5,1,4,6]=>[[[[],[],[[]]]]]=>1
[1,2,5,1,6,4]=>[[[[],[[],[]]]]]=>1
[1,2,5,4,1,6]=>[[[[[[[]]]]]]]=>1
[1,2,5,4,6,1]=>[[[[[[],[]]]]]]=>1
[1,2,5,6,1,4]=>[[[],[[[],[]]]]]=>1
[1,2,5,6,4,1]=>[[[[]],[[[]]]]]=>1
[1,2,6,1,4,5]=>[[[],[[[[]]]]]]=>1
[1,2,6,1,5,4]=>[[[[[]],[[]]]]]=>1
[1,2,6,4,1,5]=>[[[[],[],[[]]]]]=>1
[1,2,6,4,5,1]=>[[[[]],[[[]]]]]=>1
[1,2,6,5,1,4]=>[[[[[],[[]]]]]]=>1
[1,2,6,5,4,1]=>[[[[],[[],[]]]]]=>1
[1,4,1,2,5,6]=>[[[],[[],[[]]]]]=>1
[1,4,1,2,6,5]=>[[[[[],[[]]]]]]=>1
[1,4,1,5,2,6]=>[[[[],[],[],[]]]]=>1
[1,4,1,5,6,2]=>[[[],[[[],[]]]]]=>1
[1,4,1,6,2,5]=>[[[],[[]],[[]]]]=>1
[1,4,1,6,5,2]=>[[[[[],[[]]]]]]=>1
[1,4,2,1,5,6]=>[[[[[[[]]]]]]]=>1
[1,4,2,1,6,5]=>[[[[],[[],[]]]]]=>1
[1,4,2,5,1,6]=>[[[],[],[[],[]]]]=>1
[1,4,2,5,6,1]=>[[[[[]]],[[]]]]=>1
[1,4,2,6,1,5]=>[[[[],[[[]]]]]]=>1
[1,4,2,6,5,1]=>[[[[]],[[[]]]]]=>1
[1,4,5,1,2,6]=>[[[],[[],[[]]]]]=>1
[1,4,5,1,6,2]=>[[[],[[]],[[]]]]=>1
[1,4,5,2,1,6]=>[[[[[[[]]]]]]]=>1
[1,4,5,2,6,1]=>[[[[[],[[]]]]]]=>1
[1,4,5,6,1,2]=>[[[[],[],[[]]]]]=>1
[1,4,5,6,2,1]=>[[[[]],[[],[]]]]=>1
[1,4,6,1,2,5]=>[[[],[[[],[]]]]]=>1
[1,4,6,1,5,2]=>[[[[],[[],[]]]]]=>1
[1,4,6,2,1,5]=>[[[[]],[[[]]]]]=>1
[1,4,6,2,5,1]=>[[[],[],[],[[]]]]=>1
[1,4,6,5,1,2]=>[[[],[[[[]]]]]]=>1
[1,4,6,5,2,1]=>[[[[[],[[]]]]]]=>1
[1,5,1,2,4,6]=>[[[[[[],[]]]]]]=>1
[1,5,1,2,6,4]=>[[[[[]]],[[]]]]=>1
[1,5,1,4,2,6]=>[[[],[[[],[]]]]]=>1
[1,5,1,4,6,2]=>[[[[],[],[[]]]]]=>1
[1,5,1,6,2,4]=>[[[[[],[[]]]]]]=>1
[1,5,1,6,4,2]=>[[[[],[],[[]]]]]=>1
[1,5,2,1,4,6]=>[[[],[[[[]]]]]]=>1
[1,5,2,1,6,4]=>[[[],[[],[[]]]]]=>1
[1,5,2,4,1,6]=>[[[],[[]],[[]]]]=>1
[1,5,2,4,6,1]=>[[[],[[],[],[]]]]=>1
[1,5,2,6,1,4]=>[[[],[],[[[]]]]]=>1
[1,5,2,6,4,1]=>[[[],[],[],[[]]]]=>1
[1,5,4,1,2,6]=>[[[],[[]],[[]]]]=>1
[1,5,4,1,6,2]=>[[[],[[[[]]]]]]=>1
[1,5,4,2,1,6]=>[[[[],[[],[]]]]]=>1
[1,5,4,2,6,1]=>[[[[[]]],[[]]]]=>1
[1,5,4,6,1,2]=>[[[[],[[[]]]]]]=>1
[1,5,4,6,2,1]=>[[[[[[],[]]]]]]=>1
[1,5,6,1,2,4]=>[[[[],[[],[]]]]]=>1
[1,5,6,1,4,2]=>[[[[[[[]]]]]]]=>1
[1,5,6,2,1,4]=>[[[[[],[[]]]]]]=>1
[1,5,6,2,4,1]=>[[[],[[[[]]]]]]=>1
[1,5,6,4,1,2]=>[[[[]],[[],[]]]]=>1
[1,5,6,4,2,1]=>[[[[[],[[]]]]]]=>1
[1,6,1,2,4,5]=>[[[[],[[],[]]]]]=>1
[1,6,1,2,5,4]=>[[[[[[[]]]]]]]=>1
[1,6,1,4,2,5]=>[[[],[[],[[]]]]]=>1
[1,6,1,4,5,2]=>[[[[[[[]]]]]]]=>1
[1,6,1,5,2,4]=>[[[[],[[],[]]]]]=>1
[1,6,1,5,4,2]=>[[[[[]]],[[]]]]=>1
[1,6,2,1,4,5]=>[[[[],[[[]]]]]]=>1
[1,6,2,1,5,4]=>[[[[],[[[]]]]]]=>1
[1,6,2,4,1,5]=>[[[[],[[[]]]]]]=>1
[1,6,2,4,5,1]=>[[[[[[],[]]]]]]=>1
[1,6,2,5,1,4]=>[[[[],[],[],[]]]]=>1
[1,6,2,5,4,1]=>[[[[[[],[]]]]]]=>1
[1,6,4,1,2,5]=>[[[],[[[[]]]]]]=>1
[1,6,4,1,5,2]=>[[[],[[],[],[]]]]=>1
[1,6,4,2,1,5]=>[[[],[],[[[]]]]]=>1
[1,6,4,2,5,1]=>[[[],[],[[],[]]]]=>1
[1,6,4,5,1,2]=>[[[],[[[],[]]]]]=>1
[1,6,4,5,2,1]=>[[[],[[[[]]]]]]=>1
[1,6,5,1,2,4]=>[[[[[[[]]]]]]]=>1
[1,6,5,1,4,2]=>[[[[]],[[],[]]]]=>1
[1,6,5,2,1,4]=>[[[[[],[[]]]]]]=>1
[1,6,5,2,4,1]=>[[[[[],[[]]]]]]=>1
[1,6,5,4,1,2]=>[[[[[[],[]]]]]]=>1
[1,6,5,4,2,1]=>[[[],[[],[],[]]]]=>1
[2,1,1,4,5,6]=>[[],[[[],[[]]]]]=>2
[2,1,1,4,6,5]=>[[],[[[[],[]]]]]=>2
[2,1,1,5,4,6]=>[[],[[[],[[]]]]]=>2
[2,1,1,5,6,4]=>[[],[[[[[]]]]]]=>2
[2,1,1,6,4,5]=>[[],[[],[[[]]]]]=>2
[2,1,1,6,5,4]=>[[],[[[],[],[]]]]=>2
[2,1,4,1,5,6]=>[[[[[],[[]]]]]]=>1
[2,1,4,1,6,5]=>[[[[]],[[[]]]]]=>1
[2,1,4,5,1,6]=>[[[[[],[[]]]]]]=>1
[2,1,4,5,6,1]=>[[[[[],[[]]]]]]=>1
[2,1,4,6,1,5]=>[[[[[],[[]]]]]]=>1
[2,1,4,6,5,1]=>[[[[]],[[],[]]]]=>1
[2,1,5,1,4,6]=>[[[[[],[[]]]]]]=>1
[2,1,5,1,6,4]=>[[[[[]],[[]]]]]=>1
[2,1,5,4,1,6]=>[[[],[[[],[]]]]]=>1
[2,1,5,4,6,1]=>[[[],[[],[[]]]]]=>1
[2,1,5,6,1,4]=>[[[[[[[]]]]]]]=>1
[2,1,5,6,4,1]=>[[[[],[[[]]]]]]=>1
[2,1,6,1,4,5]=>[[[[[[[]]]]]]]=>1
[2,1,6,1,5,4]=>[[[[[]]],[[]]]]=>1
[2,1,6,4,1,5]=>[[[[],[[],[]]]]]=>1
[2,1,6,4,5,1]=>[[[[[[],[]]]]]]=>1
[2,1,6,5,1,4]=>[[[],[[],[[]]]]]=>1
[2,1,6,5,4,1]=>[[[],[],[[[]]]]]=>1
[2,4,1,1,5,6]=>[[],[[[]],[[]]]]=>2
[2,4,1,1,6,5]=>[[],[[[[[]]]]]]=>2
[2,4,1,5,1,6]=>[[[[],[[[]]]]]]=>1
[2,4,1,5,6,1]=>[[[],[[[],[]]]]]=>1
[2,4,1,6,1,5]=>[[[[]],[[],[]]]]=>1
[2,4,1,6,5,1]=>[[[[[[[]]]]]]]=>1
[2,4,5,1,1,6]=>[[[[[]]]],[[]]]=>2
[2,4,5,1,6,1]=>[[[],[[[[]]]]]]=>1
[2,4,5,6,1,1]=>[[],[[],[[],[]]]]=>2
[2,4,6,1,1,5]=>[[[]],[[],[],[]]]=>2
[2,4,6,1,5,1]=>[[[],[],[[[]]]]]=>1
[2,4,6,5,1,1]=>[[[]],[[[],[]]]]=>2
[2,5,1,1,4,6]=>[[],[[],[],[[]]]]=>2
[2,5,1,1,6,4]=>[[[],[]],[[],[]]]=>2
[2,5,1,4,1,6]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,6,1]=>[[[],[],[[],[]]]]=>1
[2,5,1,6,1,4]=>[[[],[],[[[]]]]]=>1
[2,5,1,6,4,1]=>[[[],[[],[[]]]]]=>1
[2,5,4,1,1,6]=>[[[[]]],[[[]]]]=>2
[2,5,4,1,6,1]=>[[[[[[[]]]]]]]=>1
[2,5,4,6,1,1]=>[[[[]]],[[],[]]]=>2
[2,5,6,1,1,4]=>[[[[]]],[[],[]]]=>2
[2,5,6,1,4,1]=>[[[[[]]],[[]]]]=>1
[2,5,6,4,1,1]=>[[],[[[[[]]]]]]=>2
[2,6,1,1,4,5]=>[[[[]]],[[[]]]]=>2
[2,6,1,1,5,4]=>[[[]],[[],[[]]]]=>2
[2,6,1,4,1,5]=>[[[],[],[[[]]]]]=>1
[2,6,1,4,5,1]=>[[[[[],[[]]]]]]=>1
[2,6,1,5,1,4]=>[[[[]],[[],[]]]]=>1
[2,6,1,5,4,1]=>[[[],[[]],[[]]]]=>1
[2,6,4,1,1,5]=>[[[]],[[],[],[]]]=>2
[2,6,4,1,5,1]=>[[[],[[]],[[]]]]=>1
[2,6,4,5,1,1]=>[[],[[[[[]]]]]]=>2
[2,6,5,1,1,4]=>[[],[[[]],[[]]]]=>2
[2,6,5,1,4,1]=>[[[[]],[[],[]]]]=>1
[2,6,5,4,1,1]=>[[[],[]],[[],[]]]=>2
[4,1,1,2,5,6]=>[[[]],[[],[[]]]]=>2
[4,1,1,2,6,5]=>[[],[[[],[[]]]]]=>2
[4,1,1,5,2,6]=>[[],[[],[],[],[]]]=>2
[4,1,1,5,6,2]=>[[],[[],[[[]]]]]=>2
[4,1,1,6,2,5]=>[[],[[[],[[]]]]]=>2
[4,1,1,6,5,2]=>[[],[[[],[[]]]]]=>2
[4,1,2,1,5,6]=>[[[],[[],[[]]]]]=>1
[4,1,2,1,6,5]=>[[[[[]],[[]]]]]=>1
[4,1,2,5,1,6]=>[[[[[]],[[]]]]]=>1
[4,1,2,5,6,1]=>[[[[[]],[[]]]]]=>1
[4,1,2,6,1,5]=>[[[],[[]],[[]]]]=>1
[4,1,2,6,5,1]=>[[[[]],[[[]]]]]=>1
[4,1,5,1,2,6]=>[[[],[],[[[]]]]]=>1
[4,1,5,1,6,2]=>[[[],[[[],[]]]]]=>1
[4,1,5,2,1,6]=>[[[],[],[[[]]]]]=>1
[4,1,5,2,6,1]=>[[[],[],[],[[]]]]=>1
[4,1,5,6,1,2]=>[[[],[[],[[]]]]]=>1
[4,1,5,6,2,1]=>[[[],[[[[]]]]]]=>1
[4,1,6,1,2,5]=>[[[[[[[]]]]]]]=>1
[4,1,6,1,5,2]=>[[[],[[]],[[]]]]=>1
[4,1,6,2,1,5]=>[[[[]],[[[]]]]]=>1
[4,1,6,2,5,1]=>[[[[],[],[[]]]]]=>1
[4,1,6,5,1,2]=>[[[[[[[]]]]]]]=>1
[4,1,6,5,2,1]=>[[[],[[],[[]]]]]=>1
[4,2,1,1,5,6]=>[[[[[]]]],[[]]]=>2
[4,2,1,1,6,5]=>[[],[[],[[],[]]]]=>2
[4,2,1,5,1,6]=>[[[[[]]],[[]]]]=>1
[4,2,1,5,6,1]=>[[[[[[[]]]]]]]=>1
[4,2,1,6,1,5]=>[[[],[[[[]]]]]]=>1
[4,2,1,6,5,1]=>[[[],[[[],[]]]]]=>1
[4,2,5,1,1,6]=>[[[],[]],[[],[]]]=>2
[4,2,5,1,6,1]=>[[[[]],[[],[]]]]=>1
[4,2,5,6,1,1]=>[[],[[[[[]]]]]]=>2
[4,2,6,1,1,5]=>[[[[]]],[[],[]]]=>2
[4,2,6,1,5,1]=>[[[[[],[[]]]]]]=>1
[4,2,6,5,1,1]=>[[[[]]],[[[]]]]=>2
[4,5,1,1,2,6]=>[[[]],[[],[[]]]]=>2
[4,5,1,1,6,2]=>[[],[[[],[[]]]]]=>2
[4,5,1,2,1,6]=>[[[[]],[[[]]]]]=>1
[4,5,1,2,6,1]=>[[[[]],[[[]]]]]=>1
[4,5,1,6,1,2]=>[[[],[[[[]]]]]]=>1
[4,5,1,6,2,1]=>[[[[],[[[]]]]]]=>1
[4,5,2,1,1,6]=>[[[[]]],[[[]]]]=>2
[4,5,2,1,6,1]=>[[[[[[[]]]]]]]=>1
[4,5,2,6,1,1]=>[[],[[[],[[]]]]]=>2
[4,5,6,1,1,2]=>[[[]],[[],[],[]]]=>2
[4,5,6,1,2,1]=>[[[],[[]],[[]]]]=>1
[4,5,6,2,1,1]=>[[],[[[[],[]]]]]=>2
[4,6,1,1,2,5]=>[[[[]]],[[],[]]]=>2
[4,6,1,1,5,2]=>[[[],[]],[[],[]]]=>2
[4,6,1,2,1,5]=>[[[],[[[[]]]]]]=>1
[4,6,1,2,5,1]=>[[[],[[[],[]]]]]=>1
[4,6,1,5,1,2]=>[[[],[[[[]]]]]]=>1
[4,6,1,5,2,1]=>[[[],[[],[[]]]]]=>1
[4,6,2,1,1,5]=>[[],[[[[[]]]]]]=>2
[4,6,2,1,5,1]=>[[[[[],[[]]]]]]=>1
[4,6,2,5,1,1]=>[[],[[],[],[[]]]]=>2
[4,6,5,1,1,2]=>[[[[[]]]],[[]]]=>2
[4,6,5,1,2,1]=>[[[[],[[[]]]]]]=>1
[4,6,5,2,1,1]=>[[],[[[]],[[]]]]=>2
[5,1,1,2,4,6]=>[[[[],[]]],[[]]]=>2
[5,1,1,2,6,4]=>[[[[[]]]],[[]]]=>2
[5,1,1,4,2,6]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,6,2]=>[[],[[],[],[[]]]]=>2
[5,1,1,6,2,4]=>[[],[[[],[[]]]]]=>2
[5,1,1,6,4,2]=>[[],[[],[],[[]]]]=>2
[5,1,2,1,4,6]=>[[[],[[[[]]]]]]=>1
[5,1,2,1,6,4]=>[[[[],[[[]]]]]]=>1
[5,1,2,4,1,6]=>[[[[[[[]]]]]]]=>1
[5,1,2,4,6,1]=>[[[[[],[],[]]]]]=>1
[5,1,2,6,1,4]=>[[[],[[[[]]]]]]=>1
[5,1,2,6,4,1]=>[[[[[],[[]]]]]]=>1
[5,1,4,1,2,6]=>[[[],[[],[[]]]]]=>1
[5,1,4,1,6,2]=>[[[],[],[[[]]]]]=>1
[5,1,4,2,1,6]=>[[[],[[[],[]]]]]=>1
[5,1,4,2,6,1]=>[[[],[[[[]]]]]]=>1
[5,1,4,6,1,2]=>[[[],[[],[[]]]]]=>1
[5,1,4,6,2,1]=>[[[],[[]],[[]]]]=>1
[5,1,6,1,2,4]=>[[[[[[],[]]]]]]=>1
[5,1,6,1,4,2]=>[[[[]],[[],[]]]]=>1
[5,1,6,2,1,4]=>[[[],[[]],[[]]]]=>1
[5,1,6,2,4,1]=>[[[[[]]],[[]]]]=>1
[5,1,6,4,1,2]=>[[[[],[[[]]]]]]=>1
[5,1,6,4,2,1]=>[[[[],[],[[]]]]]=>1
[5,2,1,1,4,6]=>[[],[[[[[]]]]]]=>2
[5,2,1,1,6,4]=>[[],[[[]],[[]]]]=>2
[5,2,1,4,1,6]=>[[[[]],[[[]]]]]=>1
[5,2,1,4,6,1]=>[[[[[],[[]]]]]]=>1
[5,2,1,6,1,4]=>[[[[[[[]]]]]]]=>1
[5,2,1,6,4,1]=>[[[[]],[[],[]]]]=>1
[5,2,4,1,1,6]=>[[[]],[[],[[]]]]=>2
[5,2,4,1,6,1]=>[[[],[[[],[]]]]]=>1
[5,2,4,6,1,1]=>[[],[[],[],[[]]]]=>2
[5,2,6,1,1,4]=>[[[[],[]]],[[]]]=>2
[5,2,6,1,4,1]=>[[[],[],[[[]]]]]=>1
[5,2,6,4,1,1]=>[[],[[],[],[[]]]]=>2
[5,4,1,1,2,6]=>[[],[[[],[[]]]]]=>2
[5,4,1,1,6,2]=>[[[]],[[[[]]]]]=>2
[5,4,1,2,1,6]=>[[[[]],[[[]]]]]=>1
[5,4,1,2,6,1]=>[[[[[],[[]]]]]]=>1
[5,4,1,6,1,2]=>[[[[[[[]]]]]]]=>1
[5,4,1,6,2,1]=>[[[[[]]],[[]]]]=>1
[5,4,2,1,1,6]=>[[],[[],[[],[]]]]=>2
[5,4,2,1,6,1]=>[[[],[[[],[]]]]]=>1
[5,4,2,6,1,1]=>[[[[[]]]],[[]]]=>2
[5,4,6,1,1,2]=>[[[[]]],[[],[]]]=>2
[5,4,6,1,2,1]=>[[[],[[[],[]]]]]=>1
[5,4,6,2,1,1]=>[[],[[],[[[]]]]]=>2
[5,6,1,1,2,4]=>[[],[[],[[],[]]]]=>2
[5,6,1,1,4,2]=>[[[[]]],[[[]]]]=>2
[5,6,1,2,1,4]=>[[[[]],[[[]]]]]=>1
[5,6,1,2,4,1]=>[[[],[[],[[]]]]]=>1
[5,6,1,4,1,2]=>[[[],[[[[]]]]]]=>1
[5,6,1,4,2,1]=>[[[[[[[]]]]]]]=>1
[5,6,2,1,1,4]=>[[],[[[]],[[]]]]=>2
[5,6,2,1,4,1]=>[[[[],[[[]]]]]]=>1
[5,6,2,4,1,1]=>[[],[[[[[]]]]]]=>2
[5,6,4,1,1,2]=>[[[[]]],[[],[]]]=>2
[5,6,4,1,2,1]=>[[[[]],[[[]]]]]=>1
[5,6,4,2,1,1]=>[[[]],[[],[[]]]]=>2
[6,1,1,2,4,5]=>[[],[[],[[],[]]]]=>2
[6,1,1,2,5,4]=>[[[[[]]]],[[]]]=>2
[6,1,1,4,2,5]=>[[[]],[[],[[]]]]=>2
[6,1,1,4,5,2]=>[[[]],[[[[]]]]]=>2
[6,1,1,5,2,4]=>[[],[[],[[],[]]]]=>2
[6,1,1,5,4,2]=>[[[]],[[[[]]]]]=>2
[6,1,2,1,4,5]=>[[[[[]],[[]]]]]=>1
[6,1,2,1,5,4]=>[[[[[],[[]]]]]]=>1
[6,1,2,4,1,5]=>[[[[]],[[],[]]]]=>1
[6,1,2,4,5,1]=>[[[],[[],[[]]]]]=>1
[6,1,2,5,1,4]=>[[[[[],[],[]]]]]=>1
[6,1,2,5,4,1]=>[[[[[[[]]]]]]]=>1
[6,1,4,1,2,5]=>[[[[],[[[]]]]]]=>1
[6,1,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[6,1,4,2,1,5]=>[[[[[[[]]]]]]]=>1
[6,1,4,2,5,1]=>[[[[[],[],[]]]]]=>1
[6,1,4,5,1,2]=>[[[[],[[],[]]]]]=>1
[6,1,4,5,2,1]=>[[[[[[[]]]]]]]=>1
[6,1,5,1,2,4]=>[[[],[[[[]]]]]]=>1
[6,1,5,1,4,2]=>[[[[[]],[[]]]]]=>1
[6,1,5,2,1,4]=>[[[[],[[[]]]]]]=>1
[6,1,5,2,4,1]=>[[[],[[],[],[]]]]=>1
[6,1,5,4,1,2]=>[[[[],[[[]]]]]]=>1
[6,1,5,4,2,1]=>[[[[[]],[[]]]]]=>1
[6,2,1,1,4,5]=>[[],[[],[[[]]]]]=>2
[6,2,1,1,5,4]=>[[[]],[[[],[]]]]=>2
[6,2,1,4,1,5]=>[[[],[[],[[]]]]]=>1
[6,2,1,4,5,1]=>[[[],[[]],[[]]]]=>1
[6,2,1,5,1,4]=>[[[],[[]],[[]]]]=>1
[6,2,1,5,4,1]=>[[[[],[[],[]]]]]=>1
[6,2,4,1,1,5]=>[[],[[],[[[]]]]]=>2
[6,2,4,1,5,1]=>[[[],[[],[[]]]]]=>1
[6,2,4,5,1,1]=>[[],[[],[[[]]]]]=>2
[6,2,5,1,1,4]=>[[],[[],[],[],[]]]=>2
[6,2,5,1,4,1]=>[[[],[],[],[[]]]]=>1
[6,2,5,4,1,1]=>[[[]],[[[],[]]]]=>2
[6,4,1,1,2,5]=>[[[[]]],[[[]]]]=>2
[6,4,1,1,5,2]=>[[],[[],[],[[]]]]=>2
[6,4,1,2,1,5]=>[[[[],[[[]]]]]]=>1
[6,4,1,2,5,1]=>[[[[],[[[]]]]]]=>1
[6,4,1,5,1,2]=>[[[[],[[[]]]]]]=>1
[6,4,1,5,2,1]=>[[[[[],[],[]]]]]=>1
[6,4,2,1,1,5]=>[[[[]]],[[],[]]]=>2
[6,4,2,1,5,1]=>[[[],[[[[]]]]]]=>1
[6,4,2,5,1,1]=>[[],[[],[[],[]]]]=>2
[6,4,5,1,1,2]=>[[[[]]],[[],[]]]=>2
[6,4,5,1,2,1]=>[[[[[],[[]]]]]]=>1
[6,4,5,2,1,1]=>[[[]],[[[[]]]]]=>2
[6,5,1,1,2,4]=>[[[[[]]]],[[]]]=>2
[6,5,1,1,4,2]=>[[],[[],[[[]]]]]=>2
[6,5,1,2,1,4]=>[[[[]],[[],[]]]]=>1
[6,5,1,2,4,1]=>[[[[[[[]]]]]]]=>1
[6,5,1,4,1,2]=>[[[[[[],[]]]]]]=>1
[6,5,1,4,2,1]=>[[[],[[[],[]]]]]=>1
[6,5,2,1,1,4]=>[[],[[[],[[]]]]]=>2
[6,5,2,1,4,1]=>[[[],[[],[[]]]]]=>1
[6,5,2,4,1,1]=>[[[]],[[],[[]]]]=>2
[6,5,4,1,1,2]=>[[[[],[]]],[[]]]=>2
[6,5,4,1,2,1]=>[[[],[],[[[]]]]]=>1
[6,5,4,2,1,1]=>[[[]],[[],[],[]]]=>2
[1,1,3,3,3,3]=>[[],[],[],[],[[]]]=>5
[1,3,1,3,3,3]=>[[],[[]],[[],[]]]=>3
[1,3,3,1,3,3]=>[[],[],[[],[[]]]]=>3
[1,3,3,3,1,3]=>[[],[],[[[],[]]]]=>3
[1,3,3,3,3,1]=>[[],[],[[]],[[]]]=>4
[3,1,1,3,3,3]=>[[],[],[[]],[[]]]=>4
[3,1,3,1,3,3]=>[[],[[],[[],[]]]]=>2
[3,1,3,3,1,3]=>[[],[[],[[],[]]]]=>2
[3,1,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,3,1,1,3,3]=>[[],[],[],[[[]]]]=>4
[3,3,1,3,1,3]=>[[],[[],[[],[]]]]=>2
[3,3,1,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,3,3,1,1,3]=>[[],[],[[]],[[]]]=>4
[3,3,3,1,3,1]=>[[],[],[[],[[]]]]=>3
[3,3,3,3,1,1]=>[[],[],[],[],[[]]]=>5
[1,1,3,3,3,4]=>[[],[],[[]],[[]]]=>4
[1,1,3,3,4,3]=>[[],[[[]]],[[]]]=>3
[1,1,3,4,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,4,3,3,3]=>[[],[],[],[[[]]]]=>4
[1,3,1,3,3,4]=>[[[]],[[],[[]]]]=>2
[1,3,1,3,4,3]=>[[[],[[[[]]]]]]=>1
[1,3,1,4,3,3]=>[[[[]]],[[[]]]]=>2
[1,3,3,1,3,4]=>[[],[[[],[[]]]]]=>2
[1,3,3,1,4,3]=>[[[]],[[[[]]]]]=>2
[1,3,3,3,1,4]=>[[],[[]],[[[]]]]=>3
[1,3,3,3,4,1]=>[[],[[[]]],[[]]]=>3
[1,3,3,4,1,3]=>[[],[[[[],[]]]]]=>2
[1,3,3,4,3,1]=>[[[[[]]]],[[]]]=>2
[1,3,4,1,3,3]=>[[],[[],[[[]]]]]=>2
[1,3,4,3,1,3]=>[[[[]],[[[]]]]]=>1
[1,3,4,3,3,1]=>[[],[[[[[]]]]]]=>2
[1,4,1,3,3,3]=>[[],[],[[[[]]]]]=>3
[1,4,3,1,3,3]=>[[[[]]],[[[]]]]=>2
[1,4,3,3,1,3]=>[[],[[[[[]]]]]]=>2
[1,4,3,3,3,1]=>[[],[[]],[[[]]]]=>3
[3,1,1,3,3,4]=>[[],[[]],[[[]]]]=>3
[3,1,1,3,4,3]=>[[],[[[[[]]]]]]=>2
[3,1,1,4,3,3]=>[[],[[]],[[[]]]]=>3
[3,1,3,1,3,4]=>[[[],[[],[[]]]]]=>1
[3,1,3,1,4,3]=>[[[[]],[[[]]]]]=>1
[3,1,3,3,1,4]=>[[[]],[[],[[]]]]=>2
[3,1,3,3,4,1]=>[[[[]]],[[[]]]]=>2
[3,1,3,4,1,3]=>[[[[[[],[]]]]]]=>1
[3,1,3,4,3,1]=>[[[],[[[[]]]]]]=>1
[3,1,4,1,3,3]=>[[],[[[[[]]]]]]=>2
[3,1,4,3,1,3]=>[[[],[[[[]]]]]]=>1
[3,1,4,3,3,1]=>[[],[[],[[[]]]]]=>2
[3,3,1,1,3,4]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,4,3]=>[[],[],[[[[]]]]]=>3
[3,3,1,3,1,4]=>[[],[[[]],[[]]]]=>2
[3,3,1,3,4,1]=>[[],[[[[[]]]]]]=>2
[3,3,1,4,1,3]=>[[],[[[[[]]]]]]=>2
[3,3,1,4,3,1]=>[[],[[],[[[]]]]]=>2
[3,3,3,1,1,4]=>[[],[],[[]],[[]]]=>4
[3,3,3,1,4,1]=>[[],[],[[[[]]]]]=>3
[3,3,3,4,1,1]=>[[],[],[],[[[]]]]=>4
[3,3,4,1,1,3]=>[[],[[]],[[[]]]]=>3
[3,3,4,1,3,1]=>[[],[[[[[]]]]]]=>2
[3,3,4,3,1,1]=>[[],[[]],[[[]]]]=>3
[3,4,1,1,3,3]=>[[],[[]],[[[]]]]=>3
[3,4,1,3,1,3]=>[[[[[[],[]]]]]]=>1
[3,4,1,3,3,1]=>[[[[[]]]],[[]]]=>2
[3,4,3,1,1,3]=>[[[[[]]]],[[]]]=>2
[3,4,3,1,3,1]=>[[[[[],[[]]]]]]=>1
[3,4,3,3,1,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,3,3,3]=>[[],[],[],[[[]]]]=>4
[4,1,3,1,3,3]=>[[],[[],[[[]]]]]=>2
[4,1,3,3,1,3]=>[[[]],[[[],[]]]]=>2
[4,1,3,3,3,1]=>[[[]],[[]],[[]]]=>3
[4,3,1,1,3,3]=>[[],[[[]]],[[]]]=>3
[4,3,1,3,1,3]=>[[[[],[[],[]]]]]=>1
[4,3,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[4,3,3,1,1,3]=>[[],[[[]]],[[]]]=>3
[4,3,3,1,3,1]=>[[],[[[]],[[]]]]=>2
[4,3,3,3,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,3,3,3,5]=>[[],[],[],[[],[]]]=>4
[1,1,3,3,5,3]=>[[],[],[[],[[]]]]=>3
[1,1,3,5,3,3]=>[[],[],[[[],[]]]]=>3
[1,1,5,3,3,3]=>[[],[],[[]],[[]]]=>4
[1,3,1,3,3,5]=>[[[]],[[],[],[]]]=>2
[1,3,1,3,5,3]=>[[[],[],[[],[]]]]=>1
[1,3,1,5,3,3]=>[[],[[[]],[[]]]]=>2
[1,3,3,1,3,5]=>[[],[[[],[],[]]]]=>2
[1,3,3,1,5,3]=>[[[]],[[],[[]]]]=>2
[1,3,3,3,1,5]=>[[],[[]],[[[]]]]=>3
[1,3,3,3,5,1]=>[[],[],[[],[[]]]]=>3
[1,3,3,5,1,3]=>[[],[[],[],[[]]]]=>2
[1,3,3,5,3,1]=>[[],[[],[[],[]]]]=>2
[1,3,5,1,3,3]=>[[],[[],[],[[]]]]=>2
[1,3,5,3,1,3]=>[[[],[],[[],[]]]]=>1
[1,3,5,3,3,1]=>[[],[[],[[],[]]]]=>2
[1,5,1,3,3,3]=>[[],[],[[[[]]]]]=>3
[1,5,3,1,3,3]=>[[],[[[],[[]]]]]=>2
[1,5,3,3,1,3]=>[[[]],[[],[[]]]]=>2
[1,5,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,3,3,5]=>[[],[[]],[[],[]]]=>3
[3,1,1,3,5,3]=>[[],[[],[[],[]]]]=>2
[3,1,1,5,3,3]=>[[],[],[[],[[]]]]=>3
[3,1,3,1,3,5]=>[[[],[[],[],[]]]]=>1
[3,1,3,1,5,3]=>[[[],[[]],[[]]]]=>1
[3,1,3,3,1,5]=>[[[]],[[],[[]]]]=>2
[3,1,3,3,5,1]=>[[[]],[[],[[]]]]=>2
[3,1,3,5,1,3]=>[[[[[],[],[]]]]]=>1
[3,1,3,5,3,1]=>[[[],[],[[],[]]]]=>1
[3,1,5,1,3,3]=>[[],[[[[[]]]]]]=>2
[3,1,5,3,1,3]=>[[[],[[]],[[]]]]=>1
[3,1,5,3,3,1]=>[[[]],[[],[],[]]]=>2
[3,3,1,1,3,5]=>[[],[],[[],[[]]]]=>3
[3,3,1,1,5,3]=>[[],[],[[[],[]]]]=>3
[3,3,1,3,1,5]=>[[],[[[]],[[]]]]=>2
[3,3,1,3,5,1]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,1,3]=>[[],[[[[[]]]]]]=>2
[3,3,1,5,3,1]=>[[],[[],[],[[]]]]=>2
[3,3,3,1,1,5]=>[[],[],[[]],[[]]]=>4
[3,3,3,1,5,1]=>[[],[],[[[[]]]]]=>3
[3,3,3,5,1,1]=>[[],[],[],[[[]]]]=>4
[3,3,5,1,1,3]=>[[],[[]],[[],[]]]=>3
[3,3,5,1,3,1]=>[[],[[[]],[[]]]]=>2
[3,3,5,3,1,1]=>[[],[],[[],[[]]]]=>3
[3,5,1,1,3,3]=>[[],[[]],[[],[]]]=>3
[3,5,1,3,1,3]=>[[[],[[]],[[]]]]=>1
[3,5,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[3,5,3,1,1,3]=>[[[],[]],[[],[]]]=>2
[3,5,3,1,3,1]=>[[[],[[],[],[]]]]=>1
[3,5,3,3,1,1]=>[[],[],[[],[[]]]]=>3
[5,1,1,3,3,3]=>[[],[],[[]],[[]]]=>4
[5,1,3,1,3,3]=>[[],[[[]],[[]]]]=>2
[5,1,3,3,1,3]=>[[],[[[],[[]]]]]=>2
[5,1,3,3,3,1]=>[[],[[[]]],[[]]]=>3
[5,3,1,1,3,3]=>[[],[],[[[],[]]]]=>3
[5,3,1,3,1,3]=>[[[],[],[[],[]]]]=>1
[5,3,1,3,3,1]=>[[[]],[[],[],[]]]=>2
[5,3,3,1,1,3]=>[[],[[]],[[],[]]]=>3
[5,3,3,1,3,1]=>[[],[[],[],[[]]]]=>2
[5,3,3,3,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,3,3,3,6]=>[[],[],[[]],[[]]]=>4
[1,1,3,3,6,3]=>[[],[[]],[[[]]]]=>3
[1,1,3,6,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,6,3,3,3]=>[[],[],[[]],[[]]]=>4
[1,3,1,3,3,6]=>[[[]],[[],[[]]]]=>2
[1,3,1,3,6,3]=>[[[[[]]],[[]]]]=>1
[1,3,1,6,3,3]=>[[],[[[],[[]]]]]=>2
[1,3,3,1,3,6]=>[[],[[[],[[]]]]]=>2
[1,3,3,1,6,3]=>[[[]],[[],[[]]]]=>2
[1,3,3,3,1,6]=>[[],[[]],[[],[]]]=>3
[1,3,3,3,6,1]=>[[],[],[[[],[]]]]=>3
[1,3,3,6,1,3]=>[[],[[[],[],[]]]]=>2
[1,3,3,6,3,1]=>[[[]],[[[[]]]]]=>2
[1,3,6,1,3,3]=>[[],[[],[],[[]]]]=>2
[1,3,6,3,1,3]=>[[[],[[[[]]]]]]=>1
[1,3,6,3,3,1]=>[[[[[]]]],[[]]]=>2
[1,6,1,3,3,3]=>[[],[[]],[[],[]]]=>3
[1,6,3,1,3,3]=>[[],[[[],[[]]]]]=>2
[1,6,3,3,1,3]=>[[[]],[[],[[]]]]=>2
[1,6,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,3,3,6]=>[[],[[[]]],[[]]]=>3
[3,1,1,3,6,3]=>[[[[[]]]],[[]]]=>2
[3,1,1,6,3,3]=>[[],[],[[[],[]]]]=>3
[3,1,3,1,3,6]=>[[[],[[],[[]]]]]=>1
[3,1,3,1,6,3]=>[[[],[[]],[[]]]]=>1
[3,1,3,3,1,6]=>[[[]],[[],[],[]]]=>2
[3,1,3,3,6,1]=>[[[[],[]]],[[]]]=>2
[3,1,3,6,1,3]=>[[[[],[],[[]]]]]=>1
[3,1,3,6,3,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,1,3,3]=>[[],[[],[[],[]]]]=>2
[3,1,6,3,1,3]=>[[[],[[]],[[]]]]=>1
[3,1,6,3,3,1]=>[[[]],[[],[],[]]]=>2
[3,3,1,1,3,6]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,6,3]=>[[],[],[[],[[]]]]=>3
[3,3,1,3,1,6]=>[[],[[],[],[[]]]]=>2
[3,3,1,3,6,1]=>[[],[[[[],[]]]]]=>2
[3,3,1,6,1,3]=>[[],[[],[[],[]]]]=>2
[3,3,1,6,3,1]=>[[],[[],[],[[]]]]=>2
[3,3,3,1,1,6]=>[[],[],[],[[],[]]]=>4
[3,3,3,1,6,1]=>[[],[],[[],[[]]]]=>3
[3,3,3,6,1,1]=>[[],[],[],[[[]]]]=>4
[3,3,6,1,1,3]=>[[],[],[[],[[]]]]=>3
[3,3,6,1,3,1]=>[[],[[[],[[]]]]]=>2
[3,3,6,3,1,1]=>[[],[],[[[[]]]]]=>3
[3,6,1,1,3,3]=>[[],[],[[],[[]]]]=>3
[3,6,1,3,1,3]=>[[[[],[],[[]]]]]=>1
[3,6,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[3,6,3,1,1,3]=>[[[]],[[[[]]]]]=>2
[3,6,3,1,3,1]=>[[[[],[[[]]]]]]=>1
[3,6,3,3,1,1]=>[[],[[]],[[[]]]]=>3
[6,1,1,3,3,3]=>[[],[],[],[[],[]]]=>4
[6,1,3,1,3,3]=>[[],[[],[],[[]]]]=>2
[6,1,3,3,1,3]=>[[],[[[],[],[]]]]=>2
[6,1,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[6,3,1,1,3,3]=>[[],[[[]]],[[]]]=>3
[6,3,1,3,1,3]=>[[[[],[[],[]]]]]=>1
[6,3,1,3,3,1]=>[[[[]]],[[],[]]]=>2
[6,3,3,1,1,3]=>[[],[[]],[[[]]]]=>3
[6,3,3,1,3,1]=>[[],[[],[[[]]]]]=>2
[6,3,3,3,1,1]=>[[],[],[],[[[]]]]=>4
[1,1,3,3,4,4]=>[[],[],[[]],[[]]]=>4
[1,1,3,4,3,4]=>[[],[[[],[[]]]]]=>2
[1,1,3,4,4,3]=>[[],[[[]]],[[]]]=>3
[1,1,4,3,3,4]=>[[],[],[[[[]]]]]=>3
[1,1,4,3,4,3]=>[[],[[[],[[]]]]]=>2
[1,1,4,4,3,3]=>[[],[],[[]],[[]]]=>4
[1,3,1,3,4,4]=>[[],[[[],[[]]]]]=>2
[1,3,1,4,3,4]=>[[[[[[[]]]]]]]=>1
[1,3,1,4,4,3]=>[[[]],[[[[]]]]]=>2
[1,3,3,1,4,4]=>[[],[[]],[[[]]]]=>3
[1,3,3,4,1,4]=>[[[[[]]]],[[]]]=>2
[1,3,3,4,4,1]=>[[[]],[[]],[[]]]=>3
[1,3,4,1,3,4]=>[[[[]],[[],[]]]]=>1
[1,3,4,1,4,3]=>[[[[[[[]]]]]]]=>1
[1,3,4,3,1,4]=>[[[[[[[]]]]]]]=>1
[1,3,4,3,4,1]=>[[[[],[[[]]]]]]=>1
[1,3,4,4,1,3]=>[[[]],[[[],[]]]]=>2
[1,3,4,4,3,1]=>[[[[]]],[[[]]]]=>2
[1,4,1,3,3,4]=>[[[]],[[[[]]]]]=>2
[1,4,1,3,4,3]=>[[[[[[[]]]]]]]=>1
[1,4,1,4,3,3]=>[[],[[[],[[]]]]]=>2
[1,4,3,1,3,4]=>[[[[[[[]]]]]]]=>1
[1,4,3,1,4,3]=>[[[],[[],[[]]]]]=>1
[1,4,3,3,1,4]=>[[],[[[],[[]]]]]=>2
[1,4,3,3,4,1]=>[[],[[[[[]]]]]]=>2
[1,4,3,4,1,3]=>[[[[[[[]]]]]]]=>1
[1,4,3,4,3,1]=>[[[[[],[[]]]]]]=>1
[1,4,4,1,3,3]=>[[],[[[]]],[[]]]=>3
[1,4,4,3,1,3]=>[[[]],[[[[]]]]]=>2
[1,4,4,3,3,1]=>[[],[],[[[[]]]]]=>3
[3,1,1,3,4,4]=>[[],[],[[[[]]]]]=>3
[3,1,1,4,3,4]=>[[],[[[[[]]]]]]=>2
[3,1,1,4,4,3]=>[[],[[]],[[[]]]]=>3
[3,1,3,1,4,4]=>[[],[[[],[[]]]]]=>2
[3,1,3,4,1,4]=>[[[[[[[]]]]]]]=>1
[3,1,3,4,4,1]=>[[[[[]]]],[[]]]=>2
[3,1,4,1,3,4]=>[[[[[[[]]]]]]]=>1
[3,1,4,1,4,3]=>[[[[[],[[]]]]]]=>1
[3,1,4,3,1,4]=>[[[],[[],[[]]]]]=>1
[3,1,4,3,4,1]=>[[[[[[[]]]]]]]=>1
[3,1,4,4,1,3]=>[[[[]]],[[[]]]]=>2
[3,1,4,4,3,1]=>[[[]],[[[],[]]]]=>2
[3,3,1,1,4,4]=>[[],[],[],[[[]]]]=>4
[3,3,1,4,1,4]=>[[],[[[[],[]]]]]=>2
[3,3,1,4,4,1]=>[[],[[[]]],[[]]]=>3
[3,3,4,1,1,4]=>[[],[[]],[[[]]]]=>3
[3,3,4,1,4,1]=>[[],[[[],[[]]]]]=>2
[3,3,4,4,1,1]=>[[],[],[[]],[[]]]=>4
[3,4,1,1,3,4]=>[[[[],[]]],[[]]]=>2
[3,4,1,1,4,3]=>[[[[]]],[[[]]]]=>2
[3,4,1,3,1,4]=>[[[[[[[]]]]]]]=>1
[3,4,1,3,4,1]=>[[[[]],[[],[]]]]=>1
[3,4,1,4,1,3]=>[[[[[]],[[]]]]]=>1
[3,4,1,4,3,1]=>[[[[[[[]]]]]]]=>1
[3,4,3,1,1,4]=>[[[[[]]]],[[]]]=>2
[3,4,3,1,4,1]=>[[[[[[[]]]]]]]=>1
[3,4,3,4,1,1]=>[[[[],[]]],[[]]]=>2
[3,4,4,1,1,3]=>[[[]],[[]],[[]]]=>3
[3,4,4,1,3,1]=>[[[]],[[[[]]]]]=>2
[3,4,4,3,1,1]=>[[[]],[[]],[[]]]=>3
[4,1,1,3,3,4]=>[[[]],[[]],[[]]]=>3
[4,1,1,3,4,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,3,3]=>[[],[],[[[[]]]]]=>3
[4,1,3,1,3,4]=>[[[[[],[[]]]]]]=>1
[4,1,3,1,4,3]=>[[[[[[[]]]]]]]=>1
[4,1,3,3,1,4]=>[[[[]]],[[[]]]]=>2
[4,1,3,3,4,1]=>[[[[],[]]],[[]]]=>2
[4,1,3,4,1,3]=>[[[[]],[[],[]]]]=>1
[4,1,3,4,3,1]=>[[[[[[[]]]]]]]=>1
[4,1,4,1,3,3]=>[[],[[[],[[]]]]]=>2
[4,1,4,3,1,3]=>[[[[[[[]]]]]]]=>1
[4,1,4,3,3,1]=>[[[]],[[[[]]]]]=>2
[4,3,1,1,3,4]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,4,3]=>[[],[[[],[[]]]]]=>2
[4,3,1,3,1,4]=>[[[[[],[[]]]]]]=>1
[4,3,1,3,4,1]=>[[[[[[[]]]]]]]=>1
[4,3,1,4,1,3]=>[[[[[[[]]]]]]]=>1
[4,3,1,4,3,1]=>[[[[]],[[],[]]]]=>1
[4,3,3,1,1,4]=>[[],[[[]]],[[]]]=>3
[4,3,3,1,4,1]=>[[],[[[[[]]]]]]=>2
[4,3,3,4,1,1]=>[[],[[[]]],[[]]]=>3
[4,3,4,1,1,3]=>[[[[]]],[[[]]]]=>2
[4,3,4,1,3,1]=>[[[[[[[]]]]]]]=>1
[4,3,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[4,4,1,1,3,3]=>[[],[],[[]],[[]]]=>4
[4,4,1,3,1,3]=>[[],[[[[],[]]]]]=>2
[4,4,1,3,3,1]=>[[],[[[]]],[[]]]=>3
[4,4,3,1,1,3]=>[[],[[[]]],[[]]]=>3
[4,4,3,1,3,1]=>[[],[[[],[[]]]]]=>2
[4,4,3,3,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,3,3,4,5]=>[[],[[]],[[],[]]]=>3
[1,1,3,3,5,4]=>[[],[],[[],[[]]]]=>3
[1,1,3,4,3,5]=>[[],[[],[[[]]]]]=>2
[1,1,3,4,5,3]=>[[],[[[],[[]]]]]=>2
[1,1,3,5,3,4]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,4,3]=>[[],[[],[[],[]]]]=>2
[1,1,4,3,3,5]=>[[],[],[[[[]]]]]=>3
[1,1,4,3,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,4,5,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,5,3,3,4]=>[[],[[]],[[[]]]]=>3
[1,1,5,3,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,5,4,3,3]=>[[],[],[[],[[]]]]=>3
[1,3,1,3,4,5]=>[[[],[[],[[]]]]]=>1
[1,3,1,3,5,4]=>[[[],[],[[[]]]]]=>1
[1,3,1,4,3,5]=>[[[[]],[[[]]]]]=>1
[1,3,1,4,5,3]=>[[[[],[[[]]]]]]=>1
[1,3,1,5,3,4]=>[[[[[]],[[]]]]]=>1
[1,3,1,5,4,3]=>[[[[[],[[]]]]]]=>1
[1,3,3,1,4,5]=>[[[]],[[[[]]]]]=>2
[1,3,3,1,5,4]=>[[[]],[[[[]]]]]=>2
[1,3,3,4,1,5]=>[[[[],[]]],[[]]]=>2
[1,3,3,4,5,1]=>[[[]],[[],[[]]]]=>2
[1,3,3,5,1,4]=>[[],[[],[[],[]]]]=>2
[1,3,3,5,4,1]=>[[],[[],[[[]]]]]=>2
[1,3,4,1,3,5]=>[[[],[],[[[]]]]]=>1
[1,3,4,1,5,3]=>[[[[[],[[]]]]]]=>1
[1,3,4,3,1,5]=>[[[[[[[]]]]]]]=>1
[1,3,4,3,5,1]=>[[[],[[[[]]]]]]=>1
[1,3,4,5,1,3]=>[[[],[[[],[]]]]]=>1
[1,3,4,5,3,1]=>[[[[],[[],[]]]]]=>1
[1,3,5,1,3,4]=>[[[],[[]],[[]]]]=>1
[1,3,5,1,4,3]=>[[[],[[],[[]]]]]=>1
[1,3,5,3,1,4]=>[[[],[[],[[]]]]]=>1
[1,3,5,3,4,1]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,1,3]=>[[[],[[]],[[]]]]=>1
[1,3,5,4,3,1]=>[[[],[[],[[]]]]]=>1
[1,4,1,3,3,5]=>[[],[[],[[[]]]]]=>2
[1,4,1,3,5,3]=>[[[[[]],[[]]]]]=>1
[1,4,1,5,3,3]=>[[],[[[],[[]]]]]=>2
[1,4,3,1,3,5]=>[[[[[],[[]]]]]]=>1
[1,4,3,1,5,3]=>[[[[[],[[]]]]]]=>1
[1,4,3,3,1,5]=>[[[]],[[[[]]]]]=>2
[1,4,3,3,5,1]=>[[],[[[],[[]]]]]=>2
[1,4,3,5,1,3]=>[[[],[[],[[]]]]]=>1
[1,4,3,5,3,1]=>[[[[[],[[]]]]]]=>1
[1,4,5,1,3,3]=>[[],[[[],[[]]]]]=>2
[1,4,5,3,1,3]=>[[[[[],[[]]]]]]=>1
[1,4,5,3,3,1]=>[[],[[],[[[]]]]]=>2
[1,5,1,3,3,4]=>[[[]],[[[[]]]]]=>2
[1,5,1,3,4,3]=>[[[[[[[]]]]]]]=>1
[1,5,1,4,3,3]=>[[],[[[],[[]]]]]=>2
[1,5,3,1,3,4]=>[[[[],[[[]]]]]]=>1
[1,5,3,1,4,3]=>[[[[[[],[]]]]]]=>1
[1,5,3,3,1,4]=>[[[]],[[],[[]]]]=>2
[1,5,3,3,4,1]=>[[[[],[]]],[[]]]=>2
[1,5,3,4,1,3]=>[[[[[]]],[[]]]]=>1
[1,5,3,4,3,1]=>[[[[],[[[]]]]]]=>1
[1,5,4,1,3,3]=>[[[[],[]]],[[]]]=>2
[1,5,4,3,1,3]=>[[[[[[],[]]]]]]=>1
[1,5,4,3,3,1]=>[[[]],[[[],[]]]]=>2
[3,1,1,3,4,5]=>[[],[[[],[[]]]]]=>2
[3,1,1,3,5,4]=>[[],[[],[[[]]]]]=>2
[3,1,1,4,3,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,4,5,3]=>[[],[[[[],[]]]]]=>2
[3,1,1,5,3,4]=>[[],[[[],[[]]]]]=>2
[3,1,1,5,4,3]=>[[],[[[],[[]]]]]=>2
[3,1,3,1,4,5]=>[[[[]],[[[]]]]]=>1
[3,1,3,1,5,4]=>[[[[]],[[[]]]]]=>1
[3,1,3,4,1,5]=>[[[[],[[[]]]]]]=>1
[3,1,3,4,5,1]=>[[[[[]],[[]]]]]=>1
[3,1,3,5,1,4]=>[[[[],[[],[]]]]]=>1
[3,1,3,5,4,1]=>[[[[[[],[]]]]]]=>1
[3,1,4,1,3,5]=>[[[[],[[[]]]]]]=>1
[3,1,4,1,5,3]=>[[[],[[],[[]]]]]=>1
[3,1,4,3,1,5]=>[[[[]],[[[]]]]]=>1
[3,1,4,3,5,1]=>[[[[[],[[]]]]]]=>1
[3,1,4,5,1,3]=>[[[[[],[[]]]]]]=>1
[3,1,4,5,3,1]=>[[[],[],[[[]]]]]=>1
[3,1,5,1,3,4]=>[[[[[[[]]]]]]]=>1
[3,1,5,1,4,3]=>[[[[[],[[]]]]]]=>1
[3,1,5,3,1,4]=>[[[],[[]],[[]]]]=>1
[3,1,5,3,4,1]=>[[[],[[[],[]]]]]=>1
[3,1,5,4,1,3]=>[[[[],[[[]]]]]]=>1
[3,1,5,4,3,1]=>[[[[]],[[],[]]]]=>1
[3,3,1,1,4,5]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,5,4]=>[[],[],[[[[]]]]]=>3
[3,3,1,4,1,5]=>[[],[[[],[[]]]]]=>2
[3,3,1,4,5,1]=>[[],[[[[],[]]]]]=>2
[3,3,1,5,1,4]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,4,1]=>[[],[[[],[[]]]]]=>2
[3,3,4,1,1,5]=>[[],[],[[],[[]]]]=>3
[3,3,4,1,5,1]=>[[],[[[],[[]]]]]=>2
[3,3,4,5,1,1]=>[[],[],[[[],[]]]]=>3
[3,3,5,1,1,4]=>[[],[],[[],[[]]]]=>3
[3,3,5,1,4,1]=>[[],[[[],[[]]]]]=>2
[3,3,5,4,1,1]=>[[],[[]],[[[]]]]=>3
[3,4,1,1,3,5]=>[[[[]]],[[],[]]]=>2
[3,4,1,1,5,3]=>[[],[[[]],[[]]]]=>2
[3,4,1,3,1,5]=>[[[[],[[[]]]]]]=>1
[3,4,1,3,5,1]=>[[[[[],[[]]]]]]=>1
[3,4,1,5,1,3]=>[[[[],[[[]]]]]]=>1
[3,4,1,5,3,1]=>[[[[],[[],[]]]]]=>1
[3,4,3,1,1,5]=>[[[[[]]]],[[]]]=>2
[3,4,3,1,5,1]=>[[[[[[[]]]]]]]=>1
[3,4,3,5,1,1]=>[[[[]]],[[[]]]]=>2
[3,4,5,1,1,3]=>[[[]],[[[],[]]]]=>2
[3,4,5,1,3,1]=>[[[],[[[[]]]]]]=>1
[3,4,5,3,1,1]=>[[],[[],[[],[]]]]=>2
[3,5,1,1,3,4]=>[[[]],[[],[[]]]]=>2
[3,5,1,1,4,3]=>[[],[[[]],[[]]]]=>2
[3,5,1,3,1,4]=>[[[],[[[],[]]]]]=>1
[3,5,1,3,4,1]=>[[[[[]]],[[]]]]=>1
[3,5,1,4,1,3]=>[[[],[[[],[]]]]]=>1
[3,5,1,4,3,1]=>[[[[],[[[]]]]]]=>1
[3,5,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[3,5,3,1,4,1]=>[[[[],[[[]]]]]]=>1
[3,5,3,4,1,1]=>[[],[[[[[]]]]]]=>2
[3,5,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[3,5,4,1,3,1]=>[[[[]],[[[]]]]]=>1
[3,5,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,3,3,5]=>[[],[],[[],[[]]]]=>3
[4,1,1,3,5,3]=>[[],[[[]],[[]]]]=>2
[4,1,1,5,3,3]=>[[],[],[[[],[]]]]=>3
[4,1,3,1,3,5]=>[[[[],[],[[]]]]]=>1
[4,1,3,1,5,3]=>[[[],[[],[[]]]]]=>1
[4,1,3,3,1,5]=>[[[]],[[[],[]]]]=>2
[4,1,3,3,5,1]=>[[],[[[]],[[]]]]=>2
[4,1,3,5,1,3]=>[[[[],[],[[]]]]]=>1
[4,1,3,5,3,1]=>[[[[],[[],[]]]]]=>1
[4,1,5,1,3,3]=>[[],[[[[],[]]]]]=>2
[4,1,5,3,1,3]=>[[[],[[],[[]]]]]=>1
[4,1,5,3,3,1]=>[[[],[]],[[],[]]]=>2
[4,3,1,1,3,5]=>[[],[[[]],[[]]]]=>2
[4,3,1,1,5,3]=>[[],[[[],[[]]]]]=>2
[4,3,1,3,1,5]=>[[[[[],[[]]]]]]=>1
[4,3,1,3,5,1]=>[[[[[],[[]]]]]]=>1
[4,3,1,5,1,3]=>[[[[[[[]]]]]]]=>1
[4,3,1,5,3,1]=>[[[[],[],[[]]]]]=>1
[4,3,3,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,3,3,1,5,1]=>[[],[[[[[]]]]]]=>2
[4,3,3,5,1,1]=>[[],[[[]]],[[]]]=>3
[4,3,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,3,5,1,3,1]=>[[[[[],[[]]]]]]=>1
[4,3,5,3,1,1]=>[[[]],[[],[[]]]]=>2
[4,5,1,1,3,3]=>[[],[[]],[[[]]]]=>3
[4,5,1,3,1,3]=>[[[[[],[[]]]]]]=>1
[4,5,1,3,3,1]=>[[[[[]]]],[[]]]=>2
[4,5,3,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,5,3,1,3,1]=>[[[[],[],[[]]]]]=>1
[4,5,3,3,1,1]=>[[],[],[[],[[]]]]=>3
[5,1,1,3,3,4]=>[[[]],[[]],[[]]]=>3
[5,1,1,3,4,3]=>[[[[[]]]],[[]]]=>2
[5,1,1,4,3,3]=>[[],[],[[[],[]]]]=>3
[5,1,3,1,3,4]=>[[[[[]],[[]]]]]=>1
[5,1,3,1,4,3]=>[[[],[[[[]]]]]]=>1
[5,1,3,3,1,4]=>[[[]],[[[],[]]]]=>2
[5,1,3,3,4,1]=>[[[[]]],[[[]]]]=>2
[5,1,3,4,1,3]=>[[[[],[[[]]]]]]=>1
[5,1,3,4,3,1]=>[[[[[[[]]]]]]]=>1
[5,1,4,1,3,3]=>[[],[[[[],[]]]]]=>2
[5,1,4,3,1,3]=>[[[],[[[[]]]]]]=>1
[5,1,4,3,3,1]=>[[],[[[[],[]]]]]=>2
[5,3,1,1,3,4]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,4,3]=>[[],[[[[],[]]]]]=>2
[5,3,1,3,1,4]=>[[[],[[]],[[]]]]=>1
[5,3,1,3,4,1]=>[[[],[[[[]]]]]]=>1
[5,3,1,4,1,3]=>[[[],[[[[]]]]]]=>1
[5,3,1,4,3,1]=>[[[],[],[[[]]]]]=>1
[5,3,3,1,1,4]=>[[],[[]],[[],[]]]=>3
[5,3,3,1,4,1]=>[[],[[],[[[]]]]]=>2
[5,3,3,4,1,1]=>[[],[],[[[[]]]]]=>3
[5,3,4,1,1,3]=>[[[]],[[[[]]]]]=>2
[5,3,4,1,3,1]=>[[[],[[[[]]]]]]=>1
[5,3,4,3,1,1]=>[[[[]]],[[],[]]]=>2
[5,4,1,1,3,3]=>[[[]],[[]],[[]]]=>3
[5,4,1,3,1,3]=>[[[[],[[[]]]]]]=>1
[5,4,1,3,3,1]=>[[[[]]],[[[]]]]=>2
[5,4,3,1,1,3]=>[[[[],[]]],[[]]]=>2
[5,4,3,1,3,1]=>[[[],[[],[[]]]]]=>1
[5,4,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,3,4,6]=>[[],[],[[[],[]]]]=>3
[1,1,3,3,6,4]=>[[],[[]],[[[]]]]=>3
[1,1,3,4,3,6]=>[[],[[[[[]]]]]]=>2
[1,1,3,4,6,3]=>[[],[[[]],[[]]]]=>2
[1,1,3,6,3,4]=>[[],[[[[[]]]]]]=>2
[1,1,3,6,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,3,6]=>[[],[],[[],[[]]]]=>3
[1,1,4,3,6,3]=>[[],[[],[[[]]]]]=>2
[1,1,4,6,3,3]=>[[],[],[[[[]]]]]=>3
[1,1,6,3,3,4]=>[[],[[]],[[[]]]]=>3
[1,1,6,3,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,4,3,3]=>[[],[[]],[[],[]]]=>3
[1,3,1,3,4,6]=>[[[],[],[[[]]]]]=>1
[1,3,1,3,6,4]=>[[[],[[[],[]]]]]=>1
[1,3,1,4,3,6]=>[[[[[]],[[]]]]]=>1
[1,3,1,4,6,3]=>[[[[[]]],[[]]]]=>1
[1,3,1,6,3,4]=>[[[[],[[[]]]]]]=>1
[1,3,1,6,4,3]=>[[[[],[],[[]]]]]=>1
[1,3,3,1,4,6]=>[[],[[[[],[]]]]]=>2
[1,3,3,1,6,4]=>[[[]],[[],[],[]]]=>2
[1,3,3,4,1,6]=>[[[[[]]]],[[]]]=>2
[1,3,3,4,6,1]=>[[],[[[],[],[]]]]=>2
[1,3,3,6,1,4]=>[[],[[],[[],[]]]]=>2
[1,3,3,6,4,1]=>[[[]],[[[[]]]]]=>2
[1,3,4,1,3,6]=>[[[[]],[[[]]]]]=>1
[1,3,4,1,6,3]=>[[[[[],[[]]]]]]=>1
[1,3,4,3,1,6]=>[[[[[[],[]]]]]]=>1
[1,3,4,3,6,1]=>[[[[]],[[[]]]]]=>1
[1,3,4,6,1,3]=>[[[],[],[],[[]]]]=>1
[1,3,4,6,3,1]=>[[[[]],[[[]]]]]=>1
[1,3,6,1,3,4]=>[[[],[[]],[[]]]]=>1
[1,3,6,1,4,3]=>[[[],[[],[[]]]]]=>1
[1,3,6,3,1,4]=>[[[[[[],[]]]]]]=>1
[1,3,6,3,4,1]=>[[[[[],[[]]]]]]=>1
[1,3,6,4,1,3]=>[[[],[[[[]]]]]]=>1
[1,3,6,4,3,1]=>[[[[],[[[]]]]]]=>1
[1,4,1,3,3,6]=>[[[[]]],[[],[]]]=>2
[1,4,1,3,6,3]=>[[[[]],[[],[]]]]=>1
[1,4,1,6,3,3]=>[[],[[],[[[]]]]]=>2
[1,4,3,1,3,6]=>[[[[[]]],[[]]]]=>1
[1,4,3,1,6,3]=>[[[[],[[[]]]]]]=>1
[1,4,3,3,1,6]=>[[[]],[[],[[]]]]=>2
[1,4,3,3,6,1]=>[[],[[],[[[]]]]]=>2
[1,4,3,6,1,3]=>[[[],[[],[[]]]]]=>1
[1,4,3,6,3,1]=>[[[],[[[[]]]]]]=>1
[1,4,6,1,3,3]=>[[],[[],[],[[]]]]=>2
[1,4,6,3,1,3]=>[[[[[[],[]]]]]]=>1
[1,4,6,3,3,1]=>[[[[[]]]],[[]]]=>2
[1,6,1,3,3,4]=>[[[]],[[],[[]]]]=>2
[1,6,1,3,4,3]=>[[[[[[],[]]]]]]=>1
[1,6,1,4,3,3]=>[[[]],[[[[]]]]]=>2
[1,6,3,1,3,4]=>[[[[[]]],[[]]]]=>1
[1,6,3,1,4,3]=>[[[],[[[[]]]]]]=>1
[1,6,3,3,1,4]=>[[[]],[[],[[]]]]=>2
[1,6,3,3,4,1]=>[[[[],[]]],[[]]]=>2
[1,6,3,4,1,3]=>[[[[[],[[]]]]]]=>1
[1,6,3,4,3,1]=>[[[[]],[[[]]]]]=>1
[1,6,4,1,3,3]=>[[],[[[[],[]]]]]=>2
[1,6,4,3,1,3]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,3,1]=>[[],[[],[],[[]]]]=>2
[3,1,1,3,4,6]=>[[],[[],[[[]]]]]=>2
[3,1,1,3,6,4]=>[[],[[[[],[]]]]]=>2
[3,1,1,4,3,6]=>[[],[[[]],[[]]]]=>2
[3,1,1,4,6,3]=>[[[[[]]]],[[]]]=>2
[3,1,1,6,3,4]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,4,3]=>[[],[[],[],[[]]]]=>2
[3,1,3,1,4,6]=>[[[],[[[],[]]]]]=>1
[3,1,3,1,6,4]=>[[[],[],[],[[]]]]=>1
[3,1,3,4,1,6]=>[[[],[[[[]]]]]]=>1
[3,1,3,4,6,1]=>[[[[],[],[[]]]]]=>1
[3,1,3,6,1,4]=>[[[[],[[],[]]]]]=>1
[3,1,3,6,4,1]=>[[[[[]]],[[]]]]=>1
[3,1,4,1,3,6]=>[[[[[[],[]]]]]]=>1
[3,1,4,1,6,3]=>[[[[]],[[],[]]]]=>1
[3,1,4,3,1,6]=>[[[],[[]],[[]]]]=>1
[3,1,4,3,6,1]=>[[[[],[[[]]]]]]=>1
[3,1,4,6,1,3]=>[[[[],[],[[]]]]]=>1
[3,1,4,6,3,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,1,3,4]=>[[[],[[],[[]]]]]=>1
[3,1,6,1,4,3]=>[[[],[[[[]]]]]]=>1
[3,1,6,3,1,4]=>[[[],[[]],[[]]]]=>1
[3,1,6,3,4,1]=>[[[],[[[],[]]]]]=>1
[3,1,6,4,1,3]=>[[[],[],[[[]]]]]=>1
[3,1,6,4,3,1]=>[[[],[],[],[[]]]]=>1
[3,3,1,1,4,6]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,6,4]=>[[],[],[[],[],[]]]=>3
[3,3,1,4,1,6]=>[[],[[],[[[]]]]]=>2
[3,3,1,4,6,1]=>[[],[[[],[[]]]]]=>2
[3,3,1,6,1,4]=>[[],[[],[[[]]]]]=>2
[3,3,1,6,4,1]=>[[],[[],[],[[]]]]=>2
[3,3,4,1,1,6]=>[[],[[[]]],[[]]]=>3
[3,3,4,1,6,1]=>[[],[[[[[]]]]]]=>2
[3,3,4,6,1,1]=>[[],[],[[],[[]]]]=>3
[3,3,6,1,1,4]=>[[],[[]],[[],[]]]=>3
[3,3,6,1,4,1]=>[[],[[[]],[[]]]]=>2
[3,3,6,4,1,1]=>[[],[],[[[[]]]]]=>3
[3,4,1,1,3,6]=>[[[[]]],[[[]]]]=>2
[3,4,1,1,6,3]=>[[],[[[],[[]]]]]=>2
[3,4,1,3,1,6]=>[[[[[],[[]]]]]]=>1
[3,4,1,3,6,1]=>[[[[[],[[]]]]]]=>1
[3,4,1,6,1,3]=>[[[[[],[[]]]]]]=>1
[3,4,1,6,3,1]=>[[[[],[[],[]]]]]=>1
[3,4,3,1,1,6]=>[[],[[],[[[]]]]]=>2
[3,4,3,1,6,1]=>[[[[[[],[]]]]]]=>1
[3,4,3,6,1,1]=>[[[[]]],[[[]]]]=>2
[3,4,6,1,1,3]=>[[],[[],[],[[]]]]=>2
[3,4,6,1,3,1]=>[[[[],[],[[]]]]]=>1
[3,4,6,3,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,1,1,3,4]=>[[],[[[]],[[]]]]=>2
[3,6,1,1,4,3]=>[[[]],[[],[[]]]]=>2
[3,6,1,3,1,4]=>[[[],[[[],[]]]]]=>1
[3,6,1,3,4,1]=>[[[[],[[[]]]]]]=>1
[3,6,1,4,1,3]=>[[[],[[[],[]]]]]=>1
[3,6,1,4,3,1]=>[[[[]],[[[]]]]]=>1
[3,6,3,1,1,4]=>[[[[]]],[[],[]]]=>2
[3,6,3,1,4,1]=>[[[[]],[[],[]]]]=>1
[3,6,3,4,1,1]=>[[],[[[]],[[]]]]=>2
[3,6,4,1,1,3]=>[[[]],[[[[]]]]]=>2
[3,6,4,1,3,1]=>[[[[[[],[]]]]]]=>1
[3,6,4,3,1,1]=>[[[[]]],[[],[]]]=>2
[4,1,1,3,3,6]=>[[[]],[[]],[[]]]=>3
[4,1,1,3,6,3]=>[[],[[[[],[]]]]]=>2
[4,1,1,6,3,3]=>[[],[],[[],[[]]]]=>3
[4,1,3,1,3,6]=>[[[[[],[[]]]]]]=>1
[4,1,3,1,6,3]=>[[[],[[],[[]]]]]=>1
[4,1,3,3,1,6]=>[[[]],[[],[[]]]]=>2
[4,1,3,3,6,1]=>[[],[[[],[[]]]]]=>2
[4,1,3,6,1,3]=>[[[[[],[],[]]]]]=>1
[4,1,3,6,3,1]=>[[[[[]]],[[]]]]=>1
[4,1,6,1,3,3]=>[[],[[[]],[[]]]]=>2
[4,1,6,3,1,3]=>[[[],[[],[[]]]]]=>1
[4,1,6,3,3,1]=>[[[],[]],[[],[]]]=>2
[4,3,1,1,3,6]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,6,3]=>[[],[[],[[[]]]]]=>2
[4,3,1,3,1,6]=>[[[[],[],[[]]]]]=>1
[4,3,1,3,6,1]=>[[[[],[[[]]]]]]=>1
[4,3,1,6,1,3]=>[[[[],[[],[]]]]]=>1
[4,3,1,6,3,1]=>[[[[],[],[[]]]]]=>1
[4,3,3,1,1,6]=>[[],[],[[],[[]]]]=>3
[4,3,3,1,6,1]=>[[],[[],[[[]]]]]=>2
[4,3,3,6,1,1]=>[[],[[[]]],[[]]]=>3
[4,3,6,1,1,3]=>[[],[[[]],[[]]]]=>2
[4,3,6,1,3,1]=>[[[[[],[[]]]]]]=>1
[4,3,6,3,1,1]=>[[[[[]]]],[[]]]=>2
[4,6,1,1,3,3]=>[[],[],[[],[],[]]]=>3
[4,6,1,3,1,3]=>[[[],[],[],[[]]]]=>1
[4,6,1,3,3,1]=>[[[]],[[],[],[]]]=>2
[4,6,3,1,1,3]=>[[[[]]],[[],[]]]=>2
[4,6,3,1,3,1]=>[[[[]],[[],[]]]]=>1
[4,6,3,3,1,1]=>[[],[],[[[[]]]]]=>3
[6,1,1,3,3,4]=>[[],[[]],[[],[]]]=>3
[6,1,1,3,4,3]=>[[],[[],[[[]]]]]=>2
[6,1,1,4,3,3]=>[[],[[]],[[[]]]]=>3
[6,1,3,1,3,4]=>[[[],[[]],[[]]]]=>1
[6,1,3,1,4,3]=>[[[],[[[[]]]]]]=>1
[6,1,3,3,1,4]=>[[[[]]],[[],[]]]=>2
[6,1,3,3,4,1]=>[[[[]]],[[],[]]]=>2
[6,1,3,4,1,3]=>[[[],[],[[[]]]]]=>1
[6,1,3,4,3,1]=>[[[],[[[[]]]]]]=>1
[6,1,4,1,3,3]=>[[],[[],[[[]]]]]=>2
[6,1,4,3,1,3]=>[[[[]],[[[]]]]]=>1
[6,1,4,3,3,1]=>[[],[[[[[]]]]]]=>2
[6,3,1,1,3,4]=>[[[[]]],[[[]]]]=>2
[6,3,1,1,4,3]=>[[[[[]]]],[[]]]=>2
[6,3,1,3,1,4]=>[[[[[],[[]]]]]]=>1
[6,3,1,3,4,1]=>[[[],[[[[]]]]]]=>1
[6,3,1,4,1,3]=>[[[[]],[[[]]]]]=>1
[6,3,1,4,3,1]=>[[[[],[[[]]]]]]=>1
[6,3,3,1,1,4]=>[[],[[]],[[[]]]]=>3
[6,3,3,1,4,1]=>[[],[[[[],[]]]]]=>2
[6,3,3,4,1,1]=>[[],[],[[],[[]]]]=>3
[6,3,4,1,1,3]=>[[[]],[[],[[]]]]=>2
[6,3,4,1,3,1]=>[[[[]],[[[]]]]]=>1
[6,3,4,3,1,1]=>[[[[]]],[[[]]]]=>2
[6,4,1,1,3,3]=>[[],[[[]]],[[]]]=>3
[6,4,1,3,1,3]=>[[[[]],[[],[]]]]=>1
[6,4,1,3,3,1]=>[[[[]]],[[],[]]]=>2
[6,4,3,1,1,3]=>[[[[]]],[[],[]]]=>2
[6,4,3,1,3,1]=>[[[],[[]],[[]]]]=>1
[6,4,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,3,5,5]=>[[],[],[],[[],[]]]=>4
[1,1,3,5,3,5]=>[[],[[],[],[[]]]]=>2
[1,1,3,5,5,3]=>[[],[[]],[[],[]]]=>3
[1,1,5,3,3,5]=>[[],[[]],[[[]]]]=>3
[1,1,5,3,5,3]=>[[],[[[[],[]]]]]=>2
[1,1,5,5,3,3]=>[[],[],[],[[[]]]]=>4
[1,3,1,3,5,5]=>[[],[[],[],[[]]]]=>2
[1,3,1,5,3,5]=>[[[],[[],[[]]]]]=>1
[1,3,1,5,5,3]=>[[[]],[[],[[]]]]=>2
[1,3,3,1,5,5]=>[[],[[]],[[[]]]]=>3
[1,3,3,5,1,5]=>[[],[[],[[[]]]]]=>2
[1,3,3,5,5,1]=>[[],[[]],[[],[]]]=>3
[1,3,5,1,3,5]=>[[[],[],[],[[]]]]=>1
[1,3,5,1,5,3]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,1,5]=>[[[],[[],[[]]]]]=>1
[1,3,5,3,5,1]=>[[[],[[]],[[]]]]=>1
[1,3,5,5,1,3]=>[[],[[[],[],[]]]]=>2
[1,3,5,5,3,1]=>[[[],[]],[[],[]]]=>2
[1,5,1,3,3,5]=>[[],[[],[[[]]]]]=>2
[1,5,1,3,5,3]=>[[[[[]],[[]]]]]=>1
[1,5,1,5,3,3]=>[[],[[[],[[]]]]]=>2
[1,5,3,1,3,5]=>[[[[],[[],[]]]]]=>1
[1,5,3,1,5,3]=>[[[],[[],[],[]]]]=>1
[1,5,3,3,1,5]=>[[],[[],[[],[]]]]=>2
[1,5,3,3,5,1]=>[[[[]]],[[[]]]]=>2
[1,5,3,5,1,3]=>[[[[],[[[]]]]]]=>1
[1,5,3,5,3,1]=>[[[[],[],[[]]]]]=>1
[1,5,5,1,3,3]=>[[],[[[]]],[[]]]=>3
[1,5,5,3,1,3]=>[[],[[[]],[[]]]]=>2
[1,5,5,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,1,1,3,5,5]=>[[],[],[[],[[]]]]=>3
[3,1,1,5,3,5]=>[[],[[[],[[]]]]]=>2
[3,1,1,5,5,3]=>[[],[[]],[[],[]]]=>3
[3,1,3,1,5,5]=>[[],[[[],[[]]]]]=>2
[3,1,3,5,1,5]=>[[[[],[[[]]]]]]=>1
[3,1,3,5,5,1]=>[[[]],[[],[[]]]]=>2
[3,1,5,1,3,5]=>[[[[],[[[]]]]]]=>1
[3,1,5,1,5,3]=>[[[],[[],[[]]]]]=>1
[3,1,5,3,1,5]=>[[[],[],[[],[]]]]=>1
[3,1,5,3,5,1]=>[[[[[]]],[[]]]]=>1
[3,1,5,5,1,3]=>[[[[]]],[[[]]]]=>2
[3,1,5,5,3,1]=>[[],[[],[],[[]]]]=>2
[3,3,1,1,5,5]=>[[],[],[],[[[]]]]=>4
[3,3,1,5,1,5]=>[[],[[[[],[]]]]]=>2
[3,3,1,5,5,1]=>[[],[[]],[[[]]]]=>3
[3,3,5,1,1,5]=>[[],[[[]]],[[]]]=>3
[3,3,5,1,5,1]=>[[],[[[],[[]]]]]=>2
[3,3,5,5,1,1]=>[[],[],[[]],[[]]]=>4
[3,5,1,1,3,5]=>[[[]],[[],[],[]]]=>2
[3,5,1,1,5,3]=>[[[[]]],[[[]]]]=>2
[3,5,1,3,1,5]=>[[[[]],[[[]]]]]=>1
[3,5,1,3,5,1]=>[[[],[],[[],[]]]]=>1
[3,5,1,5,1,3]=>[[[],[[],[[]]]]]=>1
[3,5,1,5,3,1]=>[[[[[],[[]]]]]]=>1
[3,5,3,1,1,5]=>[[[]],[[],[[]]]]=>2
[3,5,3,1,5,1]=>[[[[],[[[]]]]]]=>1
[3,5,3,5,1,1]=>[[],[[[],[[]]]]]=>2
[3,5,5,1,1,3]=>[[],[[]],[[],[]]]=>3
[3,5,5,1,3,1]=>[[],[[[],[[]]]]]=>2
[3,5,5,3,1,1]=>[[],[[]],[[],[]]]=>3
[5,1,1,3,3,5]=>[[],[[]],[[],[]]]=>3
[5,1,1,3,5,3]=>[[[]],[[],[[]]]]=>2
[5,1,1,5,3,3]=>[[],[],[[[[]]]]]=>3
[5,1,3,1,3,5]=>[[[[[],[],[]]]]]=>1
[5,1,3,1,5,3]=>[[[[[],[[]]]]]]=>1
[5,1,3,3,1,5]=>[[[[]]],[[[]]]]=>2
[5,1,3,3,5,1]=>[[],[[],[[],[]]]]=>2
[5,1,3,5,1,3]=>[[[],[[],[],[]]]]=>1
[5,1,3,5,3,1]=>[[[[],[[],[]]]]]=>1
[5,1,5,1,3,3]=>[[],[[[],[[]]]]]=>2
[5,1,5,3,1,3]=>[[[[[]],[[]]]]]=>1
[5,1,5,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,3,1,1,3,5]=>[[],[[],[[],[]]]]=>2
[5,3,1,1,5,3]=>[[],[[[],[],[]]]]=>2
[5,3,1,3,1,5]=>[[[],[[]],[[]]]]=>1
[5,3,1,3,5,1]=>[[[],[[],[[]]]]]=>1
[5,3,1,5,1,3]=>[[[],[[[[]]]]]]=>1
[5,3,1,5,3,1]=>[[[],[],[],[[]]]]=>1
[5,3,3,1,1,5]=>[[],[[]],[[],[]]]=>3
[5,3,3,1,5,1]=>[[],[[],[[[]]]]]=>2
[5,3,3,5,1,1]=>[[],[],[[[[]]]]]=>3
[5,3,5,1,1,3]=>[[[[]]],[[],[]]]=>2
[5,3,5,1,3,1]=>[[[],[[],[[]]]]]=>1
[5,3,5,3,1,1]=>[[],[[],[],[[]]]]=>2
[5,5,1,1,3,3]=>[[],[],[[]],[[]]]=>4
[5,5,1,3,1,3]=>[[],[[[],[[]]]]]=>2
[5,5,1,3,3,1]=>[[],[[[]]],[[]]]=>3
[5,5,3,1,1,3]=>[[],[[]],[[],[]]]=>3
[5,5,3,1,3,1]=>[[],[[],[],[[]]]]=>2
[5,5,3,3,1,1]=>[[],[],[],[[],[]]]=>4
[1,1,3,3,5,6]=>[[],[],[[],[[]]]]=>3
[1,1,3,3,6,5]=>[[],[[]],[[[]]]]=>3
[1,1,3,5,3,6]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,6,3]=>[[],[[],[[[]]]]]=>2
[1,1,3,6,3,5]=>[[],[[],[[[]]]]]=>2
[1,1,3,6,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,3,6]=>[[],[[]],[[[]]]]=>3
[1,1,5,3,6,3]=>[[],[[],[[[]]]]]=>2
[1,1,5,6,3,3]=>[[],[],[[],[[]]]]=>3
[1,1,6,3,3,5]=>[[],[[]],[[[]]]]=>3
[1,1,6,3,5,3]=>[[],[[],[[[]]]]]=>2
[1,1,6,5,3,3]=>[[],[[]],[[],[]]]=>3
[1,3,1,3,5,6]=>[[[],[[]],[[]]]]=>1
[1,3,1,3,6,5]=>[[[],[[[[]]]]]]=>1
[1,3,1,5,3,6]=>[[[[[],[[]]]]]]=>1
[1,3,1,5,6,3]=>[[[[[[],[]]]]]]=>1
[1,3,1,6,3,5]=>[[[],[[[],[]]]]]=>1
[1,3,1,6,5,3]=>[[[[],[],[[]]]]]=>1
[1,3,3,1,5,6]=>[[[]],[[[[]]]]]=>2
[1,3,3,1,6,5]=>[[[]],[[],[[]]]]=>2
[1,3,3,5,1,6]=>[[],[[],[[[]]]]]=>2
[1,3,3,5,6,1]=>[[],[[],[],[[]]]]=>2
[1,3,3,6,1,5]=>[[],[[[],[[]]]]]=>2
[1,3,3,6,5,1]=>[[[]],[[],[[]]]]=>2
[1,3,5,1,3,6]=>[[[],[],[[],[]]]]=>1
[1,3,5,1,6,3]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,1,6]=>[[[],[[],[],[]]]]=>1
[1,3,5,3,6,1]=>[[[],[],[[[]]]]]=>1
[1,3,5,6,1,3]=>[[[],[],[],[[]]]]=>1
[1,3,5,6,3,1]=>[[[],[[[[]]]]]]=>1
[1,3,6,1,3,5]=>[[[],[],[],[[]]]]=>1
[1,3,6,1,5,3]=>[[[[]],[[[]]]]]=>1
[1,3,6,3,1,5]=>[[[[],[[[]]]]]]=>1
[1,3,6,3,5,1]=>[[[[]],[[],[]]]]=>1
[1,3,6,5,1,3]=>[[[[]],[[],[]]]]=>1
[1,3,6,5,3,1]=>[[[[[],[[]]]]]]=>1
[1,5,1,3,3,6]=>[[[]],[[],[[]]]]=>2
[1,5,1,3,6,3]=>[[[],[[],[[]]]]]=>1
[1,5,1,6,3,3]=>[[],[[],[[[]]]]]=>2
[1,5,3,1,3,6]=>[[[[],[[[]]]]]]=>1
[1,5,3,1,6,3]=>[[[],[[],[],[]]]]=>1
[1,5,3,3,1,6]=>[[],[[],[],[[]]]]=>2
[1,5,3,3,6,1]=>[[[[]]],[[[]]]]=>2
[1,5,3,6,1,3]=>[[[[[],[[]]]]]]=>1
[1,5,3,6,3,1]=>[[[[]],[[],[]]]]=>1
[1,5,6,1,3,3]=>[[],[[],[[[]]]]]=>2
[1,5,6,3,1,3]=>[[[[]],[[[]]]]]=>1
[1,5,6,3,3,1]=>[[[]],[[],[[]]]]=>2
[1,6,1,3,3,5]=>[[[]],[[],[],[]]]=>2
[1,6,1,3,5,3]=>[[[],[[],[],[]]]]=>1
[1,6,1,5,3,3]=>[[],[[],[[[]]]]]=>2
[1,6,3,1,3,5]=>[[[],[[],[[]]]]]=>1
[1,6,3,1,5,3]=>[[[],[],[[],[]]]]=>1
[1,6,3,3,1,5]=>[[],[[],[[],[]]]]=>2
[1,6,3,3,5,1]=>[[[[]]],[[[]]]]=>2
[1,6,3,5,1,3]=>[[[[[],[[]]]]]]=>1
[1,6,3,5,3,1]=>[[[],[[]],[[]]]]=>1
[1,6,5,1,3,3]=>[[[[[]]]],[[]]]=>2
[1,6,5,3,1,3]=>[[[],[],[[[]]]]]=>1
[1,6,5,3,3,1]=>[[],[[],[],[[]]]]=>2
[3,1,1,3,5,6]=>[[],[[[]],[[]]]]=>2
[3,1,1,3,6,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,5,3,6]=>[[],[[[],[[]]]]]=>2
[3,1,1,5,6,3]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,3,5]=>[[],[[],[[[]]]]]=>2
[3,1,1,6,5,3]=>[[],[[],[],[[]]]]=>2
[3,1,3,1,5,6]=>[[[[]],[[[]]]]]=>1
[3,1,3,1,6,5]=>[[[],[[]],[[]]]]=>1
[3,1,3,5,1,6]=>[[[],[[[],[]]]]]=>1
[3,1,3,5,6,1]=>[[[[[],[],[]]]]]=>1
[3,1,3,6,1,5]=>[[[[[],[[]]]]]]=>1
[3,1,3,6,5,1]=>[[[[[]],[[]]]]]=>1
[3,1,5,1,3,6]=>[[[[[],[[]]]]]]=>1
[3,1,5,1,6,3]=>[[[[]],[[],[]]]]=>1
[3,1,5,3,1,6]=>[[[],[],[],[[]]]]=>1
[3,1,5,3,6,1]=>[[[[[]]],[[]]]]=>1
[3,1,5,6,1,3]=>[[[[],[[[]]]]]]=>1
[3,1,5,6,3,1]=>[[[],[[],[[]]]]]=>1
[3,1,6,1,3,5]=>[[[],[[],[],[]]]]=>1
[3,1,6,1,5,3]=>[[[],[],[[[]]]]]=>1
[3,1,6,3,1,5]=>[[[],[],[[],[]]]]=>1
[3,1,6,3,5,1]=>[[[],[[[[]]]]]]=>1
[3,1,6,5,1,3]=>[[[],[[[[]]]]]]=>1
[3,1,6,5,3,1]=>[[[],[],[],[[]]]]=>1
[3,3,1,1,5,6]=>[[],[[[]]],[[]]]=>3
[3,3,1,1,6,5]=>[[],[],[[],[[]]]]=>3
[3,3,1,5,1,6]=>[[],[[],[[[]]]]]=>2
[3,3,1,5,6,1]=>[[],[[[[[]]]]]]=>2
[3,3,1,6,1,5]=>[[],[[],[[[]]]]]=>2
[3,3,1,6,5,1]=>[[],[[],[[[]]]]]=>2
[3,3,5,1,1,6]=>[[],[[[]]],[[]]]=>3
[3,3,5,1,6,1]=>[[],[[],[[[]]]]]=>2
[3,3,5,6,1,1]=>[[],[],[[],[[]]]]=>3
[3,3,6,1,1,5]=>[[],[[[]]],[[]]]=>3
[3,3,6,1,5,1]=>[[],[[],[[[]]]]]=>2
[3,3,6,5,1,1]=>[[],[[]],[[],[]]]=>3
[3,5,1,1,3,6]=>[[],[[],[[],[]]]]=>2
[3,5,1,1,6,3]=>[[[[]]],[[[]]]]=>2
[3,5,1,3,1,6]=>[[[[]],[[],[]]]]=>1
[3,5,1,3,6,1]=>[[[],[],[[],[]]]]=>1
[3,5,1,6,1,3]=>[[[],[],[[[]]]]]=>1
[3,5,1,6,3,1]=>[[[[],[[[]]]]]]=>1
[3,5,3,1,1,6]=>[[],[[],[],[[]]]]=>2
[3,5,3,1,6,1]=>[[[],[[],[],[]]]]=>1
[3,5,3,6,1,1]=>[[],[[],[[[]]]]]=>2
[3,5,6,1,1,3]=>[[],[[],[],[[]]]]=>2
[3,5,6,1,3,1]=>[[[],[[]],[[]]]]=>1
[3,5,6,3,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,1,1,3,5]=>[[],[[],[],[[]]]]=>2
[3,6,1,1,5,3]=>[[[[]]],[[[]]]]=>2
[3,6,1,3,1,5]=>[[[[],[[[]]]]]]=>1
[3,6,1,3,5,1]=>[[[],[[],[],[]]]]=>1
[3,6,1,5,1,3]=>[[[[]],[[],[]]]]=>1
[3,6,1,5,3,1]=>[[[[],[[[]]]]]]=>1
[3,6,3,1,1,5]=>[[[[]]],[[],[]]]=>2
[3,6,3,1,5,1]=>[[[],[[],[[]]]]]=>1
[3,6,3,5,1,1]=>[[],[[],[[[]]]]]=>2
[3,6,5,1,1,3]=>[[[[]]],[[],[]]]=>2
[3,6,5,1,3,1]=>[[[],[[[[]]]]]]=>1
[3,6,5,3,1,1]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,3,6]=>[[],[[]],[[],[]]]=>3
[5,1,1,3,6,3]=>[[],[[[],[[]]]]]=>2
[5,1,1,6,3,3]=>[[],[],[[[[]]]]]=>3
[5,1,3,1,3,6]=>[[[],[[],[[]]]]]=>1
[5,1,3,1,6,3]=>[[[[[]],[[]]]]]=>1
[5,1,3,3,1,6]=>[[[[]]],[[],[]]]=>2
[5,1,3,3,6,1]=>[[],[[],[[],[]]]]=>2
[5,1,3,6,1,3]=>[[[],[[],[],[]]]]=>1
[5,1,3,6,3,1]=>[[[[]],[[[]]]]]=>1
[5,1,6,1,3,3]=>[[],[[],[[[]]]]]=>2
[5,1,6,3,1,3]=>[[[[[],[[]]]]]]=>1
[5,1,6,3,3,1]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,3,6]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,6,3]=>[[],[[],[],[[]]]]=>2
[5,3,1,3,1,6]=>[[[],[],[],[[]]]]=>1
[5,3,1,3,6,1]=>[[[],[[[],[]]]]]=>1
[5,3,1,6,1,3]=>[[[],[],[[],[]]]]=>1
[5,3,1,6,3,1]=>[[[],[],[],[[]]]]=>1
[5,3,3,1,1,6]=>[[],[],[[],[],[]]]=>3
[5,3,3,1,6,1]=>[[],[[],[],[[]]]]=>2
[5,3,3,6,1,1]=>[[],[],[[[[]]]]]=>3
[5,3,6,1,1,3]=>[[[]],[[],[[]]]]=>2
[5,3,6,1,3,1]=>[[[],[[],[[]]]]]=>1
[5,3,6,3,1,1]=>[[],[[],[[[]]]]]=>2
[5,6,1,1,3,3]=>[[],[],[[],[[]]]]=>3
[5,6,1,3,1,3]=>[[[[],[],[[]]]]]=>1
[5,6,1,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,6,3,1,1,3]=>[[[]],[[[[]]]]]=>2
[5,6,3,1,3,1]=>[[[[[[],[]]]]]]=>1
[5,6,3,3,1,1]=>[[],[],[[[[]]]]]=>3
[6,1,1,3,3,5]=>[[],[],[[],[],[]]]=>3
[6,1,1,3,5,3]=>[[],[[],[],[[]]]]=>2
[6,1,1,5,3,3]=>[[],[[]],[[[]]]]=>3
[6,1,3,1,3,5]=>[[[],[],[],[[]]]]=>1
[6,1,3,1,5,3]=>[[[],[[],[[]]]]]=>1
[6,1,3,3,1,5]=>[[[[]]],[[],[]]]=>2
[6,1,3,3,5,1]=>[[],[[],[],[[]]]]=>2
[6,1,3,5,1,3]=>[[[],[],[],[[]]]]=>1
[6,1,3,5,3,1]=>[[[],[],[[],[]]]]=>1
[6,1,5,1,3,3]=>[[],[[],[[[]]]]]=>2
[6,1,5,3,1,3]=>[[[],[[],[[]]]]]=>1
[6,1,5,3,3,1]=>[[[[]]],[[],[]]]=>2
[6,3,1,1,3,5]=>[[[]],[[],[[]]]]=>2
[6,3,1,1,5,3]=>[[],[[],[[],[]]]]=>2
[6,3,1,3,1,5]=>[[[],[[],[[]]]]]=>1
[6,3,1,3,5,1]=>[[[[[]],[[]]]]]=>1
[6,3,1,5,1,3]=>[[[[[]]],[[]]]]=>1
[6,3,1,5,3,1]=>[[[],[[],[],[]]]]=>1
[6,3,3,1,1,5]=>[[],[[]],[[],[]]]=>3
[6,3,3,1,5,1]=>[[],[[[],[[]]]]]=>2
[6,3,3,5,1,1]=>[[],[[[]]],[[]]]=>3
[6,3,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[6,3,5,1,3,1]=>[[[[[],[[]]]]]]=>1
[6,3,5,3,1,1]=>[[],[[[]],[[]]]]=>2
[6,5,1,1,3,3]=>[[[]],[[]],[[]]]=>3
[6,5,1,3,1,3]=>[[[[[]],[[]]]]]=>1
[6,5,1,3,3,1]=>[[[[]]],[[[]]]]=>2
[6,5,3,1,1,3]=>[[[[]]],[[],[]]]=>2
[6,5,3,1,3,1]=>[[[[],[],[[]]]]]=>1
[6,5,3,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,4,4,4]=>[[],[],[],[[[]]]]=>4
[1,1,4,3,4,4]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,3,4]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,4,3]=>[[],[],[[]],[[]]]=>4
[1,3,1,4,4,4]=>[[],[[]],[[[]]]]=>3
[1,3,4,1,4,4]=>[[],[[[[[]]]]]]=>2
[1,3,4,4,1,4]=>[[[[]]],[[[]]]]=>2
[1,3,4,4,4,1]=>[[],[[[]]],[[]]]=>3
[1,4,1,3,4,4]=>[[],[[[[[]]]]]]=>2
[1,4,1,4,3,4]=>[[[[]],[[[]]]]]=>1
[1,4,1,4,4,3]=>[[[]],[[],[[]]]]=>2
[1,4,3,1,4,4]=>[[[]],[[],[[]]]]=>2
[1,4,3,4,1,4]=>[[[[[]]],[[]]]]=>1
[1,4,3,4,4,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,1,3,4]=>[[[]],[[[[]]]]]=>2
[1,4,4,1,4,3]=>[[],[[[],[[]]]]]=>2
[1,4,4,3,1,4]=>[[],[[[],[[]]]]]=>2
[1,4,4,3,4,1]=>[[[]],[[[[]]]]]=>2
[1,4,4,4,1,3]=>[[],[[]],[[[]]]]=>3
[1,4,4,4,3,1]=>[[],[[]],[[[]]]]=>3
[3,1,1,4,4,4]=>[[],[],[[]],[[]]]=>4
[3,1,4,1,4,4]=>[[],[[],[[[]]]]]=>2
[3,1,4,4,1,4]=>[[[[],[]]],[[]]]=>2
[3,1,4,4,4,1]=>[[[]],[[]],[[]]]=>3
[3,4,1,1,4,4]=>[[],[[]],[[[]]]]=>3
[3,4,1,4,1,4]=>[[[[],[[],[]]]]]=>1
[3,4,1,4,4,1]=>[[[]],[[],[[]]]]=>2
[3,4,4,1,1,4]=>[[[]],[[]],[[]]]=>3
[3,4,4,1,4,1]=>[[[]],[[],[[]]]]=>2
[3,4,4,4,1,1]=>[[],[],[[]],[[]]]=>4
[4,1,1,3,4,4]=>[[],[[[]]],[[]]]=>3
[4,1,1,4,3,4]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,4,3]=>[[],[[[]]],[[]]]=>3
[4,1,3,1,4,4]=>[[],[[[[[]]]]]]=>2
[4,1,3,4,1,4]=>[[[[[]]],[[]]]]=>1
[4,1,3,4,4,1]=>[[[[]]],[[],[]]]=>2
[4,1,4,1,3,4]=>[[[[[]]],[[]]]]=>1
[4,1,4,1,4,3]=>[[[],[[],[[]]]]]=>1
[4,1,4,3,1,4]=>[[[[[],[[]]]]]]=>1
[4,1,4,3,4,1]=>[[[[]],[[[]]]]]=>1
[4,1,4,4,1,3]=>[[[]],[[],[[]]]]=>2
[4,1,4,4,3,1]=>[[[]],[[[[]]]]]=>2
[4,3,1,1,4,4]=>[[],[[[]]],[[]]]=>3
[4,3,1,4,1,4]=>[[[[],[[[]]]]]]=>1
[4,3,1,4,4,1]=>[[[[]]],[[[]]]]=>2
[4,3,4,1,1,4]=>[[[[]]],[[[]]]]=>2
[4,3,4,1,4,1]=>[[[[[]],[[]]]]]=>1
[4,3,4,4,1,1]=>[[[]],[[]],[[]]]=>3
[4,4,1,1,3,4]=>[[],[[[]]],[[]]]=>3
[4,4,1,1,4,3]=>[[],[[[]]],[[]]]=>3
[4,4,1,3,1,4]=>[[],[[[[[]]]]]]=>2
[4,4,1,3,4,1]=>[[],[[],[[[]]]]]=>2
[4,4,1,4,1,3]=>[[],[[[]],[[]]]]=>2
[4,4,1,4,3,1]=>[[],[[[[[]]]]]]=>2
[4,4,3,1,1,4]=>[[],[[[]]],[[]]]=>3
[4,4,3,1,4,1]=>[[],[[[[[]]]]]]=>2
[4,4,3,4,1,1]=>[[],[[[]]],[[]]]=>3
[4,4,4,1,1,3]=>[[],[],[[]],[[]]]=>4
[4,4,4,1,3,1]=>[[],[],[[[[]]]]]=>3
[4,4,4,3,1,1]=>[[],[],[[]],[[]]]=>4
[1,1,3,4,4,5]=>[[],[],[[],[[]]]]=>3
[1,1,3,4,5,4]=>[[],[[[],[[]]]]]=>2
[1,1,3,5,4,4]=>[[],[],[[[],[]]]]=>3
[1,1,4,3,4,5]=>[[],[[[[],[]]]]]=>2
[1,1,4,3,5,4]=>[[],[[[],[[]]]]]=>2
[1,1,4,4,3,5]=>[[],[[]],[[[]]]]=>3
[1,1,4,4,5,3]=>[[],[[[]]],[[]]]=>3
[1,1,4,5,3,4]=>[[],[[[],[[]]]]]=>2
[1,1,4,5,4,3]=>[[],[[[[],[]]]]]=>2
[1,1,5,3,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,5,4,3,4]=>[[],[[[],[[]]]]]=>2
[1,1,5,4,4,3]=>[[],[[]],[[],[]]]=>3
[1,3,1,4,4,5]=>[[[]],[[[[]]]]]=>2
[1,3,1,4,5,4]=>[[[[[[[]]]]]]]=>1
[1,3,1,5,4,4]=>[[[[]]],[[[]]]]=>2
[1,3,4,1,4,5]=>[[[[],[[[]]]]]]=>1
[1,3,4,1,5,4]=>[[[[[],[[]]]]]]=>1
[1,3,4,4,1,5]=>[[[[]]],[[],[]]]=>2
[1,3,4,4,5,1]=>[[],[[[]],[[]]]]=>2
[1,3,4,5,1,4]=>[[[[],[[],[]]]]]=>1
[1,3,4,5,4,1]=>[[[[],[[[]]]]]]=>1
[1,3,5,1,4,4]=>[[],[[],[[],[]]]]=>2
[1,3,5,4,1,4]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,4,1]=>[[],[[[[],[]]]]]=>2
[1,4,1,3,4,5]=>[[[[[[],[]]]]]]=>1
[1,4,1,3,5,4]=>[[[[[]],[[]]]]]=>1
[1,4,1,4,3,5]=>[[[[]],[[[]]]]]=>1
[1,4,1,4,5,3]=>[[[[[]]],[[]]]]=>1
[1,4,1,5,3,4]=>[[[[],[[[]]]]]]=>1
[1,4,1,5,4,3]=>[[[[],[[],[]]]]]=>1
[1,4,3,1,4,5]=>[[[[[]]],[[]]]]=>1
[1,4,3,1,5,4]=>[[[[[],[[]]]]]]=>1
[1,4,3,4,1,5]=>[[[[[],[[]]]]]]=>1
[1,4,3,4,5,1]=>[[[[]],[[],[]]]]=>1
[1,4,3,5,1,4]=>[[[],[[]],[[]]]]=>1
[1,4,3,5,4,1]=>[[[[[],[[]]]]]]=>1
[1,4,4,1,3,5]=>[[[]],[[[],[]]]]=>2
[1,4,4,1,5,3]=>[[],[[[]],[[]]]]=>2
[1,4,4,3,1,5]=>[[],[[[[[]]]]]]=>2
[1,4,4,3,5,1]=>[[],[[[],[[]]]]]=>2
[1,4,4,5,1,3]=>[[],[[[],[[]]]]]=>2
[1,4,4,5,3,1]=>[[[[],[]]],[[]]]=>2
[1,4,5,1,3,4]=>[[[],[[[],[]]]]]=>1
[1,4,5,1,4,3]=>[[[],[[]],[[]]]]=>1
[1,4,5,3,1,4]=>[[[],[[],[[]]]]]=>1
[1,4,5,3,4,1]=>[[[[[],[[]]]]]]=>1
[1,4,5,4,1,3]=>[[[[[[[]]]]]]]=>1
[1,4,5,4,3,1]=>[[[[[]],[[]]]]]=>1
[1,5,1,3,4,4]=>[[],[[[[[]]]]]]=>2
[1,5,1,4,3,4]=>[[[[],[[[]]]]]]=>1
[1,5,1,4,4,3]=>[[[]],[[],[[]]]]=>2
[1,5,3,1,4,4]=>[[],[[[],[[]]]]]=>2
[1,5,3,4,1,4]=>[[[[[]]],[[]]]]=>1
[1,5,3,4,4,1]=>[[[[]]],[[],[]]]=>2
[1,5,4,1,3,4]=>[[[],[[[[]]]]]]=>1
[1,5,4,1,4,3]=>[[[],[[[],[]]]]]=>1
[1,5,4,3,1,4]=>[[[[[[],[]]]]]]=>1
[1,5,4,3,4,1]=>[[[[]],[[],[]]]]=>1
[1,5,4,4,1,3]=>[[],[[],[[[]]]]]=>2
[1,5,4,4,3,1]=>[[],[[],[[[]]]]]=>2
[3,1,1,4,4,5]=>[[],[[]],[[[]]]]=>3
[3,1,1,4,5,4]=>[[],[[[[[]]]]]]=>2
[3,1,1,5,4,4]=>[[],[[]],[[[]]]]=>3
[3,1,4,1,4,5]=>[[[[[],[[]]]]]]=>1
[3,1,4,1,5,4]=>[[[[[],[[]]]]]]=>1
[3,1,4,4,1,5]=>[[[]],[[],[[]]]]=>2
[3,1,4,4,5,1]=>[[[[],[]]],[[]]]=>2
[3,1,4,5,1,4]=>[[[[],[],[[]]]]]=>1
[3,1,4,5,4,1]=>[[[[[[[]]]]]]]=>1
[3,1,5,1,4,4]=>[[],[[[]],[[]]]]=>2
[3,1,5,4,1,4]=>[[[[],[[[]]]]]]=>1
[3,1,5,4,4,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,1,4,5]=>[[[[],[]]],[[]]]=>2
[3,4,1,1,5,4]=>[[],[[[]],[[]]]]=>2
[3,4,1,4,1,5]=>[[[[],[],[[]]]]]=>1
[3,4,1,4,5,1]=>[[[],[[],[[]]]]]=>1
[3,4,1,5,1,4]=>[[[[],[[],[]]]]]=>1
[3,4,1,5,4,1]=>[[[[],[],[[]]]]]=>1
[3,4,4,1,1,5]=>[[],[[]],[[],[]]]=>3
[3,4,4,1,5,1]=>[[[]],[[],[[]]]]=>2
[3,4,4,5,1,1]=>[[],[],[[[],[]]]]=>3
[3,4,5,1,1,4]=>[[],[[],[[],[]]]]=>2
[3,4,5,1,4,1]=>[[[],[[],[[]]]]]=>1
[3,4,5,4,1,1]=>[[[]],[[[],[]]]]=>2
[3,5,1,1,4,4]=>[[],[],[[],[[]]]]=>3
[3,5,1,4,1,4]=>[[[[],[],[[]]]]]=>1
[3,5,1,4,4,1]=>[[[]],[[],[[]]]]=>2
[3,5,4,1,1,4]=>[[[[[]]]],[[]]]=>2
[3,5,4,1,4,1]=>[[[[[]],[[]]]]]=>1
[3,5,4,4,1,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,3,4,5]=>[[[[],[]]],[[]]]=>2
[4,1,1,3,5,4]=>[[],[[[]],[[]]]]=>2
[4,1,1,4,3,5]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,5,3]=>[[[[[]]]],[[]]]=>2
[4,1,1,5,3,4]=>[[],[[],[[[]]]]]=>2
[4,1,1,5,4,3]=>[[],[[],[[],[]]]]=>2
[4,1,3,1,4,5]=>[[[[[[[]]]]]]]=>1
[4,1,3,1,5,4]=>[[[],[[[[]]]]]]=>1
[4,1,3,4,1,5]=>[[[],[],[[[]]]]]=>1
[4,1,3,4,5,1]=>[[[[[],[[]]]]]]=>1
[4,1,3,5,1,4]=>[[[[],[[],[]]]]]=>1
[4,1,3,5,4,1]=>[[[],[[[],[]]]]]=>1
[4,1,4,1,3,5]=>[[[[]],[[],[]]]]=>1
[4,1,4,1,5,3]=>[[[],[[]],[[]]]]=>1
[4,1,4,3,1,5]=>[[[[[]]],[[]]]]=>1
[4,1,4,3,5,1]=>[[[[[],[[]]]]]]=>1
[4,1,4,5,1,3]=>[[[[[]],[[]]]]]=>1
[4,1,4,5,3,1]=>[[[[],[[[]]]]]]=>1
[4,1,5,1,3,4]=>[[[],[[[[]]]]]]=>1
[4,1,5,1,4,3]=>[[[],[[],[[]]]]]=>1
[4,1,5,3,1,4]=>[[[],[[],[[]]]]]=>1
[4,1,5,3,4,1]=>[[[],[],[[[]]]]]=>1
[4,1,5,4,1,3]=>[[[],[],[[[]]]]]=>1
[4,1,5,4,3,1]=>[[[],[[[],[]]]]]=>1
[4,3,1,1,4,5]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,5,4]=>[[],[[[],[[]]]]]=>2
[4,3,1,4,1,5]=>[[[[[]],[[]]]]]=>1
[4,3,1,4,5,1]=>[[[[],[[[]]]]]]=>1
[4,3,1,5,1,4]=>[[[[[]],[[]]]]]=>1
[4,3,1,5,4,1]=>[[[],[[],[[]]]]]=>1
[4,3,4,1,1,5]=>[[],[[[]],[[]]]]=>2
[4,3,4,1,5,1]=>[[[[[],[[]]]]]]=>1
[4,3,4,5,1,1]=>[[[[],[]]],[[]]]=>2
[4,3,5,1,1,4]=>[[],[[[]],[[]]]]=>2
[4,3,5,1,4,1]=>[[[[[],[[]]]]]]=>1
[4,3,5,4,1,1]=>[[[]],[[],[[]]]]=>2
[4,4,1,1,3,5]=>[[],[[]],[[],[]]]=>3
[4,4,1,1,5,3]=>[[],[],[[],[[]]]]=>3
[4,4,1,3,1,5]=>[[],[[],[[[]]]]]=>2
[4,4,1,3,5,1]=>[[],[[[],[[]]]]]=>2
[4,4,1,5,1,3]=>[[],[[],[[[]]]]]=>2
[4,4,1,5,3,1]=>[[],[[],[[],[]]]]=>2
[4,4,3,1,1,5]=>[[],[[[]]],[[]]]=>3
[4,4,3,1,5,1]=>[[],[[[[[]]]]]]=>2
[4,4,3,5,1,1]=>[[],[[[]]],[[]]]=>3
[4,4,5,1,1,3]=>[[],[[]],[[[]]]]=>3
[4,4,5,1,3,1]=>[[],[[[[[]]]]]]=>2
[4,4,5,3,1,1]=>[[],[],[[],[[]]]]=>3
[4,5,1,1,3,4]=>[[[[],[]]],[[]]]=>2
[4,5,1,1,4,3]=>[[],[[[]],[[]]]]=>2
[4,5,1,3,1,4]=>[[[[],[[[]]]]]]=>1
[4,5,1,3,4,1]=>[[[[[]]],[[]]]]=>1
[4,5,1,4,1,3]=>[[[[],[[[]]]]]]=>1
[4,5,1,4,3,1]=>[[[[],[[[]]]]]]=>1
[4,5,3,1,1,4]=>[[[]],[[],[[]]]]=>2
[4,5,3,1,4,1]=>[[[[],[[[]]]]]]=>1
[4,5,3,4,1,1]=>[[],[[[],[[]]]]]=>2
[4,5,4,1,1,3]=>[[[[[]]]],[[]]]=>2
[4,5,4,1,3,1]=>[[[[[[[]]]]]]]=>1
[4,5,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,4,4]=>[[],[[[]]],[[]]]=>3
[5,1,1,4,3,4]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,4,3]=>[[],[[]],[[],[]]]=>3
[5,1,3,1,4,4]=>[[],[[],[[[]]]]]=>2
[5,1,3,4,1,4]=>[[[],[[[[]]]]]]=>1
[5,1,3,4,4,1]=>[[[[[]]]],[[]]]=>2
[5,1,4,1,3,4]=>[[[],[[[[]]]]]]=>1
[5,1,4,1,4,3]=>[[[],[[]],[[]]]]=>1
[5,1,4,3,1,4]=>[[[],[[]],[[]]]]=>1
[5,1,4,3,4,1]=>[[[],[[[[]]]]]]=>1
[5,1,4,4,1,3]=>[[[[]]],[[],[]]]=>2
[5,1,4,4,3,1]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,4,4]=>[[],[],[[[],[]]]]=>3
[5,3,1,4,1,4]=>[[[],[[[],[]]]]]=>1
[5,3,1,4,4,1]=>[[[[],[]]],[[]]]=>2
[5,3,4,1,1,4]=>[[[]],[[[[]]]]]=>2
[5,3,4,1,4,1]=>[[[[[],[[]]]]]]=>1
[5,3,4,4,1,1]=>[[],[[]],[[[]]]]=>3
[5,4,1,1,3,4]=>[[[[[]]]],[[]]]=>2
[5,4,1,1,4,3]=>[[[[],[]]],[[]]]=>2
[5,4,1,3,1,4]=>[[[[[[[]]]]]]]=>1
[5,4,1,3,4,1]=>[[[[],[[[]]]]]]=>1
[5,4,1,4,1,3]=>[[[[[],[[]]]]]]=>1
[5,4,1,4,3,1]=>[[[[]],[[[]]]]]=>1
[5,4,3,1,1,4]=>[[[[],[]]],[[]]]=>2
[5,4,3,1,4,1]=>[[[],[[[[]]]]]]=>1
[5,4,3,4,1,1]=>[[[[]]],[[],[]]]=>2
[5,4,4,1,1,3]=>[[],[[[]]],[[]]]=>3
[5,4,4,1,3,1]=>[[],[[[[[]]]]]]=>2
[5,4,4,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,4,4,6]=>[[],[[]],[[],[]]]=>3
[1,1,3,4,6,4]=>[[],[[[]],[[]]]]=>2
[1,1,3,6,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,4,3,4,6]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,6,4]=>[[],[[],[[[]]]]]=>2
[1,1,4,4,3,6]=>[[],[],[[[],[]]]]=>3
[1,1,4,4,6,3]=>[[],[[[]]],[[]]]=>3
[1,1,4,6,3,4]=>[[],[[[[[]]]]]]=>2
[1,1,4,6,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,4,4]=>[[],[],[[[[]]]]]=>3
[1,1,6,4,3,4]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,4,3]=>[[],[],[[[],[]]]]=>3
[1,3,1,4,4,6]=>[[[[]]],[[],[]]]=>2
[1,3,1,4,6,4]=>[[[[]],[[],[]]]]=>1
[1,3,1,6,4,4]=>[[],[[],[],[[]]]]=>2
[1,3,4,1,4,6]=>[[[],[[[[]]]]]]=>1
[1,3,4,1,6,4]=>[[[[[[],[]]]]]]=>1
[1,3,4,4,1,6]=>[[[[]]],[[[]]]]=>2
[1,3,4,4,6,1]=>[[[]],[[],[],[]]]=>2
[1,3,4,6,1,4]=>[[[],[[]],[[]]]]=>1
[1,3,4,6,4,1]=>[[[[]],[[[]]]]]=>1
[1,3,6,1,4,4]=>[[],[[],[[],[]]]]=>2
[1,3,6,4,1,4]=>[[[[[[],[]]]]]]=>1
[1,3,6,4,4,1]=>[[[]],[[[[]]]]]=>2
[1,4,1,3,4,6]=>[[[[[],[[]]]]]]=>1
[1,4,1,3,6,4]=>[[[[[]]],[[]]]]=>1
[1,4,1,4,3,6]=>[[[],[],[[[]]]]]=>1
[1,4,1,4,6,3]=>[[[],[[[],[]]]]]=>1
[1,4,1,6,3,4]=>[[[[[],[[]]]]]]=>1
[1,4,1,6,4,3]=>[[[[],[[[]]]]]]=>1
[1,4,3,1,4,6]=>[[[[[]]],[[]]]]=>1
[1,4,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[1,4,3,4,1,6]=>[[[[[[[]]]]]]]=>1
[1,4,3,4,6,1]=>[[[[[],[[]]]]]]=>1
[1,4,3,6,1,4]=>[[[],[[]],[[]]]]=>1
[1,4,3,6,4,1]=>[[[],[[[[]]]]]]=>1
[1,4,4,1,3,6]=>[[],[[[[],[]]]]]=>2
[1,4,4,1,6,3]=>[[],[[],[[[]]]]]=>2
[1,4,4,3,1,6]=>[[],[[[],[[]]]]]=>2
[1,4,4,3,6,1]=>[[],[[[[],[]]]]]=>2
[1,4,4,6,1,3]=>[[[]],[[],[],[]]]=>2
[1,4,4,6,3,1]=>[[[[[]]]],[[]]]=>2
[1,4,6,1,3,4]=>[[[[],[],[[]]]]]=>1
[1,4,6,1,4,3]=>[[[[]],[[],[]]]]=>1
[1,4,6,3,1,4]=>[[[],[[[[]]]]]]=>1
[1,4,6,3,4,1]=>[[[[[],[[]]]]]]=>1
[1,4,6,4,1,3]=>[[[[[[],[]]]]]]=>1
[1,4,6,4,3,1]=>[[[[[],[[]]]]]]=>1
[1,6,1,3,4,4]=>[[],[[[],[[]]]]]=>2
[1,6,1,4,3,4]=>[[[[[[[]]]]]]]=>1
[1,6,1,4,4,3]=>[[[[]]],[[[]]]]=>2
[1,6,3,1,4,4]=>[[],[[[],[[]]]]]=>2
[1,6,3,4,1,4]=>[[[[[],[[]]]]]]=>1
[1,6,3,4,4,1]=>[[[[]]],[[],[]]]=>2
[1,6,4,1,3,4]=>[[[],[[[[]]]]]]=>1
[1,6,4,1,4,3]=>[[[],[[[[]]]]]]=>1
[1,6,4,3,1,4]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,4,1]=>[[[],[[[[]]]]]]=>1
[1,6,4,4,1,3]=>[[[[]]],[[],[]]]=>2
[1,6,4,4,3,1]=>[[],[[[],[],[]]]]=>2
[3,1,1,4,4,6]=>[[],[[]],[[[]]]]=>3
[3,1,1,4,6,4]=>[[],[[[[],[]]]]]=>2
[3,1,1,6,4,4]=>[[],[],[[],[],[]]]=>3
[3,1,4,1,4,6]=>[[[[[],[[]]]]]]=>1
[3,1,4,1,6,4]=>[[[],[[]],[[]]]]=>1
[3,1,4,4,1,6]=>[[[]],[[[],[]]]]=>2
[3,1,4,4,6,1]=>[[[]],[[],[[]]]]=>2
[3,1,4,6,1,4]=>[[[[],[[],[]]]]]=>1
[3,1,4,6,4,1]=>[[[[[]]],[[]]]]=>1
[3,1,6,1,4,4]=>[[],[[[[],[]]]]]=>2
[3,1,6,4,1,4]=>[[[],[],[[[]]]]]=>1
[3,1,6,4,4,1]=>[[[]],[[],[],[]]]=>2
[3,4,1,1,4,6]=>[[[[]]],[[[]]]]=>2
[3,4,1,1,6,4]=>[[],[[],[[[]]]]]=>2
[3,4,1,4,1,6]=>[[[[[]],[[]]]]]=>1
[3,4,1,4,6,1]=>[[[[[[],[]]]]]]=>1
[3,4,1,6,1,4]=>[[[[[[[]]]]]]]=>1
[3,4,1,6,4,1]=>[[[[],[[],[]]]]]=>1
[3,4,4,1,1,6]=>[[[]],[[]],[[]]]=>3
[3,4,4,1,6,1]=>[[[]],[[[[]]]]]=>2
[3,4,4,6,1,1]=>[[],[[]],[[],[]]]=>3
[3,4,6,1,1,4]=>[[[]],[[],[[]]]]=>2
[3,4,6,1,4,1]=>[[[[],[[[]]]]]]=>1
[3,4,6,4,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,1,1,4,4]=>[[],[[]],[[],[]]]=>3
[3,6,1,4,1,4]=>[[[],[[]],[[]]]]=>1
[3,6,1,4,4,1]=>[[[]],[[],[[]]]]=>2
[3,6,4,1,1,4]=>[[[[]]],[[],[]]]=>2
[3,6,4,1,4,1]=>[[[[]],[[],[]]]]=>1
[3,6,4,4,1,1]=>[[],[[]],[[[]]]]=>3
[4,1,1,3,4,6]=>[[[]],[[],[[]]]]=>2
[4,1,1,3,6,4]=>[[[[[]]]],[[]]]=>2
[4,1,1,4,3,6]=>[[],[[],[[[]]]]]=>2
[4,1,1,4,6,3]=>[[],[[[[],[]]]]]=>2
[4,1,1,6,3,4]=>[[],[[[],[[]]]]]=>2
[4,1,1,6,4,3]=>[[],[[],[[[]]]]]=>2
[4,1,3,1,4,6]=>[[[[[[],[]]]]]]=>1
[4,1,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[4,1,3,4,1,6]=>[[[[[]]],[[]]]]=>1
[4,1,3,4,6,1]=>[[[[[],[],[]]]]]=>1
[4,1,3,6,1,4]=>[[[[],[[],[]]]]]=>1
[4,1,3,6,4,1]=>[[[],[[[[]]]]]]=>1
[4,1,4,1,3,6]=>[[[],[[[],[]]]]]=>1
[4,1,4,1,6,3]=>[[[],[],[[[]]]]]=>1
[4,1,4,3,1,6]=>[[[[[]],[[]]]]]=>1
[4,1,4,3,6,1]=>[[[[[[],[]]]]]]=>1
[4,1,4,6,1,3]=>[[[[],[],[[]]]]]=>1
[4,1,4,6,3,1]=>[[[[[]]],[[]]]]=>1
[4,1,6,1,3,4]=>[[[[[]],[[]]]]]=>1
[4,1,6,1,4,3]=>[[[[[[[]]]]]]]=>1
[4,1,6,3,1,4]=>[[[],[[],[[]]]]]=>1
[4,1,6,3,4,1]=>[[[],[],[[[]]]]]=>1
[4,1,6,4,1,3]=>[[[[]],[[],[]]]]=>1
[4,1,6,4,3,1]=>[[[[],[],[[]]]]]=>1
[4,3,1,1,4,6]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,6,4]=>[[],[[],[],[[]]]]=>2
[4,3,1,4,1,6]=>[[[[],[[[]]]]]]=>1
[4,3,1,4,6,1]=>[[[[[]],[[]]]]]=>1
[4,3,1,6,1,4]=>[[[[[[],[]]]]]]=>1
[4,3,1,6,4,1]=>[[[[[],[],[]]]]]=>1
[4,3,4,1,1,6]=>[[[[]]],[[[]]]]=>2
[4,3,4,1,6,1]=>[[[[[[[]]]]]]]=>1
[4,3,4,6,1,1]=>[[[]],[[],[[]]]]=>2
[4,3,6,1,1,4]=>[[[]],[[],[[]]]]=>2
[4,3,6,1,4,1]=>[[[[[],[[]]]]]]=>1
[4,3,6,4,1,1]=>[[[[[]]]],[[]]]=>2
[4,4,1,1,3,6]=>[[],[[[]]],[[]]]=>3
[4,4,1,1,6,3]=>[[],[],[[[],[]]]]=>3
[4,4,1,3,1,6]=>[[],[[[],[[]]]]]=>2
[4,4,1,3,6,1]=>[[],[[[],[[]]]]]=>2
[4,4,1,6,1,3]=>[[],[[[],[[]]]]]=>2
[4,4,1,6,3,1]=>[[],[[],[[],[]]]]=>2
[4,4,3,1,1,6]=>[[],[],[[],[[]]]]=>3
[4,4,3,1,6,1]=>[[],[[[[],[]]]]]=>2
[4,4,3,6,1,1]=>[[],[[[]]],[[]]]=>3
[4,4,6,1,1,3]=>[[],[],[[],[],[]]]=>3
[4,4,6,1,3,1]=>[[],[[],[],[[]]]]=>2
[4,4,6,3,1,1]=>[[],[],[[[[]]]]]=>3
[4,6,1,1,3,4]=>[[],[[],[],[[]]]]=>2
[4,6,1,1,4,3]=>[[[[]]],[[],[]]]=>2
[4,6,1,3,1,4]=>[[[],[],[[[]]]]]=>1
[4,6,1,3,4,1]=>[[[],[],[[[]]]]]=>1
[4,6,1,4,1,3]=>[[[],[],[[[]]]]]=>1
[4,6,1,4,3,1]=>[[[],[[[[]]]]]]=>1
[4,6,3,1,1,4]=>[[[]],[[[[]]]]]=>2
[4,6,3,1,4,1]=>[[[[[[],[]]]]]]=>1
[4,6,3,4,1,1]=>[[],[[[]],[[]]]]=>2
[4,6,4,1,1,3]=>[[[[]]],[[],[]]]=>2
[4,6,4,1,3,1]=>[[[[]],[[],[]]]]=>1
[4,6,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[6,1,1,3,4,4]=>[[],[],[[[],[]]]]=>3
[6,1,1,4,3,4]=>[[[]],[[[[]]]]]=>2
[6,1,1,4,4,3]=>[[[]],[[]],[[]]]=>3
[6,1,3,1,4,4]=>[[],[[[[],[]]]]]=>2
[6,1,3,4,1,4]=>[[[],[[[[]]]]]]=>1
[6,1,3,4,4,1]=>[[[[],[]]],[[]]]=>2
[6,1,4,1,3,4]=>[[[[]],[[[]]]]]=>1
[6,1,4,1,4,3]=>[[[[[],[[]]]]]]=>1
[6,1,4,3,1,4]=>[[[[[],[[]]]]]]=>1
[6,1,4,3,4,1]=>[[[[[[[]]]]]]]=>1
[6,1,4,4,1,3]=>[[[]],[[[],[]]]]=>2
[6,1,4,4,3,1]=>[[[[]]],[[[]]]]=>2
[6,3,1,1,4,4]=>[[],[[[]]],[[]]]=>3
[6,3,1,4,1,4]=>[[[[]],[[],[]]]]=>1
[6,3,1,4,4,1]=>[[[[]]],[[],[]]]=>2
[6,3,4,1,1,4]=>[[[]],[[],[[]]]]=>2
[6,3,4,1,4,1]=>[[[],[[]],[[]]]]=>1
[6,3,4,4,1,1]=>[[],[[]],[[],[]]]=>3
[6,4,1,1,3,4]=>[[[[]]],[[[]]]]=>2
[6,4,1,1,4,3]=>[[[[[]]]],[[]]]=>2
[6,4,1,3,1,4]=>[[[[[]]],[[]]]]=>1
[6,4,1,3,4,1]=>[[[[[[],[]]]]]]=>1
[6,4,1,4,1,3]=>[[[[[],[[]]]]]]=>1
[6,4,1,4,3,1]=>[[[[]],[[[]]]]]=>1
[6,4,3,1,1,4]=>[[[[]]],[[],[]]]=>2
[6,4,3,1,4,1]=>[[[],[[[[]]]]]]=>1
[6,4,3,4,1,1]=>[[[[[]]]],[[]]]=>2
[6,4,4,1,1,3]=>[[],[[]],[[[]]]]=>3
[6,4,4,1,3,1]=>[[],[[[[],[]]]]]=>2
[6,4,4,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,4,5,5]=>[[],[],[[],[[]]]]=>3
[1,1,3,5,4,5]=>[[],[[],[[[]]]]]=>2
[1,1,3,5,5,4]=>[[],[[]],[[],[]]]=>3
[1,1,4,3,5,5]=>[[],[[]],[[[]]]]=>3
[1,1,4,5,3,5]=>[[],[[[[[]]]]]]=>2
[1,1,4,5,5,3]=>[[],[[[]]],[[]]]=>3
[1,1,5,3,4,5]=>[[],[[[],[[]]]]]=>2
[1,1,5,3,5,4]=>[[],[[[[[]]]]]]=>2
[1,1,5,4,3,5]=>[[],[[[],[[]]]]]=>2
[1,1,5,4,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,5,5,3,4]=>[[],[[]],[[[]]]]=>3
[1,1,5,5,4,3]=>[[],[],[[],[[]]]]=>3
[1,3,1,4,5,5]=>[[],[[[[[]]]]]]=>2
[1,3,1,5,4,5]=>[[[[[[[]]]]]]]=>1
[1,3,1,5,5,4]=>[[[]],[[[[]]]]]=>2
[1,3,4,1,5,5]=>[[],[[],[[[]]]]]=>2
[1,3,4,5,1,5]=>[[[[],[[[]]]]]]=>1
[1,3,4,5,5,1]=>[[[]],[[],[[]]]]=>2
[1,3,5,1,4,5]=>[[[],[[],[[]]]]]=>1
[1,3,5,1,5,4]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,1,5]=>[[[],[[[],[]]]]]=>1
[1,3,5,4,5,1]=>[[[],[[[[]]]]]]=>1
[1,3,5,5,1,4]=>[[[],[]],[[],[]]]=>2
[1,3,5,5,4,1]=>[[[[]]],[[],[]]]=>2
[1,4,1,3,5,5]=>[[],[[],[[[]]]]]=>2
[1,4,1,5,3,5]=>[[[[],[[[]]]]]]=>1
[1,4,1,5,5,3]=>[[[]],[[],[[]]]]=>2
[1,4,3,1,5,5]=>[[[[[]]]],[[]]]=>2
[1,4,3,5,1,5]=>[[[[]],[[[]]]]]=>1
[1,4,3,5,5,1]=>[[[]],[[],[[]]]]=>2
[1,4,5,1,3,5]=>[[[[]],[[],[]]]]=>1
[1,4,5,1,5,3]=>[[[[]],[[[]]]]]=>1
[1,4,5,3,1,5]=>[[[[[]],[[]]]]]=>1
[1,4,5,3,5,1]=>[[[],[[[[]]]]]]=>1
[1,4,5,5,1,3]=>[[[]],[[],[[]]]]=>2
[1,4,5,5,3,1]=>[[[[]]],[[],[]]]=>2
[1,5,1,3,4,5]=>[[[[[[],[]]]]]]=>1
[1,5,1,3,5,4]=>[[[[[]],[[]]]]]=>1
[1,5,1,4,3,5]=>[[[[],[[[]]]]]]=>1
[1,5,1,4,5,3]=>[[[[],[[[]]]]]]=>1
[1,5,1,5,3,4]=>[[[[]],[[[]]]]]=>1
[1,5,1,5,4,3]=>[[[],[[],[[]]]]]=>1
[1,5,3,1,4,5]=>[[[[],[[[]]]]]]=>1
[1,5,3,1,5,4]=>[[[],[[[],[]]]]]=>1
[1,5,3,4,1,5]=>[[[],[[]],[[]]]]=>1
[1,5,3,4,5,1]=>[[[[[]],[[]]]]]=>1
[1,5,3,5,1,4]=>[[[[[],[[]]]]]]=>1
[1,5,3,5,4,1]=>[[[[]],[[[]]]]]=>1
[1,5,4,1,3,5]=>[[[],[[],[[]]]]]=>1
[1,5,4,1,5,3]=>[[[],[],[[[]]]]]=>1
[1,5,4,3,1,5]=>[[[[]],[[],[]]]]=>1
[1,5,4,3,5,1]=>[[[[],[[[]]]]]]=>1
[1,5,4,5,1,3]=>[[[[[[[]]]]]]]=>1
[1,5,4,5,3,1]=>[[[[[]],[[]]]]]=>1
[1,5,5,1,3,4]=>[[[[[]]]],[[]]]=>2
[1,5,5,1,4,3]=>[[],[[[]],[[]]]]=>2
[1,5,5,3,1,4]=>[[],[[[]],[[]]]]=>2
[1,5,5,3,4,1]=>[[],[[[[],[]]]]]=>2
[1,5,5,4,1,3]=>[[],[[[[],[]]]]]=>2
[1,5,5,4,3,1]=>[[],[[],[[[]]]]]=>2
[3,1,1,4,5,5]=>[[],[],[[[[]]]]]=>3
[3,1,1,5,4,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,5,5,4]=>[[],[[]],[[[]]]]=>3
[3,1,4,1,5,5]=>[[],[[[]],[[]]]]=>2
[3,1,4,5,1,5]=>[[[[[],[[]]]]]]=>1
[3,1,4,5,5,1]=>[[[[]]],[[],[]]]=>2
[3,1,5,1,4,5]=>[[[[[]],[[]]]]]=>1
[3,1,5,1,5,4]=>[[[[[],[[]]]]]]=>1
[3,1,5,4,1,5]=>[[[[],[],[[]]]]]=>1
[3,1,5,4,5,1]=>[[[[[[[]]]]]]]=>1
[3,1,5,5,1,4]=>[[[]],[[],[[]]]]=>2
[3,1,5,5,4,1]=>[[],[[[],[[]]]]]=>2
[3,4,1,1,5,5]=>[[],[],[[],[[]]]]=>3
[3,4,1,5,1,5]=>[[[[],[],[[]]]]]=>1
[3,4,1,5,5,1]=>[[[]],[[],[[]]]]=>2
[3,4,5,1,1,5]=>[[[[],[]]],[[]]]=>2
[3,4,5,1,5,1]=>[[[],[[],[[]]]]]=>1
[3,4,5,5,1,1]=>[[],[[]],[[],[]]]=>3
[3,5,1,1,4,5]=>[[],[[[]],[[]]]]=>2
[3,5,1,1,5,4]=>[[[[]]],[[[]]]]=>2
[3,5,1,4,1,5]=>[[[[],[[],[]]]]]=>1
[3,5,1,4,5,1]=>[[[[],[],[[]]]]]=>1
[3,5,1,5,1,4]=>[[[[[],[],[]]]]]=>1
[3,5,1,5,4,1]=>[[[[],[[[]]]]]]=>1
[3,5,4,1,1,5]=>[[],[[],[[[]]]]]=>2
[3,5,4,1,5,1]=>[[[[],[[[]]]]]]=>1
[3,5,4,5,1,1]=>[[[[]]],[[[]]]]=>2
[3,5,5,1,1,4]=>[[],[[]],[[],[]]]=>3
[3,5,5,1,4,1]=>[[[]],[[],[[]]]]=>2
[3,5,5,4,1,1]=>[[[]],[[]],[[]]]=>3
[4,1,1,3,5,5]=>[[],[],[[],[[]]]]=>3
[4,1,1,5,3,5]=>[[],[[],[[[]]]]]=>2
[4,1,1,5,5,3]=>[[],[[]],[[],[]]]=>3
[4,1,3,1,5,5]=>[[],[[],[[[]]]]]=>2
[4,1,3,5,1,5]=>[[[],[[[],[]]]]]=>1
[4,1,3,5,5,1]=>[[[]],[[],[[]]]]=>2
[4,1,5,1,3,5]=>[[[],[[[],[]]]]]=>1
[4,1,5,1,5,3]=>[[[],[[]],[[]]]]=>1
[4,1,5,3,1,5]=>[[[],[],[[],[]]]]=>1
[4,1,5,3,5,1]=>[[[],[[[[]]]]]]=>1
[4,1,5,5,1,3]=>[[[[]]],[[],[]]]=>2
[4,1,5,5,3,1]=>[[],[[],[[],[]]]]=>2
[4,3,1,1,5,5]=>[[],[[[]]],[[]]]=>3
[4,3,1,5,1,5]=>[[[[],[[[]]]]]]=>1
[4,3,1,5,5,1]=>[[[[]]],[[[]]]]=>2
[4,3,5,1,1,5]=>[[[[]]],[[[]]]]=>2
[4,3,5,1,5,1]=>[[[[[]],[[]]]]]=>1
[4,3,5,5,1,1]=>[[[]],[[]],[[]]]=>3
[4,5,1,1,3,5]=>[[[[]]],[[],[]]]=>2
[4,5,1,1,5,3]=>[[[[]]],[[[]]]]=>2
[4,5,1,3,1,5]=>[[[[[[[]]]]]]]=>1
[4,5,1,3,5,1]=>[[[[],[[],[]]]]]=>1
[4,5,1,5,1,3]=>[[[[[]],[[]]]]]=>1
[4,5,1,5,3,1]=>[[[[[],[[]]]]]]=>1
[4,5,3,1,1,5]=>[[[]],[[],[[]]]]=>2
[4,5,3,1,5,1]=>[[[[],[[[]]]]]]=>1
[4,5,3,5,1,1]=>[[],[[[[[]]]]]]=>2
[4,5,5,1,1,3]=>[[[]],[[]],[[]]]=>3
[4,5,5,1,3,1]=>[[[]],[[[[]]]]]=>2
[4,5,5,3,1,1]=>[[],[[]],[[],[]]]=>3
[5,1,1,3,4,5]=>[[[[],[]]],[[]]]=>2
[5,1,1,3,5,4]=>[[[]],[[],[[]]]]=>2
[5,1,1,4,3,5]=>[[],[[],[[[]]]]]=>2
[5,1,1,4,5,3]=>[[],[[],[[[]]]]]=>2
[5,1,1,5,3,4]=>[[[]],[[[[]]]]]=>2
[5,1,1,5,4,3]=>[[],[[[],[[]]]]]=>2
[5,1,3,1,4,5]=>[[[[]],[[[]]]]]=>1
[5,1,3,1,5,4]=>[[[[[[[]]]]]]]=>1
[5,1,3,4,1,5]=>[[[[[[],[]]]]]]=>1
[5,1,3,4,5,1]=>[[[],[[],[[]]]]]=>1
[5,1,3,5,1,4]=>[[[],[],[[],[]]]]=>1
[5,1,3,5,4,1]=>[[[[],[[[]]]]]]=>1
[5,1,4,1,3,5]=>[[[],[[[],[]]]]]=>1
[5,1,4,1,5,3]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,1,5]=>[[[],[[[[]]]]]]=>1
[5,1,4,3,5,1]=>[[[],[[]],[[]]]]=>1
[5,1,4,5,1,3]=>[[[],[[]],[[]]]]=>1
[5,1,4,5,3,1]=>[[[],[[[],[]]]]]=>1
[5,1,5,1,3,4]=>[[[[[]]],[[]]]]=>1
[5,1,5,1,4,3]=>[[[],[[]],[[]]]]=>1
[5,1,5,3,1,4]=>[[[],[[],[[]]]]]=>1
[5,1,5,3,4,1]=>[[[[[[],[]]]]]]=>1
[5,1,5,4,1,3]=>[[[[[[],[]]]]]]=>1
[5,1,5,4,3,1]=>[[[[],[[[]]]]]]=>1
[5,3,1,1,4,5]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,5,4]=>[[],[[[[],[]]]]]=>2
[5,3,1,4,1,5]=>[[[],[[],[[]]]]]=>1
[5,3,1,4,5,1]=>[[[],[[[],[]]]]]=>1
[5,3,1,5,1,4]=>[[[],[[],[[]]]]]=>1
[5,3,1,5,4,1]=>[[[],[[],[[]]]]]=>1
[5,3,4,1,1,5]=>[[[]],[[],[[]]]]=>2
[5,3,4,1,5,1]=>[[[[[]],[[]]]]]=>1
[5,3,4,5,1,1]=>[[],[[[],[[]]]]]=>2
[5,3,5,1,1,4]=>[[[]],[[],[[]]]]=>2
[5,3,5,1,4,1]=>[[[[[]],[[]]]]]=>1
[5,3,5,4,1,1]=>[[[[]]],[[[]]]]=>2
[5,4,1,1,3,5]=>[[[]],[[],[[]]]]=>2
[5,4,1,1,5,3]=>[[],[[],[[[]]]]]=>2
[5,4,1,3,1,5]=>[[[[],[[[]]]]]]=>1
[5,4,1,3,5,1]=>[[[[[],[[]]]]]]=>1
[5,4,1,5,1,3]=>[[[[[[],[]]]]]]=>1
[5,4,1,5,3,1]=>[[[[],[[],[]]]]]=>1
[5,4,3,1,1,5]=>[[[[],[]]],[[]]]=>2
[5,4,3,1,5,1]=>[[[],[[[[]]]]]]=>1
[5,4,3,5,1,1]=>[[[[]]],[[],[]]]=>2
[5,4,5,1,1,3]=>[[[[]]],[[[]]]]=>2
[5,4,5,1,3,1]=>[[[[[[[]]]]]]]=>1
[5,4,5,3,1,1]=>[[[]],[[],[[]]]]=>2
[5,5,1,1,3,4]=>[[],[[[]]],[[]]]=>3
[5,5,1,1,4,3]=>[[],[],[[],[[]]]]=>3
[5,5,1,3,1,4]=>[[],[[],[[[]]]]]=>2
[5,5,1,3,4,1]=>[[],[[[[[]]]]]]=>2
[5,5,1,4,1,3]=>[[],[[],[[[]]]]]=>2
[5,5,1,4,3,1]=>[[],[[],[[[]]]]]=>2
[5,5,3,1,1,4]=>[[],[[]],[[],[]]]=>3
[5,5,3,1,4,1]=>[[],[[],[[[]]]]]=>2
[5,5,3,4,1,1]=>[[],[],[[[[]]]]]=>3
[5,5,4,1,1,3]=>[[],[[[]]],[[]]]=>3
[5,5,4,1,3,1]=>[[],[[[[[]]]]]]=>2
[5,5,4,3,1,1]=>[[],[[]],[[],[]]]=>3
[1,1,3,4,5,6]=>[[],[[[],[],[]]]]=>2
[1,1,3,4,6,5]=>[[],[[[]],[[]]]]=>2
[1,1,3,5,4,6]=>[[],[[],[],[[]]]]=>2
[1,1,3,5,6,4]=>[[],[[],[[[]]]]]=>2
[1,1,3,6,4,5]=>[[],[[[[[]]]]]]=>2
[1,1,3,6,5,4]=>[[],[[[[],[]]]]]=>2
[1,1,4,3,5,6]=>[[],[[[[[]]]]]]=>2
[1,1,4,3,6,5]=>[[],[[],[[],[]]]]=>2
[1,1,4,5,3,6]=>[[],[[],[[[]]]]]=>2
[1,1,4,5,6,3]=>[[],[[[],[[]]]]]=>2
[1,1,4,6,3,5]=>[[],[[[],[[]]]]]=>2
[1,1,4,6,5,3]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,4,6]=>[[],[[[[[]]]]]]=>2
[1,1,5,3,6,4]=>[[],[[[[],[]]]]]=>2
[1,1,5,4,3,6]=>[[],[[[],[[]]]]]=>2
[1,1,5,4,6,3]=>[[],[[[]],[[]]]]=>2
[1,1,5,6,3,4]=>[[],[[],[[],[]]]]=>2
[1,1,5,6,4,3]=>[[],[[[[[]]]]]]=>2
[1,1,6,3,4,5]=>[[],[[[],[[]]]]]=>2
[1,1,6,3,5,4]=>[[],[[[[[]]]]]]=>2
[1,1,6,4,3,5]=>[[],[[],[[[]]]]]=>2
[1,1,6,4,5,3]=>[[],[[],[],[[]]]]=>2
[1,1,6,5,3,4]=>[[],[[],[[[]]]]]=>2
[1,1,6,5,4,3]=>[[],[[[],[],[]]]]=>2
[1,3,1,4,5,6]=>[[[[[],[[]]]]]]=>1
[1,3,1,4,6,5]=>[[[[]],[[[]]]]]=>1
[1,3,1,5,4,6]=>[[[[]],[[[]]]]]=>1
[1,3,1,5,6,4]=>[[[[],[[[]]]]]]=>1
[1,3,1,6,4,5]=>[[[[],[],[[]]]]]=>1
[1,3,1,6,5,4]=>[[[[],[[],[]]]]]=>1
[1,3,4,1,5,6]=>[[[[],[[],[]]]]]=>1
[1,3,4,1,6,5]=>[[[[[[[]]]]]]]=>1
[1,3,4,5,1,6]=>[[[[],[[[]]]]]]=>1
[1,3,4,5,6,1]=>[[[],[[],[],[]]]]=>1
[1,3,4,6,1,5]=>[[[],[[]],[[]]]]=>1
[1,3,4,6,5,1]=>[[[[]],[[[]]]]]=>1
[1,3,5,1,4,6]=>[[[],[],[[],[]]]]=>1
[1,3,5,1,6,4]=>[[[],[[[],[]]]]]=>1
[1,3,5,4,1,6]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,6,1]=>[[[],[],[],[[]]]]=>1
[1,3,5,6,1,4]=>[[[],[[]],[[]]]]=>1
[1,3,5,6,4,1]=>[[[],[[[[]]]]]]=>1
[1,3,6,1,4,5]=>[[[],[[],[[]]]]]=>1
[1,3,6,1,5,4]=>[[[[]],[[[]]]]]=>1
[1,3,6,4,1,5]=>[[[[[],[[]]]]]]=>1
[1,3,6,4,5,1]=>[[[[],[[[]]]]]]=>1
[1,3,6,5,1,4]=>[[[[[],[],[]]]]]=>1
[1,3,6,5,4,1]=>[[[[[]],[[]]]]]=>1
[1,4,1,3,5,6]=>[[[[[],[[]]]]]]=>1
[1,4,1,3,6,5]=>[[[[[]]],[[]]]]=>1
[1,4,1,5,3,6]=>[[[],[[[],[]]]]]=>1
[1,4,1,5,6,3]=>[[[[],[],[[]]]]]=>1
[1,4,1,6,3,5]=>[[[[[],[[]]]]]]=>1
[1,4,1,6,5,3]=>[[[[[],[[]]]]]]=>1
[1,4,3,1,5,6]=>[[[[[[[]]]]]]]=>1
[1,4,3,1,6,5]=>[[[[],[[],[]]]]]=>1
[1,4,3,5,1,6]=>[[[[]],[[[]]]]]=>1
[1,4,3,5,6,1]=>[[[[[],[[]]]]]]=>1
[1,4,3,6,1,5]=>[[[],[[[[]]]]]]=>1
[1,4,3,6,5,1]=>[[[],[],[[],[]]]]=>1
[1,4,5,1,3,6]=>[[[],[[]],[[]]]]=>1
[1,4,5,1,6,3]=>[[[[]],[[[]]]]]=>1
[1,4,5,3,1,6]=>[[[[],[],[[]]]]]=>1
[1,4,5,3,6,1]=>[[[[]],[[[]]]]]=>1
[1,4,5,6,1,3]=>[[[[],[[],[]]]]]=>1
[1,4,5,6,3,1]=>[[[[],[[[]]]]]]=>1
[1,4,6,1,3,5]=>[[[[],[],[],[]]]]=>1
[1,4,6,1,5,3]=>[[[[],[[[]]]]]]=>1
[1,4,6,3,1,5]=>[[[[[],[[]]]]]]=>1
[1,4,6,3,5,1]=>[[[],[[],[[]]]]]=>1
[1,4,6,5,1,3]=>[[[],[[],[[]]]]]=>1
[1,4,6,5,3,1]=>[[[[],[[[]]]]]]=>1
[1,5,1,3,4,6]=>[[[[[],[[]]]]]]=>1
[1,5,1,3,6,4]=>[[[[[],[[]]]]]]=>1
[1,5,1,4,3,6]=>[[[[[],[],[]]]]]=>1
[1,5,1,4,6,3]=>[[[],[[[],[]]]]]=>1
[1,5,1,6,3,4]=>[[[[]],[[[]]]]]=>1
[1,5,1,6,4,3]=>[[[[[],[[]]]]]]=>1
[1,5,3,1,4,6]=>[[[[],[[[]]]]]]=>1
[1,5,3,1,6,4]=>[[[[],[],[],[]]]]=>1
[1,5,3,4,1,6]=>[[[[]],[[],[]]]]=>1
[1,5,3,4,6,1]=>[[[[[],[[]]]]]]=>1
[1,5,3,6,1,4]=>[[[[],[[[]]]]]]=>1
[1,5,3,6,4,1]=>[[[],[[],[[]]]]]=>1
[1,5,4,1,3,6]=>[[[],[[[[]]]]]]=>1
[1,5,4,1,6,3]=>[[[],[[]],[[]]]]=>1
[1,5,4,3,1,6]=>[[[[],[[],[]]]]]=>1
[1,5,4,3,6,1]=>[[[[],[[[]]]]]]=>1
[1,5,4,6,1,3]=>[[[[],[],[[]]]]]=>1
[1,5,4,6,3,1]=>[[[[]],[[[]]]]]=>1
[1,5,6,1,3,4]=>[[[[],[[],[]]]]]=>1
[1,5,6,1,4,3]=>[[[[[[[]]]]]]]=>1
[1,5,6,3,1,4]=>[[[[]],[[[]]]]]=>1
[1,5,6,3,4,1]=>[[[],[],[[],[]]]]=>1
[1,5,6,4,1,3]=>[[[[]],[[[]]]]]=>1
[1,5,6,4,3,1]=>[[[[[]],[[]]]]]=>1
[1,6,1,3,4,5]=>[[[[],[[],[]]]]]=>1
[1,6,1,3,5,4]=>[[[[[],[],[]]]]]=>1
[1,6,1,4,3,5]=>[[[[],[[[]]]]]]=>1
[1,6,1,4,5,3]=>[[[],[[[[]]]]]]=>1
[1,6,1,5,3,4]=>[[[[]],[[[]]]]]=>1
[1,6,1,5,4,3]=>[[[[],[[[]]]]]]=>1
[1,6,3,1,4,5]=>[[[[[]]],[[]]]]=>1
[1,6,3,1,5,4]=>[[[],[[[],[]]]]]=>1
[1,6,3,4,1,5]=>[[[[],[],[[]]]]]=>1
[1,6,3,4,5,1]=>[[[[[]],[[]]]]]=>1
[1,6,3,5,1,4]=>[[[[],[[[]]]]]]=>1
[1,6,3,5,4,1]=>[[[[],[[[]]]]]]=>1
[1,6,4,1,3,5]=>[[[],[[],[[]]]]]=>1
[1,6,4,1,5,3]=>[[[],[],[[],[]]]]=>1
[1,6,4,3,1,5]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,5,1]=>[[[],[[[[]]]]]]=>1
[1,6,4,5,1,3]=>[[[],[[[[]]]]]]=>1
[1,6,4,5,3,1]=>[[[],[],[],[[]]]]=>1
[1,6,5,1,3,4]=>[[[[[[[]]]]]]]=>1
[1,6,5,1,4,3]=>[[[[],[[],[]]]]]=>1
[1,6,5,3,1,4]=>[[[],[],[[[]]]]]=>1
[1,6,5,3,4,1]=>[[[],[[[[]]]]]]=>1
[1,6,5,4,1,3]=>[[[[[[],[]]]]]]=>1
[1,6,5,4,3,1]=>[[[],[[],[],[]]]]=>1
[3,1,1,4,5,6]=>[[],[[[],[[]]]]]=>2
[3,1,1,4,6,5]=>[[],[[[[[]]]]]]=>2
[3,1,1,5,4,6]=>[[],[[[[[]]]]]]=>2
[3,1,1,5,6,4]=>[[],[[[[],[]]]]]=>2
[3,1,1,6,4,5]=>[[],[[],[],[[]]]]=>2
[3,1,1,6,5,4]=>[[],[[],[[],[]]]]=>2
[3,1,4,1,5,6]=>[[[[[]],[[]]]]]=>1
[3,1,4,1,6,5]=>[[[[]],[[[]]]]]=>1
[3,1,4,5,1,6]=>[[[],[[],[[]]]]]=>1
[3,1,4,5,6,1]=>[[[[[]],[[]]]]]=>1
[3,1,4,6,1,5]=>[[[[[]],[[]]]]]=>1
[3,1,4,6,5,1]=>[[[[],[[[]]]]]]=>1
[3,1,5,1,4,6]=>[[[[[]],[[]]]]]=>1
[3,1,5,1,6,4]=>[[[],[[]],[[]]]]=>1
[3,1,5,4,1,6]=>[[[[]],[[],[]]]]=>1
[3,1,5,4,6,1]=>[[[[[]],[[]]]]]=>1
[3,1,5,6,1,4]=>[[[[[[[]]]]]]]=>1
[3,1,5,6,4,1]=>[[[[]],[[],[]]]]=>1
[3,1,6,1,4,5]=>[[[],[[[[]]]]]]=>1
[3,1,6,1,5,4]=>[[[],[[[[]]]]]]=>1
[3,1,6,4,1,5]=>[[[],[],[[],[]]]]=>1
[3,1,6,4,5,1]=>[[[],[],[[[]]]]]=>1
[3,1,6,5,1,4]=>[[[],[[],[[]]]]]=>1
[3,1,6,5,4,1]=>[[[],[[[],[]]]]]=>1
[3,4,1,1,5,6]=>[[],[[],[[],[]]]]=>2
[3,4,1,1,6,5]=>[[],[[[[[]]]]]]=>2
[3,4,1,5,1,6]=>[[[[],[[[]]]]]]=>1
[3,4,1,5,6,1]=>[[[[]],[[],[]]]]=>1
[3,4,1,6,1,5]=>[[[[],[[[]]]]]]=>1
[3,4,1,6,5,1]=>[[[[[[[]]]]]]]=>1
[3,4,5,1,1,6]=>[[[[],[]]],[[]]]=>2
[3,4,5,1,6,1]=>[[[],[[[[]]]]]]=>1
[3,4,5,6,1,1]=>[[],[[[],[],[]]]]=>2
[3,4,6,1,1,5]=>[[[]],[[],[[]]]]=>2
[3,4,6,1,5,1]=>[[[[],[[[]]]]]]=>1
[3,4,6,5,1,1]=>[[[]],[[[[]]]]]=>2
[3,5,1,1,4,6]=>[[],[[],[[],[]]]]=>2
[3,5,1,1,6,4]=>[[[[]]],[[],[]]]=>2
[3,5,1,4,1,6]=>[[[[],[[[]]]]]]=>1
[3,5,1,4,6,1]=>[[[],[],[[],[]]]]=>1
[3,5,1,6,1,4]=>[[[[]],[[],[]]]]=>1
[3,5,1,6,4,1]=>[[[[[]],[[]]]]]=>1
[3,5,4,1,1,6]=>[[[]],[[[[]]]]]=>2
[3,5,4,1,6,1]=>[[[[[]]],[[]]]]=>1
[3,5,4,6,1,1]=>[[[]],[[],[],[]]]=>2
[3,5,6,1,1,4]=>[[[]],[[],[[]]]]=>2
[3,5,6,1,4,1]=>[[[[]],[[[]]]]]=>1
[3,5,6,4,1,1]=>[[],[[[[[]]]]]]=>2
[3,6,1,1,4,5]=>[[[]],[[],[[]]]]=>2
[3,6,1,1,5,4]=>[[[[]]],[[[]]]]=>2
[3,6,1,4,1,5]=>[[[[]],[[],[]]]]=>1
[3,6,1,4,5,1]=>[[[],[[]],[[]]]]=>1
[3,6,1,5,1,4]=>[[[],[],[[[]]]]]=>1
[3,6,1,5,4,1]=>[[[[[],[[]]]]]]=>1
[3,6,4,1,1,5]=>[[[]],[[],[[]]]]=>2
[3,6,4,1,5,1]=>[[[],[[],[[]]]]]=>1
[3,6,4,5,1,1]=>[[],[[],[[[]]]]]=>2
[3,6,5,1,1,4]=>[[],[[],[],[[]]]]=>2
[3,6,5,1,4,1]=>[[[],[],[[[]]]]]=>1
[3,6,5,4,1,1]=>[[[]],[[],[[]]]]=>2
[4,1,1,3,5,6]=>[[[]],[[],[[]]]]=>2
[4,1,1,3,6,5]=>[[[[[]]]],[[]]]=>2
[4,1,1,5,3,6]=>[[],[[],[[[]]]]]=>2
[4,1,1,5,6,3]=>[[],[[],[],[[]]]]=>2
[4,1,1,6,3,5]=>[[],[[[],[[]]]]]=>2
[4,1,1,6,5,3]=>[[],[[[]],[[]]]]=>2
[4,1,3,1,5,6]=>[[[[]],[[[]]]]]=>1
[4,1,3,1,6,5]=>[[[[[],[[]]]]]]=>1
[4,1,3,5,1,6]=>[[[[],[[[]]]]]]=>1
[4,1,3,5,6,1]=>[[[[],[],[[]]]]]=>1
[4,1,3,6,1,5]=>[[[],[[],[[]]]]]=>1
[4,1,3,6,5,1]=>[[[[[],[[]]]]]]=>1
[4,1,5,1,3,6]=>[[[],[[],[[]]]]]=>1
[4,1,5,1,6,3]=>[[[],[],[[[]]]]]=>1
[4,1,5,3,1,6]=>[[[],[[],[],[]]]]=>1
[4,1,5,3,6,1]=>[[[],[[[[]]]]]]=>1
[4,1,5,6,1,3]=>[[[],[[[],[]]]]]=>1
[4,1,5,6,3,1]=>[[[],[[]],[[]]]]=>1
[4,1,6,1,3,5]=>[[[[],[],[[]]]]]=>1
[4,1,6,1,5,3]=>[[[[]],[[],[]]]]=>1
[4,1,6,3,1,5]=>[[[],[],[[],[]]]]=>1
[4,1,6,3,5,1]=>[[[[[]]],[[]]]]=>1
[4,1,6,5,1,3]=>[[[[[[[]]]]]]]=>1
[4,1,6,5,3,1]=>[[[[],[],[[]]]]]=>1
[4,3,1,1,5,6]=>[[[[[]]]],[[]]]=>2
[4,3,1,1,6,5]=>[[],[[],[[],[]]]]=>2
[4,3,1,5,1,6]=>[[[[],[[[]]]]]]=>1
[4,3,1,5,6,1]=>[[[[[[[]]]]]]]=>1
[4,3,1,6,1,5]=>[[[[[[],[]]]]]]=>1
[4,3,1,6,5,1]=>[[[],[[[],[]]]]]=>1
[4,3,5,1,1,6]=>[[[[]]],[[[]]]]=>2
[4,3,5,1,6,1]=>[[[[],[[[]]]]]]=>1
[4,3,5,6,1,1]=>[[[]],[[],[[]]]]=>2
[4,3,6,1,1,5]=>[[[[]]],[[[]]]]=>2
[4,3,6,1,5,1]=>[[[[],[[[]]]]]]=>1
[4,3,6,5,1,1]=>[[[],[]],[[],[]]]=>2
[4,5,1,1,3,6]=>[[],[[[],[[]]]]]=>2
[4,5,1,1,6,3]=>[[[[]]],[[[]]]]=>2
[4,5,1,3,1,6]=>[[[[[[],[]]]]]]=>1
[4,5,1,3,6,1]=>[[[[],[[],[]]]]]=>1
[4,5,1,6,1,3]=>[[[[[[],[]]]]]]=>1
[4,5,1,6,3,1]=>[[[[[[],[]]]]]]=>1
[4,5,3,1,1,6]=>[[],[[],[],[[]]]]=>2
[4,5,3,1,6,1]=>[[[[],[],[[]]]]]=>1
[4,5,3,6,1,1]=>[[],[[[[[]]]]]]=>2
[4,5,6,1,1,3]=>[[],[[],[[],[]]]]=>2
[4,5,6,1,3,1]=>[[[],[[],[[]]]]]=>1
[4,5,6,3,1,1]=>[[],[[[[],[]]]]]=>2
[4,6,1,1,3,5]=>[[],[[],[],[],[]]]=>2
[4,6,1,1,5,3]=>[[[[]]],[[],[]]]=>2
[4,6,1,3,1,5]=>[[[],[],[[[]]]]]=>1
[4,6,1,3,5,1]=>[[[],[],[],[[]]]]=>1
[4,6,1,5,1,3]=>[[[],[],[[[]]]]]=>1
[4,6,1,5,3,1]=>[[[],[[[],[]]]]]=>1
[4,6,3,1,1,5]=>[[[]],[[],[[]]]]=>2
[4,6,3,1,5,1]=>[[[[[],[[]]]]]]=>1
[4,6,3,5,1,1]=>[[],[[[],[[]]]]]=>2
[4,6,5,1,1,3]=>[[[]],[[],[[]]]]=>2
[4,6,5,1,3,1]=>[[[[]],[[[]]]]]=>1
[4,6,5,3,1,1]=>[[[[]]],[[],[]]]=>2
[5,1,1,3,4,6]=>[[[]],[[],[[]]]]=>2
[5,1,1,3,6,4]=>[[],[[[],[[]]]]]=>2
[5,1,1,4,3,6]=>[[],[[],[],[[]]]]=>2
[5,1,1,4,6,3]=>[[],[[],[[[]]]]]=>2
[5,1,1,6,3,4]=>[[[]],[[[[]]]]]=>2
[5,1,1,6,4,3]=>[[],[[[]],[[]]]]=>2
[5,1,3,1,4,6]=>[[[[]],[[],[]]]]=>1
[5,1,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[5,1,3,4,1,6]=>[[[[[[[]]]]]]]=>1
[5,1,3,4,6,1]=>[[[[],[],[[]]]]]=>1
[5,1,3,6,1,4]=>[[[],[],[[],[]]]]=>1
[5,1,3,6,4,1]=>[[[[]],[[[]]]]]=>1
[5,1,4,1,3,6]=>[[[],[],[[[]]]]]=>1
[5,1,4,1,6,3]=>[[[],[[[],[]]]]]=>1
[5,1,4,3,1,6]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,6,1]=>[[[],[],[[[]]]]]=>1
[5,1,4,6,1,3]=>[[[],[[],[],[]]]]=>1
[5,1,4,6,3,1]=>[[[],[[[[]]]]]]=>1
[5,1,6,1,3,4]=>[[[[[],[[]]]]]]=>1
[5,1,6,1,4,3]=>[[[[]],[[[]]]]]=>1
[5,1,6,3,1,4]=>[[[],[[],[[]]]]]=>1
[5,1,6,3,4,1]=>[[[[],[[[]]]]]]=>1
[5,1,6,4,1,3]=>[[[[],[[[]]]]]]=>1
[5,1,6,4,3,1]=>[[[[[],[],[]]]]]=>1
[5,3,1,1,4,6]=>[[[[]]],[[],[]]]=>2
[5,3,1,1,6,4]=>[[],[[],[],[],[]]]=>2
[5,3,1,4,1,6]=>[[[],[],[[[]]]]]=>1
[5,3,1,4,6,1]=>[[[],[[],[[]]]]]=>1
[5,3,1,6,1,4]=>[[[],[],[[[]]]]]=>1
[5,3,1,6,4,1]=>[[[],[],[],[[]]]]=>1
[5,3,4,1,1,6]=>[[[[]]],[[],[]]]=>2
[5,3,4,1,6,1]=>[[[[]],[[[]]]]]=>1
[5,3,4,6,1,1]=>[[],[[[]],[[]]]]=>2
[5,3,6,1,1,4]=>[[[[]]],[[],[]]]=>2
[5,3,6,1,4,1]=>[[[[[],[[]]]]]]=>1
[5,3,6,4,1,1]=>[[],[[[],[[]]]]]=>2
[5,4,1,1,3,6]=>[[[[[]]]],[[]]]=>2
[5,4,1,1,6,3]=>[[],[[[],[[]]]]]=>2
[5,4,1,3,1,6]=>[[[[[]],[[]]]]]=>1
[5,4,1,3,6,1]=>[[[[[]],[[]]]]]=>1
[5,4,1,6,1,3]=>[[[[[]],[[]]]]]=>1
[5,4,1,6,3,1]=>[[[[],[[],[]]]]]=>1
[5,4,3,1,1,6]=>[[],[[],[[],[]]]]=>2
[5,4,3,1,6,1]=>[[[],[[[],[]]]]]=>1
[5,4,3,6,1,1]=>[[[[]]],[[],[]]]=>2
[5,4,6,1,1,3]=>[[],[[],[],[[]]]]=>2
[5,4,6,1,3,1]=>[[[[[],[],[]]]]]=>1
[5,4,6,3,1,1]=>[[[[[]]]],[[]]]=>2
[5,6,1,1,3,4]=>[[],[[],[[],[]]]]=>2
[5,6,1,1,4,3]=>[[[[]]],[[[]]]]=>2
[5,6,1,3,1,4]=>[[[[],[[[]]]]]]=>1
[5,6,1,3,4,1]=>[[[[]],[[],[]]]]=>1
[5,6,1,4,1,3]=>[[[[],[[[]]]]]]=>1
[5,6,1,4,3,1]=>[[[[[[[]]]]]]]=>1
[5,6,3,1,1,4]=>[[[]],[[[[]]]]]=>2
[5,6,3,1,4,1]=>[[[[],[[[]]]]]]=>1
[5,6,3,4,1,1]=>[[],[[],[[],[]]]]=>2
[5,6,4,1,1,3]=>[[[]],[[[[]]]]]=>2
[5,6,4,1,3,1]=>[[[[],[[[]]]]]]=>1
[5,6,4,3,1,1]=>[[[]],[[],[[]]]]=>2
[6,1,1,3,4,5]=>[[],[[],[[],[]]]]=>2
[6,1,1,3,5,4]=>[[],[[],[],[[]]]]=>2
[6,1,1,4,3,5]=>[[],[[[[],[]]]]]=>2
[6,1,1,4,5,3]=>[[[]],[[[[]]]]]=>2
[6,1,1,5,3,4]=>[[[]],[[[[]]]]]=>2
[6,1,1,5,4,3]=>[[[]],[[[],[]]]]=>2
[6,1,3,1,4,5]=>[[[],[[[[]]]]]]=>1
[6,1,3,1,5,4]=>[[[],[[[[]]]]]]=>1
[6,1,3,4,1,5]=>[[[],[[[],[]]]]]=>1
[6,1,3,4,5,1]=>[[[],[[],[[]]]]]=>1
[6,1,3,5,1,4]=>[[[],[],[[],[]]]]=>1
[6,1,3,5,4,1]=>[[[],[],[[[]]]]]=>1
[6,1,4,1,3,5]=>[[[],[],[[[]]]]]=>1
[6,1,4,1,5,3]=>[[[[[]],[[]]]]]=>1
[6,1,4,3,1,5]=>[[[[[[[]]]]]]]=>1
[6,1,4,3,5,1]=>[[[],[[],[[]]]]]=>1
[6,1,4,5,1,3]=>[[[],[[],[[]]]]]=>1
[6,1,4,5,3,1]=>[[[[[[],[]]]]]]=>1
[6,1,5,1,3,4]=>[[[[]],[[[]]]]]=>1
[6,1,5,1,4,3]=>[[[[[]],[[]]]]]=>1
[6,1,5,3,1,4]=>[[[[[]],[[]]]]]=>1
[6,1,5,3,4,1]=>[[[[],[[[]]]]]]=>1
[6,1,5,4,1,3]=>[[[[]],[[],[]]]]=>1
[6,1,5,4,3,1]=>[[[[],[[[]]]]]]=>1
[6,3,1,1,4,5]=>[[[[]]],[[[]]]]=>2
[6,3,1,1,5,4]=>[[],[[],[[[]]]]]=>2
[6,3,1,4,1,5]=>[[[],[[]],[[]]]]=>1
[6,3,1,4,5,1]=>[[[[],[[[]]]]]]=>1
[6,3,1,5,1,4]=>[[[],[[],[[]]]]]=>1
[6,3,1,5,4,1]=>[[[],[[]],[[]]]]=>1
[6,3,4,1,1,5]=>[[],[[],[],[[]]]]=>2
[6,3,4,1,5,1]=>[[[],[[]],[[]]]]=>1
[6,3,4,5,1,1]=>[[],[[[],[[]]]]]=>2
[6,3,5,1,1,4]=>[[],[[],[[[]]]]]=>2
[6,3,5,1,4,1]=>[[[],[[],[[]]]]]=>1
[6,3,5,4,1,1]=>[[[[]]],[[],[]]]=>2
[6,4,1,1,3,5]=>[[[]],[[],[[]]]]=>2
[6,4,1,1,5,3]=>[[],[[],[[],[]]]]=>2
[6,4,1,3,1,5]=>[[[[]],[[],[]]]]=>1
[6,4,1,3,5,1]=>[[[[[]],[[]]]]]=>1
[6,4,1,5,1,3]=>[[[[],[[[]]]]]]=>1
[6,4,1,5,3,1]=>[[[],[],[[],[]]]]=>1
[6,4,3,1,1,5]=>[[[[]]],[[],[]]]=>2
[6,4,3,1,5,1]=>[[[],[[[[]]]]]]=>1
[6,4,3,5,1,1]=>[[[[[]]]],[[]]]=>2
[6,4,5,1,1,3]=>[[[]],[[[[]]]]]=>2
[6,4,5,1,3,1]=>[[[],[[[[]]]]]]=>1
[6,4,5,3,1,1]=>[[],[[],[],[[]]]]=>2
[6,5,1,1,3,4]=>[[[[[]]]],[[]]]=>2
[6,5,1,1,4,3]=>[[],[[],[[],[]]]]=>2
[6,5,1,3,1,4]=>[[[[],[[[]]]]]]=>1
[6,5,1,3,4,1]=>[[[[[[[]]]]]]]=>1
[6,5,1,4,1,3]=>[[[[[[],[]]]]]]=>1
[6,5,1,4,3,1]=>[[[[]],[[],[]]]]=>1
[6,5,3,1,1,4]=>[[[[]]],[[],[]]]=>2
[6,5,3,1,4,1]=>[[[[[[],[]]]]]]=>1
[6,5,3,4,1,1]=>[[[[[]]]],[[]]]=>2
[6,5,4,1,1,3]=>[[[[],[]]],[[]]]=>2
[6,5,4,1,3,1]=>[[[],[[[[]]]]]]=>1
[6,5,4,3,1,1]=>[[[]],[[],[],[]]]=>2
[1,2,2,2,2,2]=>[[],[],[],[],[[]]]=>5
[2,1,2,2,2,2]=>[[],[],[[]],[[]]]=>4
[2,2,1,2,2,2]=>[[],[],[[]],[[]]]=>4
[2,2,2,1,2,2]=>[[],[],[[]],[[]]]=>4
[2,2,2,2,1,2]=>[[],[],[],[[[]]]]=>4
[2,2,2,2,2,1]=>[[],[],[],[],[[]]]=>5
[1,2,2,2,2,3]=>[[],[],[],[[],[]]]=>4
[1,2,2,2,3,2]=>[[],[],[[],[[]]]]=>3
[1,2,2,3,2,2]=>[[],[],[[[],[]]]]=>3
[1,2,3,2,2,2]=>[[],[],[[[],[]]]]=>3
[1,3,2,2,2,2]=>[[],[],[],[[[]]]]=>4
[2,1,2,2,2,3]=>[[],[],[[],[[]]]]=>3
[2,1,2,2,3,2]=>[[],[[],[[],[]]]]=>2
[2,1,2,3,2,2]=>[[],[[],[[],[]]]]=>2
[2,1,3,2,2,2]=>[[],[],[[],[[]]]]=>3
[2,2,1,2,2,3]=>[[],[],[[],[[]]]]=>3
[2,2,1,2,3,2]=>[[],[[],[[],[]]]]=>2
[2,2,1,3,2,2]=>[[],[],[[],[[]]]]=>3
[2,2,2,1,2,3]=>[[],[],[[[],[]]]]=>3
[2,2,2,1,3,2]=>[[],[],[[],[[]]]]=>3
[2,2,2,2,1,3]=>[[],[],[],[[[]]]]=>4
[2,2,2,2,3,1]=>[[],[],[],[[[]]]]=>4
[2,2,2,3,1,2]=>[[],[],[[],[[]]]]=>3
[2,2,2,3,2,1]=>[[],[],[[[],[]]]]=>3
[2,2,3,1,2,2]=>[[],[],[[],[[]]]]=>3
[2,2,3,2,1,2]=>[[],[[],[[],[]]]]=>2
[2,2,3,2,2,1]=>[[],[],[[],[[]]]]=>3
[2,3,1,2,2,2]=>[[],[[]],[[],[]]]=>3
[2,3,2,1,2,2]=>[[[],[]],[[],[]]]=>2
[2,3,2,2,1,2]=>[[],[[],[[],[]]]]=>2
[2,3,2,2,2,1]=>[[],[],[[],[[]]]]=>3
[3,1,2,2,2,2]=>[[],[],[[]],[[]]]=>4
[3,2,1,2,2,2]=>[[],[[]],[[],[]]]=>3
[3,2,2,1,2,2]=>[[],[[]],[[],[]]]=>3
[3,2,2,2,1,2]=>[[],[],[[],[[]]]]=>3
[3,2,2,2,2,1]=>[[],[],[],[[],[]]]=>4
[1,2,2,2,2,4]=>[[],[],[[]],[[]]]=>4
[1,2,2,2,4,2]=>[[],[[]],[[[]]]]=>3
[1,2,2,4,2,2]=>[[],[[]],[[[]]]]=>3
[1,2,4,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,4,2,2,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,2,2,2,4]=>[[],[[]],[[[]]]]=>3
[2,1,2,2,4,2]=>[[[]],[[[[]]]]]=>2
[2,1,2,4,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,4,2,2,2]=>[[],[[[]]],[[]]]=>3
[2,2,1,2,2,4]=>[[],[[]],[[[]]]]=>3
[2,2,1,2,4,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,2,2]=>[[],[[[]]],[[]]]=>3
[2,2,2,1,2,4]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,4,2]=>[[],[],[[[[]]]]]=>3
[2,2,2,2,1,4]=>[[],[],[],[[[]]]]=>4
[2,2,2,2,4,1]=>[[],[],[],[[[]]]]=>4
[2,2,2,4,1,2]=>[[],[],[[[[]]]]]=>3
[2,2,2,4,2,1]=>[[],[],[[[[]]]]]=>3
[2,2,4,1,2,2]=>[[],[],[[[[]]]]]=>3
[2,2,4,2,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,4,2,2,1]=>[[],[],[[[[]]]]]=>3
[2,4,1,2,2,2]=>[[],[],[[[[]]]]]=>3
[2,4,2,1,2,2]=>[[[[[]]]],[[]]]=>2
[2,4,2,2,1,2]=>[[],[[[[[]]]]]]=>2
[2,4,2,2,2,1]=>[[],[],[[[[]]]]]=>3
[4,1,2,2,2,2]=>[[],[],[[]],[[]]]=>4
[4,2,1,2,2,2]=>[[[]],[[]],[[]]]=>3
[4,2,2,1,2,2]=>[[],[[[]]],[[]]]=>3
[4,2,2,2,1,2]=>[[],[],[[[[]]]]]=>3
[4,2,2,2,2,1]=>[[],[],[],[[[]]]]=>4
[1,2,2,2,2,5]=>[[],[],[[]],[[]]]=>4
[1,2,2,2,5,2]=>[[],[[]],[[[]]]]=>3
[1,2,2,5,2,2]=>[[],[[]],[[[]]]]=>3
[1,2,5,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,5,2,2,2,2]=>[[],[],[],[[],[]]]=>4
[2,1,2,2,2,5]=>[[],[[]],[[[]]]]=>3
[2,1,2,2,5,2]=>[[[]],[[[[]]]]]=>2
[2,1,2,5,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,5,2,2,2]=>[[],[[]],[[],[]]]=>3
[2,2,1,2,2,5]=>[[],[[]],[[[]]]]=>3
[2,2,1,2,5,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,2,2]=>[[],[[]],[[],[]]]=>3
[2,2,2,1,2,5]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,5,2]=>[[],[],[[[],[]]]]=>3
[2,2,2,2,1,5]=>[[],[],[],[[[]]]]=>4
[2,2,2,2,5,1]=>[[],[],[],[[],[]]]=>4
[2,2,2,5,1,2]=>[[],[],[[],[[]]]]=>3
[2,2,2,5,2,1]=>[[],[],[[[[]]]]]=>3
[2,2,5,1,2,2]=>[[],[],[[[],[]]]]=>3
[2,2,5,2,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,5,2,2,1]=>[[],[[[]]],[[]]]=>3
[2,5,1,2,2,2]=>[[],[],[[[],[]]]]=>3
[2,5,2,1,2,2]=>[[[]],[[[[]]]]]=>2
[2,5,2,2,1,2]=>[[[[]]],[[[]]]]=>2
[2,5,2,2,2,1]=>[[[]],[[]],[[]]]=>3
[5,1,2,2,2,2]=>[[],[],[],[[[]]]]=>4
[5,2,1,2,2,2]=>[[],[[[]]],[[]]]=>3
[5,2,2,1,2,2]=>[[],[[]],[[[]]]]=>3
[5,2,2,2,1,2]=>[[],[[]],[[[]]]]=>3
[5,2,2,2,2,1]=>[[],[],[[]],[[]]]=>4
[1,2,2,2,2,6]=>[[],[],[[]],[[]]]=>4
[1,2,2,2,6,2]=>[[],[[]],[[[]]]]=>3
[1,2,2,6,2,2]=>[[],[[]],[[[]]]]=>3
[1,2,6,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,6,2,2,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,2,2,2,6]=>[[],[[]],[[[]]]]=>3
[2,1,2,2,6,2]=>[[[]],[[[[]]]]]=>2
[2,1,2,6,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,6,2,2,2]=>[[[]],[[]],[[]]]=>3
[2,2,1,2,2,6]=>[[],[[]],[[[]]]]=>3
[2,2,1,2,6,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,2,2]=>[[],[[[]]],[[]]]=>3
[2,2,2,1,2,6]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,6,2]=>[[],[],[[[[]]]]]=>3
[2,2,2,2,1,6]=>[[],[],[],[[[]]]]=>4
[2,2,2,2,6,1]=>[[],[],[],[[[]]]]=>4
[2,2,2,6,1,2]=>[[],[],[[[[]]]]]=>3
[2,2,2,6,2,1]=>[[],[],[[[[]]]]]=>3
[2,2,6,1,2,2]=>[[],[],[[[[]]]]]=>3
[2,2,6,2,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,6,2,2,1]=>[[],[[[]]],[[]]]=>3
[2,6,1,2,2,2]=>[[],[],[[[[]]]]]=>3
[2,6,2,1,2,2]=>[[[]],[[[[]]]]]=>2
[2,6,2,2,1,2]=>[[[[]]],[[[]]]]=>2
[2,6,2,2,2,1]=>[[[]],[[]],[[]]]=>3
[6,1,2,2,2,2]=>[[],[],[],[[[]]]]=>4
[6,2,1,2,2,2]=>[[],[[]],[[[]]]]=>3
[6,2,2,1,2,2]=>[[[]],[[]],[[]]]=>3
[6,2,2,2,1,2]=>[[],[[]],[[[]]]]=>3
[6,2,2,2,2,1]=>[[],[],[[]],[[]]]=>4
[1,2,2,2,3,3]=>[[],[],[],[[],[]]]=>4
[1,2,2,3,2,3]=>[[],[[],[],[[]]]]=>2
[1,2,2,3,3,2]=>[[],[[]],[[],[]]]=>3
[1,2,3,2,2,3]=>[[],[[],[],[[]]]]=>2
[1,2,3,2,3,2]=>[[[],[],[[],[]]]]=>1
[1,2,3,3,2,2]=>[[],[[]],[[],[]]]=>3
[1,3,2,2,2,3]=>[[],[],[[[[]]]]]=>3
[1,3,2,2,3,2]=>[[],[[[],[[]]]]]=>2
[1,3,2,3,2,2]=>[[],[[[]],[[]]]]=>2
[1,3,3,2,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,2,2,3,3]=>[[],[[]],[[],[]]]=>3
[2,1,2,3,2,3]=>[[[],[[],[],[]]]]=>1
[2,1,2,3,3,2]=>[[[],[]],[[],[]]]=>2
[2,1,3,2,2,3]=>[[],[[[],[[]]]]]=>2
[2,1,3,2,3,2]=>[[[],[[]],[[]]]]=>1
[2,1,3,3,2,2]=>[[],[[]],[[],[]]]=>3
[2,2,1,2,3,3]=>[[],[[]],[[],[]]]=>3
[2,2,1,3,2,3]=>[[],[[[]],[[]]]]=>2
[2,2,1,3,3,2]=>[[],[[]],[[],[]]]=>3
[2,2,2,1,3,3]=>[[],[],[[]],[[]]]=>4
[2,2,2,3,1,3]=>[[],[],[[[[]]]]]=>3
[2,2,2,3,3,1]=>[[],[],[[]],[[]]]=>4
[2,2,3,1,2,3]=>[[],[[],[],[[]]]]=>2
[2,2,3,1,3,2]=>[[],[[[[[]]]]]]=>2
[2,2,3,2,1,3]=>[[],[[[],[[]]]]]=>2
[2,2,3,2,3,1]=>[[],[[],[[[]]]]]=>2
[2,2,3,3,1,2]=>[[],[],[[[],[]]]]=>3
[2,2,3,3,2,1]=>[[],[[]],[[],[]]]=>3
[2,3,1,2,2,3]=>[[[]],[[],[],[]]]=>2
[2,3,1,2,3,2]=>[[[],[],[[[]]]]]=>1
[2,3,1,3,2,2]=>[[[[]]],[[[]]]]=>2
[2,3,2,1,2,3]=>[[[],[],[[],[]]]]=>1
[2,3,2,1,3,2]=>[[[[],[],[[]]]]]=>1
[2,3,2,2,1,3]=>[[],[[[]],[[]]]]=>2
[2,3,2,2,3,1]=>[[],[[],[[[]]]]]=>2
[2,3,2,3,1,2]=>[[[],[[]],[[]]]]=>1
[2,3,2,3,2,1]=>[[[],[[],[],[]]]]=>1
[2,3,3,1,2,2]=>[[],[],[[],[[]]]]=>3
[2,3,3,2,1,2]=>[[],[[],[[],[]]]]=>2
[2,3,3,2,2,1]=>[[],[[]],[[],[]]]=>3
[3,1,2,2,2,3]=>[[],[[]],[[],[]]]=>3
[3,1,2,2,3,2]=>[[],[[],[[[]]]]]=>2
[3,1,2,3,2,2]=>[[[]],[[[],[]]]]=>2
[3,1,3,2,2,2]=>[[],[[]],[[[]]]]=>3
[3,2,1,2,2,3]=>[[],[[],[[],[]]]]=>2
[3,2,1,2,3,2]=>[[[],[],[[],[]]]]=>1
[3,2,1,3,2,2]=>[[],[[],[],[[]]]]=>2
[3,2,2,1,2,3]=>[[],[[],[[],[]]]]=>2
[3,2,2,1,3,2]=>[[],[[],[],[[]]]]=>2
[3,2,2,2,1,3]=>[[],[],[[],[[]]]]=>3
[3,2,2,2,3,1]=>[[],[],[[[[]]]]]=>3
[3,2,2,3,1,2]=>[[],[[[]],[[]]]]=>2
[3,2,2,3,2,1]=>[[],[[[],[],[]]]]=>2
[3,2,3,1,2,2]=>[[[]],[[],[[]]]]=>2
[3,2,3,2,1,2]=>[[[],[],[[],[]]]]=>1
[3,2,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[3,3,1,2,2,2]=>[[],[],[[]],[[]]]=>4
[3,3,2,1,2,2]=>[[],[[]],[[],[]]]=>3
[3,3,2,2,1,2]=>[[],[],[[],[[]]]]=>3
[3,3,2,2,2,1]=>[[],[],[],[[],[]]]=>4
[1,2,2,2,3,4]=>[[],[],[[],[],[]]]=>3
[1,2,2,2,4,3]=>[[],[[]],[[[]]]]=>3
[1,2,2,3,2,4]=>[[],[[],[[[]]]]]=>2
[1,2,2,3,4,2]=>[[],[[],[],[[]]]]=>2
[1,2,2,4,2,3]=>[[],[[[[],[]]]]]=>2
[1,2,2,4,3,2]=>[[[]],[[[],[]]]]=>2
[1,2,3,2,2,4]=>[[],[[[[],[]]]]]=>2
[1,2,3,2,4,2]=>[[[],[[[[]]]]]]=>1
[1,2,3,4,2,2]=>[[],[[[],[],[]]]]=>2
[1,2,4,2,2,3]=>[[[[]]],[[],[]]]=>2
[1,2,4,2,3,2]=>[[[],[[[[]]]]]]=>1
[1,2,4,3,2,2]=>[[],[[],[[[]]]]]=>2
[1,3,2,2,2,4]=>[[],[],[[],[[]]]]=>3
[1,3,2,2,4,2]=>[[],[[],[[[]]]]]=>2
[1,3,2,4,2,2]=>[[[[],[]]],[[]]]=>2
[1,3,4,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,4,2,2,2,3]=>[[],[[]],[[[]]]]=>3
[1,4,2,2,3,2]=>[[],[[[[[]]]]]]=>2
[1,4,2,3,2,2]=>[[[[]]],[[[]]]]=>2
[1,4,3,2,2,2]=>[[],[],[[],[[]]]]=>3
[2,1,2,2,3,4]=>[[],[[],[],[[]]]]=>2
[2,1,2,2,4,3]=>[[[]],[[[],[]]]]=>2
[2,1,2,3,2,4]=>[[[[]],[[],[]]]]=>1
[2,1,2,3,4,2]=>[[[[[],[],[]]]]]=>1
[2,1,2,4,2,3]=>[[[[],[[[]]]]]]=>1
[2,1,2,4,3,2]=>[[[],[],[[[]]]]]=>1
[2,1,3,2,2,4]=>[[],[[],[[],[]]]]=>2
[2,1,3,2,4,2]=>[[[],[[[],[]]]]]=>1
[2,1,3,4,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,4,2,2,3]=>[[[[]]],[[[]]]]=>2
[2,1,4,2,3,2]=>[[[[]],[[[]]]]]=>1
[2,1,4,3,2,2]=>[[],[[],[],[[]]]]=>2
[2,2,1,2,3,4]=>[[],[[[],[],[]]]]=>2
[2,2,1,2,4,3]=>[[],[[],[[[]]]]]=>2
[2,2,1,3,2,4]=>[[],[[],[[],[]]]]=>2
[2,2,1,3,4,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,2,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,3,2]=>[[],[[],[],[[]]]]=>2
[2,2,2,1,3,4]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,4,3]=>[[],[],[[],[[]]]]=>3
[2,2,2,3,1,4]=>[[],[],[[[[]]]]]=>3
[2,2,2,3,4,1]=>[[],[],[[],[[]]]]=>3
[2,2,2,4,1,3]=>[[],[],[[],[[]]]]=>3
[2,2,2,4,3,1]=>[[],[],[[[[]]]]]=>3
[2,2,3,1,2,4]=>[[],[[[]],[[]]]]=>2
[2,2,3,1,4,2]=>[[],[[[],[[]]]]]=>2
[2,2,3,2,1,4]=>[[],[[[],[[]]]]]=>2
[2,2,3,2,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,3,4,1,2]=>[[],[[],[],[[]]]]=>2
[2,2,3,4,2,1]=>[[],[[],[[[]]]]]=>2
[2,2,4,1,2,3]=>[[],[[[[],[]]]]]=>2
[2,2,4,1,3,2]=>[[],[[[]],[[]]]]=>2
[2,2,4,2,1,3]=>[[],[[[]],[[]]]]=>2
[2,2,4,2,3,1]=>[[],[[[],[[]]]]]=>2
[2,2,4,3,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,4,3,2,1]=>[[],[[[],[],[]]]]=>2
[2,3,1,2,2,4]=>[[[]],[[],[[]]]]=>2
[2,3,1,2,4,2]=>[[[],[[[],[]]]]]=>1
[2,3,1,4,2,2]=>[[],[[[]],[[]]]]=>2
[2,3,2,1,2,4]=>[[[],[[[],[]]]]]=>1
[2,3,2,1,4,2]=>[[[[],[[[]]]]]]=>1
[2,3,2,2,1,4]=>[[],[[[]],[[]]]]=>2
[2,3,2,2,4,1]=>[[],[[[[[]]]]]]=>2
[2,3,2,4,1,2]=>[[[[[]]],[[]]]]=>1
[2,3,2,4,2,1]=>[[[[],[[[]]]]]]=>1
[2,3,4,1,2,2]=>[[],[[],[],[[]]]]=>2
[2,3,4,2,1,2]=>[[[],[[]],[[]]]]=>1
[2,3,4,2,2,1]=>[[],[[[[],[]]]]]=>2
[2,4,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[2,4,1,2,3,2]=>[[[[[],[[]]]]]]=>1
[2,4,1,3,2,2]=>[[],[[[],[[]]]]]=>2
[2,4,2,1,2,3]=>[[[[[],[[]]]]]]=>1
[2,4,2,1,3,2]=>[[[],[[],[[]]]]]=>1
[2,4,2,2,1,3]=>[[],[[[],[[]]]]]=>2
[2,4,2,2,3,1]=>[[],[[[],[[]]]]]=>2
[2,4,2,3,1,2]=>[[[[],[[],[]]]]]=>1
[2,4,2,3,2,1]=>[[[[[],[[]]]]]]=>1
[2,4,3,1,2,2]=>[[[[]]],[[[]]]]=>2
[2,4,3,2,1,2]=>[[[[],[],[[]]]]]=>1
[2,4,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[3,1,2,2,2,4]=>[[[]],[[]],[[]]]=>3
[3,1,2,2,4,2]=>[[[]],[[[],[]]]]=>2
[3,1,2,4,2,2]=>[[],[[],[[[]]]]]=>2
[3,1,4,2,2,2]=>[[],[],[[],[[]]]]=>3
[3,2,1,2,2,4]=>[[[]],[[[],[]]]]=>2
[3,2,1,2,4,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,2,2]=>[[[[]]],[[],[]]]=>2
[3,2,2,1,2,4]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,4,2]=>[[],[[],[[[]]]]]=>2
[3,2,2,2,1,4]=>[[],[],[[],[[]]]]=>3
[3,2,2,2,4,1]=>[[],[],[[[[]]]]]=>3
[3,2,2,4,1,2]=>[[],[[[[[]]]]]]=>2
[3,2,2,4,2,1]=>[[],[[[[],[]]]]]=>2
[3,2,4,1,2,2]=>[[[[[]]]],[[]]]=>2
[3,2,4,2,1,2]=>[[[],[[[[]]]]]]=>1
[3,2,4,2,2,1]=>[[],[[],[[[]]]]]=>2
[3,4,1,2,2,2]=>[[],[],[[],[[]]]]=>3
[3,4,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[3,4,2,2,1,2]=>[[],[[[],[[]]]]]=>2
[3,4,2,2,2,1]=>[[],[],[[[[]]]]]=>3
[4,1,2,2,2,3]=>[[],[[]],[[],[]]]=>3
[4,1,2,2,3,2]=>[[[]],[[],[[]]]]=>2
[4,1,2,3,2,2]=>[[],[[[],[[]]]]]=>2
[4,1,3,2,2,2]=>[[],[[]],[[[]]]]=>3
[4,2,1,2,2,3]=>[[[]],[[],[[]]]]=>2
[4,2,1,2,3,2]=>[[[[],[[],[]]]]]=>1
[4,2,1,3,2,2]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,2,3]=>[[],[[[],[[]]]]]=>2
[4,2,2,1,3,2]=>[[],[[[]],[[]]]]=>2
[4,2,2,2,1,3]=>[[],[],[[[[]]]]]=>3
[4,2,2,2,3,1]=>[[],[],[[[],[]]]]=>3
[4,2,2,3,1,2]=>[[],[[],[[],[]]]]=>2
[4,2,2,3,2,1]=>[[],[[[],[[]]]]]=>2
[4,2,3,1,2,2]=>[[],[[],[[],[]]]]=>2
[4,2,3,2,1,2]=>[[[[],[[],[]]]]]=>1
[4,2,3,2,2,1]=>[[],[[[]],[[]]]]=>2
[4,3,1,2,2,2]=>[[[]],[[]],[[]]]=>3
[4,3,2,1,2,2]=>[[[]],[[],[],[]]]=>2
[4,3,2,2,1,2]=>[[],[[],[],[[]]]]=>2
[4,3,2,2,2,1]=>[[],[],[[],[],[]]]=>3
[1,2,2,2,3,5]=>[[],[],[[],[[]]]]=>3
[1,2,2,2,5,3]=>[[],[[]],[[[]]]]=>3
[1,2,2,3,2,5]=>[[],[[],[[[]]]]]=>2
[1,2,2,3,5,2]=>[[],[[],[[[]]]]]=>2
[1,2,2,5,2,3]=>[[],[[[[],[]]]]]=>2
[1,2,2,5,3,2]=>[[[]],[[[[]]]]]=>2
[1,2,3,2,2,5]=>[[],[[[[],[]]]]]=>2
[1,2,3,2,5,2]=>[[[],[[[[]]]]]]=>1
[1,2,3,5,2,2]=>[[],[[[[],[]]]]]=>2
[1,2,5,2,2,3]=>[[[[]]],[[],[]]]=>2
[1,2,5,2,3,2]=>[[[[[]]],[[]]]]=>1
[1,2,5,3,2,2]=>[[[[[]]]],[[]]]=>2
[1,3,2,2,2,5]=>[[],[],[[[[]]]]]=>3
[1,3,2,2,5,2]=>[[],[[[[[]]]]]]=>2
[1,3,2,5,2,2]=>[[[[]]],[[[]]]]=>2
[1,3,5,2,2,2]=>[[],[],[[[],[]]]]=>3
[1,5,2,2,2,3]=>[[],[[]],[[],[]]]=>3
[1,5,2,2,3,2]=>[[[[]]],[[],[]]]=>2
[1,5,2,3,2,2]=>[[],[[[[],[]]]]]=>2
[1,5,3,2,2,2]=>[[[]],[[]],[[]]]=>3
[2,1,2,2,3,5]=>[[],[[],[[[]]]]]=>2
[2,1,2,2,5,3]=>[[[]],[[[[]]]]]=>2
[2,1,2,3,2,5]=>[[[[]],[[],[]]]]=>1
[2,1,2,3,5,2]=>[[[[[[],[]]]]]]=>1
[2,1,2,5,2,3]=>[[[[],[[[]]]]]]=>1
[2,1,2,5,3,2]=>[[[],[[[[]]]]]]=>1
[2,1,3,2,2,5]=>[[],[[[],[[]]]]]=>2
[2,1,3,2,5,2]=>[[[[]],[[[]]]]]=>1
[2,1,3,5,2,2]=>[[[[],[]]],[[]]]=>2
[2,1,5,2,2,3]=>[[[[]]],[[],[]]]=>2
[2,1,5,2,3,2]=>[[[],[[[],[]]]]]=>1
[2,1,5,3,2,2]=>[[[]],[[],[[]]]]=>2
[2,2,1,2,3,5]=>[[],[[[[],[]]]]]=>2
[2,2,1,2,5,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,3,2,5]=>[[],[[[]],[[]]]]=>2
[2,2,1,3,5,2]=>[[],[[[[],[]]]]]=>2
[2,2,1,5,2,3]=>[[],[[[[],[]]]]]=>2
[2,2,1,5,3,2]=>[[],[[[]],[[]]]]=>2
[2,2,2,1,3,5]=>[[],[],[[[],[]]]]=>3
[2,2,2,1,5,3]=>[[],[],[[[[]]]]]=>3
[2,2,2,3,1,5]=>[[],[],[[[[]]]]]=>3
[2,2,2,3,5,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,5,1,3]=>[[],[],[[],[[]]]]=>3
[2,2,2,5,3,1]=>[[],[],[[[],[]]]]=>3
[2,2,3,1,2,5]=>[[],[[[]],[[]]]]=>2
[2,2,3,1,5,2]=>[[],[[[[],[]]]]]=>2
[2,2,3,2,1,5]=>[[],[[[],[[]]]]]=>2
[2,2,3,2,5,1]=>[[],[[[[],[]]]]]=>2
[2,2,3,5,1,2]=>[[],[[],[[[]]]]]=>2
[2,2,3,5,2,1]=>[[],[[[[[]]]]]]=>2
[2,2,5,1,2,3]=>[[],[[],[[],[]]]]=>2
[2,2,5,1,3,2]=>[[],[[],[[[]]]]]=>2
[2,2,5,2,1,3]=>[[],[[[[[]]]]]]=>2
[2,2,5,2,3,1]=>[[],[[[[[]]]]]]=>2
[2,2,5,3,1,2]=>[[],[[[],[[]]]]]=>2
[2,2,5,3,2,1]=>[[],[[[],[[]]]]]=>2
[2,3,1,2,2,5]=>[[[]],[[],[[]]]]=>2
[2,3,1,2,5,2]=>[[[[[]]],[[]]]]=>1
[2,3,1,5,2,2]=>[[],[[],[[[]]]]]=>2
[2,3,2,1,2,5]=>[[[],[[[],[]]]]]=>1
[2,3,2,1,5,2]=>[[[[],[[],[]]]]]=>1
[2,3,2,2,1,5]=>[[],[[[]],[[]]]]=>2
[2,3,2,2,5,1]=>[[],[[],[[[]]]]]=>2
[2,3,2,5,1,2]=>[[[[]],[[],[]]]]=>1
[2,3,2,5,2,1]=>[[[[],[[[]]]]]]=>1
[2,3,5,1,2,2]=>[[],[[],[[[]]]]]=>2
[2,3,5,2,1,2]=>[[[],[[[[]]]]]]=>1
[2,3,5,2,2,1]=>[[[[[]]]],[[]]]=>2
[2,5,1,2,2,3]=>[[],[[],[[],[]]]]=>2
[2,5,1,2,3,2]=>[[[],[[],[[]]]]]=>1
[2,5,1,3,2,2]=>[[],[[[[],[]]]]]=>2
[2,5,2,1,2,3]=>[[[[[],[[]]]]]]=>1
[2,5,2,1,3,2]=>[[[[],[[[]]]]]]=>1
[2,5,2,2,1,3]=>[[[[]]],[[[]]]]=>2
[2,5,2,2,3,1]=>[[[[]]],[[[]]]]=>2
[2,5,2,3,1,2]=>[[[[],[[[]]]]]]=>1
[2,5,2,3,2,1]=>[[[[[],[[]]]]]]=>1
[2,5,3,1,2,2]=>[[],[[[],[[]]]]]=>2
[2,5,3,2,1,2]=>[[[[],[[[]]]]]]=>1
[2,5,3,2,2,1]=>[[],[[[]],[[]]]]=>2
[3,1,2,2,2,5]=>[[[]],[[]],[[]]]=>3
[3,1,2,2,5,2]=>[[[[]]],[[[]]]]=>2
[3,1,2,5,2,2]=>[[],[[[[[]]]]]]=>2
[3,1,5,2,2,2]=>[[],[[]],[[],[]]]=>3
[3,2,1,2,2,5]=>[[[]],[[[],[]]]]=>2
[3,2,1,2,5,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,2,2]=>[[[],[]],[[],[]]]=>2
[3,2,2,1,2,5]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,5,2]=>[[],[[],[[],[]]]]=>2
[3,2,2,2,1,5]=>[[],[],[[],[[]]]]=>3
[3,2,2,2,5,1]=>[[],[],[[],[[]]]]=>3
[3,2,2,5,1,2]=>[[],[[],[[[]]]]]=>2
[3,2,2,5,2,1]=>[[],[[[[],[]]]]]=>2
[3,2,5,1,2,2]=>[[[[],[]]],[[]]]=>2
[3,2,5,2,1,2]=>[[[[]],[[[]]]]]=>1
[3,2,5,2,2,1]=>[[[[]]],[[],[]]]=>2
[3,5,1,2,2,2]=>[[],[],[[[[]]]]]=>3
[3,5,2,1,2,2]=>[[[]],[[[[]]]]]=>2
[3,5,2,2,1,2]=>[[[[]]],[[[]]]]=>2
[3,5,2,2,2,1]=>[[],[[[]]],[[]]]=>3
[5,1,2,2,2,3]=>[[],[],[[],[[]]]]=>3
[5,1,2,2,3,2]=>[[],[[[]],[[]]]]=>2
[5,1,2,3,2,2]=>[[],[[[],[[]]]]]=>2
[5,1,3,2,2,2]=>[[],[],[[[[]]]]]=>3
[5,2,1,2,2,3]=>[[],[[[]],[[]]]]=>2
[5,2,1,2,3,2]=>[[[[],[[],[]]]]]=>1
[5,2,1,3,2,2]=>[[],[[],[[[]]]]]=>2
[5,2,2,1,2,3]=>[[],[[[],[[]]]]]=>2
[5,2,2,1,3,2]=>[[],[[],[[[]]]]]=>2
[5,2,2,2,1,3]=>[[],[[]],[[[]]]]=>3
[5,2,2,2,3,1]=>[[],[[[]]],[[]]]=>3
[5,2,2,3,1,2]=>[[],[[],[[[]]]]]=>2
[5,2,2,3,2,1]=>[[],[[[],[[]]]]]=>2
[5,2,3,1,2,2]=>[[],[[],[[[]]]]]=>2
[5,2,3,2,1,2]=>[[[[],[[],[]]]]]=>1
[5,2,3,2,2,1]=>[[[]],[[],[[]]]]=>2
[5,3,1,2,2,2]=>[[],[[]],[[],[]]]=>3
[5,3,2,1,2,2]=>[[[[]]],[[],[]]]=>2
[5,3,2,2,1,2]=>[[],[[],[[[]]]]]=>2
[5,3,2,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,2,3,6]=>[[],[],[[],[[]]]]=>3
[1,2,2,2,6,3]=>[[],[[]],[[],[]]]=>3
[1,2,2,3,2,6]=>[[],[[],[[[]]]]]=>2
[1,2,2,3,6,2]=>[[],[[],[[],[]]]]=>2
[1,2,2,6,2,3]=>[[],[[[[],[]]]]]=>2
[1,2,2,6,3,2]=>[[[]],[[],[[]]]]=>2
[1,2,3,2,2,6]=>[[],[[[[],[]]]]]=>2
[1,2,3,2,6,2]=>[[[],[[[[]]]]]]=>1
[1,2,3,6,2,2]=>[[],[[],[[],[]]]]=>2
[1,2,6,2,2,3]=>[[[[]]],[[],[]]]=>2
[1,2,6,2,3,2]=>[[[[[]]],[[]]]]=>1
[1,2,6,3,2,2]=>[[],[[[],[[]]]]]=>2
[1,3,2,2,2,6]=>[[],[],[[[[]]]]]=>3
[1,3,2,2,6,2]=>[[],[[[[[]]]]]]=>2
[1,3,2,6,2,2]=>[[[[]]],[[[]]]]=>2
[1,3,6,2,2,2]=>[[],[],[[],[[]]]]=>3
[1,6,2,2,2,3]=>[[[]],[[]],[[]]]=>3
[1,6,2,2,3,2]=>[[[[[]]]],[[]]]=>2
[1,6,2,3,2,2]=>[[[]],[[[[]]]]]=>2
[1,6,3,2,2,2]=>[[[]],[[]],[[]]]=>3
[2,1,2,2,3,6]=>[[],[[],[[[]]]]]=>2
[2,1,2,2,6,3]=>[[[]],[[],[[]]]]=>2
[2,1,2,3,2,6]=>[[[[]],[[],[]]]]=>1
[2,1,2,3,6,2]=>[[[[],[[],[]]]]]=>1
[2,1,2,6,2,3]=>[[[[],[[[]]]]]]=>1
[2,1,2,6,3,2]=>[[[],[[],[[]]]]]=>1
[2,1,3,2,2,6]=>[[],[[[],[[]]]]]=>2
[2,1,3,2,6,2]=>[[[[]],[[[]]]]]=>1
[2,1,3,6,2,2]=>[[[]],[[],[[]]]]=>2
[2,1,6,2,2,3]=>[[[[]]],[[[]]]]=>2
[2,1,6,2,3,2]=>[[[[[]]],[[]]]]=>1
[2,1,6,3,2,2]=>[[[]],[[],[[]]]]=>2
[2,2,1,2,3,6]=>[[],[[[[],[]]]]]=>2
[2,2,1,2,6,3]=>[[],[[[],[[]]]]]=>2
[2,2,1,3,2,6]=>[[],[[[]],[[]]]]=>2
[2,2,1,3,6,2]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,2,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,3,2]=>[[],[[[]],[[]]]]=>2
[2,2,2,1,3,6]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,6,3]=>[[],[],[[[[]]]]]=>3
[2,2,2,3,1,6]=>[[],[],[[[],[]]]]=>3
[2,2,2,3,6,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,6,1,3]=>[[],[],[[[],[]]]]=>3
[2,2,2,6,3,1]=>[[],[],[[],[[]]]]=>3
[2,2,3,1,2,6]=>[[],[[[]],[[]]]]=>2
[2,2,3,1,6,2]=>[[],[[[],[[]]]]]=>2
[2,2,3,2,1,6]=>[[],[[[],[[]]]]]=>2
[2,2,3,2,6,1]=>[[],[[[[[]]]]]]=>2
[2,2,3,6,1,2]=>[[],[[],[[[]]]]]=>2
[2,2,3,6,2,1]=>[[],[[[],[[]]]]]=>2
[2,2,6,1,2,3]=>[[],[[[[],[]]]]]=>2
[2,2,6,1,3,2]=>[[],[[[],[[]]]]]=>2
[2,2,6,2,1,3]=>[[],[[[[[]]]]]]=>2
[2,2,6,2,3,1]=>[[],[[[[[]]]]]]=>2
[2,2,6,3,1,2]=>[[],[[],[[[]]]]]=>2
[2,2,6,3,2,1]=>[[],[[],[[],[]]]]=>2
[2,3,1,2,2,6]=>[[[]],[[],[[]]]]=>2
[2,3,1,2,6,2]=>[[[[[]]],[[]]]]=>1
[2,3,1,6,2,2]=>[[],[[[],[[]]]]]=>2
[2,3,2,1,2,6]=>[[[],[[[],[]]]]]=>1
[2,3,2,1,6,2]=>[[[[],[[[]]]]]]=>1
[2,3,2,2,1,6]=>[[],[[[]],[[]]]]=>2
[2,3,2,2,6,1]=>[[],[[[[[]]]]]]=>2
[2,3,2,6,1,2]=>[[[[[]]],[[]]]]=>1
[2,3,2,6,2,1]=>[[[[],[[[]]]]]]=>1
[2,3,6,1,2,2]=>[[],[[],[[[]]]]]=>2
[2,3,6,2,1,2]=>[[[],[[[],[]]]]]=>1
[2,3,6,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,6,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[2,6,1,2,3,2]=>[[[[[]],[[]]]]]=>1
[2,6,1,3,2,2]=>[[],[[[],[[]]]]]=>2
[2,6,2,1,2,3]=>[[[[],[[[]]]]]]=>1
[2,6,2,1,3,2]=>[[[[[],[[]]]]]]=>1
[2,6,2,2,1,3]=>[[[[]]],[[[]]]]=>2
[2,6,2,2,3,1]=>[[[[]]],[[[]]]]=>2
[2,6,2,3,1,2]=>[[[[[],[[]]]]]]=>1
[2,6,2,3,2,1]=>[[[[],[[[]]]]]]=>1
[2,6,3,1,2,2]=>[[],[[[[],[]]]]]=>2
[2,6,3,2,1,2]=>[[[],[[],[[]]]]]=>1
[2,6,3,2,2,1]=>[[[],[]],[[],[]]]=>2
[3,1,2,2,2,6]=>[[[]],[[]],[[]]]=>3
[3,1,2,2,6,2]=>[[[[]]],[[[]]]]=>2
[3,1,2,6,2,2]=>[[],[[[[[]]]]]]=>2
[3,1,6,2,2,2]=>[[],[[]],[[],[]]]=>3
[3,2,1,2,2,6]=>[[[]],[[[],[]]]]=>2
[3,2,1,2,6,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,2,2]=>[[[[]]],[[],[]]]=>2
[3,2,2,1,2,6]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,6,2]=>[[],[[],[[[]]]]]=>2
[3,2,2,2,1,6]=>[[],[],[[],[[]]]]=>3
[3,2,2,2,6,1]=>[[],[],[[[[]]]]]=>3
[3,2,2,6,1,2]=>[[],[[[[[]]]]]]=>2
[3,2,2,6,2,1]=>[[],[[[[],[]]]]]=>2
[3,2,6,1,2,2]=>[[[[[]]]],[[]]]=>2
[3,2,6,2,1,2]=>[[[[]],[[[]]]]]=>1
[3,2,6,2,2,1]=>[[[[]]],[[],[]]]=>2
[3,6,1,2,2,2]=>[[],[],[[[[]]]]]=>3
[3,6,2,1,2,2]=>[[[]],[[[],[]]]]=>2
[3,6,2,2,1,2]=>[[[[]]],[[],[]]]=>2
[3,6,2,2,2,1]=>[[],[[]],[[],[]]]=>3
[6,1,2,2,2,3]=>[[],[],[[],[[]]]]=>3
[6,1,2,2,3,2]=>[[],[[[]],[[]]]]=>2
[6,1,2,3,2,2]=>[[],[[[],[[]]]]]=>2
[6,1,3,2,2,2]=>[[],[],[[[],[]]]]=>3
[6,2,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[6,2,1,2,3,2]=>[[[[],[[],[]]]]]=>1
[6,2,1,3,2,2]=>[[],[[[]],[[]]]]=>2
[6,2,2,1,2,3]=>[[[]],[[[],[]]]]=>2
[6,2,2,1,3,2]=>[[[]],[[],[[]]]]=>2
[6,2,2,2,1,3]=>[[],[[]],[[[]]]]=>3
[6,2,2,2,3,1]=>[[],[[[]]],[[]]]=>3
[6,2,2,3,1,2]=>[[[]],[[],[[]]]]=>2
[6,2,2,3,2,1]=>[[[[],[]]],[[]]]=>2
[6,2,3,1,2,2]=>[[],[[[]],[[]]]]=>2
[6,2,3,2,1,2]=>[[[[],[[],[]]]]]=>1
[6,2,3,2,2,1]=>[[],[[],[[[]]]]]=>2
[6,3,1,2,2,2]=>[[],[[[]]],[[]]]=>3
[6,3,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[6,3,2,2,1,2]=>[[[]],[[],[[]]]]=>2
[6,3,2,2,2,1]=>[[],[[]],[[],[]]]=>3
[1,2,2,2,4,4]=>[[],[],[[]],[[]]]=>4
[1,2,2,4,2,4]=>[[[]],[[],[[]]]]=>2
[1,2,2,4,4,2]=>[[[]],[[]],[[]]]=>3
[1,2,4,2,2,4]=>[[[]],[[],[[]]]]=>2
[1,2,4,2,4,2]=>[[[[],[[],[]]]]]=>1
[1,2,4,4,2,2]=>[[],[[[]]],[[]]]=>3
[1,4,2,2,2,4]=>[[],[[]],[[[]]]]=>3
[1,4,2,2,4,2]=>[[],[[[],[[]]]]]=>2
[1,4,2,4,2,2]=>[[],[[[]],[[]]]]=>2
[1,4,4,2,2,2]=>[[],[],[],[[[]]]]=>4
[2,1,2,2,4,4]=>[[[]],[[]],[[]]]=>3
[2,1,2,4,2,4]=>[[[[[]],[[]]]]]=>1
[2,1,2,4,4,2]=>[[[[]]],[[[]]]]=>2
[2,1,4,2,2,4]=>[[[[]]],[[[]]]]=>2
[2,1,4,2,4,2]=>[[[[[]],[[]]]]]=>1
[2,1,4,4,2,2]=>[[[]],[[]],[[]]]=>3
[2,2,1,2,4,4]=>[[],[[[]]],[[]]]=>3
[2,2,1,4,2,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,4,2]=>[[],[[]],[[[]]]]=>3
[2,2,2,1,4,4]=>[[],[],[[]],[[]]]=>4
[2,2,2,4,1,4]=>[[],[],[[[[]]]]]=>3
[2,2,2,4,4,1]=>[[],[],[[]],[[]]]=>4
[2,2,4,1,2,4]=>[[],[[],[[[]]]]]=>2
[2,2,4,1,4,2]=>[[],[[[[[]]]]]]=>2
[2,2,4,2,1,4]=>[[],[[[[[]]]]]]=>2
[2,2,4,2,4,1]=>[[],[[[]],[[]]]]=>2
[2,2,4,4,1,2]=>[[],[[]],[[[]]]]=>3
[2,2,4,4,2,1]=>[[],[[]],[[[]]]]=>3
[2,4,1,2,2,4]=>[[[[]]],[[],[]]]=>2
[2,4,1,2,4,2]=>[[[[[]]],[[]]]]=>1
[2,4,1,4,2,2]=>[[],[[[[[]]]]]]=>2
[2,4,2,1,2,4]=>[[[[[]]],[[]]]]=>1
[2,4,2,1,4,2]=>[[[[[],[[]]]]]]=>1
[2,4,2,2,1,4]=>[[],[[[[[]]]]]]=>2
[2,4,2,2,4,1]=>[[[]],[[],[[]]]]=>2
[2,4,2,4,1,2]=>[[[[[]]],[[]]]]=>1
[2,4,2,4,2,1]=>[[[],[[],[[]]]]]=>1
[2,4,4,1,2,2]=>[[],[[[]]],[[]]]=>3
[2,4,4,2,1,2]=>[[[]],[[[[]]]]]=>2
[2,4,4,2,2,1]=>[[],[[]],[[[]]]]=>3
[4,1,2,2,2,4]=>[[],[[[]]],[[]]]=>3
[4,1,2,2,4,2]=>[[[[]]],[[[]]]]=>2
[4,1,2,4,2,2]=>[[],[[[[[]]]]]]=>2
[4,1,4,2,2,2]=>[[],[[]],[[[]]]]=>3
[4,2,1,2,2,4]=>[[[[]]],[[[]]]]=>2
[4,2,1,2,4,2]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,2,2]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,2,4]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,4,2]=>[[],[[[],[[]]]]]=>2
[4,2,2,2,1,4]=>[[],[],[[[[]]]]]=>3
[4,2,2,2,4,1]=>[[],[[[]]],[[]]]=>3
[4,2,2,4,1,2]=>[[[[[]]]],[[]]]=>2
[4,2,2,4,2,1]=>[[],[[[],[[]]]]]=>2
[4,2,4,1,2,2]=>[[],[[[[[]]]]]]=>2
[4,2,4,2,1,2]=>[[[[[]]],[[]]]]=>1
[4,2,4,2,2,1]=>[[],[[[],[[]]]]]=>2
[4,4,1,2,2,2]=>[[],[],[],[[[]]]]=>4
[4,4,2,1,2,2]=>[[],[[[]]],[[]]]=>3
[4,4,2,2,1,2]=>[[],[],[[[[]]]]]=>3
[4,4,2,2,2,1]=>[[],[],[],[[[]]]]=>4
[1,2,2,2,4,5]=>[[],[],[[[],[]]]]=>3
[1,2,2,2,5,4]=>[[],[[]],[[[]]]]=>3
[1,2,2,4,2,5]=>[[[]],[[[[]]]]]=>2
[1,2,2,4,5,2]=>[[],[[[],[[]]]]]=>2
[1,2,2,5,2,4]=>[[[]],[[[[]]]]]=>2
[1,2,2,5,4,2]=>[[[]],[[[[]]]]]=>2
[1,2,4,2,2,5]=>[[[]],[[[[]]]]]=>2
[1,2,4,2,5,2]=>[[[[[[[]]]]]]]=>1
[1,2,4,5,2,2]=>[[],[[[],[[]]]]]=>2
[1,2,5,2,2,4]=>[[[]],[[[[]]]]]=>2
[1,2,5,2,4,2]=>[[[[[[[]]]]]]]=>1
[1,2,5,4,2,2]=>[[[]],[[[[]]]]]=>2
[1,4,2,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,4,2,2,5,2]=>[[[]],[[],[[]]]]=>2
[1,4,2,5,2,2]=>[[],[[[],[[]]]]]=>2
[1,4,5,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,5,2,2,2,4]=>[[],[[]],[[],[]]]=>3
[1,5,2,2,4,2]=>[[[[]]],[[],[]]]=>2
[1,5,2,4,2,2]=>[[],[[[[],[]]]]]=>2
[1,5,4,2,2,2]=>[[[]],[[]],[[]]]=>3
[2,1,2,2,4,5]=>[[],[[[],[[]]]]]=>2
[2,1,2,2,5,4]=>[[[]],[[[],[]]]]=>2
[2,1,2,4,2,5]=>[[[[[[[]]]]]]]=>1
[2,1,2,4,5,2]=>[[[[[],[[]]]]]]=>1
[2,1,2,5,2,4]=>[[[[[[[]]]]]]]=>1
[2,1,2,5,4,2]=>[[[[[]]],[[]]]]=>1
[2,1,4,2,2,5]=>[[[]],[[],[[]]]]=>2
[2,1,4,2,5,2]=>[[[[[],[[]]]]]]=>1
[2,1,4,5,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,5,2,2,4]=>[[[[]]],[[],[]]]=>2
[2,1,5,2,4,2]=>[[[[[[],[]]]]]]=>1
[2,1,5,4,2,2]=>[[[[]]],[[],[]]]=>2
[2,2,1,2,4,5]=>[[],[[[],[[]]]]]=>2
[2,2,1,2,5,4]=>[[],[[],[[[]]]]]=>2
[2,2,1,4,2,5]=>[[],[[[],[[]]]]]=>2
[2,2,1,4,5,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,2,4]=>[[],[[[[],[]]]]]=>2
[2,2,1,5,4,2]=>[[],[[],[[[]]]]]=>2
[2,2,2,1,4,5]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,5,4]=>[[],[],[[],[[]]]]=>3
[2,2,2,4,1,5]=>[[],[],[[[],[]]]]=>3
[2,2,2,4,5,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,5,1,4]=>[[],[],[[],[],[]]]=>3
[2,2,2,5,4,1]=>[[],[],[[[[]]]]]=>3
[2,2,4,1,2,5]=>[[],[[[[[]]]]]]=>2
[2,2,4,1,5,2]=>[[],[[[],[],[]]]]=>2
[2,2,4,2,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,4,2,5,1]=>[[],[[[[],[]]]]]=>2
[2,2,4,5,1,2]=>[[],[[[],[[]]]]]=>2
[2,2,4,5,2,1]=>[[],[[[[[]]]]]]=>2
[2,2,5,1,2,4]=>[[],[[],[[[]]]]]=>2
[2,2,5,1,4,2]=>[[],[[],[],[[]]]]=>2
[2,2,5,2,1,4]=>[[],[[],[[[]]]]]=>2
[2,2,5,2,4,1]=>[[],[[[],[[]]]]]=>2
[2,2,5,4,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,5,4,2,1]=>[[],[[[[],[]]]]]=>2
[2,4,1,2,2,5]=>[[[[[]]]],[[]]]=>2
[2,4,1,2,5,2]=>[[[[],[[[]]]]]]=>1
[2,4,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[2,4,2,1,2,5]=>[[[[[[[]]]]]]]=>1
[2,4,2,1,5,2]=>[[[[[],[[]]]]]]=>1
[2,4,2,2,1,5]=>[[],[[[[[]]]]]]=>2
[2,4,2,2,5,1]=>[[],[[],[[[]]]]]=>2
[2,4,2,5,1,2]=>[[[[[],[[]]]]]]=>1
[2,4,2,5,2,1]=>[[[[[[[]]]]]]]=>1
[2,4,5,1,2,2]=>[[],[[[]],[[]]]]=>2
[2,4,5,2,1,2]=>[[[[],[[[]]]]]]=>1
[2,4,5,2,2,1]=>[[[[[]]]],[[]]]=>2
[2,5,1,2,2,4]=>[[[[],[]]],[[]]]=>2
[2,5,1,2,4,2]=>[[[],[[[[]]]]]]=>1
[2,5,1,4,2,2]=>[[],[[[],[],[]]]]=>2
[2,5,2,1,2,4]=>[[[[[[[]]]]]]]=>1
[2,5,2,1,4,2]=>[[[[]],[[[]]]]]=>1
[2,5,2,2,1,4]=>[[[]],[[[],[]]]]=>2
[2,5,2,2,4,1]=>[[],[[[],[[]]]]]=>2
[2,5,2,4,1,2]=>[[[[[]],[[]]]]]=>1
[2,5,2,4,2,1]=>[[[[[[[]]]]]]]=>1
[2,5,4,1,2,2]=>[[[[]]],[[[]]]]=>2
[2,5,4,2,1,2]=>[[[[[[],[]]]]]]=>1
[2,5,4,2,2,1]=>[[],[[],[[[]]]]]=>2
[4,1,2,2,2,5]=>[[],[[[]]],[[]]]=>3
[4,1,2,2,5,2]=>[[[]],[[[],[]]]]=>2
[4,1,2,5,2,2]=>[[],[[],[[[]]]]]=>2
[4,1,5,2,2,2]=>[[],[],[[],[],[]]]=>3
[4,2,1,2,2,5]=>[[[[]]],[[[]]]]=>2
[4,2,1,2,5,2]=>[[[[[[[]]]]]]]=>1
[4,2,1,5,2,2]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,2,5]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,5,2]=>[[],[[[],[[]]]]]=>2
[4,2,2,2,1,5]=>[[],[],[[[[]]]]]=>3
[4,2,2,2,5,1]=>[[],[],[[],[[]]]]=>3
[4,2,2,5,1,2]=>[[],[[[]],[[]]]]=>2
[4,2,2,5,2,1]=>[[],[[[[[]]]]]]=>2
[4,2,5,1,2,2]=>[[],[[[],[[]]]]]=>2
[4,2,5,2,1,2]=>[[[[[[[]]]]]]]=>1
[4,2,5,2,2,1]=>[[[[]]],[[[]]]]=>2
[4,5,1,2,2,2]=>[[],[],[[],[[]]]]=>3
[4,5,2,1,2,2]=>[[[[]]],[[],[]]]=>2
[4,5,2,2,1,2]=>[[[]],[[[],[]]]]=>2
[4,5,2,2,2,1]=>[[],[[[]]],[[]]]=>3
[5,1,2,2,2,4]=>[[],[[[]]],[[]]]=>3
[5,1,2,2,4,2]=>[[[[]]],[[[]]]]=>2
[5,1,2,4,2,2]=>[[],[[[[[]]]]]]=>2
[5,1,4,2,2,2]=>[[],[],[[[],[]]]]=>3
[5,2,1,2,2,4]=>[[[]],[[[[]]]]]=>2
[5,2,1,2,4,2]=>[[[[[[[]]]]]]]=>1
[5,2,1,4,2,2]=>[[[[[]]]],[[]]]=>2
[5,2,2,1,2,4]=>[[[]],[[[[]]]]]=>2
[5,2,2,1,4,2]=>[[],[[[[[]]]]]]=>2
[5,2,2,2,1,4]=>[[],[[]],[[[]]]]=>3
[5,2,2,2,4,1]=>[[],[],[[[],[]]]]=>3
[5,2,2,4,1,2]=>[[],[[[],[[]]]]]=>2
[5,2,2,4,2,1]=>[[],[[[[[]]]]]]=>2
[5,2,4,1,2,2]=>[[],[[[],[[]]]]]=>2
[5,2,4,2,1,2]=>[[[[[[[]]]]]]]=>1
[5,2,4,2,2,1]=>[[[]],[[[[]]]]]=>2
[5,4,1,2,2,2]=>[[],[[[]]],[[]]]=>3
[5,4,2,1,2,2]=>[[[[]]],[[],[]]]=>2
[5,4,2,2,1,2]=>[[],[[],[[[]]]]]=>2
[5,4,2,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,2,4,6]=>[[],[[]],[[],[]]]=>3
[1,2,2,2,6,4]=>[[],[[]],[[[]]]]=>3
[1,2,2,4,2,6]=>[[[]],[[[[]]]]]=>2
[1,2,2,4,6,2]=>[[[]],[[],[[]]]]=>2
[1,2,2,6,2,4]=>[[[]],[[[[]]]]]=>2
[1,2,2,6,4,2]=>[[[]],[[[],[]]]]=>2
[1,2,4,2,2,6]=>[[[]],[[[[]]]]]=>2
[1,2,4,2,6,2]=>[[[[[[[]]]]]]]=>1
[1,2,4,6,2,2]=>[[],[[[],[[]]]]]=>2
[1,2,6,2,2,4]=>[[[]],[[[[]]]]]=>2
[1,2,6,2,4,2]=>[[[[[[[]]]]]]]=>1
[1,2,6,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,4,2,2,2,6]=>[[[]],[[]],[[]]]=>3
[1,4,2,2,6,2]=>[[[[],[]]],[[]]]=>2
[1,4,2,6,2,2]=>[[],[[],[[[]]]]]=>2
[1,4,6,2,2,2]=>[[],[],[[],[[]]]]=>3
[1,6,2,2,2,4]=>[[[]],[[]],[[]]]=>3
[1,6,2,2,4,2]=>[[[[],[]]],[[]]]=>2
[1,6,2,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,6,4,2,2,2]=>[[],[],[[],[],[]]]=>3
[2,1,2,2,4,6]=>[[[]],[[],[[]]]]=>2
[2,1,2,2,6,4]=>[[[]],[[[[]]]]]=>2
[2,1,2,4,2,6]=>[[[[[[[]]]]]]]=>1
[2,1,2,4,6,2]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,2,4]=>[[[[[[[]]]]]]]=>1
[2,1,2,6,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,4,2,2,6]=>[[[[]]],[[[]]]]=>2
[2,1,4,2,6,2]=>[[[[],[[[]]]]]]=>1
[2,1,4,6,2,2]=>[[[]],[[],[[]]]]=>2
[2,1,6,2,2,4]=>[[[[]]],[[[]]]]=>2
[2,1,6,2,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,6,4,2,2]=>[[[]],[[],[],[]]]=>2
[2,2,1,2,4,6]=>[[],[[[],[[]]]]]=>2
[2,2,1,2,6,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,2,6]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,6,2]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,2,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,4,2]=>[[],[[[],[],[]]]]=>2
[2,2,2,1,4,6]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,6,4]=>[[],[],[[[],[]]]]=>3
[2,2,2,4,1,6]=>[[],[],[[[[]]]]]=>3
[2,2,2,4,6,1]=>[[],[],[[],[],[]]]=>3
[2,2,2,6,1,4]=>[[],[],[[[[]]]]]=>3
[2,2,2,6,4,1]=>[[],[],[[],[[]]]]=>3
[2,2,4,1,2,6]=>[[],[[[],[[]]]]]=>2
[2,2,4,1,6,2]=>[[],[[[[[]]]]]]=>2
[2,2,4,2,1,6]=>[[],[[[],[[]]]]]=>2
[2,2,4,2,6,1]=>[[],[[],[[[]]]]]=>2
[2,2,4,6,1,2]=>[[],[[],[],[[]]]]=>2
[2,2,4,6,2,1]=>[[],[[],[[[]]]]]=>2
[2,2,6,1,2,4]=>[[],[[[],[[]]]]]=>2
[2,2,6,1,4,2]=>[[],[[[[[]]]]]]=>2
[2,2,6,2,1,4]=>[[],[[[[],[]]]]]=>2
[2,2,6,2,4,1]=>[[],[[],[[[]]]]]=>2
[2,2,6,4,1,2]=>[[],[[[]],[[]]]]=>2
[2,2,6,4,2,1]=>[[],[[[[],[]]]]]=>2
[2,4,1,2,2,6]=>[[[]],[[],[[]]]]=>2
[2,4,1,2,6,2]=>[[[[[]],[[]]]]]=>1
[2,4,1,6,2,2]=>[[],[[[[[]]]]]]=>2
[2,4,2,1,2,6]=>[[[[[[[]]]]]]]=>1
[2,4,2,1,6,2]=>[[[[[[],[]]]]]]=>1
[2,4,2,2,1,6]=>[[],[[[],[[]]]]]=>2
[2,4,2,2,6,1]=>[[[[],[]]],[[]]]=>2
[2,4,2,6,1,2]=>[[[[]],[[[]]]]]=>1
[2,4,2,6,2,1]=>[[[[[[[]]]]]]]=>1
[2,4,6,1,2,2]=>[[],[[[],[],[]]]]=>2
[2,4,6,2,1,2]=>[[[],[[[[]]]]]]=>1
[2,4,6,2,2,1]=>[[[[],[]]],[[]]]=>2
[2,6,1,2,2,4]=>[[[]],[[],[[]]]]=>2
[2,6,1,2,4,2]=>[[[[[],[[]]]]]]=>1
[2,6,1,4,2,2]=>[[],[[[[[]]]]]]=>2
[2,6,2,1,2,4]=>[[[[[[[]]]]]]]=>1
[2,6,2,1,4,2]=>[[[[],[[[]]]]]]=>1
[2,6,2,2,1,4]=>[[[]],[[[],[]]]]=>2
[2,6,2,2,4,1]=>[[[[],[]]],[[]]]=>2
[2,6,2,4,1,2]=>[[[[]],[[[]]]]]=>1
[2,6,2,4,2,1]=>[[[[[[[]]]]]]]=>1
[2,6,4,1,2,2]=>[[],[[[],[[]]]]]=>2
[2,6,4,2,1,2]=>[[[[[[],[]]]]]]=>1
[2,6,4,2,2,1]=>[[[]],[[[],[]]]]=>2
[4,1,2,2,2,6]=>[[],[[]],[[],[]]]=>3
[4,1,2,2,6,2]=>[[[]],[[],[[]]]]=>2
[4,1,2,6,2,2]=>[[],[[[],[[]]]]]=>2
[4,1,6,2,2,2]=>[[],[[[]]],[[]]]=>3
[4,2,1,2,2,6]=>[[[[]]],[[[]]]]=>2
[4,2,1,2,6,2]=>[[[[[[[]]]]]]]=>1
[4,2,1,6,2,2]=>[[[[],[]]],[[]]]=>2
[4,2,2,1,2,6]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,6,2]=>[[],[[[[],[]]]]]=>2
[4,2,2,2,1,6]=>[[],[],[[[],[]]]]=>3
[4,2,2,2,6,1]=>[[],[[[]]],[[]]]=>3
[4,2,2,6,1,2]=>[[[[[]]]],[[]]]=>2
[4,2,2,6,2,1]=>[[],[[[[[]]]]]]=>2
[4,2,6,1,2,2]=>[[],[[[[[]]]]]]=>2
[4,2,6,2,1,2]=>[[[[[[[]]]]]]]=>1
[4,2,6,2,2,1]=>[[[[]]],[[[]]]]=>2
[4,6,1,2,2,2]=>[[],[],[[[],[]]]]=>3
[4,6,2,1,2,2]=>[[[]],[[[[]]]]]=>2
[4,6,2,2,1,2]=>[[[[]]],[[[]]]]=>2
[4,6,2,2,2,1]=>[[],[[[]]],[[]]]=>3
[6,1,2,2,2,4]=>[[],[[]],[[],[]]]=>3
[6,1,2,2,4,2]=>[[[]],[[],[[]]]]=>2
[6,1,2,4,2,2]=>[[],[[[],[[]]]]]=>2
[6,1,4,2,2,2]=>[[],[],[[[[]]]]]=>3
[6,2,1,2,2,4]=>[[[]],[[[[]]]]]=>2
[6,2,1,2,4,2]=>[[[[[[[]]]]]]]=>1
[6,2,1,4,2,2]=>[[[[],[]]],[[]]]=>2
[6,2,2,1,2,4]=>[[[]],[[[[]]]]]=>2
[6,2,2,1,4,2]=>[[],[[[[],[]]]]]=>2
[6,2,2,2,1,4]=>[[],[],[[[],[]]]]=>3
[6,2,2,2,4,1]=>[[],[[[]]],[[]]]=>3
[6,2,2,4,1,2]=>[[[[[]]]],[[]]]=>2
[6,2,2,4,2,1]=>[[[[[]]]],[[]]]=>2
[6,2,4,1,2,2]=>[[],[[[[[]]]]]]=>2
[6,2,4,2,1,2]=>[[[[[[[]]]]]]]=>1
[6,2,4,2,2,1]=>[[],[[[[[]]]]]]=>2
[6,4,1,2,2,2]=>[[],[[[]]],[[]]]=>3
[6,4,2,1,2,2]=>[[[[],[]]],[[]]]=>2
[6,4,2,2,1,2]=>[[],[[[[],[]]]]]=>2
[6,4,2,2,2,1]=>[[],[],[[[],[]]]]=>3
[1,2,2,2,5,5]=>[[],[],[[]],[[]]]=>4
[1,2,2,5,2,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,5,2]=>[[[]],[[]],[[]]]=>3
[1,2,5,2,2,5]=>[[[]],[[],[[]]]]=>2
[1,2,5,2,5,2]=>[[[[],[[],[]]]]]=>1
[1,2,5,5,2,2]=>[[],[[[]]],[[]]]=>3
[1,5,2,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,5,2,2,5,2]=>[[],[[[],[],[]]]]=>2
[1,5,2,5,2,2]=>[[],[[],[],[[]]]]=>2
[1,5,5,2,2,2]=>[[],[],[],[[],[]]]=>4
[2,1,2,2,5,5]=>[[[]],[[]],[[]]]=>3
[2,1,2,5,2,5]=>[[[[[]],[[]]]]]=>1
[2,1,2,5,5,2]=>[[[[]]],[[[]]]]=>2
[2,1,5,2,2,5]=>[[[[]]],[[],[]]]=>2
[2,1,5,2,5,2]=>[[[[],[],[[]]]]]=>1
[2,1,5,5,2,2]=>[[],[[]],[[],[]]]=>3
[2,2,1,2,5,5]=>[[],[[[]]],[[]]]=>3
[2,2,1,5,2,5]=>[[],[[[[],[]]]]]=>2
[2,2,1,5,5,2]=>[[],[],[[],[[]]]]=>3
[2,2,2,1,5,5]=>[[],[],[[]],[[]]]=>4
[2,2,2,5,1,5]=>[[],[],[[],[[]]]]=>3
[2,2,2,5,5,1]=>[[],[],[],[[],[]]]=>4
[2,2,5,1,2,5]=>[[],[[],[],[[]]]]=>2
[2,2,5,1,5,2]=>[[],[[],[[],[]]]]=>2
[2,2,5,2,1,5]=>[[],[[[[],[]]]]]=>2
[2,2,5,2,5,1]=>[[],[[],[],[[]]]]=>2
[2,2,5,5,1,2]=>[[],[],[[],[[]]]]=>3
[2,2,5,5,2,1]=>[[],[[]],[[[]]]]=>3
[2,5,1,2,2,5]=>[[[]],[[],[],[]]]=>2
[2,5,1,2,5,2]=>[[[],[[]],[[]]]]=>1
[2,5,1,5,2,2]=>[[],[[],[[],[]]]]=>2
[2,5,2,1,2,5]=>[[[[]],[[[]]]]]=>1
[2,5,2,1,5,2]=>[[[[],[],[[]]]]]=>1
[2,5,2,2,1,5]=>[[[]],[[[],[]]]]=>2
[2,5,2,2,5,1]=>[[[]],[[],[],[]]]=>2
[2,5,2,5,1,2]=>[[[],[[]],[[]]]]=>1
[2,5,2,5,2,1]=>[[[],[[],[[]]]]]=>1
[2,5,5,1,2,2]=>[[],[],[[[],[]]]]=>3
[2,5,5,2,1,2]=>[[[]],[[[[]]]]]=>2
[2,5,5,2,2,1]=>[[],[[[]]],[[]]]=>3
[5,1,2,2,2,5]=>[[],[[]],[[],[]]]=>3
[5,1,2,2,5,2]=>[[[]],[[],[[]]]]=>2
[5,1,2,5,2,2]=>[[],[[[],[[]]]]]=>2
[5,1,5,2,2,2]=>[[],[],[[],[[]]]]=>3
[5,2,1,2,2,5]=>[[[]],[[[[]]]]]=>2
[5,2,1,2,5,2]=>[[[[[]]],[[]]]]=>1
[5,2,1,5,2,2]=>[[[]],[[],[],[]]]=>2
[5,2,2,1,2,5]=>[[[]],[[[[]]]]]=>2
[5,2,2,1,5,2]=>[[],[[[],[],[]]]]=>2
[5,2,2,2,1,5]=>[[],[],[[[],[]]]]=>3
[5,2,2,2,5,1]=>[[],[[]],[[],[]]]=>3
[5,2,2,5,1,2]=>[[[]],[[],[[]]]]=>2
[5,2,2,5,2,1]=>[[],[[[],[[]]]]]=>2
[5,2,5,1,2,2]=>[[],[[[],[[]]]]]=>2
[5,2,5,2,1,2]=>[[[[]],[[[]]]]]=>1
[5,2,5,2,2,1]=>[[[]],[[],[[]]]]=>2
[5,5,1,2,2,2]=>[[],[],[],[[[]]]]=>4
[5,5,2,1,2,2]=>[[],[[]],[[[]]]]=>3
[5,5,2,2,1,2]=>[[],[[]],[[[]]]]=>3
[5,5,2,2,2,1]=>[[],[],[[]],[[]]]=>4
[1,2,2,2,5,6]=>[[],[],[[[],[]]]]=>3
[1,2,2,2,6,5]=>[[],[[]],[[[]]]]=>3
[1,2,2,5,2,6]=>[[[]],[[[],[]]]]=>2
[1,2,2,5,6,2]=>[[],[[],[[],[]]]]=>2
[1,2,2,6,2,5]=>[[[]],[[[],[]]]]=>2
[1,2,2,6,5,2]=>[[[]],[[],[[]]]]=>2
[1,2,5,2,2,6]=>[[],[[],[[[]]]]]=>2
[1,2,5,2,6,2]=>[[[[],[[],[]]]]]=>1
[1,2,5,6,2,2]=>[[],[[],[[],[]]]]=>2
[1,2,6,2,2,5]=>[[],[[],[[[]]]]]=>2
[1,2,6,2,5,2]=>[[[[],[[],[]]]]]=>1
[1,2,6,5,2,2]=>[[[]],[[],[[]]]]=>2
[1,5,2,2,2,6]=>[[],[],[[],[],[]]]=>3
[1,5,2,2,6,2]=>[[],[[],[],[[]]]]=>2
[1,5,2,6,2,2]=>[[],[[[],[],[]]]]=>2
[1,5,6,2,2,2]=>[[],[],[[[[]]]]]=>3
[1,6,2,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,6,2,2,5,2]=>[[[]],[[],[[]]]]=>2
[1,6,2,5,2,2]=>[[],[[[],[[]]]]]=>2
[1,6,5,2,2,2]=>[[[]],[[]],[[]]]=>3
[2,1,2,2,5,6]=>[[],[[[],[[]]]]]=>2
[2,1,2,2,6,5]=>[[[]],[[[],[]]]]=>2
[2,1,2,5,2,6]=>[[[[],[[[]]]]]]=>1
[2,1,2,5,6,2]=>[[[[],[[],[]]]]]=>1
[2,1,2,6,2,5]=>[[[[],[[[]]]]]]=>1
[2,1,2,6,5,2]=>[[[],[[],[[]]]]]=>1
[2,1,5,2,2,6]=>[[],[[],[],[[]]]]=>2
[2,1,5,2,6,2]=>[[[[[],[],[]]]]]=>1
[2,1,5,6,2,2]=>[[[[[]]]],[[]]]=>2
[2,1,6,2,2,5]=>[[[]],[[],[[]]]]=>2
[2,1,6,2,5,2]=>[[[[[],[[]]]]]]=>1
[2,1,6,5,2,2]=>[[[[]]],[[],[]]]=>2
[2,2,1,2,5,6]=>[[],[[[],[[]]]]]=>2
[2,2,1,2,6,5]=>[[],[[],[[[]]]]]=>2
[2,2,1,5,2,6]=>[[],[[[],[],[]]]]=>2
[2,2,1,5,6,2]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,2,5]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,5,2]=>[[],[[],[[[]]]]]=>2
[2,2,2,1,5,6]=>[[],[],[[[[]]]]]=>3
[2,2,2,1,6,5]=>[[],[],[[],[[]]]]=>3
[2,2,2,5,1,6]=>[[],[],[[],[[]]]]=>3
[2,2,2,5,6,1]=>[[],[],[[[[]]]]]=>3
[2,2,2,6,1,5]=>[[],[],[[],[[]]]]=>3
[2,2,2,6,5,1]=>[[],[],[[[[]]]]]=>3
[2,2,5,1,2,6]=>[[],[[],[[[]]]]]=>2
[2,2,5,1,6,2]=>[[],[[],[],[[]]]]=>2
[2,2,5,2,1,6]=>[[],[[[[[]]]]]]=>2
[2,2,5,2,6,1]=>[[],[[[],[[]]]]]=>2
[2,2,5,6,1,2]=>[[],[[[],[[]]]]]=>2
[2,2,5,6,2,1]=>[[],[[[]],[[]]]]=>2
[2,2,6,1,2,5]=>[[],[[[[[]]]]]]=>2
[2,2,6,1,5,2]=>[[],[[],[],[[]]]]=>2
[2,2,6,2,1,5]=>[[],[[],[[[]]]]]=>2
[2,2,6,2,5,1]=>[[],[[[],[],[]]]]=>2
[2,2,6,5,1,2]=>[[],[[[[[]]]]]]=>2
[2,2,6,5,2,1]=>[[],[[],[[],[]]]]=>2
[2,5,1,2,2,6]=>[[[[],[]]],[[]]]=>2
[2,5,1,2,6,2]=>[[[],[],[[[]]]]]=>1
[2,5,1,6,2,2]=>[[],[[],[],[[]]]]=>2
[2,5,2,1,2,6]=>[[[[[],[[]]]]]]=>1
[2,5,2,1,6,2]=>[[[[[]]],[[]]]]=>1
[2,5,2,2,1,6]=>[[[]],[[[[]]]]]=>2
[2,5,2,2,6,1]=>[[],[[[]],[[]]]]=>2
[2,5,2,6,1,2]=>[[[[],[[[]]]]]]=>1
[2,5,2,6,2,1]=>[[[[]],[[],[]]]]=>1
[2,5,6,1,2,2]=>[[],[[[]],[[]]]]=>2
[2,5,6,2,1,2]=>[[[],[[[],[]]]]]=>1
[2,5,6,2,2,1]=>[[[]],[[],[[]]]]=>2
[2,6,1,2,2,5]=>[[[[[]]]],[[]]]=>2
[2,6,1,2,5,2]=>[[[],[[[[]]]]]]=>1
[2,6,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[2,6,2,1,2,5]=>[[[[[],[[]]]]]]=>1
[2,6,2,1,5,2]=>[[[],[[]],[[]]]]=>1
[2,6,2,2,1,5]=>[[[]],[[[],[]]]]=>2
[2,6,2,2,5,1]=>[[[]],[[],[],[]]]=>2
[2,6,2,5,1,2]=>[[[[],[],[[]]]]]=>1
[2,6,2,5,2,1]=>[[[[]],[[],[]]]]=>1
[2,6,5,1,2,2]=>[[[[]]],[[[]]]]=>2
[2,6,5,2,1,2]=>[[[],[[],[[]]]]]=>1
[2,6,5,2,2,1]=>[[[],[]],[[],[]]]=>2
[5,1,2,2,2,6]=>[[],[[[]]],[[]]]=>3
[5,1,2,2,6,2]=>[[[]],[[[],[]]]]=>2
[5,1,2,6,2,2]=>[[],[[],[[[]]]]]=>2
[5,1,6,2,2,2]=>[[],[[]],[[],[]]]=>3
[5,2,1,2,2,6]=>[[[]],[[],[[]]]]=>2
[5,2,1,2,6,2]=>[[[[]],[[[]]]]]=>1
[5,2,1,6,2,2]=>[[[[[]]]],[[]]]=>2
[5,2,2,1,2,6]=>[[],[[[],[[]]]]]=>2
[5,2,2,1,6,2]=>[[],[[[[[]]]]]]=>2
[5,2,2,2,1,6]=>[[],[],[[[[]]]]]=>3
[5,2,2,2,6,1]=>[[],[],[[],[[]]]]=>3
[5,2,2,6,1,2]=>[[],[[],[[[]]]]]=>2
[5,2,2,6,2,1]=>[[],[[],[[[]]]]]=>2
[5,2,6,1,2,2]=>[[],[[[[],[]]]]]=>2
[5,2,6,2,1,2]=>[[[],[[[[]]]]]]=>1
[5,2,6,2,2,1]=>[[[[],[]]],[[]]]=>2
[5,6,1,2,2,2]=>[[],[],[[],[[]]]]=>3
[5,6,2,1,2,2]=>[[[[]]],[[],[]]]=>2
[5,6,2,2,1,2]=>[[[]],[[[],[]]]]=>2
[5,6,2,2,2,1]=>[[],[[[]]],[[]]]=>3
[6,1,2,2,2,5]=>[[],[[[]]],[[]]]=>3
[6,1,2,2,5,2]=>[[[[]]],[[[]]]]=>2
[6,1,2,5,2,2]=>[[],[[[[[]]]]]]=>2
[6,1,5,2,2,2]=>[[],[],[[],[[]]]]=>3
[6,2,1,2,2,5]=>[[[]],[[],[[]]]]=>2
[6,2,1,2,5,2]=>[[[[]],[[[]]]]]=>1
[6,2,1,5,2,2]=>[[[]],[[],[[]]]]=>2
[6,2,2,1,2,5]=>[[],[[[],[[]]]]]=>2
[6,2,2,1,5,2]=>[[],[[[],[[]]]]]=>2
[6,2,2,2,1,5]=>[[],[[]],[[[]]]]=>3
[6,2,2,2,5,1]=>[[],[],[[],[],[]]]=>3
[6,2,2,5,1,2]=>[[],[[],[],[[]]]]=>2
[6,2,2,5,2,1]=>[[],[[],[[[]]]]]=>2
[6,2,5,1,2,2]=>[[],[[[],[],[]]]]=>2
[6,2,5,2,1,2]=>[[[],[[[[]]]]]]=>1
[6,2,5,2,2,1]=>[[[[],[]]],[[]]]=>2
[6,5,1,2,2,2]=>[[],[[[]]],[[]]]=>3
[6,5,2,1,2,2]=>[[[]],[[],[[]]]]=>2
[6,5,2,2,1,2]=>[[[]],[[],[[]]]]=>2
[6,5,2,2,2,1]=>[[],[[]],[[],[]]]=>3
[1,2,2,3,3,3]=>[[],[],[],[[],[]]]=>4
[1,2,3,2,3,3]=>[[[]],[[],[],[]]]=>2
[1,2,3,3,2,3]=>[[],[[[],[],[]]]]=>2
[1,2,3,3,3,2]=>[[],[[]],[[],[]]]=>3
[1,3,2,2,3,3]=>[[],[[]],[[[]]]]=>3
[1,3,2,3,2,3]=>[[[[],[[],[]]]]]=>1
[1,3,2,3,3,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,2,2,3]=>[[],[[[]]],[[]]]=>3
[1,3,3,2,3,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,3,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,2,3,3,3]=>[[],[[]],[[],[]]]=>3
[2,1,3,2,3,3]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,2,3]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,3,2]=>[[],[[]],[[],[]]]=>3
[2,2,1,3,3,3]=>[[],[],[[]],[[]]]=>4
[2,2,3,1,3,3]=>[[],[],[[[[]]]]]=>3
[2,2,3,3,1,3]=>[[],[[]],[[[]]]]=>3
[2,2,3,3,3,1]=>[[],[],[[]],[[]]]=>4
[2,3,1,2,3,3]=>[[],[[],[],[[]]]]=>2
[2,3,1,3,2,3]=>[[[[]],[[[]]]]]=>1
[2,3,1,3,3,2]=>[[[]],[[[[]]]]]=>2
[2,3,2,1,3,3]=>[[[]],[[],[[]]]]=>2
[2,3,2,3,1,3]=>[[[],[[[[]]]]]]=>1
[2,3,2,3,3,1]=>[[[[]]],[[],[]]]=>2
[2,3,3,1,2,3]=>[[],[[[],[],[]]]]=>2
[2,3,3,1,3,2]=>[[[]],[[[[]]]]]=>2
[2,3,3,2,1,3]=>[[[]],[[],[[]]]]=>2
[2,3,3,2,3,1]=>[[],[[[[],[]]]]]=>2
[2,3,3,3,1,2]=>[[],[],[[[],[]]]]=>3
[2,3,3,3,2,1]=>[[],[[]],[[],[]]]=>3
[3,1,2,2,3,3]=>[[],[],[[],[[]]]]=>3
[3,1,2,3,2,3]=>[[[[],[],[[]]]]]=>1
[3,1,2,3,3,2]=>[[[[]]],[[],[]]]=>2
[3,1,3,2,2,3]=>[[[[[]]]],[[]]]=>2
[3,1,3,2,3,2]=>[[[[[]],[[]]]]]=>1
[3,1,3,3,2,2]=>[[[]],[[]],[[]]]=>3
[3,2,1,2,3,3]=>[[[],[]],[[],[]]]=>2
[3,2,1,3,2,3]=>[[[],[[]],[[]]]]=>1
[3,2,1,3,3,2]=>[[[]],[[],[],[]]]=>2
[3,2,2,1,3,3]=>[[],[[]],[[],[]]]=>3
[3,2,2,3,1,3]=>[[],[[[[[]]]]]]=>2
[3,2,2,3,3,1]=>[[],[[]],[[[]]]]=>3
[3,2,3,1,2,3]=>[[[[],[],[[]]]]]=>1
[3,2,3,1,3,2]=>[[[[]],[[[]]]]]=>1
[3,2,3,2,1,3]=>[[[],[[]],[[]]]]=>1
[3,2,3,2,3,1]=>[[[],[[[],[]]]]]=>1
[3,2,3,3,1,2]=>[[],[[[],[[]]]]]=>2
[3,2,3,3,2,1]=>[[[]],[[],[],[]]]=>2
[3,3,1,2,2,3]=>[[],[[]],[[],[]]]=>3
[3,3,1,2,3,2]=>[[],[[[[],[]]]]]=>2
[3,3,1,3,2,2]=>[[],[[]],[[[]]]]=>3
[3,3,2,1,2,3]=>[[],[[],[[],[]]]]=>2
[3,3,2,1,3,2]=>[[],[[],[],[[]]]]=>2
[3,3,2,2,1,3]=>[[],[],[[],[[]]]]=>3
[3,3,2,2,3,1]=>[[],[],[[[[]]]]]=>3
[3,3,2,3,1,2]=>[[],[[[],[[]]]]]=>2
[3,3,2,3,2,1]=>[[],[[],[],[[]]]]=>2
[3,3,3,1,2,2]=>[[],[],[],[[[]]]]=>4
[3,3,3,2,1,2]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,2,1]=>[[],[],[],[[],[]]]=>4
[1,2,2,3,3,4]=>[[],[],[[],[],[]]]=>3
[1,2,2,3,4,3]=>[[],[[],[],[[]]]]=>2
[1,2,2,4,3,3]=>[[],[[]],[[[]]]]=>3
[1,2,3,2,3,4]=>[[[],[],[],[[]]]]=>1
[1,2,3,2,4,3]=>[[[],[[],[[]]]]]=>1
[1,2,3,3,2,4]=>[[[[]]],[[],[]]]=>2
[1,2,3,3,4,2]=>[[],[[],[],[[]]]]=>2
[1,2,3,4,2,3]=>[[[],[],[],[[]]]]=>1
[1,2,3,4,3,2]=>[[[],[],[[],[]]]]=>1
[1,2,4,2,3,3]=>[[],[[],[[[]]]]]=>2
[1,2,4,3,2,3]=>[[[],[[],[[]]]]]=>1
[1,2,4,3,3,2]=>[[],[[],[[[]]]]]=>2
[1,3,2,2,3,4]=>[[],[[],[[[]]]]]=>2
[1,3,2,2,4,3]=>[[],[[],[[],[]]]]=>2
[1,3,2,3,2,4]=>[[[],[[],[[]]]]]=>1
[1,3,2,3,4,2]=>[[[[[[],[]]]]]]=>1
[1,3,2,4,2,3]=>[[[],[[[[]]]]]]=>1
[1,3,2,4,3,2]=>[[[],[[],[],[]]]]=>1
[1,3,3,2,2,4]=>[[],[],[[],[[]]]]=>3
[1,3,3,2,4,2]=>[[],[[[[],[]]]]]=>2
[1,3,3,4,2,2]=>[[],[[]],[[[]]]]=>3
[1,3,4,2,2,3]=>[[[]],[[],[[]]]]=>2
[1,3,4,2,3,2]=>[[[[],[[[]]]]]]=>1
[1,3,4,3,2,2]=>[[],[[],[[[]]]]]=>2
[1,4,2,2,3,3]=>[[],[],[[[[]]]]]=>3
[1,4,2,3,2,3]=>[[[[[]],[[]]]]]=>1
[1,4,2,3,3,2]=>[[[]],[[[[]]]]]=>2
[1,4,3,2,2,3]=>[[],[[[],[[]]]]]=>2
[1,4,3,2,3,2]=>[[[[],[],[[]]]]]=>1
[1,4,3,3,2,2]=>[[],[[]],[[],[]]]=>3
[2,1,2,3,3,4]=>[[],[[],[],[[]]]]=>2
[2,1,2,3,4,3]=>[[[],[[],[],[]]]]=>1
[2,1,2,4,3,3]=>[[],[[],[[[]]]]]=>2
[2,1,3,2,3,4]=>[[[[]],[[],[]]]]=>1
[2,1,3,2,4,3]=>[[[],[],[[],[]]]]=>1
[2,1,3,3,2,4]=>[[],[[],[[],[]]]]=>2
[2,1,3,3,4,2]=>[[[[[]]]],[[]]]=>2
[2,1,3,4,2,3]=>[[[[[]],[[]]]]]=>1
[2,1,3,4,3,2]=>[[[],[],[[[]]]]]=>1
[2,1,4,2,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,4,3,2,3]=>[[[],[[]],[[]]]]=>1
[2,1,4,3,3,2]=>[[],[[],[],[[]]]]=>2
[2,2,1,3,3,4]=>[[],[[[]]],[[]]]=>3
[2,2,1,3,4,3]=>[[],[[],[[[]]]]]=>2
[2,2,1,4,3,3]=>[[],[],[[],[[]]]]=>3
[2,2,3,1,3,4]=>[[],[[],[[[]]]]]=>2
[2,2,3,1,4,3]=>[[],[[[[[]]]]]]=>2
[2,2,3,3,1,4]=>[[],[[]],[[[]]]]=>3
[2,2,3,3,4,1]=>[[],[],[[],[[]]]]=>3
[2,2,3,4,1,3]=>[[],[[],[[[]]]]]=>2
[2,2,3,4,3,1]=>[[],[[],[[[]]]]]=>2
[2,2,4,1,3,3]=>[[],[],[[],[[]]]]=>3
[2,2,4,3,1,3]=>[[],[[[]],[[]]]]=>2
[2,2,4,3,3,1]=>[[],[],[[[[]]]]]=>3
[2,3,1,2,3,4]=>[[[],[],[],[[]]]]=>1
[2,3,1,2,4,3]=>[[[],[[[[]]]]]]=>1
[2,3,1,3,2,4]=>[[[[[],[[]]]]]]=>1
[2,3,1,3,4,2]=>[[[[]],[[],[]]]]=>1
[2,3,1,4,2,3]=>[[[],[[],[[]]]]]=>1
[2,3,1,4,3,2]=>[[[[[],[[]]]]]]=>1
[2,3,2,1,3,4]=>[[[[]],[[],[]]]]=>1
[2,3,2,1,4,3]=>[[[[],[],[[]]]]]=>1
[2,3,2,3,1,4]=>[[[],[[[[]]]]]]=>1
[2,3,2,3,4,1]=>[[[],[],[[[]]]]]=>1
[2,3,2,4,1,3]=>[[[[[],[[]]]]]]=>1
[2,3,2,4,3,1]=>[[[[[]],[[]]]]]=>1
[2,3,3,1,2,4]=>[[],[[[],[[]]]]]=>2
[2,3,3,1,4,2]=>[[[]],[[],[[]]]]=>2
[2,3,3,2,1,4]=>[[[]],[[],[[]]]]=>2
[2,3,3,2,4,1]=>[[[]],[[[[]]]]]=>2
[2,3,3,4,1,2]=>[[],[[],[],[[]]]]=>2
[2,3,3,4,2,1]=>[[],[[],[[[]]]]]=>2
[2,3,4,1,2,3]=>[[[],[],[],[[]]]]=>1
[2,3,4,1,3,2]=>[[[],[[[[]]]]]]=>1
[2,3,4,2,1,3]=>[[[],[[[[]]]]]]=>1
[2,3,4,2,3,1]=>[[[],[],[[],[]]]]=>1
[2,3,4,3,1,2]=>[[[],[[]],[[]]]]=>1
[2,3,4,3,2,1]=>[[[],[[],[],[]]]]=>1
[2,4,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[2,4,1,3,2,3]=>[[[[]],[[[]]]]]=>1
[2,4,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[2,4,2,1,3,3]=>[[[]],[[],[[]]]]=>2
[2,4,2,3,1,3]=>[[[],[[],[[]]]]]=>1
[2,4,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[2,4,3,1,2,3]=>[[[[[],[[]]]]]]=>1
[2,4,3,1,3,2]=>[[[],[[],[[]]]]]=>1
[2,4,3,2,1,3]=>[[[],[[],[],[]]]]=>1
[2,4,3,2,3,1]=>[[[[],[[[]]]]]]=>1
[2,4,3,3,1,2]=>[[],[[[[[]]]]]]=>2
[2,4,3,3,2,1]=>[[],[[],[],[[]]]]=>2
[3,1,2,2,3,4]=>[[],[[],[],[[]]]]=>2
[3,1,2,2,4,3]=>[[[]],[[[[]]]]]=>2
[3,1,2,3,2,4]=>[[[[[[],[]]]]]]=>1
[3,1,2,3,4,2]=>[[[],[[],[],[]]]]=>1
[3,1,2,4,2,3]=>[[[[]],[[],[]]]]=>1
[3,1,2,4,3,2]=>[[[[],[[[]]]]]]=>1
[3,1,3,2,2,4]=>[[[]],[[],[[]]]]=>2
[3,1,3,2,4,2]=>[[[[]],[[],[]]]]=>1
[3,1,3,4,2,2]=>[[],[[],[[[]]]]]=>2
[3,1,4,2,2,3]=>[[[]],[[],[[]]]]=>2
[3,1,4,2,3,2]=>[[[[]],[[[]]]]]=>1
[3,1,4,3,2,2]=>[[[]],[[],[[]]]]=>2
[3,2,1,2,3,4]=>[[[],[[],[],[]]]]=>1
[3,2,1,2,4,3]=>[[[],[],[[[]]]]]=>1
[3,2,1,3,2,4]=>[[[],[],[[],[]]]]=>1
[3,2,1,3,4,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,2,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,3,2]=>[[[],[],[],[[]]]]=>1
[3,2,2,1,3,4]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,4,3]=>[[],[[],[],[[]]]]=>2
[3,2,2,3,1,4]=>[[],[[[[[]]]]]]=>2
[3,2,2,3,4,1]=>[[],[[],[[[]]]]]=>2
[3,2,2,4,1,3]=>[[],[[[]],[[]]]]=>2
[3,2,2,4,3,1]=>[[],[[[],[[]]]]]=>2
[3,2,3,1,2,4]=>[[[[[],[[]]]]]]=>1
[3,2,3,1,4,2]=>[[[[[]],[[]]]]]=>1
[3,2,3,2,1,4]=>[[[],[[]],[[]]]]=>1
[3,2,3,2,4,1]=>[[[[]],[[[]]]]]=>1
[3,2,3,4,1,2]=>[[[[],[],[[]]]]]=>1
[3,2,3,4,2,1]=>[[[],[[[],[]]]]]=>1
[3,2,4,1,2,3]=>[[[[],[[[]]]]]]=>1
[3,2,4,1,3,2]=>[[[],[[],[[]]]]]=>1
[3,2,4,2,1,3]=>[[[],[[],[[]]]]]=>1
[3,2,4,2,3,1]=>[[[[[]],[[]]]]]=>1
[3,2,4,3,1,2]=>[[[[[]]],[[]]]]=>1
[3,2,4,3,2,1]=>[[[],[],[],[[]]]]=>1
[3,3,1,2,2,4]=>[[],[[[]]],[[]]]=>3
[3,3,1,2,4,2]=>[[],[[],[[[]]]]]=>2
[3,3,1,4,2,2]=>[[],[],[[],[[]]]]=>3
[3,3,2,1,2,4]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,4,2]=>[[],[[],[[[]]]]]=>2
[3,3,2,2,1,4]=>[[],[],[[],[[]]]]=>3
[3,3,2,2,4,1]=>[[],[],[[[[]]]]]=>3
[3,3,2,4,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,2,4,2,1]=>[[],[[],[[[]]]]]=>2
[3,3,4,1,2,2]=>[[],[],[[],[[]]]]=>3
[3,3,4,2,1,2]=>[[],[[[]],[[]]]]=>2
[3,3,4,2,2,1]=>[[],[],[[[[]]]]]=>3
[3,4,1,2,2,3]=>[[],[[],[],[[]]]]=>2
[3,4,1,2,3,2]=>[[[],[[]],[[]]]]=>1
[3,4,1,3,2,2]=>[[],[[[[[]]]]]]=>2
[3,4,2,1,2,3]=>[[[],[[]],[[]]]]=>1
[3,4,2,1,3,2]=>[[[[[],[[]]]]]]=>1
[3,4,2,2,1,3]=>[[],[[[[[]]]]]]=>2
[3,4,2,2,3,1]=>[[],[[],[[],[]]]]=>2
[3,4,2,3,1,2]=>[[[],[],[[],[]]]]=>1
[3,4,2,3,2,1]=>[[[],[[],[[]]]]]=>1
[3,4,3,1,2,2]=>[[[]],[[],[[]]]]=>2
[3,4,3,2,1,2]=>[[[],[[],[],[]]]]=>1
[3,4,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[4,1,2,2,3,3]=>[[],[[]],[[],[]]]=>3
[4,1,2,3,2,3]=>[[[[[],[],[]]]]]=>1
[4,1,2,3,3,2]=>[[[]],[[],[[]]]]=>2
[4,1,3,2,2,3]=>[[],[[[[[]]]]]]=>2
[4,1,3,2,3,2]=>[[[[[],[[]]]]]]=>1
[4,1,3,3,2,2]=>[[],[[]],[[[]]]]=>3
[4,2,1,2,3,3]=>[[[]],[[],[[]]]]=>2
[4,2,1,3,2,3]=>[[[[[],[[]]]]]]=>1
[4,2,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,3,3]=>[[],[[[]]],[[]]]=>3
[4,2,2,3,1,3]=>[[],[[[],[[]]]]]=>2
[4,2,2,3,3,1]=>[[],[[]],[[],[]]]=>3
[4,2,3,1,2,3]=>[[[],[[],[],[]]]]=>1
[4,2,3,1,3,2]=>[[[[]],[[[]]]]]=>1
[4,2,3,2,1,3]=>[[[[[],[[]]]]]]=>1
[4,2,3,2,3,1]=>[[[[]],[[],[]]]]=>1
[4,2,3,3,1,2]=>[[],[[],[[],[]]]]=>2
[4,2,3,3,2,1]=>[[[]],[[],[[]]]]=>2
[4,3,1,2,2,3]=>[[[]],[[],[[]]]]=>2
[4,3,1,2,3,2]=>[[[[]],[[],[]]]]=>1
[4,3,1,3,2,2]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,2,3]=>[[[],[],[[],[]]]]=>1
[4,3,2,1,3,2]=>[[[],[],[],[[]]]]=>1
[4,3,2,2,1,3]=>[[],[[],[],[[]]]]=>2
[4,3,2,2,3,1]=>[[],[[[[],[]]]]]=>2
[4,3,2,3,1,2]=>[[[],[[],[[]]]]]=>1
[4,3,2,3,2,1]=>[[[],[],[],[[]]]]=>1
[4,3,3,1,2,2]=>[[],[[[]]],[[]]]=>3
[4,3,3,2,1,2]=>[[],[[],[],[[]]]]=>2
[4,3,3,2,2,1]=>[[],[],[[],[],[]]]=>3
[1,2,2,3,3,5]=>[[],[[]],[[],[]]]=>3
[1,2,2,3,5,3]=>[[],[[],[[[]]]]]=>2
[1,2,2,5,3,3]=>[[],[[]],[[[]]]]=>3
[1,2,3,2,3,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,2,5,3]=>[[[],[[[[]]]]]]=>1
[1,2,3,3,2,5]=>[[[[]]],[[],[]]]=>2
[1,2,3,3,5,2]=>[[[[]]],[[],[]]]=>2
[1,2,3,5,2,3]=>[[[],[],[[[]]]]]=>1
[1,2,3,5,3,2]=>[[[],[[[[]]]]]]=>1
[1,2,5,2,3,3]=>[[],[[],[[[]]]]]=>2
[1,2,5,3,2,3]=>[[[[[]]],[[]]]]=>1
[1,2,5,3,3,2]=>[[],[[[[[]]]]]]=>2
[1,3,2,2,3,5]=>[[],[[[],[[]]]]]=>2
[1,3,2,2,5,3]=>[[],[[[[[]]]]]]=>2
[1,3,2,3,2,5]=>[[[[[]],[[]]]]]=>1
[1,3,2,3,5,2]=>[[[[]],[[[]]]]]=>1
[1,3,2,5,2,3]=>[[[[[[[]]]]]]]=>1
[1,3,2,5,3,2]=>[[[[[[],[]]]]]]=>1
[1,3,3,2,2,5]=>[[],[[]],[[[]]]]=>3
[1,3,3,2,5,2]=>[[[]],[[[[]]]]]=>2
[1,3,3,5,2,2]=>[[],[],[[[],[]]]]=>3
[1,3,5,2,2,3]=>[[[]],[[[],[]]]]=>2
[1,3,5,2,3,2]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,2,2]=>[[[[],[]]],[[]]]=>2
[1,5,2,2,3,3]=>[[],[[]],[[],[]]]=>3
[1,5,2,3,2,3]=>[[[],[[[],[]]]]]=>1
[1,5,2,3,3,2]=>[[[[],[]]],[[]]]=>2
[1,5,3,2,2,3]=>[[[[[]]]],[[]]]=>2
[1,5,3,2,3,2]=>[[[[[],[[]]]]]]=>1
[1,5,3,3,2,2]=>[[],[[]],[[[]]]]=>3
[2,1,2,3,3,5]=>[[[[]]],[[],[]]]=>2
[2,1,2,3,5,3]=>[[[[[[],[]]]]]]=>1
[2,1,2,5,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,3,2,3,5]=>[[[],[[],[[]]]]]=>1
[2,1,3,2,5,3]=>[[[[]],[[[]]]]]=>1
[2,1,3,3,2,5]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,5,2]=>[[],[[],[[[]]]]]=>2
[2,1,3,5,2,3]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,3,2]=>[[[],[[[],[]]]]]=>1
[2,1,5,2,3,3]=>[[[[],[]]],[[]]]=>2
[2,1,5,3,2,3]=>[[[[[]]],[[]]]]=>1
[2,1,5,3,3,2]=>[[[]],[[],[[]]]]=>2
[2,2,1,3,3,5]=>[[],[],[[],[[]]]]=>3
[2,2,1,3,5,3]=>[[],[[[[],[]]]]]=>2
[2,2,1,5,3,3]=>[[],[[[]]],[[]]]=>3
[2,2,3,1,3,5]=>[[],[[[[],[]]]]]=>2
[2,2,3,1,5,3]=>[[],[[[],[[]]]]]=>2
[2,2,3,3,1,5]=>[[],[[]],[[[]]]]=>3
[2,2,3,3,5,1]=>[[],[[]],[[[]]]]=>3
[2,2,3,5,1,3]=>[[],[[[],[[]]]]]=>2
[2,2,3,5,3,1]=>[[],[[[[],[]]]]]=>2
[2,2,5,1,3,3]=>[[],[],[[[],[]]]]=>3
[2,2,5,3,1,3]=>[[],[[[],[[]]]]]=>2
[2,2,5,3,3,1]=>[[],[],[[],[[]]]]=>3
[2,3,1,2,3,5]=>[[[],[[]],[[]]]]=>1
[2,3,1,2,5,3]=>[[[],[[[],[]]]]]=>1
[2,3,1,3,2,5]=>[[[[[[[]]]]]]]=>1
[2,3,1,3,5,2]=>[[[[[],[[]]]]]]=>1
[2,3,1,5,2,3]=>[[[],[[],[[]]]]]=>1
[2,3,1,5,3,2]=>[[[[],[[[]]]]]]=>1
[2,3,2,1,3,5]=>[[[[],[[],[]]]]]=>1
[2,3,2,1,5,3]=>[[[[],[[[]]]]]]=>1
[2,3,2,3,1,5]=>[[[],[[[[]]]]]]=>1
[2,3,2,3,5,1]=>[[[],[[[[]]]]]]=>1
[2,3,2,5,1,3]=>[[[[[[],[]]]]]]=>1
[2,3,2,5,3,1]=>[[[[[],[[]]]]]]=>1
[2,3,3,1,2,5]=>[[],[[[],[[]]]]]=>2
[2,3,3,1,5,2]=>[[[]],[[[],[]]]]=>2
[2,3,3,2,1,5]=>[[[]],[[],[[]]]]=>2
[2,3,3,2,5,1]=>[[[]],[[[],[]]]]=>2
[2,3,3,5,1,2]=>[[],[[[[],[]]]]]=>2
[2,3,3,5,2,1]=>[[[]],[[[[]]]]]=>2
[2,3,5,1,2,3]=>[[[],[],[[[]]]]]=>1
[2,3,5,1,3,2]=>[[[[[]],[[]]]]]=>1
[2,3,5,2,1,3]=>[[[[],[[[]]]]]]=>1
[2,3,5,2,3,1]=>[[[[[]]],[[]]]]=>1
[2,3,5,3,1,2]=>[[[],[[],[[]]]]]=>1
[2,3,5,3,2,1]=>[[[[[[],[]]]]]]=>1
[2,5,1,2,3,3]=>[[],[[],[[],[]]]]=>2
[2,5,1,3,2,3]=>[[[],[[[[]]]]]]=>1
[2,5,1,3,3,2]=>[[[[],[]]],[[]]]=>2
[2,5,2,1,3,3]=>[[[]],[[[[]]]]]=>2
[2,5,2,3,1,3]=>[[[[[[[]]]]]]]=>1
[2,5,2,3,3,1]=>[[[[[]]]],[[]]]=>2
[2,5,3,1,2,3]=>[[[[],[[],[]]]]]=>1
[2,5,3,1,3,2]=>[[[[],[[[]]]]]]=>1
[2,5,3,2,1,3]=>[[[[],[[[]]]]]]=>1
[2,5,3,2,3,1]=>[[[[[],[[]]]]]]=>1
[2,5,3,3,1,2]=>[[],[[[]],[[]]]]=>2
[2,5,3,3,2,1]=>[[[]],[[],[[]]]]=>2
[3,1,2,2,3,5]=>[[[]],[[],[[]]]]=>2
[3,1,2,2,5,3]=>[[[]],[[[],[]]]]=>2
[3,1,2,3,2,5]=>[[[[[[],[]]]]]]=>1
[3,1,2,3,5,2]=>[[[[],[[[]]]]]]=>1
[3,1,2,5,2,3]=>[[[[[[],[]]]]]]=>1
[3,1,2,5,3,2]=>[[[[[]]],[[]]]]=>1
[3,1,3,2,2,5]=>[[[[[]]]],[[]]]=>2
[3,1,3,2,5,2]=>[[[[[[[]]]]]]]=>1
[3,1,3,5,2,2]=>[[],[[[],[[]]]]]=>2
[3,1,5,2,2,3]=>[[[]],[[],[[]]]]=>2
[3,1,5,2,3,2]=>[[[[[[],[]]]]]]=>1
[3,1,5,3,2,2]=>[[[[]]],[[],[]]]=>2
[3,2,1,2,3,5]=>[[[],[[[],[]]]]]=>1
[3,2,1,2,5,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,3,2,5]=>[[[],[[]],[[]]]]=>1
[3,2,1,3,5,2]=>[[[],[[[],[]]]]]=>1
[3,2,1,5,2,3]=>[[[],[[[],[]]]]]=>1
[3,2,1,5,3,2]=>[[[],[[]],[[]]]]=>1
[3,2,2,1,3,5]=>[[],[[],[[],[]]]]=>2
[3,2,2,1,5,3]=>[[],[[],[[[]]]]]=>2
[3,2,2,3,1,5]=>[[],[[[[[]]]]]]=>2
[3,2,2,3,5,1]=>[[],[[[[[]]]]]]=>2
[3,2,2,5,1,3]=>[[],[[],[[[]]]]]=>2
[3,2,2,5,3,1]=>[[],[[[],[[]]]]]=>2
[3,2,3,1,2,5]=>[[[[[],[[]]]]]]=>1
[3,2,3,1,5,2]=>[[[[],[[[]]]]]]=>1
[3,2,3,2,1,5]=>[[[],[[]],[[]]]]=>1
[3,2,3,2,5,1]=>[[[[]],[[],[]]]]=>1
[3,2,3,5,1,2]=>[[[[],[[[]]]]]]=>1
[3,2,3,5,2,1]=>[[[],[[[[]]]]]]=>1
[3,2,5,1,2,3]=>[[[[],[[],[]]]]]=>1
[3,2,5,1,3,2]=>[[[],[[[],[]]]]]=>1
[3,2,5,2,1,3]=>[[[[]],[[[]]]]]=>1
[3,2,5,2,3,1]=>[[[[[[[]]]]]]]=>1
[3,2,5,3,1,2]=>[[[[[],[[]]]]]]=>1
[3,2,5,3,2,1]=>[[[],[[]],[[]]]]=>1
[3,3,1,2,2,5]=>[[],[[[]]],[[]]]=>3
[3,3,1,2,5,2]=>[[],[[[[[]]]]]]=>2
[3,3,1,5,2,2]=>[[],[],[[],[[]]]]=>3
[3,3,2,1,2,5]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,5,2]=>[[],[[],[[],[]]]]=>2
[3,3,2,2,1,5]=>[[],[],[[],[[]]]]=>3
[3,3,2,2,5,1]=>[[],[],[[],[[]]]]=>3
[3,3,2,5,1,2]=>[[],[[[[],[]]]]]=>2
[3,3,2,5,2,1]=>[[],[[],[[[]]]]]=>2
[3,3,5,1,2,2]=>[[],[],[[[[]]]]]=>3
[3,3,5,2,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,5,2,2,1]=>[[],[[[]]],[[]]]=>3
[3,5,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[3,5,1,2,3,2]=>[[[[[],[[]]]]]]=>1
[3,5,1,3,2,2]=>[[],[[[],[[]]]]]=>2
[3,5,2,1,2,3]=>[[[[[],[[]]]]]]=>1
[3,5,2,1,3,2]=>[[[[]],[[],[]]]]=>1
[3,5,2,2,1,3]=>[[[]],[[[],[]]]]=>2
[3,5,2,2,3,1]=>[[[[]]],[[[]]]]=>2
[3,5,2,3,1,2]=>[[[[[[],[]]]]]]=>1
[3,5,2,3,2,1]=>[[[[[],[[]]]]]]=>1
[3,5,3,1,2,2]=>[[],[[[],[[]]]]]=>2
[3,5,3,2,1,2]=>[[[[[[],[]]]]]]=>1
[3,5,3,2,2,1]=>[[],[[],[[[]]]]]=>2
[5,1,2,2,3,3]=>[[],[],[[],[[]]]]=>3
[5,1,2,3,2,3]=>[[[[],[],[[]]]]]=>1
[5,1,2,3,3,2]=>[[[]],[[],[[]]]]=>2
[5,1,3,2,2,3]=>[[],[[[[[]]]]]]=>2
[5,1,3,2,3,2]=>[[[[[],[[]]]]]]=>1
[5,1,3,3,2,2]=>[[],[[[]]],[[]]]=>3
[5,2,1,2,3,3]=>[[[]],[[],[[]]]]=>2
[5,2,1,3,2,3]=>[[[[[],[[]]]]]]=>1
[5,2,1,3,3,2]=>[[[[]]],[[],[]]]=>2
[5,2,2,1,3,3]=>[[],[[]],[[[]]]]=>3
[5,2,2,3,1,3]=>[[[[[]]]],[[]]]=>2
[5,2,2,3,3,1]=>[[],[[[]]],[[]]]=>3
[5,2,3,1,2,3]=>[[[[],[],[[]]]]]=>1
[5,2,3,1,3,2]=>[[[[[[[]]]]]]]=>1
[5,2,3,2,1,3]=>[[[[[]],[[]]]]]=>1
[5,2,3,2,3,1]=>[[[[],[[[]]]]]]=>1
[5,2,3,3,1,2]=>[[[]],[[[],[]]]]=>2
[5,2,3,3,2,1]=>[[[]],[[],[[]]]]=>2
[5,3,1,2,2,3]=>[[[],[]],[[],[]]]=>2
[5,3,1,2,3,2]=>[[[],[[[],[]]]]]=>1
[5,3,1,3,2,2]=>[[[[]]],[[],[]]]=>2
[5,3,2,1,2,3]=>[[[[],[[],[]]]]]=>1
[5,3,2,1,3,2]=>[[[[],[],[[]]]]]=>1
[5,3,2,2,1,3]=>[[],[[],[[[]]]]]=>2
[5,3,2,2,3,1]=>[[],[[[],[[]]]]]=>2
[5,3,2,3,1,2]=>[[[],[[],[[]]]]]=>1
[5,3,2,3,2,1]=>[[[[],[],[[]]]]]=>1
[5,3,3,1,2,2]=>[[],[],[[[],[]]]]=>3
[5,3,3,2,1,2]=>[[],[[],[[[]]]]]=>2
[5,3,3,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,3,3,6]=>[[],[[]],[[],[]]]=>3
[1,2,2,3,6,3]=>[[],[[],[[[]]]]]=>2
[1,2,2,6,3,3]=>[[],[[]],[[],[]]]=>3
[1,2,3,2,3,6]=>[[[],[],[[[]]]]]=>1
[1,2,3,2,6,3]=>[[[],[[[],[]]]]]=>1
[1,2,3,3,2,6]=>[[[[]]],[[],[]]]=>2
[1,2,3,3,6,2]=>[[[],[]],[[],[]]]=>2
[1,2,3,6,2,3]=>[[[],[],[[],[]]]]=>1
[1,2,3,6,3,2]=>[[[],[[[[]]]]]]=>1
[1,2,6,2,3,3]=>[[],[[],[[[]]]]]=>2
[1,2,6,3,2,3]=>[[[],[[[],[]]]]]=>1
[1,2,6,3,3,2]=>[[[]],[[],[[]]]]=>2
[1,3,2,2,3,6]=>[[],[[[[[]]]]]]=>2
[1,3,2,2,6,3]=>[[],[[],[[[]]]]]=>2
[1,3,2,3,2,6]=>[[[[[]],[[]]]]]=>1
[1,3,2,3,6,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,6,2,3]=>[[[[[[[]]]]]]]=>1
[1,3,2,6,3,2]=>[[[[],[[],[]]]]]=>1
[1,3,3,2,2,6]=>[[],[[]],[[[]]]]=>3
[1,3,3,2,6,2]=>[[[]],[[[[]]]]]=>2
[1,3,3,6,2,2]=>[[],[[]],[[],[]]]=>3
[1,3,6,2,2,3]=>[[[]],[[],[[]]]]=>2
[1,3,6,2,3,2]=>[[[[],[[[]]]]]]=>1
[1,3,6,3,2,2]=>[[],[[[[[]]]]]]=>2
[1,6,2,2,3,3]=>[[],[[[]]],[[]]]=>3
[1,6,2,3,2,3]=>[[[[[]],[[]]]]]=>1
[1,6,2,3,3,2]=>[[[[]]],[[[]]]]=>2
[1,6,3,2,2,3]=>[[[[[]]]],[[]]]=>2
[1,6,3,2,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,3,3,2,2]=>[[],[[]],[[[]]]]=>3
[2,1,2,3,3,6]=>[[[[]]],[[],[]]]=>2
[2,1,2,3,6,3]=>[[[[[[],[]]]]]]=>1
[2,1,2,6,3,3]=>[[[]],[[],[[]]]]=>2
[2,1,3,2,3,6]=>[[[[]],[[[]]]]]=>1
[2,1,3,2,6,3]=>[[[[]],[[],[]]]]=>1
[2,1,3,3,2,6]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,6,2]=>[[[]],[[],[[]]]]=>2
[2,1,3,6,2,3]=>[[[[[],[[]]]]]]=>1
[2,1,3,6,3,2]=>[[[],[[[[]]]]]]=>1
[2,1,6,2,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,6,3,2,3]=>[[[[[]]],[[]]]]=>1
[2,1,6,3,3,2]=>[[[]],[[],[[]]]]=>2
[2,2,1,3,3,6]=>[[],[[]],[[[]]]]=>3
[2,2,1,3,6,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,3,3]=>[[],[[[]]],[[]]]=>3
[2,2,3,1,3,6]=>[[],[[[[[]]]]]]=>2
[2,2,3,1,6,3]=>[[],[[[],[[]]]]]=>2
[2,2,3,3,1,6]=>[[],[[]],[[],[]]]=>3
[2,2,3,3,6,1]=>[[],[[]],[[[]]]]=>3
[2,2,3,6,1,3]=>[[],[[[[],[]]]]]=>2
[2,2,3,6,3,1]=>[[],[[[[[]]]]]]=>2
[2,2,6,1,3,3]=>[[],[],[[],[[]]]]=>3
[2,2,6,3,1,3]=>[[],[[],[[[]]]]]=>2
[2,2,6,3,3,1]=>[[],[[]],[[],[]]]=>3
[2,3,1,2,3,6]=>[[[],[[]],[[]]]]=>1
[2,3,1,2,6,3]=>[[[],[[],[[]]]]]=>1
[2,3,1,3,2,6]=>[[[[[[[]]]]]]]=>1
[2,3,1,3,6,2]=>[[[[[],[[]]]]]]=>1
[2,3,1,6,2,3]=>[[[],[[[],[]]]]]=>1
[2,3,1,6,3,2]=>[[[[],[[[]]]]]]=>1
[2,3,2,1,3,6]=>[[[[],[[[]]]]]]=>1
[2,3,2,1,6,3]=>[[[[],[[[]]]]]]=>1
[2,3,2,3,1,6]=>[[[],[[],[[]]]]]=>1
[2,3,2,3,6,1]=>[[[],[[[[]]]]]]=>1
[2,3,2,6,1,3]=>[[[[[],[[]]]]]]=>1
[2,3,2,6,3,1]=>[[[[[[],[]]]]]]=>1
[2,3,3,1,2,6]=>[[],[[[],[[]]]]]=>2
[2,3,3,1,6,2]=>[[[]],[[],[[]]]]=>2
[2,3,3,2,1,6]=>[[[]],[[],[[]]]]=>2
[2,3,3,2,6,1]=>[[[]],[[[[]]]]]=>2
[2,3,3,6,1,2]=>[[],[[[[],[]]]]]=>2
[2,3,3,6,2,1]=>[[[]],[[],[[]]]]=>2
[2,3,6,1,2,3]=>[[[],[],[[[]]]]]=>1
[2,3,6,1,3,2]=>[[[[[],[[]]]]]]=>1
[2,3,6,2,1,3]=>[[[[],[[[]]]]]]=>1
[2,3,6,2,3,1]=>[[[[]],[[],[]]]]=>1
[2,3,6,3,1,2]=>[[[],[[[[]]]]]]=>1
[2,3,6,3,2,1]=>[[[[[],[[]]]]]]=>1
[2,6,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[2,6,1,3,2,3]=>[[[[],[[[]]]]]]=>1
[2,6,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[2,6,2,1,3,3]=>[[[]],[[[[]]]]]=>2
[2,6,2,3,1,3]=>[[[[[[[]]]]]]]=>1
[2,6,2,3,3,1]=>[[[[[]]]],[[]]]=>2
[2,6,3,1,2,3]=>[[[],[[],[[]]]]]=>1
[2,6,3,1,3,2]=>[[[],[[[[]]]]]]=>1
[2,6,3,2,1,3]=>[[[],[[],[[]]]]]=>1
[2,6,3,2,3,1]=>[[[],[[[[]]]]]]=>1
[2,6,3,3,1,2]=>[[[[]]],[[],[]]]=>2
[2,6,3,3,2,1]=>[[],[[],[[],[]]]]=>2
[3,1,2,2,3,6]=>[[[]],[[],[[]]]]=>2
[3,1,2,2,6,3]=>[[[]],[[],[[]]]]=>2
[3,1,2,3,2,6]=>[[[[[[],[]]]]]]=>1
[3,1,2,3,6,2]=>[[[[],[[],[]]]]]=>1
[3,1,2,6,2,3]=>[[[[[[],[]]]]]]=>1
[3,1,2,6,3,2]=>[[[[[],[[]]]]]]=>1
[3,1,3,2,2,6]=>[[[[[]]]],[[]]]=>2
[3,1,3,2,6,2]=>[[[[[[[]]]]]]]=>1
[3,1,3,6,2,2]=>[[],[[[]],[[]]]]=>2
[3,1,6,2,2,3]=>[[[]],[[[],[]]]]=>2
[3,1,6,2,3,2]=>[[[],[[[[]]]]]]=>1
[3,1,6,3,2,2]=>[[[[]]],[[],[]]]=>2
[3,2,1,2,3,6]=>[[[],[[[],[]]]]]=>1
[3,2,1,2,6,3]=>[[[],[[],[[]]]]]=>1
[3,2,1,3,2,6]=>[[[],[[]],[[]]]]=>1
[3,2,1,3,6,2]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,2,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,3,2]=>[[[],[[]],[[]]]]=>1
[3,2,2,1,3,6]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,6,3]=>[[],[[],[[[]]]]]=>2
[3,2,2,3,1,6]=>[[],[[[],[[]]]]]=>2
[3,2,2,3,6,1]=>[[],[[[[[]]]]]]=>2
[3,2,2,6,1,3]=>[[],[[[],[[]]]]]=>2
[3,2,2,6,3,1]=>[[],[[],[[[]]]]]=>2
[3,2,3,1,2,6]=>[[[[[],[[]]]]]]=>1
[3,2,3,1,6,2]=>[[[[[],[[]]]]]]=>1
[3,2,3,2,1,6]=>[[[],[[]],[[]]]]=>1
[3,2,3,2,6,1]=>[[[[]],[[[]]]]]=>1
[3,2,3,6,1,2]=>[[[[],[[[]]]]]]=>1
[3,2,3,6,2,1]=>[[[],[[],[[]]]]]=>1
[3,2,6,1,2,3]=>[[[[],[[[]]]]]]=>1
[3,2,6,1,3,2]=>[[[],[[],[[]]]]]=>1
[3,2,6,2,1,3]=>[[[[]],[[[]]]]]=>1
[3,2,6,2,3,1]=>[[[[[[[]]]]]]]=>1
[3,2,6,3,1,2]=>[[[[[[],[]]]]]]=>1
[3,2,6,3,2,1]=>[[[],[],[[],[]]]]=>1
[3,3,1,2,2,6]=>[[],[[[]]],[[]]]=>3
[3,3,1,2,6,2]=>[[],[[[[[]]]]]]=>2
[3,3,1,6,2,2]=>[[],[],[[[],[]]]]=>3
[3,3,2,1,2,6]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,6,2]=>[[],[[],[[[]]]]]=>2
[3,3,2,2,1,6]=>[[],[],[[],[[]]]]=>3
[3,3,2,2,6,1]=>[[],[],[[[[]]]]]=>3
[3,3,2,6,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,2,6,2,1]=>[[],[[],[[[]]]]]=>2
[3,3,6,1,2,2]=>[[],[],[[[[]]]]]=>3
[3,3,6,2,1,2]=>[[],[[],[[[]]]]]=>2
[3,3,6,2,2,1]=>[[],[[]],[[],[]]]=>3
[3,6,1,2,2,3]=>[[],[[],[[[]]]]]=>2
[3,6,1,2,3,2]=>[[[[[],[[]]]]]]=>1
[3,6,1,3,2,2]=>[[],[[[],[[]]]]]=>2
[3,6,2,1,2,3]=>[[[],[[[],[]]]]]=>1
[3,6,2,1,3,2]=>[[[],[[],[[]]]]]=>1
[3,6,2,2,1,3]=>[[[[]]],[[],[]]]=>2
[3,6,2,2,3,1]=>[[[[]]],[[],[]]]=>2
[3,6,2,3,1,2]=>[[[],[[],[[]]]]]=>1
[3,6,2,3,2,1]=>[[[],[[[],[]]]]]=>1
[3,6,3,1,2,2]=>[[],[[[[[]]]]]]=>2
[3,6,3,2,1,2]=>[[[[[]],[[]]]]]=>1
[3,6,3,2,2,1]=>[[[]],[[],[[]]]]=>2
[6,1,2,2,3,3]=>[[],[],[[],[[]]]]=>3
[6,1,2,3,2,3]=>[[[[],[],[[]]]]]=>1
[6,1,2,3,3,2]=>[[[]],[[],[[]]]]=>2
[6,1,3,2,2,3]=>[[],[[[[],[]]]]]=>2
[6,1,3,2,3,2]=>[[[],[[],[[]]]]]=>1
[6,1,3,3,2,2]=>[[],[[]],[[],[]]]=>3
[6,2,1,2,3,3]=>[[[[]]],[[],[]]]=>2
[6,2,1,3,2,3]=>[[[[[]],[[]]]]]=>1
[6,2,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[6,2,2,1,3,3]=>[[[]],[[]],[[]]]=>3
[6,2,2,3,1,3]=>[[[[[]]]],[[]]]=>2
[6,2,2,3,3,1]=>[[[]],[[]],[[]]]=>3
[6,2,3,1,2,3]=>[[[[[],[],[]]]]]=>1
[6,2,3,1,3,2]=>[[[[[[[]]]]]]]=>1
[6,2,3,2,1,3]=>[[[[[],[[]]]]]]=>1
[6,2,3,2,3,1]=>[[[[[[],[]]]]]]=>1
[6,2,3,3,1,2]=>[[],[[[],[[]]]]]=>2
[6,2,3,3,2,1]=>[[[[]]],[[],[]]]=>2
[6,3,1,2,2,3]=>[[[]],[[],[[]]]]=>2
[6,3,1,2,3,2]=>[[[[],[[[]]]]]]=>1
[6,3,1,3,2,2]=>[[[]],[[[[]]]]]=>2
[6,3,2,1,2,3]=>[[[[],[[],[]]]]]=>1
[6,3,2,1,3,2]=>[[[[[],[],[]]]]]=>1
[6,3,2,2,1,3]=>[[[]],[[],[[]]]]=>2
[6,3,2,2,3,1]=>[[[[[]]]],[[]]]=>2
[6,3,2,3,1,2]=>[[[[[],[[]]]]]]=>1
[6,3,2,3,2,1]=>[[[[],[],[[]]]]]=>1
[6,3,3,1,2,2]=>[[],[],[[[[]]]]]=>3
[6,3,3,2,1,2]=>[[],[[[]],[[]]]]=>2
[6,3,3,2,2,1]=>[[],[[]],[[],[]]]=>3
[1,2,2,3,4,4]=>[[],[],[[],[],[]]]=>3
[1,2,2,4,3,4]=>[[],[[[[],[]]]]]=>2
[1,2,2,4,4,3]=>[[[]],[[]],[[]]]=>3
[1,2,3,2,4,4]=>[[[]],[[[],[]]]]=>2
[1,2,3,4,2,4]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,4,2]=>[[[]],[[],[],[]]]=>2
[1,2,4,2,3,4]=>[[[],[],[[[]]]]]=>1
[1,2,4,2,4,3]=>[[[[],[[[]]]]]]=>1
[1,2,4,3,2,4]=>[[[[],[[],[]]]]]=>1
[1,2,4,3,4,2]=>[[[],[[[[]]]]]]=>1
[1,2,4,4,2,3]=>[[[]],[[[],[]]]]=>2
[1,2,4,4,3,2]=>[[[[]]],[[],[]]]=>2
[1,3,2,2,4,4]=>[[],[[]],[[],[]]]=>3
[1,3,2,4,2,4]=>[[[],[[]],[[]]]]=>1
[1,3,2,4,4,2]=>[[[[]]],[[],[]]]=>2
[1,3,4,2,2,4]=>[[[[]]],[[],[]]]=>2
[1,3,4,2,4,2]=>[[[],[[],[[]]]]]=>1
[1,3,4,4,2,2]=>[[],[[[]]],[[]]]=>3
[1,4,2,2,3,4]=>[[],[[],[[[]]]]]=>2
[1,4,2,2,4,3]=>[[],[[[[[]]]]]]=>2
[1,4,2,3,2,4]=>[[[[[[[]]]]]]]=>1
[1,4,2,3,4,2]=>[[[[],[[],[]]]]]=>1
[1,4,2,4,2,3]=>[[[[[]],[[]]]]]=>1
[1,4,2,4,3,2]=>[[[[[],[[]]]]]]=>1
[1,4,3,2,2,4]=>[[],[[[],[[]]]]]=>2
[1,4,3,2,4,2]=>[[[[],[[[]]]]]]=>1
[1,4,3,4,2,2]=>[[[[]]],[[[]]]]=>2
[1,4,4,2,2,3]=>[[[]],[[]],[[]]]=>3
[1,4,4,2,3,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,3,2,2]=>[[],[],[[],[[]]]]=>3
[2,1,2,3,4,4]=>[[[]],[[],[],[]]]=>2
[2,1,2,4,3,4]=>[[[[]],[[],[]]]]=>1
[2,1,2,4,4,3]=>[[[[]]],[[],[]]]=>2
[2,1,3,2,4,4]=>[[[],[]],[[],[]]]=>2
[2,1,3,4,2,4]=>[[[[],[[[]]]]]]=>1
[2,1,3,4,4,2]=>[[[[]]],[[[]]]]=>2
[2,1,4,2,3,4]=>[[[[],[[[]]]]]]=>1
[2,1,4,2,4,3]=>[[[[]],[[[]]]]]=>1
[2,1,4,3,2,4]=>[[[],[[]],[[]]]]=>1
[2,1,4,3,4,2]=>[[[[]],[[[]]]]]=>1
[2,1,4,4,2,3]=>[[[]],[[[[]]]]]=>2
[2,1,4,4,3,2]=>[[[]],[[],[],[]]]=>2
[2,2,1,3,4,4]=>[[],[[[]]],[[]]]=>3
[2,2,1,4,3,4]=>[[],[[[]],[[]]]]=>2
[2,2,1,4,4,3]=>[[],[[]],[[],[]]]=>3
[2,2,3,1,4,4]=>[[],[],[[[[]]]]]=>3
[2,2,3,4,1,4]=>[[],[[],[[[]]]]]=>2
[2,2,3,4,4,1]=>[[],[[]],[[],[]]]=>3
[2,2,4,1,3,4]=>[[],[[[]],[[]]]]=>2
[2,2,4,1,4,3]=>[[],[[[[[]]]]]]=>2
[2,2,4,3,1,4]=>[[],[[[[[]]]]]]=>2
[2,2,4,3,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,4,4,1,3]=>[[],[],[[[],[]]]]=>3
[2,2,4,4,3,1]=>[[],[[]],[[[]]]]=>3
[2,3,1,2,4,4]=>[[],[[[],[[]]]]]=>2
[2,3,1,4,2,4]=>[[[[[]],[[]]]]]=>1
[2,3,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[2,3,2,1,4,4]=>[[[]],[[],[[]]]]=>2
[2,3,2,4,1,4]=>[[[[[[[]]]]]]]=>1
[2,3,2,4,4,1]=>[[[]],[[[[]]]]]=>2
[2,3,4,1,2,4]=>[[[],[[]],[[]]]]=>1
[2,3,4,1,4,2]=>[[[],[[[[]]]]]]=>1
[2,3,4,2,1,4]=>[[[],[[[[]]]]]]=>1
[2,3,4,2,4,1]=>[[[],[[[[]]]]]]=>1
[2,3,4,4,1,2]=>[[],[[[],[],[]]]]=>2
[2,3,4,4,2,1]=>[[[[]]],[[],[]]]=>2
[2,4,1,2,3,4]=>[[[[[],[],[]]]]]=>1
[2,4,1,2,4,3]=>[[[[[]]],[[]]]]=>1
[2,4,1,3,2,4]=>[[[],[],[[[]]]]]=>1
[2,4,1,3,4,2]=>[[[[[]]],[[]]]]=>1
[2,4,1,4,2,3]=>[[[[[[[]]]]]]]=>1
[2,4,1,4,3,2]=>[[[[[],[[]]]]]]=>1
[2,4,2,1,3,4]=>[[[[[]]],[[]]]]=>1
[2,4,2,1,4,3]=>[[[[[]],[[]]]]]=>1
[2,4,2,3,1,4]=>[[[[[]],[[]]]]]=>1
[2,4,2,3,4,1]=>[[[[[],[[]]]]]]=>1
[2,4,2,4,1,3]=>[[[],[],[[[]]]]]=>1
[2,4,2,4,3,1]=>[[[],[[[],[]]]]]=>1
[2,4,3,1,2,4]=>[[[[[]]],[[]]]]=>1
[2,4,3,1,4,2]=>[[[[[]],[[]]]]]=>1
[2,4,3,2,1,4]=>[[[[],[],[[]]]]]=>1
[2,4,3,2,4,1]=>[[[],[[[],[]]]]]=>1
[2,4,3,4,1,2]=>[[[[[],[[]]]]]]=>1
[2,4,3,4,2,1]=>[[[[],[[[]]]]]]=>1
[2,4,4,1,2,3]=>[[[]],[[[],[]]]]=>2
[2,4,4,1,3,2]=>[[],[[[],[[]]]]]=>2
[2,4,4,2,1,3]=>[[],[[[],[[]]]]]=>2
[2,4,4,2,3,1]=>[[[]],[[],[[]]]]=>2
[2,4,4,3,1,2]=>[[[]],[[[[]]]]]=>2
[2,4,4,3,2,1]=>[[[]],[[],[],[]]]=>2
[3,1,2,2,4,4]=>[[],[[]],[[[]]]]=>3
[3,1,2,4,2,4]=>[[[],[[],[[]]]]]=>1
[3,1,2,4,4,2]=>[[[[]]],[[],[]]]=>2
[3,1,4,2,2,4]=>[[[]],[[],[[]]]]=>2
[3,1,4,2,4,2]=>[[[],[[]],[[]]]]=>1
[3,1,4,4,2,2]=>[[],[[]],[[],[]]]=>3
[3,2,1,2,4,4]=>[[[[]]],[[],[]]]=>2
[3,2,1,4,2,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,4,2]=>[[[]],[[[],[]]]]=>2
[3,2,2,1,4,4]=>[[],[[]],[[],[]]]=>3
[3,2,2,4,1,4]=>[[],[[[[[]]]]]]=>2
[3,2,2,4,4,1]=>[[],[[]],[[[]]]]=>3
[3,2,4,1,2,4]=>[[[[],[[[]]]]]]=>1
[3,2,4,1,4,2]=>[[[[[[[]]]]]]]=>1
[3,2,4,2,1,4]=>[[[],[[[[]]]]]]=>1
[3,2,4,2,4,1]=>[[[[[],[[]]]]]]=>1
[3,2,4,4,1,2]=>[[[]],[[[[]]]]]=>2
[3,2,4,4,2,1]=>[[[]],[[[],[]]]]=>2
[3,4,1,2,2,4]=>[[[]],[[],[[]]]]=>2
[3,4,1,2,4,2]=>[[[[[]]],[[]]]]=>1
[3,4,1,4,2,2]=>[[],[[[[[]]]]]]=>2
[3,4,2,1,2,4]=>[[[[[]]],[[]]]]=>1
[3,4,2,1,4,2]=>[[[[[]],[[]]]]]=>1
[3,4,2,2,1,4]=>[[],[[[[[]]]]]]=>2
[3,4,2,2,4,1]=>[[[[]]],[[[]]]]=>2
[3,4,2,4,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,2,4,2,1]=>[[[[[]],[[]]]]]=>1
[3,4,4,1,2,2]=>[[],[],[[],[[]]]]=>3
[3,4,4,2,1,2]=>[[],[[[],[[]]]]]=>2
[3,4,4,2,2,1]=>[[],[[]],[[[]]]]=>3
[4,1,2,2,3,4]=>[[[]],[[],[],[]]]=>2
[4,1,2,2,4,3]=>[[[[]]],[[[]]]]=>2
[4,1,2,3,2,4]=>[[[[],[[[]]]]]]=>1
[4,1,2,3,4,2]=>[[[[],[],[[]]]]]=>1
[4,1,2,4,2,3]=>[[[[[[],[]]]]]]=>1
[4,1,2,4,3,2]=>[[[[],[[[]]]]]]=>1
[4,1,3,2,2,4]=>[[],[[],[[[]]]]]=>2
[4,1,3,2,4,2]=>[[[[],[[[]]]]]]=>1
[4,1,3,4,2,2]=>[[],[[[[[]]]]]]=>2
[4,1,4,2,2,3]=>[[[]],[[[[]]]]]=>2
[4,1,4,2,3,2]=>[[[[[[[]]]]]]]=>1
[4,1,4,3,2,2]=>[[],[[[]],[[]]]]=>2
[4,2,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[4,2,1,2,4,3]=>[[[[],[[[]]]]]]=>1
[4,2,1,3,2,4]=>[[[[],[[],[]]]]]=>1
[4,2,1,3,4,2]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,2,3]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,3,2]=>[[[[],[],[[]]]]]=>1
[4,2,2,1,3,4]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,4,3]=>[[],[[[]],[[]]]]=>2
[4,2,2,3,1,4]=>[[],[[[],[[]]]]]=>2
[4,2,2,3,4,1]=>[[],[[[]],[[]]]]=>2
[4,2,2,4,1,3]=>[[],[[],[[[]]]]]=>2
[4,2,2,4,3,1]=>[[],[[[[],[]]]]]=>2
[4,2,3,1,2,4]=>[[[],[[],[[]]]]]=>1
[4,2,3,1,4,2]=>[[[],[[]],[[]]]]=>1
[4,2,3,2,1,4]=>[[[[[],[[]]]]]]=>1
[4,2,3,2,4,1]=>[[[[[[[]]]]]]]=>1
[4,2,3,4,1,2]=>[[[[[],[],[]]]]]=>1
[4,2,3,4,2,1]=>[[[[]],[[],[]]]]=>1
[4,2,4,1,2,3]=>[[[[],[[[]]]]]]=>1
[4,2,4,1,3,2]=>[[[[[],[[]]]]]]=>1
[4,2,4,2,1,3]=>[[[],[[],[[]]]]]=>1
[4,2,4,2,3,1]=>[[[],[[]],[[]]]]=>1
[4,2,4,3,1,2]=>[[[],[[[[]]]]]]=>1
[4,2,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[4,3,1,2,2,4]=>[[[[]]],[[[]]]]=>2
[4,3,1,2,4,2]=>[[[[],[[[]]]]]]=>1
[4,3,1,4,2,2]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,2,4]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,4,2]=>[[[],[],[[[]]]]]=>1
[4,3,2,2,1,4]=>[[],[[],[],[[]]]]=>2
[4,3,2,2,4,1]=>[[],[[[[],[]]]]]=>2
[4,3,2,4,1,2]=>[[[],[[[[]]]]]]=>1
[4,3,2,4,2,1]=>[[[],[],[[[]]]]]=>1
[4,3,4,1,2,2]=>[[[]],[[],[[]]]]=>2
[4,3,4,2,1,2]=>[[[],[[],[[]]]]]=>1
[4,3,4,2,2,1]=>[[],[[],[[[]]]]]=>2
[4,4,1,2,2,3]=>[[],[],[[],[[]]]]=>3
[4,4,1,2,3,2]=>[[],[[[],[[]]]]]=>2
[4,4,1,3,2,2]=>[[],[],[[[[]]]]]=>3
[4,4,2,1,2,3]=>[[],[[[],[[]]]]]=>2
[4,4,2,1,3,2]=>[[],[[[],[[]]]]]=>2
[4,4,2,2,1,3]=>[[],[],[[[[]]]]]=>3
[4,4,2,2,3,1]=>[[],[],[[[],[]]]]=>3
[4,4,2,3,1,2]=>[[],[[],[[],[]]]]=>2
[4,4,2,3,2,1]=>[[],[[[],[[]]]]]=>2
[4,4,3,1,2,2]=>[[],[[[]]],[[]]]=>3
[4,4,3,2,1,2]=>[[],[[],[],[[]]]]=>2
[4,4,3,2,2,1]=>[[],[],[[],[],[]]]=>3
[1,2,2,3,4,5]=>[[],[[],[],[],[]]]=>2
[1,2,2,3,5,4]=>[[],[[],[[[]]]]]=>2
[1,2,2,4,3,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,4,5,3]=>[[],[[[],[[]]]]]=>2
[1,2,2,5,3,4]=>[[],[[[[],[]]]]]=>2
[1,2,2,5,4,3]=>[[[]],[[[],[]]]]=>2
[1,2,3,2,4,5]=>[[[],[[]],[[]]]]=>1
[1,2,3,2,5,4]=>[[[],[[],[[]]]]]=>1
[1,2,3,4,2,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,5,2]=>[[[],[],[],[[]]]]=>1
[1,2,3,5,2,4]=>[[[],[[],[[]]]]]=>1
[1,2,3,5,4,2]=>[[[],[[[[]]]]]]=>1
[1,2,4,2,3,5]=>[[[[]],[[],[]]]]=>1
[1,2,4,2,5,3]=>[[[[[],[[]]]]]]=>1
[1,2,4,3,2,5]=>[[[[[],[[]]]]]]=>1
[1,2,4,3,5,2]=>[[[[],[[[]]]]]]=>1
[1,2,4,5,2,3]=>[[[],[[]],[[]]]]=>1
[1,2,4,5,3,2]=>[[[[]],[[[]]]]]=>1
[1,2,5,2,3,4]=>[[[],[],[[[]]]]]=>1
[1,2,5,2,4,3]=>[[[[[[[]]]]]]]=>1
[1,2,5,3,2,4]=>[[[[[[[]]]]]]]=>1
[1,2,5,3,4,2]=>[[[],[[],[[]]]]]=>1
[1,2,5,4,2,3]=>[[[[]],[[[]]]]]=>1
[1,2,5,4,3,2]=>[[[[[],[],[]]]]]=>1
[1,3,2,2,4,5]=>[[],[[],[[[]]]]]=>2
[1,3,2,2,5,4]=>[[],[[[],[[]]]]]=>2
[1,3,2,4,2,5]=>[[[],[[[[]]]]]]=>1
[1,3,2,4,5,2]=>[[[],[[[[]]]]]]=>1
[1,3,2,5,2,4]=>[[[[[]]],[[]]]]=>1
[1,3,2,5,4,2]=>[[[[[],[[]]]]]]=>1
[1,3,4,2,2,5]=>[[[]],[[[[]]]]]=>2
[1,3,4,2,5,2]=>[[[[[[[]]]]]]]=>1
[1,3,4,5,2,2]=>[[],[[[],[[]]]]]=>2
[1,3,5,2,2,4]=>[[[]],[[],[],[]]]=>2
[1,3,5,2,4,2]=>[[[],[[]],[[]]]]=>1
[1,3,5,4,2,2]=>[[[]],[[[],[]]]]=>2
[1,4,2,2,3,5]=>[[[[]]],[[[]]]]=>2
[1,4,2,2,5,3]=>[[],[[],[[],[]]]]=>2
[1,4,2,3,2,5]=>[[[[]],[[[]]]]]=>1
[1,4,2,3,5,2]=>[[[[[[[]]]]]]]=>1
[1,4,2,5,2,3]=>[[[[[]]],[[]]]]=>1
[1,4,2,5,3,2]=>[[[],[[],[[]]]]]=>1
[1,4,3,2,2,5]=>[[],[[],[[],[]]]]=>2
[1,4,3,2,5,2]=>[[[],[[[],[]]]]]=>1
[1,4,3,5,2,2]=>[[[[]]],[[[]]]]=>2
[1,4,5,2,2,3]=>[[[]],[[],[[]]]]=>2
[1,4,5,2,3,2]=>[[[[[],[[]]]]]]=>1
[1,4,5,3,2,2]=>[[[[[]]]],[[]]]=>2
[1,5,2,2,3,4]=>[[[],[]],[[],[]]]=>2
[1,5,2,2,4,3]=>[[[[]]],[[],[]]]=>2
[1,5,2,3,2,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,3,4,2]=>[[[],[[],[[]]]]]=>1
[1,5,2,4,2,3]=>[[[],[[[[]]]]]]=>1
[1,5,2,4,3,2]=>[[[],[[],[[]]]]]=>1
[1,5,3,2,2,4]=>[[[[[]]]],[[]]]=>2
[1,5,3,2,4,2]=>[[[[[],[[]]]]]]=>1
[1,5,3,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,5,4,2,2,3]=>[[[[]]],[[[]]]]=>2
[1,5,4,2,3,2]=>[[[[[],[[]]]]]]=>1
[1,5,4,3,2,2]=>[[],[[],[],[[]]]]=>2
[2,1,2,3,4,5]=>[[[[],[],[],[]]]]=>1
[2,1,2,3,5,4]=>[[[],[[[],[]]]]]=>1
[2,1,2,4,3,5]=>[[[],[[],[[]]]]]=>1
[2,1,2,4,5,3]=>[[[[[],[[]]]]]]=>1
[2,1,2,5,3,4]=>[[[[],[[[]]]]]]=>1
[2,1,2,5,4,3]=>[[[],[],[[[]]]]]=>1
[2,1,3,2,4,5]=>[[[],[[[],[]]]]]=>1
[2,1,3,2,5,4]=>[[[],[[]],[[]]]]=>1
[2,1,3,4,2,5]=>[[[[[[[]]]]]]]=>1
[2,1,3,4,5,2]=>[[[[[],[[]]]]]]=>1
[2,1,3,5,2,4]=>[[[[],[],[[]]]]]=>1
[2,1,3,5,4,2]=>[[[[]],[[],[]]]]=>1
[2,1,4,2,3,5]=>[[[[[[[]]]]]]]=>1
[2,1,4,2,5,3]=>[[[[],[[],[]]]]]=>1
[2,1,4,3,2,5]=>[[[],[],[[],[]]]]=>1
[2,1,4,3,5,2]=>[[[[]],[[[]]]]]=>1
[2,1,4,5,2,3]=>[[[[[]],[[]]]]]=>1
[2,1,4,5,3,2]=>[[[],[[[[]]]]]]=>1
[2,1,5,2,3,4]=>[[[[],[[],[]]]]]=>1
[2,1,5,2,4,3]=>[[[],[[[],[]]]]]=>1
[2,1,5,3,2,4]=>[[[[[]]],[[]]]]=>1
[2,1,5,3,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,5,4,2,3]=>[[[],[[[[]]]]]]=>1
[2,1,5,4,3,2]=>[[[],[],[],[[]]]]=>1
[2,2,1,3,4,5]=>[[],[[[],[[]]]]]=>2
[2,2,1,3,5,4]=>[[],[[],[[],[]]]]=>2
[2,2,1,4,3,5]=>[[],[[[]],[[]]]]=>2
[2,2,1,4,5,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,3,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,4,3]=>[[],[[],[],[[]]]]=>2
[2,2,3,1,4,5]=>[[],[[],[[[]]]]]=>2
[2,2,3,1,5,4]=>[[],[[[[[]]]]]]=>2
[2,2,3,4,1,5]=>[[],[[],[[],[]]]]=>2
[2,2,3,4,5,1]=>[[],[[],[],[[]]]]=>2
[2,2,3,5,1,4]=>[[],[[[[],[]]]]]=>2
[2,2,3,5,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,4,1,3,5]=>[[],[[],[],[[]]]]=>2
[2,2,4,1,5,3]=>[[],[[[],[[]]]]]=>2
[2,2,4,3,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,4,3,5,1]=>[[],[[],[[[]]]]]=>2
[2,2,4,5,1,3]=>[[],[[],[[[]]]]]=>2
[2,2,4,5,3,1]=>[[],[[[[],[]]]]]=>2
[2,2,5,1,3,4]=>[[],[[],[[[]]]]]=>2
[2,2,5,1,4,3]=>[[],[[],[],[[]]]]=>2
[2,2,5,3,1,4]=>[[],[[],[[],[]]]]=>2
[2,2,5,3,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,5,4,1,3]=>[[],[[[[[]]]]]]=>2
[2,2,5,4,3,1]=>[[],[[[],[[]]]]]=>2
[2,3,1,2,4,5]=>[[[],[],[[[]]]]]=>1
[2,3,1,2,5,4]=>[[[],[[[[]]]]]]=>1
[2,3,1,4,2,5]=>[[[[],[[],[]]]]]=>1
[2,3,1,4,5,2]=>[[[[[]]],[[]]]]=>1
[2,3,1,5,2,4]=>[[[[[],[[]]]]]]=>1
[2,3,1,5,4,2]=>[[[[[]],[[]]]]]=>1
[2,3,2,1,4,5]=>[[[[]],[[],[]]]]=>1
[2,3,2,1,5,4]=>[[[[],[],[[]]]]]=>1
[2,3,2,4,1,5]=>[[[[[],[[]]]]]]=>1
[2,3,2,4,5,1]=>[[[[]],[[[]]]]]=>1
[2,3,2,5,1,4]=>[[[[[],[],[]]]]]=>1
[2,3,2,5,4,1]=>[[[[[]],[[]]]]]=>1
[2,3,4,1,2,5]=>[[[],[[]],[[]]]]=>1
[2,3,4,1,5,2]=>[[[],[[],[],[]]]]=>1
[2,3,4,2,1,5]=>[[[],[[[[]]]]]]=>1
[2,3,4,2,5,1]=>[[[],[[[],[]]]]]=>1
[2,3,4,5,1,2]=>[[[],[],[],[[]]]]=>1
[2,3,4,5,2,1]=>[[[],[],[[[]]]]]=>1
[2,3,5,1,2,4]=>[[[[]],[[],[]]]]=>1
[2,3,5,1,4,2]=>[[[[[],[[]]]]]]=>1
[2,3,5,2,1,4]=>[[[[[[[]]]]]]]=>1
[2,3,5,2,4,1]=>[[[[],[[],[]]]]]=>1
[2,3,5,4,1,2]=>[[[[]],[[[]]]]]=>1
[2,3,5,4,2,1]=>[[[[[],[[]]]]]]=>1
[2,4,1,2,3,5]=>[[[],[[],[[]]]]]=>1
[2,4,1,2,5,3]=>[[[[[[[]]]]]]]=>1
[2,4,1,3,2,5]=>[[[[]],[[[]]]]]=>1
[2,4,1,3,5,2]=>[[[],[],[[],[]]]]=>1
[2,4,1,5,2,3]=>[[[[],[],[[]]]]]=>1
[2,4,1,5,3,2]=>[[[[],[[[]]]]]]=>1
[2,4,2,1,3,5]=>[[[],[[]],[[]]]]=>1
[2,4,2,1,5,3]=>[[[[[],[[]]]]]]=>1
[2,4,2,3,1,5]=>[[[[[]],[[]]]]]=>1
[2,4,2,3,5,1]=>[[[[[]]],[[]]]]=>1
[2,4,2,5,1,3]=>[[[],[[],[[]]]]]=>1
[2,4,2,5,3,1]=>[[[[[],[],[]]]]]=>1
[2,4,3,1,2,5]=>[[[[[[[]]]]]]]=>1
[2,4,3,1,5,2]=>[[[[[],[[]]]]]]=>1
[2,4,3,2,1,5]=>[[[[],[],[[]]]]]=>1
[2,4,3,2,5,1]=>[[[[],[[],[]]]]]=>1
[2,4,3,5,1,2]=>[[[],[[[[]]]]]]=>1
[2,4,3,5,2,1]=>[[[],[[[],[]]]]]=>1
[2,4,5,1,2,3]=>[[[[],[],[[]]]]]=>1
[2,4,5,1,3,2]=>[[[[[]]],[[]]]]=>1
[2,4,5,2,1,3]=>[[[],[[[[]]]]]]=>1
[2,4,5,2,3,1]=>[[[[[]],[[]]]]]=>1
[2,4,5,3,1,2]=>[[[[],[[],[]]]]]=>1
[2,4,5,3,2,1]=>[[[[[[],[]]]]]]=>1
[2,5,1,2,3,4]=>[[[],[[],[],[]]]]=>1
[2,5,1,2,4,3]=>[[[],[[[[]]]]]]=>1
[2,5,1,3,2,4]=>[[[],[[],[[]]]]]=>1
[2,5,1,3,4,2]=>[[[],[[[[]]]]]]=>1
[2,5,1,4,2,3]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,3,2]=>[[[],[],[[],[]]]]=>1
[2,5,2,1,3,4]=>[[[[[[[]]]]]]]=>1
[2,5,2,1,4,3]=>[[[[]],[[],[]]]]=>1
[2,5,2,3,1,4]=>[[[],[[[[]]]]]]=>1
[2,5,2,3,4,1]=>[[[[],[[],[]]]]]=>1
[2,5,2,4,1,3]=>[[[[],[[],[]]]]]=>1
[2,5,2,4,3,1]=>[[[[[[[]]]]]]]=>1
[2,5,3,1,2,4]=>[[[[],[[[]]]]]]=>1
[2,5,3,1,4,2]=>[[[],[[],[],[]]]]=>1
[2,5,3,2,1,4]=>[[[[]],[[],[]]]]=>1
[2,5,3,2,4,1]=>[[[[[[[]]]]]]]=>1
[2,5,3,4,1,2]=>[[[[],[[[]]]]]]=>1
[2,5,3,4,2,1]=>[[[[[],[[]]]]]]=>1
[2,5,4,1,2,3]=>[[[[[],[[]]]]]]=>1
[2,5,4,1,3,2]=>[[[[[[],[]]]]]]=>1
[2,5,4,2,1,3]=>[[[[[[],[]]]]]]=>1
[2,5,4,2,3,1]=>[[[[[]],[[]]]]]=>1
[2,5,4,3,1,2]=>[[[[],[[[]]]]]]=>1
[2,5,4,3,2,1]=>[[[[],[],[],[]]]]=>1
[3,1,2,2,4,5]=>[[[[],[]]],[[]]]=>2
[3,1,2,2,5,4]=>[[[]],[[[[]]]]]=>2
[3,1,2,4,2,5]=>[[[[[]]],[[]]]]=>1
[3,1,2,4,5,2]=>[[[[[],[[]]]]]]=>1
[3,1,2,5,2,4]=>[[[[[[[]]]]]]]=>1
[3,1,2,5,4,2]=>[[[],[[[[]]]]]]=>1
[3,1,4,2,2,5]=>[[[],[]],[[],[]]]=>2
[3,1,4,2,5,2]=>[[[],[[],[[]]]]]=>1
[3,1,4,5,2,2]=>[[],[[[[[]]]]]]=>2
[3,1,5,2,2,4]=>[[[]],[[],[[]]]]=>2
[3,1,5,2,4,2]=>[[[],[[[],[]]]]]=>1
[3,1,5,4,2,2]=>[[[]],[[],[[]]]]=>2
[3,2,1,2,4,5]=>[[[],[[],[[]]]]]=>1
[3,2,1,2,5,4]=>[[[],[],[[[]]]]]=>1
[3,2,1,4,2,5]=>[[[],[[],[[]]]]]=>1
[3,2,1,4,5,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,2,4]=>[[[],[[[],[]]]]]=>1
[3,2,1,5,4,2]=>[[[],[],[[[]]]]]=>1
[3,2,2,1,4,5]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,5,4]=>[[],[[],[],[[]]]]=>2
[3,2,2,4,1,5]=>[[],[[[],[[]]]]]=>2
[3,2,2,4,5,1]=>[[],[[[[[]]]]]]=>2
[3,2,2,5,1,4]=>[[],[[],[],[[]]]]=>2
[3,2,2,5,4,1]=>[[],[[[],[[]]]]]=>2
[3,2,4,1,2,5]=>[[[[[[[]]]]]]]=>1
[3,2,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[3,2,4,2,1,5]=>[[[],[[[[]]]]]]=>1
[3,2,4,2,5,1]=>[[[[],[[[]]]]]]=>1
[3,2,4,5,1,2]=>[[[[[]],[[]]]]]=>1
[3,2,4,5,2,1]=>[[[],[[[[]]]]]]=>1
[3,2,5,1,2,4]=>[[[[[[],[]]]]]]=>1
[3,2,5,1,4,2]=>[[[[[],[],[]]]]]=>1
[3,2,5,2,1,4]=>[[[[]],[[],[]]]]=>1
[3,2,5,2,4,1]=>[[[[[]],[[]]]]]=>1
[3,2,5,4,1,2]=>[[[[[]]],[[]]]]=>1
[3,2,5,4,2,1]=>[[[],[],[[[]]]]]=>1
[3,4,1,2,2,5]=>[[[]],[[],[[]]]]=>2
[3,4,1,2,5,2]=>[[[],[[[],[]]]]]=>1
[3,4,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[3,4,2,1,2,5]=>[[[[[]]],[[]]]]=>1
[3,4,2,1,5,2]=>[[[[[],[[]]]]]]=>1
[3,4,2,2,1,5]=>[[],[[[[[]]]]]]=>2
[3,4,2,2,5,1]=>[[],[[],[[[]]]]]=>2
[3,4,2,5,1,2]=>[[[],[[],[[]]]]]=>1
[3,4,2,5,2,1]=>[[[[[[[]]]]]]]=>1
[3,4,5,1,2,2]=>[[],[[],[],[[]]]]=>2
[3,4,5,2,1,2]=>[[[],[],[[[]]]]]=>1
[3,4,5,2,2,1]=>[[[[],[]]],[[]]]=>2
[3,5,1,2,2,4]=>[[[[]]],[[],[]]]=>2
[3,5,1,2,4,2]=>[[[[[]]],[[]]]]=>1
[3,5,1,4,2,2]=>[[],[[[],[[]]]]]=>2
[3,5,2,1,2,4]=>[[[[]],[[[]]]]]=>1
[3,5,2,1,4,2]=>[[[[[[[]]]]]]]=>1
[3,5,2,2,1,4]=>[[[[]]],[[[]]]]=>2
[3,5,2,2,4,1]=>[[],[[],[[],[]]]]=>2
[3,5,2,4,1,2]=>[[[],[[],[[]]]]]=>1
[3,5,2,4,2,1]=>[[[],[[[[]]]]]]=>1
[3,5,4,1,2,2]=>[[[[]]],[[[]]]]=>2
[3,5,4,2,1,2]=>[[[[],[[[]]]]]]=>1
[3,5,4,2,2,1]=>[[],[[[]],[[]]]]=>2
[4,1,2,2,3,5]=>[[],[[[]],[[]]]]=>2
[4,1,2,2,5,3]=>[[[[]]],[[[]]]]=>2
[4,1,2,3,2,5]=>[[[[],[[[]]]]]]=>1
[4,1,2,3,5,2]=>[[[],[[[],[]]]]]=>1
[4,1,2,5,2,3]=>[[[[]],[[],[]]]]=>1
[4,1,2,5,3,2]=>[[[[[[[]]]]]]]=>1
[4,1,3,2,2,5]=>[[],[[[[[]]]]]]=>2
[4,1,3,2,5,2]=>[[[[]],[[[]]]]]=>1
[4,1,3,5,2,2]=>[[],[[],[[],[]]]]=>2
[4,1,5,2,2,3]=>[[[]],[[],[],[]]]=>2
[4,1,5,2,3,2]=>[[[],[],[[[]]]]]=>1
[4,1,5,3,2,2]=>[[[]],[[[],[]]]]=>2
[4,2,1,2,3,5]=>[[[[],[[[]]]]]]=>1
[4,2,1,2,5,3]=>[[[[[]]],[[]]]]=>1
[4,2,1,3,2,5]=>[[[[[],[[]]]]]]=>1
[4,2,1,3,5,2]=>[[[[],[[[]]]]]]=>1
[4,2,1,5,2,3]=>[[[[],[[[]]]]]]=>1
[4,2,1,5,3,2]=>[[[],[[],[[]]]]]=>1
[4,2,2,1,3,5]=>[[],[[[],[[]]]]]=>2
[4,2,2,1,5,3]=>[[],[[[],[[]]]]]=>2
[4,2,2,3,1,5]=>[[],[[[],[[]]]]]=>2
[4,2,2,3,5,1]=>[[[[[]]]],[[]]]=>2
[4,2,2,5,1,3]=>[[],[[[]],[[]]]]=>2
[4,2,2,5,3,1]=>[[],[[[],[],[]]]]=>2
[4,2,3,1,2,5]=>[[[],[[],[[]]]]]=>1
[4,2,3,1,5,2]=>[[[[]],[[],[]]]]=>1
[4,2,3,2,1,5]=>[[[[[],[[]]]]]]=>1
[4,2,3,2,5,1]=>[[[[],[[[]]]]]]=>1
[4,2,3,5,1,2]=>[[[[[[],[]]]]]]=>1
[4,2,3,5,2,1]=>[[[[[[[]]]]]]]=>1
[4,2,5,1,2,3]=>[[[[],[[],[]]]]]=>1
[4,2,5,1,3,2]=>[[[[[[],[]]]]]]=>1
[4,2,5,2,1,3]=>[[[[[[[]]]]]]]=>1
[4,2,5,2,3,1]=>[[[],[[[[]]]]]]=>1
[4,2,5,3,1,2]=>[[[],[[]],[[]]]]=>1
[4,2,5,3,2,1]=>[[[],[[],[[]]]]]=>1
[4,3,1,2,2,5]=>[[[[]]],[[[]]]]=>2
[4,3,1,2,5,2]=>[[[[[[[]]]]]]]=>1
[4,3,1,5,2,2]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,2,5]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,5,2]=>[[[],[],[[],[]]]]=>1
[4,3,2,2,1,5]=>[[],[[],[],[[]]]]=>2
[4,3,2,2,5,1]=>[[],[[],[[],[]]]]=>2
[4,3,2,5,1,2]=>[[[],[[[],[]]]]]=>1
[4,3,2,5,2,1]=>[[[],[],[[[]]]]]=>1
[4,3,5,1,2,2]=>[[[[[]]]],[[]]]=>2
[4,3,5,2,1,2]=>[[[[]],[[[]]]]]=>1
[4,3,5,2,2,1]=>[[[[]]],[[],[]]]=>2
[4,5,1,2,2,3]=>[[],[[],[],[[]]]]=>2
[4,5,1,2,3,2]=>[[[],[[]],[[]]]]=>1
[4,5,1,3,2,2]=>[[],[[[[[]]]]]]=>2
[4,5,2,1,2,3]=>[[[],[[]],[[]]]]=>1
[4,5,2,1,3,2]=>[[[[[[],[]]]]]]=>1
[4,5,2,2,1,3]=>[[[[]]],[[[]]]]=>2
[4,5,2,2,3,1]=>[[[]],[[],[[]]]]=>2
[4,5,2,3,1,2]=>[[[],[],[[[]]]]]=>1
[4,5,2,3,2,1]=>[[[],[[],[[]]]]]=>1
[4,5,3,1,2,2]=>[[],[[],[[],[]]]]=>2
[4,5,3,2,1,2]=>[[[[]],[[],[]]]]=>1
[4,5,3,2,2,1]=>[[],[[],[[[]]]]]=>2
[5,1,2,2,3,4]=>[[],[[],[],[[]]]]=>2
[5,1,2,2,4,3]=>[[[[]]],[[[]]]]=>2
[5,1,2,3,2,4]=>[[[[],[[[]]]]]]=>1
[5,1,2,3,4,2]=>[[[[],[],[[]]]]]=>1
[5,1,2,4,2,3]=>[[[[],[[[]]]]]]=>1
[5,1,2,4,3,2]=>[[[[[[],[]]]]]]=>1
[5,1,3,2,2,4]=>[[],[[[]],[[]]]]=>2
[5,1,3,2,4,2]=>[[[[[[],[]]]]]]=>1
[5,1,3,4,2,2]=>[[],[[[[[]]]]]]=>2
[5,1,4,2,2,3]=>[[[]],[[[],[]]]]=>2
[5,1,4,2,3,2]=>[[[],[[[[]]]]]]=>1
[5,1,4,3,2,2]=>[[],[[],[[],[]]]]=>2
[5,2,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[5,2,1,2,4,3]=>[[[[[[],[]]]]]]=>1
[5,2,1,3,2,4]=>[[[[],[[],[]]]]]=>1
[5,2,1,3,4,2]=>[[[[[[[]]]]]]]=>1
[5,2,1,4,2,3]=>[[[[[[[]]]]]]]=>1
[5,2,1,4,3,2]=>[[[[],[],[[]]]]]=>1
[5,2,2,1,3,4]=>[[[]],[[[[]]]]]=>2
[5,2,2,1,4,3]=>[[],[[],[[[]]]]]=>2
[5,2,2,3,1,4]=>[[[[[]]]],[[]]]=>2
[5,2,2,3,4,1]=>[[],[[],[[],[]]]]=>2
[5,2,2,4,1,3]=>[[],[[],[[],[]]]]=>2
[5,2,2,4,3,1]=>[[],[[[[[]]]]]]=>2
[5,2,3,1,2,4]=>[[[[[],[[]]]]]]=>1
[5,2,3,1,4,2]=>[[[[[],[[]]]]]]=>1
[5,2,3,2,1,4]=>[[[[[]],[[]]]]]=>1
[5,2,3,2,4,1]=>[[[[]],[[[]]]]]=>1
[5,2,3,4,1,2]=>[[[],[[],[],[]]]]=>1
[5,2,3,4,2,1]=>[[[[[[],[]]]]]]=>1
[5,2,4,1,2,3]=>[[[[]],[[],[]]]]=>1
[5,2,4,1,3,2]=>[[[],[[],[[]]]]]=>1
[5,2,4,2,1,3]=>[[[[[],[[]]]]]]=>1
[5,2,4,2,3,1]=>[[[[[],[[]]]]]]=>1
[5,2,4,3,1,2]=>[[[[[[[]]]]]]]=>1
[5,2,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[5,3,1,2,2,4]=>[[[[],[]]],[[]]]=>2
[5,3,1,2,4,2]=>[[[],[],[[[]]]]]=>1
[5,3,1,4,2,2]=>[[],[[],[],[[]]]]=>2
[5,3,2,1,2,4]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,4,2]=>[[[[]],[[],[]]]]=>1
[5,3,2,2,1,4]=>[[],[[],[[[]]]]]=>2
[5,3,2,2,4,1]=>[[[[[]]]],[[]]]=>2
[5,3,2,4,1,2]=>[[[[[[[]]]]]]]=>1
[5,3,2,4,2,1]=>[[[[]],[[],[]]]]=>1
[5,3,4,1,2,2]=>[[],[[],[[[]]]]]=>2
[5,3,4,2,1,2]=>[[[],[[],[[]]]]]=>1
[5,3,4,2,2,1]=>[[],[[[],[[]]]]]=>2
[5,4,1,2,2,3]=>[[],[[[]],[[]]]]=>2
[5,4,1,2,3,2]=>[[[],[[],[[]]]]]=>1
[5,4,1,3,2,2]=>[[],[[],[[[]]]]]=>2
[5,4,2,1,2,3]=>[[[],[[],[[]]]]]=>1
[5,4,2,1,3,2]=>[[[],[[]],[[]]]]=>1
[5,4,2,2,1,3]=>[[],[[],[[[]]]]]=>2
[5,4,2,2,3,1]=>[[],[[[],[[]]]]]=>2
[5,4,2,3,1,2]=>[[[[],[[],[]]]]]=>1
[5,4,2,3,2,1]=>[[[],[[]],[[]]]]=>1
[5,4,3,1,2,2]=>[[[[]]],[[],[]]]=>2
[5,4,3,2,1,2]=>[[[],[],[],[[]]]]=>1
[5,4,3,2,2,1]=>[[],[[],[],[],[]]]=>2
[1,2,2,3,4,6]=>[[],[[],[],[[]]]]=>2
[1,2,2,3,6,4]=>[[],[[],[[[]]]]]=>2
[1,2,2,4,3,6]=>[[[]],[[[[]]]]]=>2
[1,2,2,4,6,3]=>[[[]],[[],[[]]]]=>2
[1,2,2,6,3,4]=>[[],[[],[[],[]]]]=>2
[1,2,2,6,4,3]=>[[[]],[[[[]]]]]=>2
[1,2,3,2,4,6]=>[[[],[[[],[]]]]]=>1
[1,2,3,2,6,4]=>[[[],[[[[]]]]]]=>1
[1,2,3,4,2,6]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,6,2]=>[[[],[],[[[]]]]]=>1
[1,2,3,6,2,4]=>[[[],[[],[[]]]]]=>1
[1,2,3,6,4,2]=>[[[],[[[],[]]]]]=>1
[1,2,4,2,3,6]=>[[[[]],[[[]]]]]=>1
[1,2,4,2,6,3]=>[[[[[[],[]]]]]]=>1
[1,2,4,3,2,6]=>[[[[[],[[]]]]]]=>1
[1,2,4,3,6,2]=>[[[[[[],[]]]]]]=>1
[1,2,4,6,2,3]=>[[[],[[[],[]]]]]=>1
[1,2,4,6,3,2]=>[[[[],[[[]]]]]]=>1
[1,2,6,2,3,4]=>[[[],[],[[[]]]]]=>1
[1,2,6,2,4,3]=>[[[[[[[]]]]]]]=>1
[1,2,6,3,2,4]=>[[[[],[[[]]]]]]=>1
[1,2,6,3,4,2]=>[[[[]],[[],[]]]]=>1
[1,2,6,4,2,3]=>[[[],[[],[[]]]]]=>1
[1,2,6,4,3,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,2,4,6]=>[[],[[],[],[[]]]]=>2
[1,3,2,2,6,4]=>[[],[[[[[]]]]]]=>2
[1,3,2,4,2,6]=>[[[],[[[[]]]]]]=>1
[1,3,2,4,6,2]=>[[[],[],[[[]]]]]=>1
[1,3,2,6,2,4]=>[[[[[]]],[[]]]]=>1
[1,3,2,6,4,2]=>[[[[[],[[]]]]]]=>1
[1,3,4,2,2,6]=>[[[]],[[[[]]]]]=>2
[1,3,4,2,6,2]=>[[[[[[[]]]]]]]=>1
[1,3,4,6,2,2]=>[[],[[[],[[]]]]]=>2
[1,3,6,2,2,4]=>[[[],[]],[[],[]]]=>2
[1,3,6,2,4,2]=>[[[[]],[[],[]]]]=>1
[1,3,6,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,4,2,2,3,6]=>[[[[],[]]],[[]]]=>2
[1,4,2,2,6,3]=>[[[]],[[],[[]]]]=>2
[1,4,2,3,2,6]=>[[[[[[[]]]]]]]=>1
[1,4,2,3,6,2]=>[[[],[[]],[[]]]]=>1
[1,4,2,6,2,3]=>[[[[]],[[[]]]]]=>1
[1,4,2,6,3,2]=>[[[[],[[[]]]]]]=>1
[1,4,3,2,2,6]=>[[],[[[],[[]]]]]=>2
[1,4,3,2,6,2]=>[[[[]],[[],[]]]]=>1
[1,4,3,6,2,2]=>[[[]],[[],[],[]]]=>2
[1,4,6,2,2,3]=>[[[]],[[],[[]]]]=>2
[1,4,6,2,3,2]=>[[[[[]]],[[]]]]=>1
[1,4,6,3,2,2]=>[[],[[[[[]]]]]]=>2
[1,6,2,2,3,4]=>[[[]],[[],[[]]]]=>2
[1,6,2,2,4,3]=>[[[[[]]]],[[]]]=>2
[1,6,2,3,2,4]=>[[[[[[[]]]]]]]=>1
[1,6,2,3,4,2]=>[[[],[[],[[]]]]]=>1
[1,6,2,4,2,3]=>[[[[]],[[[]]]]]=>1
[1,6,2,4,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,3,2,2,4]=>[[[[[]]]],[[]]]=>2
[1,6,3,2,4,2]=>[[[[[]]],[[]]]]=>1
[1,6,3,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,6,4,2,2,3]=>[[[]],[[],[],[]]]=>2
[1,6,4,2,3,2]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,2,2]=>[[[],[]],[[],[]]]=>2
[2,1,2,3,4,6]=>[[[[[],[],[]]]]]=>1
[2,1,2,3,6,4]=>[[[[[[],[]]]]]]=>1
[2,1,2,4,3,6]=>[[[[[]]],[[]]]]=>1
[2,1,2,4,6,3]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,3,4]=>[[[[],[[],[]]]]]=>1
[2,1,2,6,4,3]=>[[[[[]]],[[]]]]=>1
[2,1,3,2,4,6]=>[[[],[[],[],[]]]]=>1
[2,1,3,2,6,4]=>[[[[]],[[[]]]]]=>1
[2,1,3,4,2,6]=>[[[[[[[]]]]]]]=>1
[2,1,3,4,6,2]=>[[[[[],[[]]]]]]=>1
[2,1,3,6,2,4]=>[[[[],[[],[]]]]]=>1
[2,1,3,6,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,4,2,3,6]=>[[[[],[[[]]]]]]=>1
[2,1,4,2,6,3]=>[[[[[]],[[]]]]]=>1
[2,1,4,3,2,6]=>[[[],[[]],[[]]]]=>1
[2,1,4,3,6,2]=>[[[],[[],[],[]]]]=>1
[2,1,4,6,2,3]=>[[[[[],[[]]]]]]=>1
[2,1,4,6,3,2]=>[[[],[[[[]]]]]]=>1
[2,1,6,2,3,4]=>[[[[[]],[[]]]]]=>1
[2,1,6,2,4,3]=>[[[[[]]],[[]]]]=>1
[2,1,6,3,2,4]=>[[[[[]]],[[]]]]=>1
[2,1,6,3,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,6,4,2,3]=>[[[[[],[],[]]]]]=>1
[2,1,6,4,3,2]=>[[[],[],[[],[]]]]=>1
[2,2,1,3,4,6]=>[[],[[[],[[]]]]]=>2
[2,2,1,3,6,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,4,3,6]=>[[],[[],[[],[]]]]=>2
[2,2,1,4,6,3]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,3,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,4,3]=>[[],[[],[[],[]]]]=>2
[2,2,3,1,4,6]=>[[],[[[[[]]]]]]=>2
[2,2,3,1,6,4]=>[[],[[[],[],[]]]]=>2
[2,2,3,4,1,6]=>[[],[[],[[[]]]]]=>2
[2,2,3,4,6,1]=>[[],[[],[[],[]]]]=>2
[2,2,3,6,1,4]=>[[],[[[],[[]]]]]=>2
[2,2,3,6,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,4,1,3,6]=>[[],[[[]],[[]]]]=>2
[2,2,4,1,6,3]=>[[],[[[],[[]]]]]=>2
[2,2,4,3,1,6]=>[[],[[[[],[]]]]]=>2
[2,2,4,3,6,1]=>[[],[[[]],[[]]]]=>2
[2,2,4,6,1,3]=>[[],[[],[],[],[]]]=>2
[2,2,4,6,3,1]=>[[],[[],[[[]]]]]=>2
[2,2,6,1,3,4]=>[[],[[[],[[]]]]]=>2
[2,2,6,1,4,3]=>[[],[[[[[]]]]]]=>2
[2,2,6,3,1,4]=>[[],[[],[[[]]]]]=>2
[2,2,6,3,4,1]=>[[],[[],[],[[]]]]=>2
[2,2,6,4,1,3]=>[[],[[[]],[[]]]]=>2
[2,2,6,4,3,1]=>[[],[[[],[[]]]]]=>2
[2,3,1,2,4,6]=>[[[],[[],[[]]]]]=>1
[2,3,1,2,6,4]=>[[[],[[[],[]]]]]=>1
[2,3,1,4,2,6]=>[[[[[]],[[]]]]]=>1
[2,3,1,4,6,2]=>[[[[[[],[]]]]]]=>1
[2,3,1,6,2,4]=>[[[[],[[[]]]]]]=>1
[2,3,1,6,4,2]=>[[[[],[],[],[]]]]=>1
[2,3,2,1,4,6]=>[[[[],[[[]]]]]]=>1
[2,3,2,1,6,4]=>[[[[],[[],[]]]]]=>1
[2,3,2,4,1,6]=>[[[[[[[]]]]]]]=>1
[2,3,2,4,6,1]=>[[[[[],[],[]]]]]=>1
[2,3,2,6,1,4]=>[[[[[[[]]]]]]]=>1
[2,3,2,6,4,1]=>[[[[[],[[]]]]]]=>1
[2,3,4,1,2,6]=>[[[],[],[[],[]]]]=>1
[2,3,4,1,6,2]=>[[[],[[[[]]]]]]=>1
[2,3,4,2,1,6]=>[[[],[[],[[]]]]]=>1
[2,3,4,2,6,1]=>[[[],[[[[]]]]]]=>1
[2,3,4,6,1,2]=>[[[],[],[[],[]]]]=>1
[2,3,4,6,2,1]=>[[[],[[[[]]]]]]=>1
[2,3,6,1,2,4]=>[[[],[[],[[]]]]]=>1
[2,3,6,1,4,2]=>[[[[[]],[[]]]]]=>1
[2,3,6,2,1,4]=>[[[[],[],[[]]]]]=>1
[2,3,6,2,4,1]=>[[[[],[[[]]]]]]=>1
[2,3,6,4,1,2]=>[[[],[[[[]]]]]]=>1
[2,3,6,4,2,1]=>[[[[[],[[]]]]]]=>1
[2,4,1,2,3,6]=>[[[[[],[[]]]]]]=>1
[2,4,1,2,6,3]=>[[[[],[],[[]]]]]=>1
[2,4,1,3,2,6]=>[[[],[[[],[]]]]]=>1
[2,4,1,3,6,2]=>[[[[]],[[],[]]]]=>1
[2,4,1,6,2,3]=>[[[[[[[]]]]]]]=>1
[2,4,1,6,3,2]=>[[[[[[],[]]]]]]=>1
[2,4,2,1,3,6]=>[[[[[]]],[[]]]]=>1
[2,4,2,1,6,3]=>[[[[[[],[]]]]]]=>1
[2,4,2,3,1,6]=>[[[[],[],[[]]]]]=>1
[2,4,2,3,6,1]=>[[[],[[[[]]]]]]=>1
[2,4,2,6,1,3]=>[[[],[[]],[[]]]]=>1
[2,4,2,6,3,1]=>[[[[],[[],[]]]]]=>1
[2,4,3,1,2,6]=>[[[[[[[]]]]]]]=>1
[2,4,3,1,6,2]=>[[[[],[[[]]]]]]=>1
[2,4,3,2,1,6]=>[[[[],[],[[]]]]]=>1
[2,4,3,2,6,1]=>[[[[]],[[],[]]]]=>1
[2,4,3,6,1,2]=>[[[[[]]],[[]]]]=>1
[2,4,3,6,2,1]=>[[[[],[[],[]]]]]=>1
[2,4,6,1,2,3]=>[[[],[],[[],[]]]]=>1
[2,4,6,1,3,2]=>[[[],[],[],[[]]]]=>1
[2,4,6,2,1,3]=>[[[],[],[[[]]]]]=>1
[2,4,6,2,3,1]=>[[[],[[[[]]]]]]=>1
[2,4,6,3,1,2]=>[[[],[[[[]]]]]]=>1
[2,4,6,3,2,1]=>[[[],[[[],[]]]]]=>1
[2,6,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[2,6,1,2,4,3]=>[[[[[],[[]]]]]]=>1
[2,6,1,3,2,4]=>[[[[[],[],[]]]]]=>1
[2,6,1,3,4,2]=>[[[[],[[[]]]]]]=>1
[2,6,1,4,2,3]=>[[[[[[[]]]]]]]=>1
[2,6,1,4,3,2]=>[[[[],[[[]]]]]]=>1
[2,6,2,1,3,4]=>[[[[[[[]]]]]]]=>1
[2,6,2,1,4,3]=>[[[[],[[],[]]]]]=>1
[2,6,2,3,1,4]=>[[[[[[],[]]]]]]=>1
[2,6,2,3,4,1]=>[[[],[[],[[]]]]]=>1
[2,6,2,4,1,3]=>[[[],[[],[[]]]]]=>1
[2,6,2,4,3,1]=>[[[[[[[]]]]]]]=>1
[2,6,3,1,2,4]=>[[[],[[[[]]]]]]=>1
[2,6,3,1,4,2]=>[[[],[[[],[]]]]]=>1
[2,6,3,2,1,4]=>[[[],[[],[[]]]]]=>1
[2,6,3,2,4,1]=>[[[],[[]],[[]]]]=>1
[2,6,3,4,1,2]=>[[[],[],[[],[]]]]=>1
[2,6,3,4,2,1]=>[[[],[[[[]]]]]]=>1
[2,6,4,1,2,3]=>[[[],[[],[[]]]]]=>1
[2,6,4,1,3,2]=>[[[],[[[[]]]]]]=>1
[2,6,4,2,1,3]=>[[[[[[],[]]]]]]=>1
[2,6,4,2,3,1]=>[[[[[],[],[]]]]]=>1
[2,6,4,3,1,2]=>[[[[],[[[]]]]]]=>1
[2,6,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[3,1,2,2,4,6]=>[[[]],[[],[[]]]]=>2
[3,1,2,2,6,4]=>[[[]],[[[],[]]]]=>2
[3,1,2,4,2,6]=>[[[[[]]],[[]]]]=>1
[3,1,2,4,6,2]=>[[[[[]],[[]]]]]=>1
[3,1,2,6,2,4]=>[[[[[[[]]]]]]]=>1
[3,1,2,6,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,4,2,2,6]=>[[[]],[[],[[]]]]=>2
[3,1,4,2,6,2]=>[[[],[[[],[]]]]]=>1
[3,1,4,6,2,2]=>[[],[[],[[[]]]]]=>2
[3,1,6,2,2,4]=>[[[]],[[[],[]]]]=>2
[3,1,6,2,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,6,4,2,2]=>[[],[[],[],[],[]]]=>2
[3,2,1,2,4,6]=>[[[],[[],[[]]]]]=>1
[3,2,1,2,6,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,2,6]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,6,2]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,2,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,4,2]=>[[[],[[],[],[]]]]=>1
[3,2,2,1,4,6]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,6,4]=>[[],[[],[[],[]]]]=>2
[3,2,2,4,1,6]=>[[],[[[[[]]]]]]=>2
[3,2,2,4,6,1]=>[[],[[],[],[[]]]]=>2
[3,2,2,6,1,4]=>[[],[[[[[]]]]]]=>2
[3,2,2,6,4,1]=>[[],[[[]],[[]]]]=>2
[3,2,4,1,2,6]=>[[[[[]],[[]]]]]=>1
[3,2,4,1,6,2]=>[[[[[[[]]]]]]]=>1
[3,2,4,2,1,6]=>[[[],[[],[[]]]]]=>1
[3,2,4,2,6,1]=>[[[[],[[[]]]]]]=>1
[3,2,4,6,1,2]=>[[[[[],[],[]]]]]=>1
[3,2,4,6,2,1]=>[[[],[[[],[]]]]]=>1
[3,2,6,1,2,4]=>[[[[[]],[[]]]]]=>1
[3,2,6,1,4,2]=>[[[[[[[]]]]]]]=>1
[3,2,6,2,1,4]=>[[[[]],[[],[]]]]=>1
[3,2,6,2,4,1]=>[[[[],[[[]]]]]]=>1
[3,2,6,4,1,2]=>[[[[[],[[]]]]]]=>1
[3,2,6,4,2,1]=>[[[[]],[[],[]]]]=>1
[3,4,1,2,2,6]=>[[[],[]],[[],[]]]=>2
[3,4,1,2,6,2]=>[[[],[[],[[]]]]]=>1
[3,4,1,6,2,2]=>[[],[[[[[]]]]]]=>2
[3,4,2,1,2,6]=>[[[[[]]],[[]]]]=>1
[3,4,2,1,6,2]=>[[[[],[[[]]]]]]=>1
[3,4,2,2,1,6]=>[[],[[[],[[]]]]]=>2
[3,4,2,2,6,1]=>[[[[]]],[[[]]]]=>2
[3,4,2,6,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,2,6,2,1]=>[[[[[[[]]]]]]]=>1
[3,4,6,1,2,2]=>[[],[[],[[],[]]]]=>2
[3,4,6,2,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,6,2,2,1]=>[[[[[]]]],[[]]]=>2
[3,6,1,2,2,4]=>[[[]],[[],[[]]]]=>2
[3,6,1,2,4,2]=>[[[[[]],[[]]]]]=>1
[3,6,1,4,2,2]=>[[],[[[],[[]]]]]=>2
[3,6,2,1,2,4]=>[[[],[[[[]]]]]]=>1
[3,6,2,1,4,2]=>[[[],[],[[[]]]]]=>1
[3,6,2,2,1,4]=>[[],[[[],[],[]]]]=>2
[3,6,2,2,4,1]=>[[[[]]],[[],[]]]=>2
[3,6,2,4,1,2]=>[[[],[[[[]]]]]]=>1
[3,6,2,4,2,1]=>[[[],[[[[]]]]]]=>1
[3,6,4,1,2,2]=>[[],[[[[[]]]]]]=>2
[3,6,4,2,1,2]=>[[[[],[[[]]]]]]=>1
[3,6,4,2,2,1]=>[[],[[[],[[]]]]]=>2
[4,1,2,2,3,6]=>[[],[[[]],[[]]]]=>2
[4,1,2,2,6,3]=>[[[]],[[],[],[]]]=>2
[4,1,2,3,2,6]=>[[[],[[[],[]]]]]=>1
[4,1,2,3,6,2]=>[[[[],[[],[]]]]]=>1
[4,1,2,6,2,3]=>[[[],[[[],[]]]]]=>1
[4,1,2,6,3,2]=>[[[],[[]],[[]]]]=>1
[4,1,3,2,2,6]=>[[],[[],[[[]]]]]=>2
[4,1,3,2,6,2]=>[[[],[[[[]]]]]]=>1
[4,1,3,6,2,2]=>[[],[[],[[[]]]]]=>2
[4,1,6,2,2,3]=>[[[]],[[[[]]]]]=>2
[4,1,6,2,3,2]=>[[[[[[[]]]]]]]=>1
[4,1,6,3,2,2]=>[[[]],[[[],[]]]]=>2
[4,2,1,2,3,6]=>[[[[],[[[]]]]]]=>1
[4,2,1,2,6,3]=>[[[[[]],[[]]]]]=>1
[4,2,1,3,2,6]=>[[[[[],[[]]]]]]=>1
[4,2,1,3,6,2]=>[[[[[]],[[]]]]]=>1
[4,2,1,6,2,3]=>[[[],[[[[]]]]]]=>1
[4,2,1,6,3,2]=>[[[],[[],[[]]]]]=>1
[4,2,2,1,3,6]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,6,3]=>[[],[[[[],[]]]]]=>2
[4,2,2,3,1,6]=>[[],[[[],[],[]]]]=>2
[4,2,2,3,6,1]=>[[[[[]]]],[[]]]=>2
[4,2,2,6,1,3]=>[[],[[[],[[]]]]]=>2
[4,2,2,6,3,1]=>[[],[[],[[],[]]]]=>2
[4,2,3,1,2,6]=>[[[],[[],[[]]]]]=>1
[4,2,3,1,6,2]=>[[[],[[]],[[]]]]=>1
[4,2,3,2,1,6]=>[[[],[[],[[]]]]]=>1
[4,2,3,2,6,1]=>[[[[[[[]]]]]]]=>1
[4,2,3,6,1,2]=>[[[[[[],[]]]]]]=>1
[4,2,3,6,2,1]=>[[[[[],[[]]]]]]=>1
[4,2,6,1,2,3]=>[[[[],[[[]]]]]]=>1
[4,2,6,1,3,2]=>[[[[[],[[]]]]]]=>1
[4,2,6,2,1,3]=>[[[[[[[]]]]]]]=>1
[4,2,6,2,3,1]=>[[[],[[[[]]]]]]=>1
[4,2,6,3,1,2]=>[[[[]],[[],[]]]]=>1
[4,2,6,3,2,1]=>[[[[],[[],[]]]]]=>1
[4,3,1,2,2,6]=>[[[[]]],[[[]]]]=>2
[4,3,1,2,6,2]=>[[[[[[[]]]]]]]=>1
[4,3,1,6,2,2]=>[[[[],[]]],[[]]]=>2
[4,3,2,1,2,6]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,6,2]=>[[[],[],[[[]]]]]=>1
[4,3,2,2,1,6]=>[[],[[],[],[[]]]]=>2
[4,3,2,2,6,1]=>[[],[[[[],[]]]]]=>2
[4,3,2,6,1,2]=>[[[],[[[[]]]]]]=>1
[4,3,2,6,2,1]=>[[[],[],[[[]]]]]=>1
[4,3,6,1,2,2]=>[[[[[]]]],[[]]]=>2
[4,3,6,2,1,2]=>[[[[]],[[],[]]]]=>1
[4,3,6,2,2,1]=>[[[],[]],[[],[]]]=>2
[4,6,1,2,2,3]=>[[],[[],[[],[]]]]=>2
[4,6,1,2,3,2]=>[[[],[[],[[]]]]]=>1
[4,6,1,3,2,2]=>[[],[[[],[],[]]]]=>2
[4,6,2,1,2,3]=>[[[[[[],[]]]]]]=>1
[4,6,2,1,3,2]=>[[[],[[],[[]]]]]=>1
[4,6,2,2,1,3]=>[[[]],[[[],[]]]]=>2
[4,6,2,2,3,1]=>[[[[]]],[[[]]]]=>2
[4,6,2,3,1,2]=>[[[[[],[[]]]]]]=>1
[4,6,2,3,2,1]=>[[[[[[],[]]]]]]=>1
[4,6,3,1,2,2]=>[[],[[[[[]]]]]]=>2
[4,6,3,2,1,2]=>[[[[[],[[]]]]]]=>1
[4,6,3,2,2,1]=>[[[[]]],[[],[]]]=>2
[6,1,2,2,3,4]=>[[],[[],[],[[]]]]=>2
[6,1,2,2,4,3]=>[[[]],[[],[[]]]]=>2
[6,1,2,3,2,4]=>[[[],[[[],[]]]]]=>1
[6,1,2,3,4,2]=>[[[[],[],[[]]]]]=>1
[6,1,2,4,2,3]=>[[[],[[[],[]]]]]=>1
[6,1,2,4,3,2]=>[[[[]],[[],[]]]]=>1
[6,1,3,2,2,4]=>[[],[[],[],[[]]]]=>2
[6,1,3,2,4,2]=>[[[],[],[[[]]]]]=>1
[6,1,3,4,2,2]=>[[],[[[[],[]]]]]=>2
[6,1,4,2,2,3]=>[[[]],[[[[]]]]]=>2
[6,1,4,2,3,2]=>[[[[[[[]]]]]]]=>1
[6,1,4,3,2,2]=>[[],[[],[[[]]]]]=>2
[6,2,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[6,2,1,2,4,3]=>[[[[],[[[]]]]]]=>1
[6,2,1,3,2,4]=>[[[[],[[],[]]]]]=>1
[6,2,1,3,4,2]=>[[[[[[[]]]]]]]=>1
[6,2,1,4,2,3]=>[[[],[[[[]]]]]]=>1
[6,2,1,4,3,2]=>[[[],[[],[],[]]]]=>1
[6,2,2,1,3,4]=>[[[]],[[[[]]]]]=>2
[6,2,2,1,4,3]=>[[],[[],[[],[]]]]=>2
[6,2,2,3,1,4]=>[[],[[[[],[]]]]]=>2
[6,2,2,3,4,1]=>[[[]],[[],[[]]]]=>2
[6,2,2,4,1,3]=>[[[]],[[],[[]]]]=>2
[6,2,2,4,3,1]=>[[[[[]]]],[[]]]=>2
[6,2,3,1,2,4]=>[[[[[]],[[]]]]]=>1
[6,2,3,1,4,2]=>[[[],[[],[[]]]]]=>1
[6,2,3,2,1,4]=>[[[],[[],[[]]]]]=>1
[6,2,3,2,4,1]=>[[[[[[[]]]]]]]=>1
[6,2,3,4,1,2]=>[[[[],[],[[]]]]]=>1
[6,2,3,4,2,1]=>[[[[],[[[]]]]]]=>1
[6,2,4,1,2,3]=>[[[[[[],[]]]]]]=>1
[6,2,4,1,3,2]=>[[[[[],[[]]]]]]=>1
[6,2,4,2,1,3]=>[[[[[],[[]]]]]]=>1
[6,2,4,2,3,1]=>[[[[[],[[]]]]]]=>1
[6,2,4,3,1,2]=>[[[[[[[]]]]]]]=>1
[6,2,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[6,3,1,2,2,4]=>[[[[[]]]],[[]]]=>2
[6,3,1,2,4,2]=>[[[[[[],[]]]]]]=>1
[6,3,1,4,2,2]=>[[],[[],[[[]]]]]=>2
[6,3,2,1,2,4]=>[[[[],[[[]]]]]]=>1
[6,3,2,1,4,2]=>[[[[[[],[]]]]]]=>1
[6,3,2,2,1,4]=>[[[]],[[],[[]]]]=>2
[6,3,2,2,4,1]=>[[],[[[],[[]]]]]=>2
[6,3,2,4,1,2]=>[[[[[]]],[[]]]]=>1
[6,3,2,4,2,1]=>[[[[],[[[]]]]]]=>1
[6,3,4,1,2,2]=>[[],[[],[[],[]]]]=>2
[6,3,4,2,1,2]=>[[[[[],[[]]]]]]=>1
[6,3,4,2,2,1]=>[[[]],[[[[]]]]]=>2
[6,4,1,2,2,3]=>[[[]],[[],[[]]]]=>2
[6,4,1,2,3,2]=>[[[[[],[[]]]]]]=>1
[6,4,1,3,2,2]=>[[[]],[[[[]]]]]=>2
[6,4,2,1,2,3]=>[[[],[[],[[]]]]]=>1
[6,4,2,1,3,2]=>[[[],[[],[[]]]]]=>1
[6,4,2,2,1,3]=>[[],[[[[],[]]]]]=>2
[6,4,2,2,3,1]=>[[],[[[],[],[]]]]=>2
[6,4,2,3,1,2]=>[[[],[],[[],[]]]]=>1
[6,4,2,3,2,1]=>[[[],[[],[[]]]]]=>1
[6,4,3,1,2,2]=>[[[[],[]]],[[]]]=>2
[6,4,3,2,1,2]=>[[[[[],[],[]]]]]=>1
[6,4,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,2,3,5,5]=>[[],[],[[[],[]]]]=>3
[1,2,2,5,3,5]=>[[[]],[[[[]]]]]=>2
[1,2,2,5,5,3]=>[[[]],[[]],[[]]]=>3
[1,2,3,2,5,5]=>[[[]],[[[],[]]]]=>2
[1,2,3,5,2,5]=>[[[],[[[[]]]]]]=>1
[1,2,3,5,5,2]=>[[[[],[]]],[[]]]=>2
[1,2,5,2,3,5]=>[[[[]],[[[]]]]]=>1
[1,2,5,2,5,3]=>[[[[[]],[[]]]]]=>1
[1,2,5,3,2,5]=>[[[[[]],[[]]]]]=>1
[1,2,5,3,5,2]=>[[[[[[[]]]]]]]=>1
[1,2,5,5,2,3]=>[[[]],[[[],[]]]]=>2
[1,2,5,5,3,2]=>[[[[]]],[[[]]]]=>2
[1,3,2,2,5,5]=>[[],[[]],[[[]]]]=>3
[1,3,2,5,2,5]=>[[[[[]],[[]]]]]=>1
[1,3,2,5,5,2]=>[[[]],[[[[]]]]]=>2
[1,3,5,2,2,5]=>[[[]],[[[],[]]]]=>2
[1,3,5,2,5,2]=>[[[],[[],[[]]]]]=>1
[1,3,5,5,2,2]=>[[],[[]],[[],[]]]=>3
[1,5,2,2,3,5]=>[[[[]]],[[],[]]]=>2
[1,5,2,2,5,3]=>[[[[]]],[[],[]]]=>2
[1,5,2,3,2,5]=>[[[],[[[[]]]]]]=>1
[1,5,2,3,5,2]=>[[[],[],[[[]]]]]=>1
[1,5,2,5,2,3]=>[[[],[[]],[[]]]]=>1
[1,5,2,5,3,2]=>[[[],[[[[]]]]]]=>1
[1,5,3,2,2,5]=>[[[[[]]]],[[]]]=>2
[1,5,3,2,5,2]=>[[[[[]]],[[]]]]=>1
[1,5,3,5,2,2]=>[[],[[],[[[]]]]]=>2
[1,5,5,2,2,3]=>[[],[[]],[[],[]]]=>3
[1,5,5,2,3,2]=>[[],[[],[[[]]]]]=>2
[1,5,5,3,2,2]=>[[],[[]],[[[]]]]=>3
[2,1,2,3,5,5]=>[[[[],[]]],[[]]]=>2
[2,1,2,5,3,5]=>[[[[[[[]]]]]]]=>1
[2,1,2,5,5,3]=>[[[[]]],[[[]]]]=>2
[2,1,3,2,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,3,5,2,5]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,5,2]=>[[[[]]],[[],[]]]=>2
[2,1,5,2,3,5]=>[[[[[[],[]]]]]]=>1
[2,1,5,2,5,3]=>[[[[[[],[]]]]]]=>1
[2,1,5,3,2,5]=>[[[[[]]],[[]]]]=>1
[2,1,5,3,5,2]=>[[[[],[[[]]]]]]=>1
[2,1,5,5,2,3]=>[[],[[],[[[]]]]]=>2
[2,1,5,5,3,2]=>[[],[[[],[[]]]]]=>2
[2,2,1,3,5,5]=>[[],[[]],[[],[]]]=>3
[2,2,1,5,3,5]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,5,3]=>[[],[[]],[[[]]]]=>3
[2,2,3,1,5,5]=>[[],[],[[[[]]]]]=>3
[2,2,3,5,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,3,5,5,1]=>[[],[[[]]],[[]]]=>3
[2,2,5,1,3,5]=>[[],[[],[[],[]]]]=>2
[2,2,5,1,5,3]=>[[],[[],[[[]]]]]=>2
[2,2,5,3,1,5]=>[[],[[[],[[]]]]]=>2
[2,2,5,3,5,1]=>[[],[[],[[[]]]]]=>2
[2,2,5,5,1,3]=>[[],[],[[],[[]]]]=>3
[2,2,5,5,3,1]=>[[],[[]],[[],[]]]=>3
[2,3,1,2,5,5]=>[[],[[[],[[]]]]]=>2
[2,3,1,5,2,5]=>[[[[[],[[]]]]]]=>1
[2,3,1,5,5,2]=>[[[[]]],[[],[]]]=>2
[2,3,2,1,5,5]=>[[[]],[[],[[]]]]=>2
[2,3,2,5,1,5]=>[[[[[[],[]]]]]]=>1
[2,3,2,5,5,1]=>[[],[[],[[[]]]]]=>2
[2,3,5,1,2,5]=>[[[],[[],[[]]]]]=>1
[2,3,5,1,5,2]=>[[[[[[],[]]]]]]=>1
[2,3,5,2,1,5]=>[[[[[],[[]]]]]]=>1
[2,3,5,2,5,1]=>[[[[[[],[]]]]]]=>1
[2,3,5,5,1,2]=>[[[]],[[[],[]]]]=>2
[2,3,5,5,2,1]=>[[[[]]],[[[]]]]=>2
[2,5,1,2,3,5]=>[[[],[[],[[]]]]]=>1
[2,5,1,2,5,3]=>[[[],[[]],[[]]]]=>1
[2,5,1,3,2,5]=>[[[],[],[[[]]]]]=>1
[2,5,1,3,5,2]=>[[[],[[],[[]]]]]=>1
[2,5,1,5,2,3]=>[[[],[[],[[]]]]]=>1
[2,5,1,5,3,2]=>[[[],[[[[]]]]]]=>1
[2,5,2,1,3,5]=>[[[[[],[[]]]]]]=>1
[2,5,2,1,5,3]=>[[[[],[[[]]]]]]=>1
[2,5,2,3,1,5]=>[[[[[[],[]]]]]]=>1
[2,5,2,3,5,1]=>[[[],[[[[]]]]]]=>1
[2,5,2,5,1,3]=>[[[],[[]],[[]]]]=>1
[2,5,2,5,3,1]=>[[[],[[],[[]]]]]=>1
[2,5,3,1,2,5]=>[[[],[[[],[]]]]]=>1
[2,5,3,1,5,2]=>[[[[],[[],[]]]]]=>1
[2,5,3,2,1,5]=>[[[[],[[[]]]]]]=>1
[2,5,3,2,5,1]=>[[[],[[]],[[]]]]=>1
[2,5,3,5,1,2]=>[[[[]],[[[]]]]]=>1
[2,5,3,5,2,1]=>[[[[[[[]]]]]]]=>1
[2,5,5,1,2,3]=>[[],[[],[[],[]]]]=>2
[2,5,5,1,3,2]=>[[],[[],[[[]]]]]=>2
[2,5,5,2,1,3]=>[[[]],[[[[]]]]]=>2
[2,5,5,2,3,1]=>[[[]],[[[[]]]]]=>2
[2,5,5,3,1,2]=>[[[]],[[],[[]]]]=>2
[2,5,5,3,2,1]=>[[],[[[],[[]]]]]=>2
[3,1,2,2,5,5]=>[[],[[]],[[[]]]]=>3
[3,1,2,5,2,5]=>[[[[[],[[]]]]]]=>1
[3,1,2,5,5,2]=>[[[[[]]]],[[]]]=>2
[3,1,5,2,2,5]=>[[[]],[[],[[]]]]=>2
[3,1,5,2,5,2]=>[[[[[],[],[]]]]]=>1
[3,1,5,5,2,2]=>[[],[],[[],[[]]]]=>3
[3,2,1,2,5,5]=>[[[[]]],[[],[]]]=>2
[3,2,1,5,2,5]=>[[[],[[[],[]]]]]=>1
[3,2,1,5,5,2]=>[[],[[],[[],[]]]]=>2
[3,2,2,1,5,5]=>[[],[[]],[[],[]]]=>3
[3,2,2,5,1,5]=>[[],[[],[[[]]]]]=>2
[3,2,2,5,5,1]=>[[],[],[[],[[]]]]=>3
[3,2,5,1,2,5]=>[[[[],[],[[]]]]]=>1
[3,2,5,1,5,2]=>[[[[],[[],[]]]]]=>1
[3,2,5,2,1,5]=>[[[[]],[[],[]]]]=>1
[3,2,5,2,5,1]=>[[[[],[],[[]]]]]=>1
[3,2,5,5,1,2]=>[[],[[],[[[]]]]]=>2
[3,2,5,5,2,1]=>[[[]],[[[],[]]]]=>2
[3,5,1,2,2,5]=>[[[]],[[],[[]]]]=>2
[3,5,1,2,5,2]=>[[[[[]],[[]]]]]=>1
[3,5,1,5,2,2]=>[[],[[],[[[]]]]]=>2
[3,5,2,1,2,5]=>[[[[[[[]]]]]]]=>1
[3,5,2,1,5,2]=>[[[[[],[],[]]]]]=>1
[3,5,2,2,1,5]=>[[],[[[],[[]]]]]=>2
[3,5,2,2,5,1]=>[[[[]]],[[],[]]]=>2
[3,5,2,5,1,2]=>[[[[[],[[]]]]]]=>1
[3,5,2,5,2,1]=>[[[[[],[[]]]]]]=>1
[3,5,5,1,2,2]=>[[],[[[]]],[[]]]=>3
[3,5,5,2,1,2]=>[[[]],[[[[]]]]]=>2
[3,5,5,2,2,1]=>[[[]],[[]],[[]]]=>3
[5,1,2,2,3,5]=>[[],[[[]],[[]]]]=>2
[5,1,2,2,5,3]=>[[[]],[[],[[]]]]=>2
[5,1,2,3,2,5]=>[[[],[[[],[]]]]]=>1
[5,1,2,3,5,2]=>[[[[],[[[]]]]]]=>1
[5,1,2,5,2,3]=>[[[],[[[],[]]]]]=>1
[5,1,2,5,3,2]=>[[[[]],[[[]]]]]=>1
[5,1,3,2,2,5]=>[[],[[],[[[]]]]]=>2
[5,1,3,2,5,2]=>[[[],[[[[]]]]]]=>1
[5,1,3,5,2,2]=>[[],[[[],[[]]]]]=>2
[5,1,5,2,2,3]=>[[[]],[[],[[]]]]=>2
[5,1,5,2,3,2]=>[[[[],[[[]]]]]]=>1
[5,1,5,3,2,2]=>[[[[]]],[[[]]]]=>2
[5,2,1,2,3,5]=>[[[[],[[[]]]]]]=>1
[5,2,1,2,5,3]=>[[[[[[[]]]]]]]=>1
[5,2,1,3,2,5]=>[[[[[],[[]]]]]]=>1
[5,2,1,3,5,2]=>[[[[]],[[],[]]]]=>1
[5,2,1,5,2,3]=>[[[],[],[[[]]]]]=>1
[5,2,1,5,3,2]=>[[[],[[],[[]]]]]=>1
[5,2,2,1,3,5]=>[[],[[[],[[]]]]]=>2
[5,2,2,1,5,3]=>[[],[[[[],[]]]]]=>2
[5,2,2,3,1,5]=>[[],[[[[],[]]]]]=>2
[5,2,2,3,5,1]=>[[[[[]]]],[[]]]=>2
[5,2,2,5,1,3]=>[[[]],[[],[[]]]]=>2
[5,2,2,5,3,1]=>[[],[[[],[[]]]]]=>2
[5,2,3,1,2,5]=>[[[[[],[[]]]]]]=>1
[5,2,3,1,5,2]=>[[[],[],[[[]]]]]=>1
[5,2,3,2,1,5]=>[[[],[[],[[]]]]]=>1
[5,2,3,2,5,1]=>[[[[],[[[]]]]]]=>1
[5,2,3,5,1,2]=>[[[[],[[[]]]]]]=>1
[5,2,3,5,2,1]=>[[[[[]]],[[]]]]=>1
[5,2,5,1,2,3]=>[[[[],[[],[]]]]]=>1
[5,2,5,1,3,2]=>[[[[],[[[]]]]]]=>1
[5,2,5,2,1,3]=>[[[[]],[[[]]]]]=>1
[5,2,5,2,3,1]=>[[[[[]]],[[]]]]=>1
[5,2,5,3,1,2]=>[[[[[]],[[]]]]]=>1
[5,2,5,3,2,1]=>[[[[[]],[[]]]]]=>1
[5,3,1,2,2,5]=>[[[[],[]]],[[]]]=>2
[5,3,1,2,5,2]=>[[[],[[[[]]]]]]=>1
[5,3,1,5,2,2]=>[[],[[],[[],[]]]]=>2
[5,3,2,1,2,5]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,5,2]=>[[[[],[[],[]]]]]=>1
[5,3,2,2,1,5]=>[[],[[],[[[]]]]]=>2
[5,3,2,2,5,1]=>[[],[[[]],[[]]]]=>2
[5,3,2,5,1,2]=>[[[[],[[[]]]]]]=>1
[5,3,2,5,2,1]=>[[[[],[[[]]]]]]=>1
[5,3,5,1,2,2]=>[[],[[[[[]]]]]]=>2
[5,3,5,2,1,2]=>[[[[[[[]]]]]]]=>1
[5,3,5,2,2,1]=>[[[[]]],[[[]]]]=>2
[5,5,1,2,2,3]=>[[],[],[[],[[]]]]=>3
[5,5,1,2,3,2]=>[[],[[[],[[]]]]]=>2
[5,5,1,3,2,2]=>[[],[],[[[[]]]]]=>3
[5,5,2,1,2,3]=>[[],[[[],[[]]]]]=>2
[5,5,2,1,3,2]=>[[],[[[[],[]]]]]=>2
[5,5,2,2,1,3]=>[[],[[]],[[[]]]]=>3
[5,5,2,2,3,1]=>[[],[[[]]],[[]]]=>3
[5,5,2,3,1,2]=>[[],[[[[],[]]]]]=>2
[5,5,2,3,2,1]=>[[],[[[],[[]]]]]=>2
[5,5,3,1,2,2]=>[[],[],[[[],[]]]]=>3
[5,5,3,2,1,2]=>[[],[[[[],[]]]]]=>2
[5,5,3,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,3,5,6]=>[[],[[],[],[[]]]]=>2
[1,2,2,3,6,5]=>[[],[[],[[[]]]]]=>2
[1,2,2,5,3,6]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,6,3]=>[[],[[[],[[]]]]]=>2
[1,2,2,6,3,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,6,5,3]=>[[[]],[[[[]]]]]=>2
[1,2,3,2,5,6]=>[[[],[[]],[[]]]]=>1
[1,2,3,2,6,5]=>[[[],[[],[[]]]]]=>1
[1,2,3,5,2,6]=>[[[],[[[],[]]]]]=>1
[1,2,3,5,6,2]=>[[[],[[]],[[]]]]=>1
[1,2,3,6,2,5]=>[[[],[[],[],[]]]]=>1
[1,2,3,6,5,2]=>[[[],[[[[]]]]]]=>1
[1,2,5,2,3,6]=>[[[[]],[[],[]]]]=>1
[1,2,5,2,6,3]=>[[[[[],[],[]]]]]=>1
[1,2,5,3,2,6]=>[[[[[[[]]]]]]]=>1
[1,2,5,3,6,2]=>[[[[],[],[[]]]]]=>1
[1,2,5,6,2,3]=>[[[],[],[[],[]]]]=>1
[1,2,5,6,3,2]=>[[[[]],[[[]]]]]=>1
[1,2,6,2,3,5]=>[[[[]],[[[]]]]]=>1
[1,2,6,2,5,3]=>[[[[[],[[]]]]]]=>1
[1,2,6,3,2,5]=>[[[[],[[[]]]]]]=>1
[1,2,6,3,5,2]=>[[[[],[],[[]]]]]=>1
[1,2,6,5,2,3]=>[[[[]],[[],[]]]]=>1
[1,2,6,5,3,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,2,5,6]=>[[],[[[[[]]]]]]=>2
[1,3,2,2,6,5]=>[[],[[[],[[]]]]]=>2
[1,3,2,5,2,6]=>[[[[[],[[]]]]]]=>1
[1,3,2,5,6,2]=>[[[[[],[[]]]]]]=>1
[1,3,2,6,2,5]=>[[[[[],[[]]]]]]=>1
[1,3,2,6,5,2]=>[[[[],[[],[]]]]]=>1
[1,3,5,2,2,6]=>[[],[[],[[],[]]]]=>2
[1,3,5,2,6,2]=>[[[],[[],[[]]]]]=>1
[1,3,5,6,2,2]=>[[],[[[[],[]]]]]=>2
[1,3,6,2,2,5]=>[[],[[],[],[[]]]]=>2
[1,3,6,2,5,2]=>[[[[],[],[[]]]]]=>1
[1,3,6,5,2,2]=>[[[]],[[[[]]]]]=>2
[1,5,2,2,3,6]=>[[[[]]],[[],[]]]=>2
[1,5,2,2,6,3]=>[[],[[],[],[],[]]]=>2
[1,5,2,3,2,6]=>[[[],[],[[[]]]]]=>1
[1,5,2,3,6,2]=>[[[],[[[],[]]]]]=>1
[1,5,2,6,2,3]=>[[[],[],[[[]]]]]=>1
[1,5,2,6,3,2]=>[[[],[],[],[[]]]]=>1
[1,5,3,2,2,6]=>[[[]],[[],[[]]]]=>2
[1,5,3,2,6,2]=>[[[[[]]],[[]]]]=>1
[1,5,3,6,2,2]=>[[],[[[]],[[]]]]=>2
[1,5,6,2,2,3]=>[[[]],[[],[[]]]]=>2
[1,5,6,2,3,2]=>[[[[[],[[]]]]]]=>1
[1,5,6,3,2,2]=>[[],[[[],[[]]]]]=>2
[1,6,2,2,3,5]=>[[[[]]],[[[]]]]=>2
[1,6,2,2,5,3]=>[[],[[],[[],[]]]]=>2
[1,6,2,3,2,5]=>[[[[],[[[]]]]]]=>1
[1,6,2,3,5,2]=>[[[[[[[]]]]]]]=>1
[1,6,2,5,2,3]=>[[[[],[[[]]]]]]=>1
[1,6,2,5,3,2]=>[[[[]],[[],[]]]]=>1
[1,6,3,2,2,5]=>[[[[[]]]],[[]]]=>2
[1,6,3,2,5,2]=>[[[[[],[[]]]]]]=>1
[1,6,3,5,2,2]=>[[],[[],[[[]]]]]=>2
[1,6,5,2,2,3]=>[[[[]]],[[[]]]]=>2
[1,6,5,2,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,5,3,2,2]=>[[[],[]],[[],[]]]=>2
[2,1,2,3,5,6]=>[[[[],[],[[]]]]]=>1
[2,1,2,3,6,5]=>[[[],[[[],[]]]]]=>1
[2,1,2,5,3,6]=>[[[[[]],[[]]]]]=>1
[2,1,2,5,6,3]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,3,5]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,5,3]=>[[[],[[[[]]]]]]=>1
[2,1,3,2,5,6]=>[[[[[]]],[[]]]]=>1
[2,1,3,2,6,5]=>[[[],[[]],[[]]]]=>1
[2,1,3,5,2,6]=>[[[[],[[],[]]]]]=>1
[2,1,3,5,6,2]=>[[[[[[],[]]]]]]=>1
[2,1,3,6,2,5]=>[[[[],[],[[]]]]]=>1
[2,1,3,6,5,2]=>[[[[[]]],[[]]]]=>1
[2,1,5,2,3,6]=>[[[[[[],[]]]]]]=>1
[2,1,5,2,6,3]=>[[[[],[],[],[]]]]=>1
[2,1,5,3,2,6]=>[[[],[[],[[]]]]]=>1
[2,1,5,3,6,2]=>[[[[[]],[[]]]]]=>1
[2,1,5,6,2,3]=>[[[[[]],[[]]]]]=>1
[2,1,5,6,3,2]=>[[[],[[],[[]]]]]=>1
[2,1,6,2,3,5]=>[[[[[[[]]]]]]]=>1
[2,1,6,2,5,3]=>[[[[],[[],[]]]]]=>1
[2,1,6,3,2,5]=>[[[[[]]],[[]]]]=>1
[2,1,6,3,5,2]=>[[[[],[[[]]]]]]=>1
[2,1,6,5,2,3]=>[[[],[[[[]]]]]]=>1
[2,1,6,5,3,2]=>[[[],[],[[],[]]]]=>1
[2,2,1,3,5,6]=>[[],[[[[],[]]]]]=>2
[2,2,1,3,6,5]=>[[],[[],[[[]]]]]=>2
[2,2,1,5,3,6]=>[[],[[[[[]]]]]]=>2
[2,2,1,5,6,3]=>[[],[[[],[[]]]]]=>2
[2,2,1,6,3,5]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,5,3]=>[[],[[],[[],[]]]]=>2
[2,2,3,1,5,6]=>[[],[[],[[[]]]]]=>2
[2,2,3,1,6,5]=>[[],[[[],[[]]]]]=>2
[2,2,3,5,1,6]=>[[],[[[[[]]]]]]=>2
[2,2,3,5,6,1]=>[[],[[],[[],[]]]]=>2
[2,2,3,6,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,3,6,5,1]=>[[],[[[],[[]]]]]=>2
[2,2,5,1,3,6]=>[[],[[],[],[[]]]]=>2
[2,2,5,1,6,3]=>[[],[[],[[[]]]]]=>2
[2,2,5,3,1,6]=>[[],[[[],[],[]]]]=>2
[2,2,5,3,6,1]=>[[],[[[]],[[]]]]=>2
[2,2,5,6,1,3]=>[[],[[[[],[]]]]]=>2
[2,2,5,6,3,1]=>[[],[[[[[]]]]]]=>2
[2,2,6,1,3,5]=>[[],[[[],[],[]]]]=>2
[2,2,6,1,5,3]=>[[],[[[]],[[]]]]=>2
[2,2,6,3,1,5]=>[[],[[],[],[[]]]]=>2
[2,2,6,3,5,1]=>[[],[[],[[[]]]]]=>2
[2,2,6,5,1,3]=>[[],[[[[[]]]]]]=>2
[2,2,6,5,3,1]=>[[],[[[],[[]]]]]=>2
[2,3,1,2,5,6]=>[[[],[],[[[]]]]]=>1
[2,3,1,2,6,5]=>[[[],[[[[]]]]]]=>1
[2,3,1,5,2,6]=>[[[[[],[],[]]]]]=>1
[2,3,1,5,6,2]=>[[[[]],[[[]]]]]=>1
[2,3,1,6,2,5]=>[[[[],[[],[]]]]]=>1
[2,3,1,6,5,2]=>[[[[],[[[]]]]]]=>1
[2,3,2,1,5,6]=>[[[[]],[[],[]]]]=>1
[2,3,2,1,6,5]=>[[[[],[],[[]]]]]=>1
[2,3,2,5,1,6]=>[[[[[[],[]]]]]]=>1
[2,3,2,5,6,1]=>[[[[[]]],[[]]]]=>1
[2,3,2,6,1,5]=>[[[[[],[[]]]]]]=>1
[2,3,2,6,5,1]=>[[[[[]],[[]]]]]=>1
[2,3,5,1,2,6]=>[[[[[]]],[[]]]]=>1
[2,3,5,1,6,2]=>[[[[[],[[]]]]]]=>1
[2,3,5,2,1,6]=>[[[[[[[]]]]]]]=>1
[2,3,5,2,6,1]=>[[[[],[[],[]]]]]=>1
[2,3,5,6,1,2]=>[[[],[],[[],[]]]]=>1
[2,3,5,6,2,1]=>[[[[]],[[[]]]]]=>1
[2,3,6,1,2,5]=>[[[[]],[[],[]]]]=>1
[2,3,6,1,5,2]=>[[[[[[],[]]]]]]=>1
[2,3,6,2,1,5]=>[[[[],[[[]]]]]]=>1
[2,3,6,2,5,1]=>[[[[],[],[],[]]]]=>1
[2,3,6,5,1,2]=>[[[[]],[[],[]]]]=>1
[2,3,6,5,2,1]=>[[[[[[],[]]]]]]=>1
[2,5,1,2,3,6]=>[[[],[],[[],[]]]]=>1
[2,5,1,2,6,3]=>[[[],[[[],[]]]]]=>1
[2,5,1,3,2,6]=>[[[],[[[[]]]]]]=>1
[2,5,1,3,6,2]=>[[[],[],[],[[]]]]=>1
[2,5,1,6,2,3]=>[[[],[[]],[[]]]]=>1
[2,5,1,6,3,2]=>[[[],[[[[]]]]]]=>1
[2,5,2,1,3,6]=>[[[[]],[[[]]]]]=>1
[2,5,2,1,6,3]=>[[[[[],[[]]]]]]=>1
[2,5,2,3,1,6]=>[[[[[],[[]]]]]]=>1
[2,5,2,3,6,1]=>[[[[[]]],[[]]]]=>1
[2,5,2,6,1,3]=>[[[[],[[],[]]]]]=>1
[2,5,2,6,3,1]=>[[[[],[],[[]]]]]=>1
[2,5,3,1,2,6]=>[[[[],[[[]]]]]]=>1
[2,5,3,1,6,2]=>[[[],[[],[],[]]]]=>1
[2,5,3,2,1,6]=>[[[[],[[],[]]]]]=>1
[2,5,3,2,6,1]=>[[[[[[[]]]]]]]=>1
[2,5,3,6,1,2]=>[[[[[]]],[[]]]]=>1
[2,5,3,6,2,1]=>[[[],[],[[[]]]]]=>1
[2,5,6,1,2,3]=>[[[[],[],[[]]]]]=>1
[2,5,6,1,3,2]=>[[[[[],[[]]]]]]=>1
[2,5,6,2,1,3]=>[[[[]],[[[]]]]]=>1
[2,5,6,2,3,1]=>[[[],[[],[[]]]]]=>1
[2,5,6,3,1,2]=>[[[[[[],[]]]]]]=>1
[2,5,6,3,2,1]=>[[[[],[[[]]]]]]=>1
[2,6,1,2,3,5]=>[[[[],[[],[]]]]]=>1
[2,6,1,2,5,3]=>[[[[[[[]]]]]]]=>1
[2,6,1,3,2,5]=>[[[[],[[[]]]]]]=>1
[2,6,1,3,5,2]=>[[[],[[],[],[]]]]=>1
[2,6,1,5,2,3]=>[[[],[[]],[[]]]]=>1
[2,6,1,5,3,2]=>[[[[]],[[[]]]]]=>1
[2,6,2,1,3,5]=>[[[[],[[[]]]]]]=>1
[2,6,2,1,5,3]=>[[[[]],[[[]]]]]=>1
[2,6,2,3,1,5]=>[[[],[[[[]]]]]]=>1
[2,6,2,3,5,1]=>[[[[],[[[]]]]]]=>1
[2,6,2,5,1,3]=>[[[[],[],[[]]]]]=>1
[2,6,2,5,3,1]=>[[[[],[[],[]]]]]=>1
[2,6,3,1,2,5]=>[[[],[[[[]]]]]]=>1
[2,6,3,1,5,2]=>[[[],[],[],[[]]]]=>1
[2,6,3,2,1,5]=>[[[],[],[[],[]]]]=>1
[2,6,3,2,5,1]=>[[[],[[],[[]]]]]=>1
[2,6,3,5,1,2]=>[[[],[[[[]]]]]]=>1
[2,6,3,5,2,1]=>[[[],[[]],[[]]]]=>1
[2,6,5,1,2,3]=>[[[[[],[[]]]]]]=>1
[2,6,5,1,3,2]=>[[[[[[],[]]]]]]=>1
[2,6,5,2,1,3]=>[[[],[[],[[]]]]]=>1
[2,6,5,2,3,1]=>[[[],[[[[]]]]]]=>1
[2,6,5,3,1,2]=>[[[[],[[[]]]]]]=>1
[2,6,5,3,2,1]=>[[[[],[],[[]]]]]=>1
[3,1,2,2,5,6]=>[[[[],[]]],[[]]]=>2
[3,1,2,2,6,5]=>[[[]],[[[[]]]]]=>2
[3,1,2,5,2,6]=>[[[[],[[[]]]]]]=>1
[3,1,2,5,6,2]=>[[[[],[[],[]]]]]=>1
[3,1,2,6,2,5]=>[[[[],[[[]]]]]]=>1
[3,1,2,6,5,2]=>[[[[[]],[[]]]]]=>1
[3,1,5,2,2,6]=>[[[]],[[],[],[]]]=>2
[3,1,5,2,6,2]=>[[[[],[],[[]]]]]=>1
[3,1,5,6,2,2]=>[[],[[[[[]]]]]]=>2
[3,1,6,2,2,5]=>[[[],[]],[[],[]]]=>2
[3,1,6,2,5,2]=>[[[],[[],[[]]]]]=>1
[3,1,6,5,2,2]=>[[[[],[]]],[[]]]=>2
[3,2,1,2,5,6]=>[[[],[[],[[]]]]]=>1
[3,2,1,2,6,5]=>[[[],[],[[[]]]]]=>1
[3,2,1,5,2,6]=>[[[],[[],[],[]]]]=>1
[3,2,1,5,6,2]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,2,5]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,5,2]=>[[[],[],[[[]]]]]=>1
[3,2,2,1,5,6]=>[[],[[],[[[]]]]]=>2
[3,2,2,1,6,5]=>[[],[[],[],[[]]]]=>2
[3,2,2,5,1,6]=>[[],[[],[[[]]]]]=>2
[3,2,2,5,6,1]=>[[],[[[[[]]]]]]=>2
[3,2,2,6,1,5]=>[[],[[[]],[[]]]]=>2
[3,2,2,6,5,1]=>[[],[[[],[[]]]]]=>2
[3,2,5,1,2,6]=>[[[[[[],[]]]]]]=>1
[3,2,5,1,6,2]=>[[[[],[],[[]]]]]=>1
[3,2,5,2,1,6]=>[[[[]],[[[]]]]]=>1
[3,2,5,2,6,1]=>[[[[[],[[]]]]]]=>1
[3,2,5,6,1,2]=>[[[[[]],[[]]]]]=>1
[3,2,5,6,2,1]=>[[[],[[],[[]]]]]=>1
[3,2,6,1,2,5]=>[[[[[[[]]]]]]]=>1
[3,2,6,1,5,2]=>[[[[],[],[[]]]]]=>1
[3,2,6,2,1,5]=>[[[[]],[[],[]]]]=>1
[3,2,6,2,5,1]=>[[[[],[],[[]]]]]=>1
[3,2,6,5,1,2]=>[[[[[]]],[[]]]]=>1
[3,2,6,5,2,1]=>[[[],[],[[],[]]]]=>1
[3,5,1,2,2,6]=>[[[[[]]]],[[]]]=>2
[3,5,1,2,6,2]=>[[[[],[[[]]]]]]=>1
[3,5,1,6,2,2]=>[[],[[[]],[[]]]]=>2
[3,5,2,1,2,6]=>[[[[[]],[[]]]]]=>1
[3,5,2,1,6,2]=>[[[[[[[]]]]]]]=>1
[3,5,2,2,1,6]=>[[],[[[[[]]]]]]=>2
[3,5,2,2,6,1]=>[[],[[],[[],[]]]]=>2
[3,5,2,6,1,2]=>[[[[]],[[],[]]]]=>1
[3,5,2,6,2,1]=>[[[[],[[[]]]]]]=>1
[3,5,6,1,2,2]=>[[],[[],[[],[]]]]=>2
[3,5,6,2,1,2]=>[[[[],[[[]]]]]]=>1
[3,5,6,2,2,1]=>[[[[[]]]],[[]]]=>2
[3,6,1,2,2,5]=>[[[[]]],[[],[]]]=>2
[3,6,1,2,5,2]=>[[[[[]]],[[]]]]=>1
[3,6,1,5,2,2]=>[[],[[],[[[]]]]]=>2
[3,6,2,1,2,5]=>[[[],[[]],[[]]]]=>1
[3,6,2,1,5,2]=>[[[],[[],[[]]]]]=>1
[3,6,2,2,1,5]=>[[[[]]],[[],[]]]=>2
[3,6,2,2,5,1]=>[[],[[],[],[],[]]]=>2
[3,6,2,5,1,2]=>[[[],[],[],[[]]]]=>1
[3,6,2,5,2,1]=>[[[],[],[[[]]]]]=>1
[3,6,5,1,2,2]=>[[[[],[]]],[[]]]=>2
[3,6,5,2,1,2]=>[[[[[],[[]]]]]]=>1
[3,6,5,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,1,2,2,3,6]=>[[],[[],[[],[]]]]=>2
[5,1,2,2,6,3]=>[[[[]]],[[],[]]]=>2
[5,1,2,3,2,6]=>[[[[],[[[]]]]]]=>1
[5,1,2,3,6,2]=>[[[],[],[[],[]]]]=>1
[5,1,2,6,2,3]=>[[[[]],[[],[]]]]=>1
[5,1,2,6,3,2]=>[[[[[]],[[]]]]]=>1
[5,1,3,2,2,6]=>[[],[[[[[]]]]]]=>2
[5,1,3,2,6,2]=>[[[[]],[[[]]]]]=>1
[5,1,3,6,2,2]=>[[],[[],[],[[]]]]=>2
[5,1,6,2,2,3]=>[[[]],[[],[[]]]]=>2
[5,1,6,2,3,2]=>[[[],[[[[]]]]]]=>1
[5,1,6,3,2,2]=>[[[]],[[[[]]]]]=>2
[5,2,1,2,3,6]=>[[[[],[[[]]]]]]=>1
[5,2,1,2,6,3]=>[[[],[[]],[[]]]]=>1
[5,2,1,3,2,6]=>[[[],[[],[[]]]]]=>1
[5,2,1,3,6,2]=>[[[[[],[[]]]]]]=>1
[5,2,1,6,2,3]=>[[[[[[[]]]]]]]=>1
[5,2,1,6,3,2]=>[[[],[[],[[]]]]]=>1
[5,2,2,1,3,6]=>[[[]],[[[[]]]]]=>2
[5,2,2,1,6,3]=>[[],[[[],[[]]]]]=>2
[5,2,2,3,1,6]=>[[],[[[],[[]]]]]=>2
[5,2,2,3,6,1]=>[[[[[]]]],[[]]]=>2
[5,2,2,6,1,3]=>[[],[[],[[],[]]]]=>2
[5,2,2,6,3,1]=>[[],[[],[],[[]]]]=>2
[5,2,3,1,2,6]=>[[[],[[],[[]]]]]=>1
[5,2,3,1,6,2]=>[[[[[]],[[]]]]]=>1
[5,2,3,2,1,6]=>[[[[[],[[]]]]]]=>1
[5,2,3,2,6,1]=>[[[],[[[[]]]]]]=>1
[5,2,3,6,1,2]=>[[[[],[[[]]]]]]=>1
[5,2,3,6,2,1]=>[[[[[]],[[]]]]]=>1
[5,2,6,1,2,3]=>[[[],[[[],[]]]]]=>1
[5,2,6,1,3,2]=>[[[],[[],[[]]]]]=>1
[5,2,6,2,1,3]=>[[[],[[[[]]]]]]=>1
[5,2,6,2,3,1]=>[[[],[[[[]]]]]]=>1
[5,2,6,3,1,2]=>[[[],[],[[[]]]]]=>1
[5,2,6,3,2,1]=>[[[],[],[[],[]]]]=>1
[5,3,1,2,2,6]=>[[[[],[]]],[[]]]=>2
[5,3,1,2,6,2]=>[[[],[[[[]]]]]]=>1
[5,3,1,6,2,2]=>[[],[[[],[],[]]]]=>2
[5,3,2,1,2,6]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,6,2]=>[[[],[[[],[]]]]]=>1
[5,3,2,2,1,6]=>[[],[[],[[],[]]]]=>2
[5,3,2,2,6,1]=>[[[[[]]]],[[]]]=>2
[5,3,2,6,1,2]=>[[[[[[[]]]]]]]=>1
[5,3,2,6,2,1]=>[[[[],[[[]]]]]]=>1
[5,3,6,1,2,2]=>[[],[[[[[]]]]]]=>2
[5,3,6,2,1,2]=>[[[[[[],[]]]]]]=>1
[5,3,6,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,6,1,2,2,3]=>[[],[[],[],[[]]]]=>2
[5,6,1,2,3,2]=>[[[],[[]],[[]]]]=>1
[5,6,1,3,2,2]=>[[],[[[],[[]]]]]=>2
[5,6,2,1,2,3]=>[[[],[],[[[]]]]]=>1
[5,6,2,1,3,2]=>[[[[[],[[]]]]]]=>1
[5,6,2,2,1,3]=>[[[[]]],[[[]]]]=>2
[5,6,2,2,3,1]=>[[[]],[[],[[]]]]=>2
[5,6,2,3,1,2]=>[[[],[[]],[[]]]]=>1
[5,6,2,3,2,1]=>[[[[]],[[],[]]]]=>1
[5,6,3,1,2,2]=>[[],[[],[[[]]]]]=>2
[5,6,3,2,1,2]=>[[[],[[],[[]]]]]=>1
[5,6,3,2,2,1]=>[[[[]]],[[],[]]]=>2
[6,1,2,2,3,5]=>[[],[[],[[],[]]]]=>2
[6,1,2,2,5,3]=>[[[[]]],[[[]]]]=>2
[6,1,2,3,2,5]=>[[[[],[[[]]]]]]=>1
[6,1,2,3,5,2]=>[[[[]],[[],[]]]]=>1
[6,1,2,5,2,3]=>[[[[],[[[]]]]]]=>1
[6,1,2,5,3,2]=>[[[[[[[]]]]]]]=>1
[6,1,3,2,2,5]=>[[],[[[[],[]]]]]=>2
[6,1,3,2,5,2]=>[[[],[[[[]]]]]]=>1
[6,1,3,5,2,2]=>[[],[[[],[],[]]]]=>2
[6,1,5,2,2,3]=>[[[]],[[],[[]]]]=>2
[6,1,5,2,3,2]=>[[[[],[[[]]]]]]=>1
[6,1,5,3,2,2]=>[[[]],[[[[]]]]]=>2
[6,2,1,2,3,5]=>[[[[[[],[]]]]]]=>1
[6,2,1,2,5,3]=>[[[[]],[[[]]]]]=>1
[6,2,1,3,2,5]=>[[[],[[],[[]]]]]=>1
[6,2,1,3,5,2]=>[[[[],[[[]]]]]]=>1
[6,2,1,5,2,3]=>[[[[],[[[]]]]]]=>1
[6,2,1,5,3,2]=>[[[[[],[[]]]]]]=>1
[6,2,2,1,3,5]=>[[[]],[[[],[]]]]=>2
[6,2,2,1,5,3]=>[[],[[[[[]]]]]]=>2
[6,2,2,3,1,5]=>[[[[[]]]],[[]]]=>2
[6,2,2,3,5,1]=>[[],[[[[],[]]]]]=>2
[6,2,2,5,1,3]=>[[],[[],[],[[]]]]=>2
[6,2,2,5,3,1]=>[[],[[],[[],[]]]]=>2
[6,2,3,1,2,5]=>[[[],[[],[[]]]]]=>1
[6,2,3,1,5,2]=>[[[[],[[[]]]]]]=>1
[6,2,3,2,1,5]=>[[[[[]],[[]]]]]=>1
[6,2,3,2,5,1]=>[[[],[],[[[]]]]]=>1
[6,2,3,5,1,2]=>[[[[]],[[],[]]]]=>1
[6,2,3,5,2,1]=>[[[[[[[]]]]]]]=>1
[6,2,5,1,2,3]=>[[[],[],[[],[]]]]=>1
[6,2,5,1,3,2]=>[[[],[],[[[]]]]]=>1
[6,2,5,2,1,3]=>[[[],[[[[]]]]]]=>1
[6,2,5,2,3,1]=>[[[],[[[[]]]]]]=>1
[6,2,5,3,1,2]=>[[[],[[],[[]]]]]=>1
[6,2,5,3,2,1]=>[[[],[[],[[]]]]]=>1
[6,3,1,2,2,5]=>[[[[[]]]],[[]]]=>2
[6,3,1,2,5,2]=>[[[],[[[[]]]]]]=>1
[6,3,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[6,3,2,1,2,5]=>[[[[],[[[]]]]]]=>1
[6,3,2,1,5,2]=>[[[],[],[[],[]]]]=>1
[6,3,2,2,1,5]=>[[],[[],[[],[]]]]=>2
[6,3,2,2,5,1]=>[[[]],[[],[[]]]]=>2
[6,3,2,5,1,2]=>[[[[],[[[]]]]]]=>1
[6,3,2,5,2,1]=>[[[[]],[[],[]]]]=>1
[6,3,5,1,2,2]=>[[],[[[[[]]]]]]=>2
[6,3,5,2,1,2]=>[[[[]],[[[]]]]]=>1
[6,3,5,2,2,1]=>[[[]],[[],[[]]]]=>2
[6,5,1,2,2,3]=>[[],[[[]],[[]]]]=>2
[6,5,1,2,3,2]=>[[[],[[],[[]]]]]=>1
[6,5,1,3,2,2]=>[[],[[],[[[]]]]]=>2
[6,5,2,1,2,3]=>[[[],[[],[[]]]]]=>1
[6,5,2,1,3,2]=>[[[],[],[[[]]]]]=>1
[6,5,2,2,1,3]=>[[[]],[[],[[]]]]=>2
[6,5,2,2,3,1]=>[[[[[]]]],[[]]]=>2
[6,5,2,3,1,2]=>[[[[],[[[]]]]]]=>1
[6,5,2,3,2,1]=>[[[],[[]],[[]]]]=>1
[6,5,3,1,2,2]=>[[[[],[]]],[[]]]=>2
[6,5,3,2,1,2]=>[[[],[],[[[]]]]]=>1
[6,5,3,2,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,2,4,4,4]=>[[],[],[[]],[[]]]=>4
[1,2,4,2,4,4]=>[[],[[[]],[[]]]]=>2
[1,2,4,4,2,4]=>[[],[[[],[[]]]]]=>2
[1,2,4,4,4,2]=>[[],[[[]]],[[]]]=>3
[1,4,2,2,4,4]=>[[],[],[[[[]]]]]=>3
[1,4,2,4,2,4]=>[[[[],[[],[]]]]]=>1
[1,4,2,4,4,2]=>[[[]],[[],[[]]]]=>2
[1,4,4,2,2,4]=>[[[]],[[]],[[]]]=>3
[1,4,4,2,4,2]=>[[[]],[[],[[]]]]=>2
[1,4,4,4,2,2]=>[[],[],[[]],[[]]]=>4
[2,1,2,4,4,4]=>[[],[[[]]],[[]]]=>3
[2,1,4,2,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,4,4,2,4]=>[[[]],[[[[]]]]]=>2
[2,1,4,4,4,2]=>[[],[[]],[[[]]]]=>3
[2,2,1,4,4,4]=>[[],[],[[]],[[]]]=>4
[2,2,4,1,4,4]=>[[],[],[[[[]]]]]=>3
[2,2,4,4,1,4]=>[[],[[]],[[[]]]]=>3
[2,2,4,4,4,1]=>[[],[],[[]],[[]]]=>4
[2,4,1,2,4,4]=>[[],[[],[[[]]]]]=>2
[2,4,1,4,2,4]=>[[[],[[[[]]]]]]=>1
[2,4,1,4,4,2]=>[[[[[]]]],[[]]]=>2
[2,4,2,1,4,4]=>[[[[[]]]],[[]]]=>2
[2,4,2,4,1,4]=>[[[[[]]],[[]]]]=>1
[2,4,2,4,4,1]=>[[[]],[[],[[]]]]=>2
[2,4,4,1,2,4]=>[[],[[[[],[]]]]]=>2
[2,4,4,1,4,2]=>[[[]],[[[[]]]]]=>2
[2,4,4,2,1,4]=>[[[]],[[[[]]]]]=>2
[2,4,4,2,4,1]=>[[],[[[],[[]]]]]=>2
[2,4,4,4,1,2]=>[[],[[]],[[[]]]]=>3
[2,4,4,4,2,1]=>[[],[[]],[[[]]]]=>3
[4,1,2,2,4,4]=>[[],[[[]]],[[]]]=>3
[4,1,2,4,2,4]=>[[[[[],[[]]]]]]=>1
[4,1,2,4,4,2]=>[[[[[]]]],[[]]]=>2
[4,1,4,2,2,4]=>[[[]],[[[[]]]]]=>2
[4,1,4,2,4,2]=>[[[[[],[[]]]]]]=>1
[4,1,4,4,2,2]=>[[],[[]],[[[]]]]=>3
[4,2,1,2,4,4]=>[[[[[]]]],[[]]]=>2
[4,2,1,4,2,4]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,4,4]=>[[],[[[]]],[[]]]=>3
[4,2,2,4,1,4]=>[[[[[]]]],[[]]]=>2
[4,2,2,4,4,1]=>[[],[[[]]],[[]]]=>3
[4,2,4,1,2,4]=>[[[[[[],[]]]]]]=>1
[4,2,4,1,4,2]=>[[[],[[[[]]]]]]=>1
[4,2,4,2,1,4]=>[[[[]],[[[]]]]]=>1
[4,2,4,2,4,1]=>[[[],[[],[[]]]]]=>1
[4,2,4,4,1,2]=>[[[[]]],[[[]]]]=>2
[4,2,4,4,2,1]=>[[[]],[[],[[]]]]=>2
[4,4,1,2,2,4]=>[[],[[[]]],[[]]]=>3
[4,4,1,2,4,2]=>[[],[[[[[]]]]]]=>2
[4,4,1,4,2,2]=>[[],[],[[[[]]]]]=>3
[4,4,2,1,2,4]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,4,2]=>[[],[[[]],[[]]]]=>2
[4,4,2,2,1,4]=>[[],[],[[[[]]]]]=>3
[4,4,2,2,4,1]=>[[],[[[]]],[[]]]=>3
[4,4,2,4,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,2,4,2,1]=>[[],[[[]],[[]]]]=>2
[4,4,4,1,2,2]=>[[],[],[],[[[]]]]=>4
[4,4,4,2,1,2]=>[[],[],[[[[]]]]]=>3
[4,4,4,2,2,1]=>[[],[],[],[[[]]]]=>4
[1,2,2,4,4,5]=>[[],[[]],[[],[]]]=>3
[1,2,2,4,5,4]=>[[],[[[],[[]]]]]=>2
[1,2,2,5,4,4]=>[[],[[]],[[[]]]]=>3
[1,2,4,2,4,5]=>[[[],[[],[[]]]]]=>1
[1,2,4,2,5,4]=>[[[[[[[]]]]]]]=>1
[1,2,4,4,2,5]=>[[[[]]],[[[]]]]=>2
[1,2,4,4,5,2]=>[[[]],[[],[[]]]]=>2
[1,2,4,5,2,4]=>[[[],[[[],[]]]]]=>1
[1,2,4,5,4,2]=>[[[[]],[[[]]]]]=>1
[1,2,5,2,4,4]=>[[],[[[[[]]]]]]=>2
[1,2,5,4,2,4]=>[[[[[[[]]]]]]]=>1
[1,2,5,4,4,2]=>[[],[[[[[]]]]]]=>2
[1,4,2,2,4,5]=>[[[[]]],[[[]]]]=>2
[1,4,2,2,5,4]=>[[],[[],[[[]]]]]=>2
[1,4,2,4,2,5]=>[[[],[[],[[]]]]]=>1
[1,4,2,4,5,2]=>[[[[[[[]]]]]]]=>1
[1,4,2,5,2,4]=>[[[[[]]],[[]]]]=>1
[1,4,2,5,4,2]=>[[[],[[[],[]]]]]=>1
[1,4,4,2,2,5]=>[[],[[]],[[],[]]]=>3
[1,4,4,2,5,2]=>[[],[[[],[[]]]]]=>2
[1,4,4,5,2,2]=>[[],[[]],[[[]]]]=>3
[1,4,5,2,2,4]=>[[[]],[[[[]]]]]=>2
[1,4,5,2,4,2]=>[[[[[[[]]]]]]]=>1
[1,4,5,4,2,2]=>[[[]],[[[[]]]]]=>2
[1,5,2,2,4,4]=>[[],[[]],[[],[]]]=>3
[1,5,2,4,2,4]=>[[[],[[[],[]]]]]=>1
[1,5,2,4,4,2]=>[[[[],[]]],[[]]]=>2
[1,5,4,2,2,4]=>[[[[]]],[[[]]]]=>2
[1,5,4,2,4,2]=>[[[[[],[[]]]]]]=>1
[1,5,4,4,2,2]=>[[],[[[]]],[[]]]=>3
[2,1,2,4,4,5]=>[[[]],[[],[[]]]]=>2
[2,1,2,4,5,4]=>[[[],[[],[[]]]]]=>1
[2,1,2,5,4,4]=>[[],[[],[[[]]]]]=>2
[2,1,4,2,4,5]=>[[[[[[[]]]]]]]=>1
[2,1,4,2,5,4]=>[[[[]],[[],[]]]]=>1
[2,1,4,4,2,5]=>[[],[[[],[[]]]]]=>2
[2,1,4,4,5,2]=>[[[[[]]]],[[]]]=>2
[2,1,4,5,2,4]=>[[[[[[[]]]]]]]=>1
[2,1,4,5,4,2]=>[[[[[]]],[[]]]]=>1
[2,1,5,2,4,4]=>[[[[],[]]],[[]]]=>2
[2,1,5,4,2,4]=>[[[],[[[[]]]]]]=>1
[2,1,5,4,4,2]=>[[[]],[[[],[]]]]=>2
[2,2,1,4,4,5]=>[[],[[[]]],[[]]]=>3
[2,2,1,4,5,4]=>[[],[[],[[[]]]]]=>2
[2,2,1,5,4,4]=>[[],[],[[],[[]]]]=>3
[2,2,4,1,4,5]=>[[],[[[[[]]]]]]=>2
[2,2,4,1,5,4]=>[[],[[[],[[]]]]]=>2
[2,2,4,4,1,5]=>[[],[[]],[[],[]]]=>3
[2,2,4,4,5,1]=>[[],[[[]]],[[]]]=>3
[2,2,4,5,1,4]=>[[],[[[[],[]]]]]=>2
[2,2,4,5,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,5,1,4,4]=>[[],[],[[],[],[]]]=>3
[2,2,5,4,1,4]=>[[],[[[]],[[]]]]=>2
[2,2,5,4,4,1]=>[[],[],[[[[]]]]]=>3
[2,4,1,2,4,5]=>[[[],[[],[[]]]]]=>1
[2,4,1,2,5,4]=>[[[[[[[]]]]]]]=>1
[2,4,1,4,2,5]=>[[[[],[[[]]]]]]=>1
[2,4,1,4,5,2]=>[[[[],[[[]]]]]]=>1
[2,4,1,5,2,4]=>[[[],[[],[],[]]]]=>1
[2,4,1,5,4,2]=>[[[[],[[[]]]]]]=>1
[2,4,2,1,4,5]=>[[[[[[[]]]]]]]=>1
[2,4,2,1,5,4]=>[[[[[]],[[]]]]]=>1
[2,4,2,4,1,5]=>[[[],[[],[[]]]]]=>1
[2,4,2,4,5,1]=>[[[[[]]],[[]]]]=>1
[2,4,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[2,4,2,5,4,1]=>[[[[[[[]]]]]]]=>1
[2,4,4,1,2,5]=>[[[]],[[[[]]]]]=>2
[2,4,4,1,5,2]=>[[[]],[[],[],[]]]=>2
[2,4,4,2,1,5]=>[[[]],[[[[]]]]]=>2
[2,4,4,2,5,1]=>[[[]],[[[],[]]]]=>2
[2,4,4,5,1,2]=>[[[]],[[],[[]]]]=>2
[2,4,4,5,2,1]=>[[[[[]]]],[[]]]=>2
[2,4,5,1,2,4]=>[[[],[[],[[]]]]]=>1
[2,4,5,1,4,2]=>[[[[[],[[]]]]]]=>1
[2,4,5,2,1,4]=>[[[[[[[]]]]]]]=>1
[2,4,5,2,4,1]=>[[[],[[],[[]]]]]=>1
[2,4,5,4,1,2]=>[[[[[]],[[]]]]]=>1
[2,4,5,4,2,1]=>[[[[[],[[]]]]]]=>1
[2,5,1,2,4,4]=>[[],[[[[],[]]]]]=>2
[2,5,1,4,2,4]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,4,2]=>[[[]],[[],[],[]]]=>2
[2,5,2,1,4,4]=>[[[[]]],[[],[]]]=>2
[2,5,2,4,1,4]=>[[[],[[],[[]]]]]=>1
[2,5,2,4,4,1]=>[[[]],[[],[[]]]]=>2
[2,5,4,1,2,4]=>[[[[[[[]]]]]]]=>1
[2,5,4,1,4,2]=>[[[[]],[[[]]]]]=>1
[2,5,4,2,1,4]=>[[[[]],[[],[]]]]=>1
[2,5,4,2,4,1]=>[[[[[[[]]]]]]]=>1
[2,5,4,4,1,2]=>[[],[[[[[]]]]]]=>2
[2,5,4,4,2,1]=>[[[]],[[[],[]]]]=>2
[4,1,2,2,4,5]=>[[],[[[],[[]]]]]=>2
[4,1,2,2,5,4]=>[[[[]]],[[[]]]]=>2
[4,1,2,4,2,5]=>[[[[[[[]]]]]]]=>1
[4,1,2,4,5,2]=>[[[],[[],[[]]]]]=>1
[4,1,2,5,2,4]=>[[[[]],[[[]]]]]=>1
[4,1,2,5,4,2]=>[[[[[[[]]]]]]]=>1
[4,1,4,2,2,5]=>[[[[]]],[[],[]]]=>2
[4,1,4,2,5,2]=>[[[],[[],[[]]]]]=>1
[4,1,4,5,2,2]=>[[],[[],[[[]]]]]=>2
[4,1,5,2,2,4]=>[[[]],[[],[],[]]]=>2
[4,1,5,2,4,2]=>[[[],[],[[[]]]]]=>1
[4,1,5,4,2,2]=>[[[[],[]]],[[]]]=>2
[4,2,1,2,4,5]=>[[[[[],[[]]]]]]=>1
[4,2,1,2,5,4]=>[[[[],[[[]]]]]]=>1
[4,2,1,4,2,5]=>[[[],[[],[[]]]]]=>1
[4,2,1,4,5,2]=>[[[[[[[]]]]]]]=>1
[4,2,1,5,2,4]=>[[[[],[[[]]]]]]=>1
[4,2,1,5,4,2]=>[[[[]],[[],[]]]]=>1
[4,2,2,1,4,5]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,5,4]=>[[],[[[]],[[]]]]=>2
[4,2,2,4,1,5]=>[[],[[[],[[]]]]]=>2
[4,2,2,4,5,1]=>[[[[[]]]],[[]]]=>2
[4,2,2,5,1,4]=>[[],[[],[],[[]]]]=>2
[4,2,2,5,4,1]=>[[],[[[[[]]]]]]=>2
[4,2,4,1,2,5]=>[[[[[[[]]]]]]]=>1
[4,2,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[4,2,4,2,1,5]=>[[[[]],[[[]]]]]=>1
[4,2,4,2,5,1]=>[[[[]],[[],[]]]]=>1
[4,2,4,5,1,2]=>[[[[[],[[]]]]]]=>1
[4,2,4,5,2,1]=>[[[[[[[]]]]]]]=>1
[4,2,5,1,2,4]=>[[[[],[[[]]]]]]=>1
[4,2,5,1,4,2]=>[[[],[[],[],[]]]]=>1
[4,2,5,2,1,4]=>[[[[],[[[]]]]]]=>1
[4,2,5,2,4,1]=>[[[[[],[[]]]]]]=>1
[4,2,5,4,1,2]=>[[[[[[[]]]]]]]=>1
[4,2,5,4,2,1]=>[[[[]],[[],[]]]]=>1
[4,4,1,2,2,5]=>[[],[[[]]],[[]]]=>3
[4,4,1,2,5,2]=>[[],[[],[[[]]]]]=>2
[4,4,1,5,2,2]=>[[],[],[[],[],[]]]=>3
[4,4,2,1,2,5]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,5,2]=>[[],[[[],[[]]]]]=>2
[4,4,2,2,1,5]=>[[],[],[[[[]]]]]=>3
[4,4,2,2,5,1]=>[[],[],[[],[[]]]]=>3
[4,4,2,5,1,2]=>[[],[[[],[[]]]]]=>2
[4,4,2,5,2,1]=>[[],[[[[[]]]]]]=>2
[4,4,5,1,2,2]=>[[],[],[[],[[]]]]=>3
[4,4,5,2,1,2]=>[[],[[],[[[]]]]]=>2
[4,4,5,2,2,1]=>[[],[[[]]],[[]]]=>3
[4,5,1,2,2,4]=>[[[]],[[],[[]]]]=>2
[4,5,1,2,4,2]=>[[[[[]]],[[]]]]=>1
[4,5,1,4,2,2]=>[[],[[[],[[]]]]]=>2
[4,5,2,1,2,4]=>[[[],[[[[]]]]]]=>1
[4,5,2,1,4,2]=>[[[[[[[]]]]]]]=>1
[4,5,2,2,1,4]=>[[[[]]],[[[]]]]=>2
[4,5,2,2,4,1]=>[[],[[[],[[]]]]]=>2
[4,5,2,4,1,2]=>[[[],[[],[[]]]]]=>1
[4,5,2,4,2,1]=>[[[[[[[]]]]]]]=>1
[4,5,4,1,2,2]=>[[[]],[[],[[]]]]=>2
[4,5,4,2,1,2]=>[[[[]],[[],[]]]]=>1
[4,5,4,2,2,1]=>[[],[[[]],[[]]]]=>2
[5,1,2,2,4,4]=>[[],[[[]]],[[]]]=>3
[5,1,2,4,2,4]=>[[[[[],[[]]]]]]=>1
[5,1,2,4,4,2]=>[[[[[]]]],[[]]]=>2
[5,1,4,2,2,4]=>[[[]],[[[],[]]]]=>2
[5,1,4,2,4,2]=>[[[],[[],[[]]]]]=>1
[5,1,4,4,2,2]=>[[],[[]],[[],[]]]=>3
[5,2,1,2,4,4]=>[[[[]]],[[[]]]]=>2
[5,2,1,4,2,4]=>[[[[[[[]]]]]]]=>1
[5,2,1,4,4,2]=>[[[[]]],[[[]]]]=>2
[5,2,2,1,4,4]=>[[],[[]],[[[]]]]=>3
[5,2,2,4,1,4]=>[[],[[[],[[]]]]]=>2
[5,2,2,4,4,1]=>[[],[[]],[[],[]]]=>3
[5,2,4,1,2,4]=>[[[],[[[],[]]]]]=>1
[5,2,4,1,4,2]=>[[[[]],[[[]]]]]=>1
[5,2,4,2,1,4]=>[[[[[[[]]]]]]]=>1
[5,2,4,2,4,1]=>[[[],[[],[[]]]]]=>1
[5,2,4,4,1,2]=>[[[]],[[],[[]]]]=>2
[5,2,4,4,2,1]=>[[[]],[[[[]]]]]=>2
[5,4,1,2,2,4]=>[[[[]]],[[[]]]]=>2
[5,4,1,2,4,2]=>[[[[[[[]]]]]]]=>1
[5,4,1,4,2,2]=>[[[[[]]]],[[]]]=>2
[5,4,2,1,2,4]=>[[[],[[[[]]]]]]=>1
[5,4,2,1,4,2]=>[[[],[[],[[]]]]]=>1
[5,4,2,2,1,4]=>[[],[[],[[[]]]]]=>2
[5,4,2,2,4,1]=>[[[[[]]]],[[]]]=>2
[5,4,2,4,1,2]=>[[[[[[[]]]]]]]=>1
[5,4,2,4,2,1]=>[[[],[[],[[]]]]]=>1
[5,4,4,1,2,2]=>[[],[[[]]],[[]]]=>3
[5,4,4,2,1,2]=>[[],[[[[],[]]]]]=>2
[5,4,4,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,4,4,6]=>[[],[[]],[[],[]]]=>3
[1,2,2,4,6,4]=>[[[]],[[],[[]]]]=>2
[1,2,2,6,4,4]=>[[],[[]],[[[]]]]=>3
[1,2,4,2,4,6]=>[[[[],[],[[]]]]]=>1
[1,2,4,2,6,4]=>[[[[[],[[]]]]]]=>1
[1,2,4,4,2,6]=>[[[[]]],[[[]]]]=>2
[1,2,4,4,6,2]=>[[],[[[]],[[]]]]=>2
[1,2,4,6,2,4]=>[[[[],[],[[]]]]]=>1
[1,2,4,6,4,2]=>[[[[],[[],[]]]]]=>1
[1,2,6,2,4,4]=>[[],[[[[[]]]]]]=>2
[1,2,6,4,2,4]=>[[[[[],[[]]]]]]=>1
[1,2,6,4,4,2]=>[[[[]]],[[],[]]]=>2
[1,4,2,2,4,6]=>[[],[[],[[[]]]]]=>2
[1,4,2,2,6,4]=>[[[]],[[[],[]]]]=>2
[1,4,2,4,2,6]=>[[[[[],[[]]]]]]=>1
[1,4,2,4,6,2]=>[[[],[[],[[]]]]]=>1
[1,4,2,6,2,4]=>[[[[]],[[[]]]]]=>1
[1,4,2,6,4,2]=>[[[[],[],[[]]]]]=>1
[1,4,4,2,2,6]=>[[],[[]],[[[]]]]=>3
[1,4,4,2,6,2]=>[[],[[[[],[]]]]]=>2
[1,4,4,6,2,2]=>[[],[],[[],[[]]]]=>3
[1,4,6,2,2,4]=>[[[],[]],[[],[]]]=>2
[1,4,6,2,4,2]=>[[[],[[],[[]]]]]=>1
[1,4,6,4,2,2]=>[[],[[],[[[]]]]]=>2
[1,6,2,2,4,4]=>[[],[[[]]],[[]]]=>3
[1,6,2,4,2,4]=>[[[],[[],[[]]]]]=>1
[1,6,2,4,4,2]=>[[[[]]],[[],[]]]=>2
[1,6,4,2,2,4]=>[[[]],[[],[],[]]]=>2
[1,6,4,2,4,2]=>[[[],[],[],[[]]]]=>1
[1,6,4,4,2,2]=>[[],[],[[],[],[]]]=>3
[2,1,2,4,4,6]=>[[],[[[]],[[]]]]=>2
[2,1,2,4,6,4]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,4,2,4,6]=>[[[[],[[[]]]]]]=>1
[2,1,4,2,6,4]=>[[[[],[[[]]]]]]=>1
[2,1,4,4,2,6]=>[[[]],[[[[]]]]]=>2
[2,1,4,4,6,2]=>[[],[[[],[[]]]]]=>2
[2,1,4,6,2,4]=>[[[[],[[],[]]]]]=>1
[2,1,4,6,4,2]=>[[[[],[[[]]]]]]=>1
[2,1,6,2,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,6,4,2,4]=>[[[[[],[],[]]]]]=>1
[2,1,6,4,4,2]=>[[],[[],[],[[]]]]=>2
[2,2,1,4,4,6]=>[[],[[[]]],[[]]]=>3
[2,2,1,4,6,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,4,4]=>[[],[[]],[[],[]]]=>3
[2,2,4,1,4,6]=>[[],[[],[[[]]]]]=>2
[2,2,4,1,6,4]=>[[],[[[[],[]]]]]=>2
[2,2,4,4,1,6]=>[[],[[]],[[[]]]]=>3
[2,2,4,4,6,1]=>[[],[],[[],[],[]]]=>3
[2,2,4,6,1,4]=>[[],[[],[],[[]]]]=>2
[2,2,4,6,4,1]=>[[],[[],[[[]]]]]=>2
[2,2,6,1,4,4]=>[[],[],[[[[]]]]]=>3
[2,2,6,4,1,4]=>[[],[[[]],[[]]]]=>2
[2,2,6,4,4,1]=>[[],[[]],[[],[]]]=>3
[2,4,1,2,4,6]=>[[[],[],[[[]]]]]=>1
[2,4,1,2,6,4]=>[[[[[]],[[]]]]]=>1
[2,4,1,4,2,6]=>[[[[[[],[]]]]]]=>1
[2,4,1,4,6,2]=>[[[],[[],[[]]]]]=>1
[2,4,1,6,2,4]=>[[[],[[[[]]]]]]=>1
[2,4,1,6,4,2]=>[[[[],[],[[]]]]]=>1
[2,4,2,1,4,6]=>[[[[[]]],[[]]]]=>1
[2,4,2,1,6,4]=>[[[[[],[],[]]]]]=>1
[2,4,2,4,1,6]=>[[[],[[[],[]]]]]=>1
[2,4,2,4,6,1]=>[[[],[],[],[[]]]]=>1
[2,4,2,6,1,4]=>[[[[]],[[[]]]]]=>1
[2,4,2,6,4,1]=>[[[[],[[],[]]]]]=>1
[2,4,4,1,2,6]=>[[[]],[[],[[]]]]=>2
[2,4,4,1,6,2]=>[[[]],[[[[]]]]]=>2
[2,4,4,2,1,6]=>[[[]],[[],[[]]]]=>2
[2,4,4,2,6,1]=>[[],[[[[],[]]]]]=>2
[2,4,4,6,1,2]=>[[],[[],[],[[]]]]=>2
[2,4,4,6,2,1]=>[[],[[],[[[]]]]]=>2
[2,4,6,1,2,4]=>[[[],[],[],[[]]]]=>1
[2,4,6,1,4,2]=>[[[],[],[[[]]]]]=>1
[2,4,6,2,1,4]=>[[[],[[],[[]]]]]=>1
[2,4,6,2,4,1]=>[[[],[[]],[[]]]]=>1
[2,4,6,4,1,2]=>[[[],[[[[]]]]]]=>1
[2,4,6,4,2,1]=>[[[],[[],[[]]]]]=>1
[2,6,1,2,4,4]=>[[],[[[]],[[]]]]=>2
[2,6,1,4,2,4]=>[[[[[[],[]]]]]]=>1
[2,6,1,4,4,2]=>[[[[[]]]],[[]]]=>2
[2,6,2,1,4,4]=>[[[[]]],[[],[]]]=>2
[2,6,2,4,1,4]=>[[[[]],[[],[]]]]=>1
[2,6,2,4,4,1]=>[[[[]]],[[],[]]]=>2
[2,6,4,1,2,4]=>[[[[[]]],[[]]]]=>1
[2,6,4,1,4,2]=>[[[],[[[],[]]]]]=>1
[2,6,4,2,1,4]=>[[[[[[],[]]]]]]=>1
[2,6,4,2,4,1]=>[[[],[[[],[]]]]]=>1
[2,6,4,4,1,2]=>[[[]],[[],[[]]]]=>2
[2,6,4,4,2,1]=>[[],[[],[[[]]]]]=>2
[4,1,2,2,4,6]=>[[[[]]],[[],[]]]=>2
[4,1,2,2,6,4]=>[[[]],[[],[[]]]]=>2
[4,1,2,4,2,6]=>[[[],[[[[]]]]]]=>1
[4,1,2,4,6,2]=>[[[[[],[[]]]]]]=>1
[4,1,2,6,2,4]=>[[[[]],[[[]]]]]=>1
[4,1,2,6,4,2]=>[[[[]],[[],[]]]]=>1
[4,1,4,2,2,6]=>[[[[]]],[[],[]]]=>2
[4,1,4,2,6,2]=>[[[[]],[[],[]]]]=>1
[4,1,4,6,2,2]=>[[],[[[]],[[]]]]=>2
[4,1,6,2,2,4]=>[[[]],[[[[]]]]]=>2
[4,1,6,2,4,2]=>[[[[[[],[]]]]]]=>1
[4,1,6,4,2,2]=>[[],[[],[],[[]]]]=>2
[4,2,1,2,4,6]=>[[[[[]],[[]]]]]=>1
[4,2,1,2,6,4]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,2,6]=>[[[[]],[[[]]]]]=>1
[4,2,1,4,6,2]=>[[[[[],[[]]]]]]=>1
[4,2,1,6,2,4]=>[[[],[[[[]]]]]]=>1
[4,2,1,6,4,2]=>[[[],[],[],[[]]]]=>1
[4,2,2,1,4,6]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,6,4]=>[[],[[[],[],[]]]]=>2
[4,2,2,4,1,6]=>[[],[[[[],[]]]]]=>2
[4,2,2,4,6,1]=>[[],[[],[],[[]]]]=>2
[4,2,2,6,1,4]=>[[[[[]]]],[[]]]=>2
[4,2,2,6,4,1]=>[[],[[],[[],[]]]]=>2
[4,2,4,1,2,6]=>[[[[[],[[]]]]]]=>1
[4,2,4,1,6,2]=>[[[[]],[[[]]]]]=>1
[4,2,4,2,1,6]=>[[[],[[]],[[]]]]=>1
[4,2,4,2,6,1]=>[[[],[[[],[]]]]]=>1
[4,2,4,6,1,2]=>[[[[],[],[[]]]]]=>1
[4,2,4,6,2,1]=>[[[[[[],[]]]]]]=>1
[4,2,6,1,2,4]=>[[[[[],[[]]]]]]=>1
[4,2,6,1,4,2]=>[[[],[[[[]]]]]]=>1
[4,2,6,2,1,4]=>[[[[],[[[]]]]]]=>1
[4,2,6,2,4,1]=>[[[[[[],[]]]]]]=>1
[4,2,6,4,1,2]=>[[[],[[],[[]]]]]=>1
[4,2,6,4,2,1]=>[[[],[],[[[]]]]]=>1
[4,4,1,2,2,6]=>[[],[[]],[[],[]]]=>3
[4,4,1,2,6,2]=>[[],[[[]],[[]]]]=>2
[4,4,1,6,2,2]=>[[],[],[[[[]]]]]=>3
[4,4,2,1,2,6]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,6,2]=>[[],[[],[[[]]]]]=>2
[4,4,2,2,1,6]=>[[],[],[[[],[]]]]=>3
[4,4,2,2,6,1]=>[[],[[[]]],[[]]]=>3
[4,4,2,6,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,2,6,2,1]=>[[],[[[[[]]]]]]=>2
[4,4,6,1,2,2]=>[[],[],[[[],[]]]]=>3
[4,4,6,2,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,6,2,2,1]=>[[],[[[]]],[[]]]=>3
[4,6,1,2,2,4]=>[[[]],[[],[],[]]]=>2
[4,6,1,2,4,2]=>[[[],[[]],[[]]]]=>1
[4,6,1,4,2,2]=>[[],[[[[],[]]]]]=>2
[4,6,2,1,2,4]=>[[[[]],[[[]]]]]=>1
[4,6,2,1,4,2]=>[[[[[[],[]]]]]]=>1
[4,6,2,2,1,4]=>[[],[[[],[[]]]]]=>2
[4,6,2,2,4,1]=>[[[]],[[],[[]]]]=>2
[4,6,2,4,1,2]=>[[[[]],[[[]]]]]=>1
[4,6,2,4,2,1]=>[[[[]],[[[]]]]]=>1
[4,6,4,1,2,2]=>[[],[[[[[]]]]]]=>2
[4,6,4,2,1,2]=>[[[[],[[[]]]]]]=>1
[4,6,4,2,2,1]=>[[],[[[],[[]]]]]=>2
[6,1,2,2,4,4]=>[[],[[]],[[],[]]]=>3
[6,1,2,4,2,4]=>[[[],[[]],[[]]]]=>1
[6,1,2,4,4,2]=>[[[]],[[],[[]]]]=>2
[6,1,4,2,2,4]=>[[[[]]],[[],[]]]=>2
[6,1,4,2,4,2]=>[[[],[[],[[]]]]]=>1
[6,1,4,4,2,2]=>[[],[[[]]],[[]]]=>3
[6,2,1,2,4,4]=>[[[[]]],[[[]]]]=>2
[6,2,1,4,2,4]=>[[[],[[[[]]]]]]=>1
[6,2,1,4,4,2]=>[[[[]]],[[],[]]]=>2
[6,2,2,1,4,4]=>[[],[[]],[[],[]]]=>3
[6,2,2,4,1,4]=>[[],[[[[],[]]]]]=>2
[6,2,2,4,4,1]=>[[[]],[[]],[[]]]=>3
[6,2,4,1,2,4]=>[[[[],[[[]]]]]]=>1
[6,2,4,1,4,2]=>[[[[[]]],[[]]]]=>1
[6,2,4,2,1,4]=>[[[[[]]],[[]]]]=>1
[6,2,4,2,4,1]=>[[[[[],[[]]]]]]=>1
[6,2,4,4,1,2]=>[[[[]]],[[[]]]]=>2
[6,2,4,4,2,1]=>[[[[]]],[[[]]]]=>2
[6,4,1,2,2,4]=>[[[[[]]]],[[]]]=>2
[6,4,1,2,4,2]=>[[[],[[[[]]]]]]=>1
[6,4,1,4,2,2]=>[[],[[],[[[]]]]]=>2
[6,4,2,1,2,4]=>[[[],[[[[]]]]]]=>1
[6,4,2,1,4,2]=>[[[],[[]],[[]]]]=>1
[6,4,2,2,1,4]=>[[],[[[[],[]]]]]=>2
[6,4,2,2,4,1]=>[[[[]]],[[],[]]]=>2
[6,4,2,4,1,2]=>[[[],[[[[]]]]]]=>1
[6,4,2,4,2,1]=>[[[],[[]],[[]]]]=>1
[6,4,4,1,2,2]=>[[],[],[[[[]]]]]=>3
[6,4,4,2,1,2]=>[[],[[],[[[]]]]]=>2
[6,4,4,2,2,1]=>[[],[],[[[],[]]]]=>3
[1,2,2,4,5,5]=>[[],[],[[],[[]]]]=>3
[1,2,2,5,4,5]=>[[],[[[[],[]]]]]=>2
[1,2,2,5,5,4]=>[[[]],[[]],[[]]]=>3
[1,2,4,2,5,5]=>[[],[[[[[]]]]]]=>2
[1,2,4,5,2,5]=>[[[[]],[[[]]]]]=>1
[1,2,4,5,5,2]=>[[[]],[[],[[]]]]=>2
[1,2,5,2,4,5]=>[[[],[[[[]]]]]]=>1
[1,2,5,2,5,4]=>[[[[[]],[[]]]]]=>1
[1,2,5,4,2,5]=>[[[[[]],[[]]]]]=>1
[1,2,5,4,5,2]=>[[[],[[[[]]]]]]=>1
[1,2,5,5,2,4]=>[[[[]]],[[[]]]]=>2
[1,2,5,5,4,2]=>[[[[]]],[[[]]]]=>2
[1,4,2,2,5,5]=>[[],[],[[],[[]]]]=>3
[1,4,2,5,2,5]=>[[[],[],[[[]]]]]=>1
[1,4,2,5,5,2]=>[[[]],[[],[[]]]]=>2
[1,4,5,2,2,5]=>[[[[]]],[[],[]]]=>2
[1,4,5,2,5,2]=>[[[],[[],[[]]]]]=>1
[1,4,5,5,2,2]=>[[],[[[]]],[[]]]=>3
[1,5,2,2,4,5]=>[[[[]]],[[],[]]]=>2
[1,5,2,2,5,4]=>[[[[]]],[[],[]]]=>2
[1,5,2,4,2,5]=>[[[],[[[[]]]]]]=>1
[1,5,2,4,5,2]=>[[[],[],[[[]]]]]=>1
[1,5,2,5,2,4]=>[[[],[[]],[[]]]]=>1
[1,5,2,5,4,2]=>[[[],[[[[]]]]]]=>1
[1,5,4,2,2,5]=>[[[[]]],[[[]]]]=>2
[1,5,4,2,5,2]=>[[[[[]]],[[]]]]=>1
[1,5,4,5,2,2]=>[[[]],[[],[[]]]]=>2
[1,5,5,2,2,4]=>[[],[[]],[[],[]]]=>3
[1,5,5,2,4,2]=>[[],[[],[[[]]]]]=>2
[1,5,5,4,2,2]=>[[],[[[]]],[[]]]=>3
[2,1,2,4,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,2,5,4,5]=>[[[[]],[[],[]]]]=>1
[2,1,2,5,5,4]=>[[[[]]],[[],[]]]=>2
[2,1,4,2,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,4,5,2,5]=>[[[[],[[[]]]]]]=>1
[2,1,4,5,5,2]=>[[[[]]],[[[]]]]=>2
[2,1,5,2,4,5]=>[[[[[[],[]]]]]]=>1
[2,1,5,2,5,4]=>[[[],[[[],[]]]]]=>1
[2,1,5,4,2,5]=>[[[],[[[[]]]]]]=>1
[2,1,5,4,5,2]=>[[[],[[],[[]]]]]=>1
[2,1,5,5,2,4]=>[[],[[],[[[]]]]]=>2
[2,1,5,5,4,2]=>[[],[[],[[[]]]]]=>2
[2,2,1,4,5,5]=>[[],[[[]]],[[]]]=>3
[2,2,1,5,4,5]=>[[],[[[]],[[]]]]=>2
[2,2,1,5,5,4]=>[[],[[]],[[],[]]]=>3
[2,2,4,1,5,5]=>[[],[],[[],[[]]]]=>3
[2,2,4,5,1,5]=>[[],[[[[[]]]]]]=>2
[2,2,4,5,5,1]=>[[],[[[]]],[[]]]=>3
[2,2,5,1,4,5]=>[[],[[],[],[[]]]]=>2
[2,2,5,1,5,4]=>[[],[[],[[[]]]]]=>2
[2,2,5,4,1,5]=>[[],[[[],[[]]]]]=>2
[2,2,5,4,5,1]=>[[],[[[]],[[]]]]=>2
[2,2,5,5,1,4]=>[[],[],[[],[],[]]]=>3
[2,2,5,5,4,1]=>[[],[[]],[[[]]]]=>3
[2,4,1,2,5,5]=>[[],[[[[[]]]]]]=>2
[2,4,1,5,2,5]=>[[[[],[],[[]]]]]=>1
[2,4,1,5,5,2]=>[[],[[],[],[[]]]]=>2
[2,4,2,1,5,5]=>[[[[[]]]],[[]]]=>2
[2,4,2,5,1,5]=>[[[[[]],[[]]]]]=>1
[2,4,2,5,5,1]=>[[[[]]],[[],[]]]=>2
[2,4,5,1,2,5]=>[[[[],[[],[]]]]]=>1
[2,4,5,1,5,2]=>[[[[[[],[]]]]]]=>1
[2,4,5,2,1,5]=>[[[[[],[[]]]]]]=>1
[2,4,5,2,5,1]=>[[[[[[],[]]]]]]=>1
[2,4,5,5,1,2]=>[[],[[[],[[]]]]]=>2
[2,4,5,5,2,1]=>[[[[]]],[[[]]]]=>2
[2,5,1,2,4,5]=>[[[],[[],[[]]]]]=>1
[2,5,1,2,5,4]=>[[[],[[]],[[]]]]=>1
[2,5,1,4,2,5]=>[[[],[],[],[[]]]]=>1
[2,5,1,4,5,2]=>[[[],[],[[[]]]]]=>1
[2,5,1,5,2,4]=>[[[],[[],[[]]]]]=>1
[2,5,1,5,4,2]=>[[[],[[[[]]]]]]=>1
[2,5,2,1,4,5]=>[[[],[[[[]]]]]]=>1
[2,5,2,1,5,4]=>[[[[],[[],[]]]]]=>1
[2,5,2,4,1,5]=>[[[[[],[],[]]]]]=>1
[2,5,2,4,5,1]=>[[[],[[[[]]]]]]=>1
[2,5,2,5,1,4]=>[[[],[],[],[[]]]]=>1
[2,5,2,5,4,1]=>[[[],[[[],[]]]]]=>1
[2,5,4,1,2,5]=>[[[[[]]],[[]]]]=>1
[2,5,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[2,5,4,2,1,5]=>[[[[],[[[]]]]]]=>1
[2,5,4,2,5,1]=>[[[],[[]],[[]]]]=>1
[2,5,4,5,1,2]=>[[[],[[],[[]]]]]=>1
[2,5,4,5,2,1]=>[[[[[[],[]]]]]]=>1
[2,5,5,1,2,4]=>[[],[[],[[[]]]]]=>2
[2,5,5,1,4,2]=>[[],[[],[],[[]]]]=>2
[2,5,5,2,1,4]=>[[],[[[[],[]]]]]=>2
[2,5,5,2,4,1]=>[[[]],[[],[[]]]]=>2
[2,5,5,4,1,2]=>[[[]],[[[[]]]]]=>2
[2,5,5,4,2,1]=>[[],[[],[[[]]]]]=>2
[4,1,2,2,5,5]=>[[],[[[]]],[[]]]=>3
[4,1,2,5,2,5]=>[[[],[[],[[]]]]]=>1
[4,1,2,5,5,2]=>[[[[]]],[[],[]]]=>2
[4,1,5,2,2,5]=>[[[]],[[],[],[]]]=>2
[4,1,5,2,5,2]=>[[[],[],[],[[]]]]=>1
[4,1,5,5,2,2]=>[[],[],[[],[],[]]]=>3
[4,2,1,2,5,5]=>[[[[[]]]],[[]]]=>2
[4,2,1,5,2,5]=>[[[[],[[[]]]]]]=>1
[4,2,1,5,5,2]=>[[[]],[[],[[]]]]=>2
[4,2,2,1,5,5]=>[[],[[[]]],[[]]]=>3
[4,2,2,5,1,5]=>[[],[[[]],[[]]]]=>2
[4,2,2,5,5,1]=>[[],[[]],[[],[]]]=>3
[4,2,5,1,2,5]=>[[[[[],[],[]]]]]=>1
[4,2,5,1,5,2]=>[[[[],[[],[]]]]]=>1
[4,2,5,2,1,5]=>[[[[],[[[]]]]]]=>1
[4,2,5,2,5,1]=>[[[[],[],[[]]]]]=>1
[4,2,5,5,1,2]=>[[[]],[[],[[]]]]=>2
[4,2,5,5,2,1]=>[[[]],[[[[]]]]]=>2
[4,5,1,2,2,5]=>[[[],[]],[[],[]]]=>2
[4,5,1,2,5,2]=>[[[],[[],[[]]]]]=>1
[4,5,1,5,2,2]=>[[],[[],[[[]]]]]=>2
[4,5,2,1,2,5]=>[[[],[[[[]]]]]]=>1
[4,5,2,1,5,2]=>[[[[],[],[[]]]]]=>1
[4,5,2,2,1,5]=>[[],[[[],[[]]]]]=>2
[4,5,2,2,5,1]=>[[[[]]],[[],[]]]=>2
[4,5,2,5,1,2]=>[[[],[[],[[]]]]]=>1
[4,5,2,5,2,1]=>[[[[[]],[[]]]]]=>1
[4,5,5,1,2,2]=>[[],[],[[],[[]]]]=>3
[4,5,5,2,1,2]=>[[],[[[[],[]]]]]=>2
[4,5,5,2,2,1]=>[[[]],[[]],[[]]]=>3
[5,1,2,2,4,5]=>[[],[[[],[[]]]]]=>2
[5,1,2,2,5,4]=>[[[]],[[],[[]]]]=>2
[5,1,2,4,2,5]=>[[[],[[[[]]]]]]=>1
[5,1,2,4,5,2]=>[[[[[]],[[]]]]]=>1
[5,1,2,5,2,4]=>[[[[]],[[[]]]]]=>1
[5,1,2,5,4,2]=>[[[[]],[[[]]]]]=>1
[5,1,4,2,2,5]=>[[[]],[[],[],[]]]=>2
[5,1,4,2,5,2]=>[[[],[[]],[[]]]]=>1
[5,1,4,5,2,2]=>[[],[[[[],[]]]]]=>2
[5,1,5,2,2,4]=>[[[]],[[],[[]]]]=>2
[5,1,5,2,4,2]=>[[[[],[[[]]]]]]=>1
[5,1,5,4,2,2]=>[[[[]]],[[[]]]]=>2
[5,2,1,2,4,5]=>[[[[[]],[[]]]]]=>1
[5,2,1,2,5,4]=>[[[[[[],[]]]]]]=>1
[5,2,1,4,2,5]=>[[[[[],[[]]]]]]=>1
[5,2,1,4,5,2]=>[[[[[]]],[[]]]]=>1
[5,2,1,5,2,4]=>[[[],[],[[[]]]]]=>1
[5,2,1,5,4,2]=>[[[],[[[],[]]]]]=>1
[5,2,2,1,4,5]=>[[[]],[[[[]]]]]=>2
[5,2,2,1,5,4]=>[[],[[],[[],[]]]]=>2
[5,2,2,4,1,5]=>[[],[[[],[],[]]]]=>2
[5,2,2,4,5,1]=>[[[[[]]]],[[]]]=>2
[5,2,2,5,1,4]=>[[],[[],[],[[]]]]=>2
[5,2,2,5,4,1]=>[[],[[[[],[]]]]]=>2
[5,2,4,1,2,5]=>[[[[[]]],[[]]]]=>1
[5,2,4,1,5,2]=>[[[],[],[],[[]]]]=>1
[5,2,4,2,1,5]=>[[[[[]]],[[]]]]=>1
[5,2,4,2,5,1]=>[[[[],[[[]]]]]]=>1
[5,2,4,5,1,2]=>[[[[[],[[]]]]]]=>1
[5,2,4,5,2,1]=>[[[[[]]],[[]]]]=>1
[5,2,5,1,2,4]=>[[[[],[[[]]]]]]=>1
[5,2,5,1,4,2]=>[[[[],[],[[]]]]]=>1
[5,2,5,2,1,4]=>[[[],[[[],[]]]]]=>1
[5,2,5,2,4,1]=>[[[],[[]],[[]]]]=>1
[5,2,5,4,1,2]=>[[[],[[[[]]]]]]=>1
[5,2,5,4,2,1]=>[[[[],[[[]]]]]]=>1
[5,4,1,2,2,5]=>[[[[]]],[[[]]]]=>2
[5,4,1,2,5,2]=>[[[[],[[[]]]]]]=>1
[5,4,1,5,2,2]=>[[[]],[[],[],[]]]=>2
[5,4,2,1,2,5]=>[[[],[[[[]]]]]]=>1
[5,4,2,1,5,2]=>[[[],[[],[[]]]]]=>1
[5,4,2,2,1,5]=>[[],[[],[[[]]]]]=>2
[5,4,2,2,5,1]=>[[],[[[]],[[]]]]=>2
[5,4,2,5,1,2]=>[[[[[],[[]]]]]]=>1
[5,4,2,5,2,1]=>[[[[[]]],[[]]]]=>1
[5,4,5,1,2,2]=>[[[]],[[],[[]]]]=>2
[5,4,5,2,1,2]=>[[[[]],[[],[]]]]=>1
[5,4,5,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,5,1,2,2,4]=>[[],[[[]]],[[]]]=>3
[5,5,1,2,4,2]=>[[],[[[[[]]]]]]=>2
[5,5,1,4,2,2]=>[[],[],[[[],[]]]]=>3
[5,5,2,1,2,4]=>[[],[[[[[]]]]]]=>2
[5,5,2,1,4,2]=>[[],[[[[[]]]]]]=>2
[5,5,2,2,1,4]=>[[],[[]],[[[]]]]=>3
[5,5,2,2,4,1]=>[[],[],[[[],[]]]]=>3
[5,5,2,4,1,2]=>[[],[[[]],[[]]]]=>2
[5,5,2,4,2,1]=>[[],[[[[[]]]]]]=>2
[5,5,4,1,2,2]=>[[],[[[]]],[[]]]=>3
[5,5,4,2,1,2]=>[[],[[],[[[]]]]]=>2
[5,5,4,2,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,2,4,5,6]=>[[],[[[],[],[]]]]=>2
[1,2,2,4,6,5]=>[[[]],[[],[[]]]]=>2
[1,2,2,5,4,6]=>[[[]],[[[[]]]]]=>2
[1,2,2,5,6,4]=>[[],[[[],[[]]]]]=>2
[1,2,2,6,4,5]=>[[],[[[[],[]]]]]=>2
[1,2,2,6,5,4]=>[[[]],[[[],[]]]]=>2
[1,2,4,2,5,6]=>[[[],[[[[]]]]]]=>1
[1,2,4,2,6,5]=>[[[[[[[]]]]]]]=>1
[1,2,4,5,2,6]=>[[[[]],[[],[]]]]=>1
[1,2,4,5,6,2]=>[[[],[[]],[[]]]]=>1
[1,2,4,6,2,5]=>[[[[],[[],[]]]]]=>1
[1,2,4,6,5,2]=>[[[[],[[[]]]]]]=>1
[1,2,5,2,4,6]=>[[[[[[],[]]]]]]=>1
[1,2,5,2,6,4]=>[[[[[],[[]]]]]]=>1
[1,2,5,4,2,6]=>[[[[[[[]]]]]]]=>1
[1,2,5,4,6,2]=>[[[[[]],[[]]]]]=>1
[1,2,5,6,2,4]=>[[[],[[],[[]]]]]=>1
[1,2,5,6,4,2]=>[[[[]],[[],[]]]]=>1
[1,2,6,2,4,5]=>[[[],[[[[]]]]]]=>1
[1,2,6,2,5,4]=>[[[[[],[[]]]]]]=>1
[1,2,6,4,2,5]=>[[[[[],[[]]]]]]=>1
[1,2,6,4,5,2]=>[[[[]],[[],[]]]]=>1
[1,2,6,5,2,4]=>[[[[],[[[]]]]]]=>1
[1,2,6,5,4,2]=>[[[[[[],[]]]]]]=>1
[1,4,2,2,5,6]=>[[[]],[[],[[]]]]=>2
[1,4,2,2,6,5]=>[[[]],[[[[]]]]]=>2
[1,4,2,5,2,6]=>[[[],[[],[[]]]]]=>1
[1,4,2,5,6,2]=>[[[],[],[[[]]]]]=>1
[1,4,2,6,2,5]=>[[[],[[]],[[]]]]=>1
[1,4,2,6,5,2]=>[[[[[],[[]]]]]]=>1
[1,4,5,2,2,6]=>[[],[[],[[[]]]]]=>2
[1,4,5,2,6,2]=>[[[],[[],[[]]]]]=>1
[1,4,5,6,2,2]=>[[],[[],[[],[]]]]=>2
[1,4,6,2,2,5]=>[[],[[],[],[[]]]]=>2
[1,4,6,2,5,2]=>[[[],[[]],[[]]]]=>1
[1,4,6,5,2,2]=>[[[]],[[[[]]]]]=>2
[1,5,2,2,4,6]=>[[[],[]],[[],[]]]=>2
[1,5,2,2,6,4]=>[[],[[],[],[[]]]]=>2
[1,5,2,4,2,6]=>[[[],[],[[[]]]]]=>1
[1,5,2,4,6,2]=>[[[],[[],[[]]]]]=>1
[1,5,2,6,2,4]=>[[[],[],[[[]]]]]=>1
[1,5,2,6,4,2]=>[[[],[],[[],[]]]]=>1
[1,5,4,2,2,6]=>[[[]],[[],[[]]]]=>2
[1,5,4,2,6,2]=>[[[[[]]],[[]]]]=>1
[1,5,4,6,2,2]=>[[[[]]],[[[]]]]=>2
[1,5,6,2,2,4]=>[[[]],[[[[]]]]]=>2
[1,5,6,2,4,2]=>[[[[[[[]]]]]]]=>1
[1,5,6,4,2,2]=>[[],[[[]],[[]]]]=>2
[1,6,2,2,4,5]=>[[[[]]],[[[]]]]=>2
[1,6,2,2,5,4]=>[[],[[],[[[]]]]]=>2
[1,6,2,4,2,5]=>[[[[]],[[],[]]]]=>1
[1,6,2,4,5,2]=>[[[[[[[]]]]]]]=>1
[1,6,2,5,2,4]=>[[[[],[[[]]]]]]=>1
[1,6,2,5,4,2]=>[[[],[[[],[]]]]]=>1
[1,6,4,2,2,5]=>[[[]],[[],[],[]]]=>2
[1,6,4,2,5,2]=>[[[],[],[[[]]]]]=>1
[1,6,4,5,2,2]=>[[],[[[[],[]]]]]=>2
[1,6,5,2,2,4]=>[[[[]]],[[[]]]]=>2
[1,6,5,2,4,2]=>[[[[[]]],[[]]]]=>1
[1,6,5,4,2,2]=>[[[],[]],[[],[]]]=>2
[2,1,2,4,5,6]=>[[[[],[],[[]]]]]=>1
[2,1,2,4,6,5]=>[[[],[[],[[]]]]]=>1
[2,1,2,5,4,6]=>[[[[]],[[[]]]]]=>1
[2,1,2,5,6,4]=>[[[[[],[[]]]]]]=>1
[2,1,2,6,4,5]=>[[[[],[[[]]]]]]=>1
[2,1,2,6,5,4]=>[[[],[],[[[]]]]]=>1
[2,1,4,2,5,6]=>[[[[[],[[]]]]]]=>1
[2,1,4,2,6,5]=>[[[[[]]],[[]]]]=>1
[2,1,4,5,2,6]=>[[[[],[[[]]]]]]=>1
[2,1,4,5,6,2]=>[[[[],[[],[]]]]]=>1
[2,1,4,6,2,5]=>[[[[],[],[[]]]]]=>1
[2,1,4,6,5,2]=>[[[[[]]],[[]]]]=>1
[2,1,5,2,4,6]=>[[[[],[[],[]]]]]=>1
[2,1,5,2,6,4]=>[[[[[],[],[]]]]]=>1
[2,1,5,4,2,6]=>[[[],[[],[[]]]]]=>1
[2,1,5,4,6,2]=>[[[[[]]],[[]]]]=>1
[2,1,5,6,2,4]=>[[[[[[[]]]]]]]=>1
[2,1,5,6,4,2]=>[[[[[]],[[]]]]]=>1
[2,1,6,2,4,5]=>[[[[[[[]]]]]]]=>1
[2,1,6,2,5,4]=>[[[[]],[[],[]]]]=>1
[2,1,6,4,2,5]=>[[[[[],[],[]]]]]=>1
[2,1,6,4,5,2]=>[[[[[[],[]]]]]]=>1
[2,1,6,5,2,4]=>[[[],[[[[]]]]]]=>1
[2,1,6,5,4,2]=>[[[],[],[[],[]]]]=>1
[2,2,1,4,5,6]=>[[],[[[],[[]]]]]=>2
[2,2,1,4,6,5]=>[[],[[],[[[]]]]]=>2
[2,2,1,5,4,6]=>[[],[[[]],[[]]]]=>2
[2,2,1,5,6,4]=>[[],[[[[[]]]]]]=>2
[2,2,1,6,4,5]=>[[],[[[[],[]]]]]=>2
[2,2,1,6,5,4]=>[[],[[],[],[[]]]]=>2
[2,2,4,1,5,6]=>[[],[[[],[[]]]]]=>2
[2,2,4,1,6,5]=>[[],[[[[[]]]]]]=>2
[2,2,4,5,1,6]=>[[],[[[[[]]]]]]=>2
[2,2,4,5,6,1]=>[[],[[],[[],[]]]]=>2
[2,2,4,6,1,5]=>[[],[[],[],[[]]]]=>2
[2,2,4,6,5,1]=>[[],[[],[[[]]]]]=>2
[2,2,5,1,4,6]=>[[],[[],[],[[]]]]=>2
[2,2,5,1,6,4]=>[[],[[],[[],[]]]]=>2
[2,2,5,4,1,6]=>[[],[[[[[]]]]]]=>2
[2,2,5,4,6,1]=>[[],[[[[],[]]]]]=>2
[2,2,5,6,1,4]=>[[],[[],[[[]]]]]=>2
[2,2,5,6,4,1]=>[[],[[[[[]]]]]]=>2
[2,2,6,1,4,5]=>[[],[[[[[]]]]]]=>2
[2,2,6,1,5,4]=>[[],[[[]],[[]]]]=>2
[2,2,6,4,1,5]=>[[],[[],[],[[]]]]=>2
[2,2,6,4,5,1]=>[[],[[[[[]]]]]]=>2
[2,2,6,5,1,4]=>[[],[[[],[[]]]]]=>2
[2,2,6,5,4,1]=>[[],[[],[[],[]]]]=>2
[2,4,1,2,5,6]=>[[[[[],[[]]]]]]=>1
[2,4,1,2,6,5]=>[[[[[]],[[]]]]]=>1
[2,4,1,5,2,6]=>[[[[],[],[],[]]]]=>1
[2,4,1,5,6,2]=>[[[[],[[[]]]]]]=>1
[2,4,1,6,2,5]=>[[[[[],[[]]]]]]=>1
[2,4,1,6,5,2]=>[[[[[],[[]]]]]]=>1
[2,4,2,1,5,6]=>[[[[[[[]]]]]]]=>1
[2,4,2,1,6,5]=>[[[[],[[],[]]]]]=>1
[2,4,2,5,1,6]=>[[[[],[[],[]]]]]=>1
[2,4,2,5,6,1]=>[[[],[[[[]]]]]]=>1
[2,4,2,6,1,5]=>[[[[]],[[],[]]]]=>1
[2,4,2,6,5,1]=>[[[[[[[]]]]]]]=>1
[2,4,5,1,2,6]=>[[[[[]],[[]]]]]=>1
[2,4,5,1,6,2]=>[[[[[],[[]]]]]]=>1
[2,4,5,2,1,6]=>[[[[[[[]]]]]]]=>1
[2,4,5,2,6,1]=>[[[],[[],[[]]]]]=>1
[2,4,5,6,1,2]=>[[[],[[],[],[]]]]=>1
[2,4,5,6,2,1]=>[[[[],[[[]]]]]]=>1
[2,4,6,1,2,5]=>[[[],[],[[[]]]]]=>1
[2,4,6,1,5,2]=>[[[],[],[[],[]]]]=>1
[2,4,6,2,1,5]=>[[[],[[[[]]]]]]=>1
[2,4,6,2,5,1]=>[[[],[[],[],[]]]]=>1
[2,4,6,5,1,2]=>[[[],[[[[]]]]]]=>1
[2,4,6,5,2,1]=>[[[],[[],[[]]]]]=>1
[2,5,1,2,4,6]=>[[[],[[[],[]]]]]=>1
[2,5,1,2,6,4]=>[[[],[[[[]]]]]]=>1
[2,5,1,4,2,6]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,6,2]=>[[[],[],[],[[]]]]=>1
[2,5,1,6,2,4]=>[[[],[[]],[[]]]]=>1
[2,5,1,6,4,2]=>[[[],[[],[],[]]]]=>1
[2,5,2,1,4,6]=>[[[],[[[[]]]]]]=>1
[2,5,2,1,6,4]=>[[[[[]],[[]]]]]=>1
[2,5,2,4,1,6]=>[[[[[],[[]]]]]]=>1
[2,5,2,4,6,1]=>[[[[],[],[[]]]]]=>1
[2,5,2,6,1,4]=>[[[],[[[],[]]]]]=>1
[2,5,2,6,4,1]=>[[[[[],[],[]]]]]=>1
[2,5,4,1,2,6]=>[[[[[]],[[]]]]]=>1
[2,5,4,1,6,2]=>[[[[[]]],[[]]]]=>1
[2,5,4,2,1,6]=>[[[[],[[],[]]]]]=>1
[2,5,4,2,6,1]=>[[[[[[[]]]]]]]=>1
[2,5,4,6,1,2]=>[[[[[[],[]]]]]]=>1
[2,5,4,6,2,1]=>[[[[]],[[],[]]]]=>1
[2,5,6,1,2,4]=>[[[[],[[],[]]]]]=>1
[2,5,6,1,4,2]=>[[[[[]]],[[]]]]=>1
[2,5,6,2,1,4]=>[[[],[[]],[[]]]]=>1
[2,5,6,2,4,1]=>[[[[]],[[[]]]]]=>1
[2,5,6,4,1,2]=>[[[[[[],[]]]]]]=>1
[2,5,6,4,2,1]=>[[[[[]],[[]]]]]=>1
[2,6,1,2,4,5]=>[[[[],[[],[]]]]]=>1
[2,6,1,2,5,4]=>[[[[[[[]]]]]]]=>1
[2,6,1,4,2,5]=>[[[[[],[[]]]]]]=>1
[2,6,1,4,5,2]=>[[[],[[[[]]]]]]=>1
[2,6,1,5,2,4]=>[[[],[],[[],[]]]]=>1
[2,6,1,5,4,2]=>[[[[]],[[[]]]]]=>1
[2,6,2,1,4,5]=>[[[[[[],[]]]]]]=>1
[2,6,2,1,5,4]=>[[[[]],[[],[]]]]=>1
[2,6,2,4,1,5]=>[[[],[],[[[]]]]]=>1
[2,6,2,4,5,1]=>[[[[],[[[]]]]]]=>1
[2,6,2,5,1,4]=>[[[[],[],[],[]]]]=>1
[2,6,2,5,4,1]=>[[[],[[[],[]]]]]=>1
[2,6,4,1,2,5]=>[[[[[]]],[[]]]]=>1
[2,6,4,1,5,2]=>[[[],[],[],[[]]]]=>1
[2,6,4,2,1,5]=>[[[[]],[[],[]]]]=>1
[2,6,4,2,5,1]=>[[[[],[[],[]]]]]=>1
[2,6,4,5,1,2]=>[[[[],[[[]]]]]]=>1
[2,6,4,5,2,1]=>[[[[]],[[[]]]]]=>1
[2,6,5,1,2,4]=>[[[[[[[]]]]]]]=>1
[2,6,5,1,4,2]=>[[[[],[[[]]]]]]=>1
[2,6,5,2,1,4]=>[[[],[[],[[]]]]]=>1
[2,6,5,2,4,1]=>[[[],[[]],[[]]]]=>1
[2,6,5,4,1,2]=>[[[],[[[],[]]]]]=>1
[2,6,5,4,2,1]=>[[[[],[],[[]]]]]=>1
[4,1,2,2,5,6]=>[[],[[[],[[]]]]]=>2
[4,1,2,2,6,5]=>[[[]],[[],[[]]]]=>2
[4,1,2,5,2,6]=>[[[],[],[[[]]]]]=>1
[4,1,2,5,6,2]=>[[[[],[[],[]]]]]=>1
[4,1,2,6,2,5]=>[[[[]],[[],[]]]]=>1
[4,1,2,6,5,2]=>[[[],[[]],[[]]]]=>1
[4,1,5,2,2,6]=>[[],[[],[],[],[]]]=>2
[4,1,5,2,6,2]=>[[[],[],[],[[]]]]=>1
[4,1,5,6,2,2]=>[[],[[[[],[]]]]]=>2
[4,1,6,2,2,5]=>[[[]],[[],[[]]]]=>2
[4,1,6,2,5,2]=>[[[],[[],[[]]]]]=>1
[4,1,6,5,2,2]=>[[[]],[[],[[]]]]=>2
[4,2,1,2,5,6]=>[[[[[],[[]]]]]]=>1
[4,2,1,2,6,5]=>[[[[],[[[]]]]]]=>1
[4,2,1,5,2,6]=>[[[[],[],[[]]]]]=>1
[4,2,1,5,6,2]=>[[[[[[[]]]]]]]=>1
[4,2,1,6,2,5]=>[[[],[[],[[]]]]]=>1
[4,2,1,6,5,2]=>[[[],[[[],[]]]]]=>1
[4,2,2,1,5,6]=>[[],[[[[[]]]]]]=>2
[4,2,2,1,6,5]=>[[],[[],[[],[]]]]=>2
[4,2,2,5,1,6]=>[[],[[],[[],[]]]]=>2
[4,2,2,5,6,1]=>[[[[[]]]],[[]]]=>2
[4,2,2,6,1,5]=>[[],[[],[[[]]]]]=>2
[4,2,2,6,5,1]=>[[],[[[[[]]]]]]=>2
[4,2,5,1,2,6]=>[[[[],[[[]]]]]]=>1
[4,2,5,1,6,2]=>[[[],[[],[],[]]]]=>1
[4,2,5,2,1,6]=>[[[[]],[[[]]]]]=>1
[4,2,5,2,6,1]=>[[[[[]],[[]]]]]=>1
[4,2,5,6,1,2]=>[[[[[],[[]]]]]]=>1
[4,2,5,6,2,1]=>[[[[[],[[]]]]]]=>1
[4,2,6,1,2,5]=>[[[[[[[]]]]]]]=>1
[4,2,6,1,5,2]=>[[[[],[],[[]]]]]=>1
[4,2,6,2,1,5]=>[[[[],[[[]]]]]]=>1
[4,2,6,2,5,1]=>[[[[],[],[[]]]]]=>1
[4,2,6,5,1,2]=>[[[[[[[]]]]]]]=>1
[4,2,6,5,2,1]=>[[[[],[[],[]]]]]=>1
[4,5,1,2,2,6]=>[[[]],[[],[[]]]]=>2
[4,5,1,2,6,2]=>[[[],[[[],[]]]]]=>1
[4,5,1,6,2,2]=>[[],[[[]],[[]]]]=>2
[4,5,2,1,2,6]=>[[[],[[],[[]]]]]=>1
[4,5,2,1,6,2]=>[[[[[[[]]]]]]]=>1
[4,5,2,2,1,6]=>[[],[[[[[]]]]]]=>2
[4,5,2,2,6,1]=>[[],[[[]],[[]]]]=>2
[4,5,2,6,1,2]=>[[[],[[[],[]]]]]=>1
[4,5,2,6,2,1]=>[[[[],[[[]]]]]]=>1
[4,5,6,1,2,2]=>[[],[[],[],[[]]]]=>2
[4,5,6,2,1,2]=>[[[],[],[[[]]]]]=>1
[4,5,6,2,2,1]=>[[[[],[]]],[[]]]=>2
[4,6,1,2,2,5]=>[[[[],[]]],[[]]]=>2
[4,6,1,2,5,2]=>[[[],[[[[]]]]]]=>1
[4,6,1,5,2,2]=>[[],[[],[[],[]]]]=>2
[4,6,2,1,2,5]=>[[[[[]],[[]]]]]=>1
[4,6,2,1,5,2]=>[[[[[],[[]]]]]]=>1
[4,6,2,2,1,5]=>[[[[]]],[[[]]]]=>2
[4,6,2,2,5,1]=>[[],[[],[],[[]]]]=>2
[4,6,2,5,1,2]=>[[[[],[],[[]]]]]=>1
[4,6,2,5,2,1]=>[[[[],[[[]]]]]]=>1
[4,6,5,1,2,2]=>[[[[]]],[[[]]]]=>2
[4,6,5,2,1,2]=>[[[[[]],[[]]]]]=>1
[4,6,5,2,2,1]=>[[[]],[[],[[]]]]=>2
[5,1,2,2,4,6]=>[[[[]]],[[],[]]]=>2
[5,1,2,2,6,4]=>[[[[]]],[[[]]]]=>2
[5,1,2,4,2,6]=>[[[[[[[]]]]]]]=>1
[5,1,2,4,6,2]=>[[[],[[],[[]]]]]=>1
[5,1,2,6,2,4]=>[[[[]],[[[]]]]]=>1
[5,1,2,6,4,2]=>[[[[],[[[]]]]]]=>1
[5,1,4,2,2,6]=>[[[]],[[[],[]]]]=>2
[5,1,4,2,6,2]=>[[[],[],[[[]]]]]=>1
[5,1,4,6,2,2]=>[[],[[],[],[[]]]]=>2
[5,1,6,2,2,4]=>[[[]],[[],[[]]]]=>2
[5,1,6,2,4,2]=>[[[],[[[],[]]]]]=>1
[5,1,6,4,2,2]=>[[],[[],[],[[]]]]=>2
[5,2,1,2,4,6]=>[[[[[],[[]]]]]]=>1
[5,2,1,2,6,4]=>[[[[]],[[[]]]]]=>1
[5,2,1,4,2,6]=>[[[[[]]],[[]]]]=>1
[5,2,1,4,6,2]=>[[[[[]],[[]]]]]=>1
[5,2,1,6,2,4]=>[[[[[[[]]]]]]]=>1
[5,2,1,6,4,2]=>[[[[],[],[[]]]]]=>1
[5,2,2,1,4,6]=>[[[]],[[[[]]]]]=>2
[5,2,2,1,6,4]=>[[],[[[],[[]]]]]=>2
[5,2,2,4,1,6]=>[[],[[[],[[]]]]]=>2
[5,2,2,4,6,1]=>[[],[[],[],[[]]]]=>2
[5,2,2,6,1,4]=>[[],[[],[[[]]]]]=>2
[5,2,2,6,4,1]=>[[],[[],[],[[]]]]=>2
[5,2,4,1,2,6]=>[[[],[[]],[[]]]]=>1
[5,2,4,1,6,2]=>[[[[]],[[[]]]]]=>1
[5,2,4,2,1,6]=>[[[[[]],[[]]]]]=>1
[5,2,4,2,6,1]=>[[[[]],[[],[]]]]=>1
[5,2,4,6,1,2]=>[[[[],[],[[]]]]]=>1
[5,2,4,6,2,1]=>[[[[],[[[]]]]]]=>1
[5,2,6,1,2,4]=>[[[],[[],[[]]]]]=>1
[5,2,6,1,4,2]=>[[[],[[[[]]]]]]=>1
[5,2,6,2,1,4]=>[[[],[[[],[]]]]]=>1
[5,2,6,2,4,1]=>[[[],[],[[[]]]]]=>1
[5,2,6,4,1,2]=>[[[],[[]],[[]]]]=>1
[5,2,6,4,2,1]=>[[[],[[[],[]]]]]=>1
[5,4,1,2,2,6]=>[[[]],[[],[[]]]]=>2
[5,4,1,2,6,2]=>[[[[[],[[]]]]]]=>1
[5,4,1,6,2,2]=>[[[[[]]]],[[]]]=>2
[5,4,2,1,2,6]=>[[[],[[[[]]]]]]=>1
[5,4,2,1,6,2]=>[[[],[[[],[]]]]]=>1
[5,4,2,2,1,6]=>[[],[[],[[],[]]]]=>2
[5,4,2,2,6,1]=>[[[[[]]]],[[]]]=>2
[5,4,2,6,1,2]=>[[[[[[[]]]]]]]=>1
[5,4,2,6,2,1]=>[[[[[]]],[[]]]]=>1
[5,4,6,1,2,2]=>[[[[],[]]],[[]]]=>2
[5,4,6,2,1,2]=>[[[[]],[[[]]]]]=>1
[5,4,6,2,2,1]=>[[[[]]],[[],[]]]=>2
[5,6,1,2,2,4]=>[[[],[]],[[],[]]]=>2
[5,6,1,2,4,2]=>[[[],[[],[[]]]]]=>1
[5,6,1,4,2,2]=>[[],[[[[[]]]]]]=>2
[5,6,2,1,2,4]=>[[[],[[[[]]]]]]=>1
[5,6,2,1,4,2]=>[[[[],[[[]]]]]]=>1
[5,6,2,2,1,4]=>[[],[[[],[[]]]]]=>2
[5,6,2,2,4,1]=>[[[[]]],[[[]]]]=>2
[5,6,2,4,1,2]=>[[[],[[[[]]]]]]=>1
[5,6,2,4,2,1]=>[[[[[[[]]]]]]]=>1
[5,6,4,1,2,2]=>[[],[[],[[[]]]]]=>2
[5,6,4,2,1,2]=>[[[[]],[[],[]]]]=>1
[5,6,4,2,2,1]=>[[],[[[],[[]]]]]=>2
[6,1,2,2,4,5]=>[[],[[],[[],[]]]]=>2
[6,1,2,2,5,4]=>[[[[]]],[[[]]]]=>2
[6,1,2,4,2,5]=>[[[[]],[[[]]]]]=>1
[6,1,2,4,5,2]=>[[[],[[],[[]]]]]=>1
[6,1,2,5,2,4]=>[[[],[[[[]]]]]]=>1
[6,1,2,5,4,2]=>[[[[[[[]]]]]]]=>1
[6,1,4,2,2,5]=>[[[]],[[],[[]]]]=>2
[6,1,4,2,5,2]=>[[[[[],[[]]]]]]=>1
[6,1,4,5,2,2]=>[[],[[[[[]]]]]]=>2
[6,1,5,2,2,4]=>[[[],[]],[[],[]]]=>2
[6,1,5,2,4,2]=>[[[[]],[[],[]]]]=>1
[6,1,5,4,2,2]=>[[[[[]]]],[[]]]=>2
[6,2,1,2,4,5]=>[[[[[],[[]]]]]]=>1
[6,2,1,2,5,4]=>[[[[]],[[],[]]]]=>1
[6,2,1,4,2,5]=>[[[],[[]],[[]]]]=>1
[6,2,1,4,5,2]=>[[[],[[[[]]]]]]=>1
[6,2,1,5,2,4]=>[[[[],[[[]]]]]]=>1
[6,2,1,5,4,2]=>[[[[],[[[]]]]]]=>1
[6,2,2,1,4,5]=>[[],[[[[],[]]]]]=>2
[6,2,2,1,5,4]=>[[],[[],[[[]]]]]=>2
[6,2,2,4,1,5]=>[[[[],[]]],[[]]]=>2
[6,2,2,4,5,1]=>[[],[[[[],[]]]]]=>2
[6,2,2,5,1,4]=>[[],[[],[],[],[]]]=>2
[6,2,2,5,4,1]=>[[],[[],[[[]]]]]=>2
[6,2,4,1,2,5]=>[[[],[[[[]]]]]]=>1
[6,2,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[6,2,4,2,1,5]=>[[[[[[[]]]]]]]=>1
[6,2,4,2,5,1]=>[[[],[],[[[]]]]]=>1
[6,2,4,5,1,2]=>[[[],[[],[[]]]]]=>1
[6,2,4,5,2,1]=>[[[[[[[]]]]]]]=>1
[6,2,5,1,2,4]=>[[[],[],[[[]]]]]=>1
[6,2,5,1,4,2]=>[[[],[],[],[[]]]]=>1
[6,2,5,2,1,4]=>[[[],[],[[[]]]]]=>1
[6,2,5,2,4,1]=>[[[],[[],[[]]]]]=>1
[6,2,5,4,1,2]=>[[[],[[[[]]]]]]=>1
[6,2,5,4,2,1]=>[[[],[[[],[]]]]]=>1
[6,4,1,2,2,5]=>[[[[[]]]],[[]]]=>2
[6,4,1,2,5,2]=>[[[[[[],[]]]]]]=>1
[6,4,1,5,2,2]=>[[],[[],[],[[]]]]=>2
[6,4,2,1,2,5]=>[[[],[[[[]]]]]]=>1
[6,4,2,1,5,2]=>[[[],[[],[[]]]]]=>1
[6,4,2,2,1,5]=>[[],[[[[],[]]]]]=>2
[6,4,2,2,5,1]=>[[],[[],[[],[]]]]=>2
[6,4,2,5,1,2]=>[[[],[[],[[]]]]]=>1
[6,4,2,5,2,1]=>[[[],[[[[]]]]]]=>1
[6,4,5,1,2,2]=>[[],[[],[[[]]]]]=>2
[6,4,5,2,1,2]=>[[[[],[[[]]]]]]=>1
[6,4,5,2,2,1]=>[[[[]]],[[[]]]]=>2
[6,5,1,2,2,4]=>[[[[]]],[[[]]]]=>2
[6,5,1,2,4,2]=>[[[[[[[]]]]]]]=>1
[6,5,1,4,2,2]=>[[[[],[]]],[[]]]=>2
[6,5,2,1,2,4]=>[[[[[]]],[[]]]]=>1
[6,5,2,1,4,2]=>[[[],[[[[]]]]]]=>1
[6,5,2,2,1,4]=>[[[]],[[],[[]]]]=>2
[6,5,2,2,4,1]=>[[],[[[],[[]]]]]=>2
[6,5,2,4,1,2]=>[[[[[],[[]]]]]]=>1
[6,5,2,4,2,1]=>[[[[]],[[[]]]]]=>1
[6,5,4,1,2,2]=>[[[[]]],[[],[]]]=>2
[6,5,4,2,1,2]=>[[[],[],[[[]]]]]=>1
[6,5,4,2,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,3,3,3,3]=>[[],[],[],[[],[]]]=>4
[1,3,2,3,3,3]=>[[],[[]],[[[]]]]=>3
[1,3,3,2,3,3]=>[[[]],[[]],[[]]]=>3
[1,3,3,3,2,3]=>[[],[[]],[[[]]]]=>3
[1,3,3,3,3,2]=>[[],[],[[]],[[]]]=>4
[2,1,3,3,3,3]=>[[],[],[[]],[[]]]=>4
[2,3,1,3,3,3]=>[[],[[]],[[[]]]]=>3
[2,3,3,1,3,3]=>[[],[[]],[[[]]]]=>3
[2,3,3,3,1,3]=>[[],[[]],[[[]]]]=>3
[2,3,3,3,3,1]=>[[],[],[[]],[[]]]=>4
[3,1,2,3,3,3]=>[[],[[]],[[],[]]]=>3
[3,1,3,2,3,3]=>[[[[]]],[[[]]]]=>2
[3,1,3,3,2,3]=>[[[]],[[[[]]]]]=>2
[3,1,3,3,3,2]=>[[],[[]],[[[]]]]=>3
[3,2,1,3,3,3]=>[[],[[]],[[],[]]]=>3
[3,2,3,1,3,3]=>[[[[[]]]],[[]]]=>2
[3,2,3,3,1,3]=>[[[]],[[[[]]]]]=>2
[3,2,3,3,3,1]=>[[],[[]],[[[]]]]=>3
[3,3,1,2,3,3]=>[[],[],[[],[[]]]]=>3
[3,3,1,3,2,3]=>[[],[[[[[]]]]]]=>2
[3,3,1,3,3,2]=>[[],[[]],[[[]]]]=>3
[3,3,2,1,3,3]=>[[],[[]],[[],[]]]=>3
[3,3,2,3,1,3]=>[[],[[[[[]]]]]]=>2
[3,3,2,3,3,1]=>[[],[[]],[[[]]]]=>3
[3,3,3,1,2,3]=>[[],[],[[[],[]]]]=>3
[3,3,3,1,3,2]=>[[],[],[[[[]]]]]=>3
[3,3,3,2,1,3]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,3,1]=>[[],[],[[[[]]]]]=>3
[3,3,3,3,1,2]=>[[],[],[],[[[]]]]=>4
[3,3,3,3,2,1]=>[[],[],[],[[],[]]]=>4
[1,2,3,3,3,4]=>[[],[],[[],[],[]]]=>3
[1,2,3,3,4,3]=>[[],[[],[],[[]]]]=>2
[1,2,3,4,3,3]=>[[],[[[],[],[]]]]=>2
[1,2,4,3,3,3]=>[[],[],[[[[]]]]]=>3
[1,3,2,3,3,4]=>[[],[[],[[[]]]]]=>2
[1,3,2,3,4,3]=>[[[[],[[],[]]]]]=>1
[1,3,2,4,3,3]=>[[],[[],[[],[]]]]=>2
[1,3,3,2,3,4]=>[[[]],[[[],[]]]]=>2
[1,3,3,2,4,3]=>[[],[[],[[],[]]]]=>2
[1,3,3,3,2,4]=>[[],[],[[[],[]]]]=>3
[1,3,3,3,4,2]=>[[],[[[]]],[[]]]=>3
[1,3,3,4,2,3]=>[[[]],[[],[[]]]]=>2
[1,3,3,4,3,2]=>[[[[],[]]],[[]]]=>2
[1,3,4,2,3,3]=>[[],[[[]],[[]]]]=>2
[1,3,4,3,2,3]=>[[[[],[[],[]]]]]=>1
[1,3,4,3,3,2]=>[[],[[],[[[]]]]]=>2
[1,4,2,3,3,3]=>[[],[[]],[[[]]]]=>3
[1,4,3,2,3,3]=>[[[]],[[],[[]]]]=>2
[1,4,3,3,2,3]=>[[],[[[]],[[]]]]=>2
[1,4,3,3,3,2]=>[[],[[]],[[],[]]]=>3
[2,1,3,3,3,4]=>[[],[[[]]],[[]]]=>3
[2,1,3,3,4,3]=>[[[[],[]]],[[]]]=>2
[2,1,3,4,3,3]=>[[],[[],[[[]]]]]=>2
[2,1,4,3,3,3]=>[[],[],[[],[[]]]]=>3
[2,3,1,3,3,4]=>[[[[]]],[[],[]]]=>2
[2,3,1,3,4,3]=>[[[[]],[[[]]]]]=>1
[2,3,1,4,3,3]=>[[[[]]],[[[]]]]=>2
[2,3,3,1,3,4]=>[[],[[[[],[]]]]]=>2
[2,3,3,1,4,3]=>[[[]],[[[[]]]]]=>2
[2,3,3,3,1,4]=>[[],[[]],[[[]]]]=>3
[2,3,3,3,4,1]=>[[],[],[[],[[]]]]=>3
[2,3,3,4,1,3]=>[[],[[],[[[]]]]]=>2
[2,3,3,4,3,1]=>[[],[[],[[[]]]]]=>2
[2,3,4,1,3,3]=>[[],[[[[],[]]]]]=>2
[2,3,4,3,1,3]=>[[[],[[[[]]]]]]=>1
[2,3,4,3,3,1]=>[[],[[[[],[]]]]]=>2
[2,4,1,3,3,3]=>[[],[],[[],[[]]]]=>3
[2,4,3,1,3,3]=>[[[]],[[],[[]]]]=>2
[2,4,3,3,1,3]=>[[],[[[],[[]]]]]=>2
[2,4,3,3,3,1]=>[[],[],[[[[]]]]]=>3
[3,1,2,3,3,4]=>[[[]],[[],[],[]]]=>2
[3,1,2,3,4,3]=>[[[[[],[],[]]]]]=>1
[3,1,2,4,3,3]=>[[[]],[[[[]]]]]=>2
[3,1,3,2,3,4]=>[[[[],[[[]]]]]]=>1
[3,1,3,2,4,3]=>[[[[],[[],[]]]]]=>1
[3,1,3,3,2,4]=>[[],[[[],[[]]]]]=>2
[3,1,3,3,4,2]=>[[[[],[]]],[[]]]=>2
[3,1,3,4,2,3]=>[[[],[[],[[]]]]]=>1
[3,1,3,4,3,2]=>[[[[],[[[]]]]]]=>1
[3,1,4,2,3,3]=>[[],[[[],[[]]]]]=>2
[3,1,4,3,2,3]=>[[[[[],[[]]]]]]=>1
[3,1,4,3,3,2]=>[[],[[[]],[[]]]]=>2
[3,2,1,3,3,4]=>[[[[],[]]],[[]]]=>2
[3,2,1,3,4,3]=>[[[],[],[[[]]]]]=>1
[3,2,1,4,3,3]=>[[],[[],[],[[]]]]=>2
[3,2,3,1,3,4]=>[[[[],[[[]]]]]]=>1
[3,2,3,1,4,3]=>[[[[]],[[[]]]]]=>1
[3,2,3,3,1,4]=>[[[]],[[[[]]]]]=>2
[3,2,3,3,4,1]=>[[],[[],[[[]]]]]=>2
[3,2,3,4,1,3]=>[[[[[[],[]]]]]]=>1
[3,2,3,4,3,1]=>[[[[]],[[],[]]]]=>1
[3,2,4,1,3,3]=>[[[]],[[],[[]]]]=>2
[3,2,4,3,1,3]=>[[[],[[],[[]]]]]=>1
[3,2,4,3,3,1]=>[[],[[[],[[]]]]]=>2
[3,3,1,2,3,4]=>[[],[[[],[],[]]]]=>2
[3,3,1,2,4,3]=>[[],[[[[[]]]]]]=>2
[3,3,1,3,2,4]=>[[],[[[],[[]]]]]=>2
[3,3,1,3,4,2]=>[[],[[],[[[]]]]]=>2
[3,3,1,4,2,3]=>[[],[[[]],[[]]]]=>2
[3,3,1,4,3,2]=>[[],[[[],[[]]]]]=>2
[3,3,2,1,3,4]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,4,3]=>[[],[[],[],[[]]]]=>2
[3,3,2,3,1,4]=>[[],[[[[[]]]]]]=>2
[3,3,2,3,4,1]=>[[],[[[[],[]]]]]=>2
[3,3,2,4,1,3]=>[[],[[[],[[]]]]]=>2
[3,3,2,4,3,1]=>[[],[[[]],[[]]]]=>2
[3,3,3,1,2,4]=>[[],[],[[[[]]]]]=>3
[3,3,3,1,4,2]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,1,4]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,4,1]=>[[],[],[[[[]]]]]=>3
[3,3,3,4,1,2]=>[[],[],[[],[[]]]]=>3
[3,3,3,4,2,1]=>[[],[],[[[[]]]]]=>3
[3,3,4,1,2,3]=>[[],[[],[],[[]]]]=>2
[3,3,4,1,3,2]=>[[],[[[[[]]]]]]=>2
[3,3,4,2,1,3]=>[[],[[[[[]]]]]]=>2
[3,3,4,2,3,1]=>[[],[[],[[],[]]]]=>2
[3,3,4,3,1,2]=>[[],[[[]],[[]]]]=>2
[3,3,4,3,2,1]=>[[],[[[],[],[]]]]=>2
[3,4,1,2,3,3]=>[[],[[],[],[[]]]]=>2
[3,4,1,3,2,3]=>[[[],[[[[]]]]]]=>1
[3,4,1,3,3,2]=>[[[[[]]]],[[]]]=>2
[3,4,2,1,3,3]=>[[[[[]]]],[[]]]=>2
[3,4,2,3,1,3]=>[[[],[[],[[]]]]]=>1
[3,4,2,3,3,1]=>[[[],[]],[[],[]]]=>2
[3,4,3,1,2,3]=>[[[],[[]],[[]]]]=>1
[3,4,3,1,3,2]=>[[[[[]],[[]]]]]=>1
[3,4,3,2,1,3]=>[[[[],[],[[]]]]]=>1
[3,4,3,2,3,1]=>[[[],[[[],[]]]]]=>1
[3,4,3,3,1,2]=>[[],[[[],[[]]]]]=>2
[3,4,3,3,2,1]=>[[],[[],[],[[]]]]=>2
[4,1,2,3,3,3]=>[[],[],[[],[[]]]]=>3
[4,1,3,2,3,3]=>[[[]],[[[[]]]]]=>2
[4,1,3,3,2,3]=>[[[[]]],[[[]]]]=>2
[4,1,3,3,3,2]=>[[[]],[[]],[[]]]=>3
[4,2,1,3,3,3]=>[[[]],[[]],[[]]]=>3
[4,2,3,1,3,3]=>[[],[[[],[[]]]]]=>2
[4,2,3,3,1,3]=>[[[]],[[],[[]]]]=>2
[4,2,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[4,3,1,2,3,3]=>[[[]],[[],[[]]]]=>2
[4,3,1,3,2,3]=>[[[[[]]],[[]]]]=>1
[4,3,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,3,3]=>[[[]],[[],[],[]]]=>2
[4,3,2,3,1,3]=>[[[],[[[[]]]]]]=>1
[4,3,2,3,3,1]=>[[[]],[[[],[]]]]=>2
[4,3,3,1,2,3]=>[[],[[[],[[]]]]]=>2
[4,3,3,1,3,2]=>[[],[[[],[[]]]]]=>2
[4,3,3,2,1,3]=>[[],[[],[],[[]]]]=>2
[4,3,3,2,3,1]=>[[],[[],[[[]]]]]=>2
[4,3,3,3,1,2]=>[[],[],[[[[]]]]]=>3
[4,3,3,3,2,1]=>[[],[],[[],[],[]]]=>3
[1,2,3,3,3,5]=>[[],[[]],[[],[]]]=>3
[1,2,3,3,5,3]=>[[[[]]],[[],[]]]=>2
[1,2,3,5,3,3]=>[[],[[[[],[]]]]]=>2
[1,2,5,3,3,3]=>[[],[],[[[[]]]]]=>3
[1,3,2,3,3,5]=>[[[]],[[],[[]]]]=>2
[1,3,2,3,5,3]=>[[[[]],[[[]]]]]=>1
[1,3,2,5,3,3]=>[[[[]]],[[[]]]]=>2
[1,3,3,2,3,5]=>[[],[[[],[[]]]]]=>2
[1,3,3,2,5,3]=>[[[]],[[[[]]]]]=>2
[1,3,3,3,2,5]=>[[],[[]],[[[]]]]=>3
[1,3,3,3,5,2]=>[[],[],[[],[[]]]]=>3
[1,3,3,5,2,3]=>[[],[[],[[[]]]]]=>2
[1,3,3,5,3,2]=>[[],[[],[[[]]]]]=>2
[1,3,5,2,3,3]=>[[],[[[[],[]]]]]=>2
[1,3,5,3,2,3]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,3,2]=>[[],[[[[],[]]]]]=>2
[1,5,2,3,3,3]=>[[],[],[[[],[]]]]=>3
[1,5,3,2,3,3]=>[[[[]]],[[[]]]]=>2
[1,5,3,3,2,3]=>[[[]],[[[[]]]]]=>2
[1,5,3,3,3,2]=>[[],[[]],[[[]]]]=>3
[2,1,3,3,3,5]=>[[],[],[[],[[]]]]=>3
[2,1,3,3,5,3]=>[[],[[],[[[]]]]]=>2
[2,1,3,5,3,3]=>[[[[],[]]],[[]]]=>2
[2,1,5,3,3,3]=>[[[]],[[]],[[]]]=>3
[2,3,1,3,3,5]=>[[[[]]],[[],[]]]=>2
[2,3,1,3,5,3]=>[[[[],[[],[]]]]]=>1
[2,3,1,5,3,3]=>[[],[[[]],[[]]]]=>2
[2,3,3,1,3,5]=>[[[]],[[[],[]]]]=>2
[2,3,3,1,5,3]=>[[[]],[[],[[]]]]=>2
[2,3,3,3,1,5]=>[[],[[]],[[[]]]]=>3
[2,3,3,3,5,1]=>[[],[[]],[[[]]]]=>3
[2,3,3,5,1,3]=>[[[]],[[],[[]]]]=>2
[2,3,3,5,3,1]=>[[[]],[[[],[]]]]=>2
[2,3,5,1,3,3]=>[[],[[[]],[[]]]]=>2
[2,3,5,3,1,3]=>[[[[],[[],[]]]]]=>1
[2,3,5,3,3,1]=>[[],[[],[[[]]]]]=>2
[2,5,1,3,3,3]=>[[],[],[[[],[]]]]=>3
[2,5,3,1,3,3]=>[[],[[[],[[]]]]]=>2
[2,5,3,3,1,3]=>[[],[[[]],[[]]]]=>2
[2,5,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,1,2,3,3,5]=>[[[]],[[],[[]]]]=>2
[3,1,2,3,5,3]=>[[[],[[[],[]]]]]=>1
[3,1,2,5,3,3]=>[[],[[],[[[]]]]]=>2
[3,1,3,2,3,5]=>[[[[[],[[]]]]]]=>1
[3,1,3,2,5,3]=>[[[[]],[[[]]]]]=>1
[3,1,3,3,2,5]=>[[[]],[[[[]]]]]=>2
[3,1,3,3,5,2]=>[[[]],[[],[[]]]]=>2
[3,1,3,5,2,3]=>[[[[],[[[]]]]]]=>1
[3,1,3,5,3,2]=>[[[[]],[[],[]]]]=>1
[3,1,5,2,3,3]=>[[],[[[],[[]]]]]=>2
[3,1,5,3,2,3]=>[[[],[[[[]]]]]]=>1
[3,1,5,3,3,2]=>[[[]],[[[],[]]]]=>2
[3,2,1,3,3,5]=>[[],[[],[[],[]]]]=>2
[3,2,1,3,5,3]=>[[[],[[[],[]]]]]=>1
[3,2,1,5,3,3]=>[[[[]]],[[],[]]]=>2
[3,2,3,1,3,5]=>[[[[],[[[]]]]]]=>1
[3,2,3,1,5,3]=>[[[[[]],[[]]]]]=>1
[3,2,3,3,1,5]=>[[[]],[[[[]]]]]=>2
[3,2,3,3,5,1]=>[[[]],[[[[]]]]]=>2
[3,2,3,5,1,3]=>[[[[[]],[[]]]]]=>1
[3,2,3,5,3,1]=>[[[[],[[[]]]]]]=>1
[3,2,5,1,3,3]=>[[[[],[]]],[[]]]=>2
[3,2,5,3,1,3]=>[[[[[],[[]]]]]]=>1
[3,2,5,3,3,1]=>[[],[[[]],[[]]]]=>2
[3,3,1,2,3,5]=>[[],[[[],[[]]]]]=>2
[3,3,1,2,5,3]=>[[],[[],[[[]]]]]=>2
[3,3,1,3,2,5]=>[[],[[[[[]]]]]]=>2
[3,3,1,3,5,2]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,2,3]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,3,2]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,3,5]=>[[],[[],[[],[]]]]=>2
[3,3,2,1,5,3]=>[[],[[],[[[]]]]]=>2
[3,3,2,3,1,5]=>[[],[[[[[]]]]]]=>2
[3,3,2,3,5,1]=>[[],[[[[[]]]]]]=>2
[3,3,2,5,1,3]=>[[],[[[[],[]]]]]=>2
[3,3,2,5,3,1]=>[[],[[[],[[]]]]]=>2
[3,3,3,1,2,5]=>[[],[],[[[[]]]]]=>3
[3,3,3,1,5,2]=>[[],[],[[[],[]]]]=>3
[3,3,3,2,1,5]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,5,1]=>[[],[],[[[],[]]]]=>3
[3,3,3,5,1,2]=>[[],[],[[[[]]]]]=>3
[3,3,3,5,2,1]=>[[],[],[[[[]]]]]=>3
[3,3,5,1,2,3]=>[[],[[[[],[]]]]]=>2
[3,3,5,1,3,2]=>[[],[[[]],[[]]]]=>2
[3,3,5,2,1,3]=>[[],[[],[[[]]]]]=>2
[3,3,5,2,3,1]=>[[],[[[[[]]]]]]=>2
[3,3,5,3,1,2]=>[[],[[[],[[]]]]]=>2
[3,3,5,3,2,1]=>[[],[[[[],[]]]]]=>2
[3,5,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[3,5,1,3,2,3]=>[[[[]],[[[]]]]]=>1
[3,5,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[3,5,2,1,3,3]=>[[[[]]],[[],[]]]=>2
[3,5,2,3,1,3]=>[[[],[[[[]]]]]]=>1
[3,5,2,3,3,1]=>[[[[[]]]],[[]]]=>2
[3,5,3,1,2,3]=>[[[[],[[],[]]]]]=>1
[3,5,3,1,3,2]=>[[[],[[[],[]]]]]=>1
[3,5,3,2,1,3]=>[[[[]],[[],[]]]]=>1
[3,5,3,2,3,1]=>[[[[[]],[[]]]]]=>1
[3,5,3,3,1,2]=>[[],[[[]],[[]]]]=>2
[3,5,3,3,2,1]=>[[],[[],[[[]]]]]=>2
[5,1,2,3,3,3]=>[[],[],[[],[[]]]]=>3
[5,1,3,2,3,3]=>[[[]],[[[[]]]]]=>2
[5,1,3,3,2,3]=>[[[[]]],[[[]]]]=>2
[5,1,3,3,3,2]=>[[],[[[]]],[[]]]=>3
[5,2,1,3,3,3]=>[[],[[[]]],[[]]]=>3
[5,2,3,1,3,3]=>[[],[[[[[]]]]]]=>2
[5,2,3,3,1,3]=>[[[[]]],[[[]]]]=>2
[5,2,3,3,3,1]=>[[[]],[[]],[[]]]=>3
[5,3,1,2,3,3]=>[[],[[],[[],[]]]]=>2
[5,3,1,3,2,3]=>[[[],[[[[]]]]]]=>1
[5,3,1,3,3,2]=>[[[]],[[[],[]]]]=>2
[5,3,2,1,3,3]=>[[[[]]],[[],[]]]=>2
[5,3,2,3,1,3]=>[[[[]],[[[]]]]]=>1
[5,3,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,3,3,1,2,3]=>[[],[[],[[],[]]]]=>2
[5,3,3,1,3,2]=>[[],[[],[[[]]]]]=>2
[5,3,3,2,1,3]=>[[],[[],[[[]]]]]=>2
[5,3,3,2,3,1]=>[[],[[[],[[]]]]]=>2
[5,3,3,3,1,2]=>[[],[],[[],[[]]]]=>3
[5,3,3,3,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,3,3,3,6]=>[[],[[]],[[],[]]]=>3
[1,2,3,3,6,3]=>[[[[]]],[[],[]]]=>2
[1,2,3,6,3,3]=>[[],[[[[],[]]]]]=>2
[1,2,6,3,3,3]=>[[],[],[[],[[]]]]=>3
[1,3,2,3,3,6]=>[[[]],[[[[]]]]]=>2
[1,3,2,3,6,3]=>[[[[[[[]]]]]]]=>1
[1,3,2,6,3,3]=>[[[[]]],[[],[]]]=>2
[1,3,3,2,3,6]=>[[[]],[[[[]]]]]=>2
[1,3,3,2,6,3]=>[[[]],[[[],[]]]]=>2
[1,3,3,3,2,6]=>[[],[[]],[[[]]]]=>3
[1,3,3,3,6,2]=>[[],[[]],[[],[]]]=>3
[1,3,3,6,2,3]=>[[[]],[[],[[]]]]=>2
[1,3,3,6,3,2]=>[[[]],[[[[]]]]]=>2
[1,3,6,2,3,3]=>[[],[[[],[[]]]]]=>2
[1,3,6,3,2,3]=>[[[[[[[]]]]]]]=>1
[1,3,6,3,3,2]=>[[[[[]]]],[[]]]=>2
[1,6,2,3,3,3]=>[[],[[[]]],[[]]]=>3
[1,6,3,2,3,3]=>[[[[]]],[[[]]]]=>2
[1,6,3,3,2,3]=>[[[]],[[[[]]]]]=>2
[1,6,3,3,3,2]=>[[],[[]],[[[]]]]=>3
[2,1,3,3,3,6]=>[[],[[]],[[[]]]]=>3
[2,1,3,3,6,3]=>[[[]],[[[[]]]]]=>2
[2,1,3,6,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,6,3,3,3]=>[[[]],[[]],[[]]]=>3
[2,3,1,3,3,6]=>[[[[[]]]],[[]]]=>2
[2,3,1,3,6,3]=>[[[[[[[]]]]]]]=>1
[2,3,1,6,3,3]=>[[],[[[],[[]]]]]=>2
[2,3,3,1,3,6]=>[[[]],[[[[]]]]]=>2
[2,3,3,1,6,3]=>[[[]],[[],[[]]]]=>2
[2,3,3,3,1,6]=>[[],[[]],[[],[]]]=>3
[2,3,3,3,6,1]=>[[],[[]],[[[]]]]=>3
[2,3,3,6,1,3]=>[[[]],[[[],[]]]]=>2
[2,3,3,6,3,1]=>[[[]],[[[[]]]]]=>2
[2,3,6,1,3,3]=>[[],[[],[[[]]]]]=>2
[2,3,6,3,1,3]=>[[[[[[[]]]]]]]=>1
[2,3,6,3,3,1]=>[[[[[]]]],[[]]]=>2
[2,6,1,3,3,3]=>[[],[],[[],[[]]]]=>3
[2,6,3,1,3,3]=>[[],[[[[],[]]]]]=>2
[2,6,3,3,1,3]=>[[[[]]],[[],[]]]=>2
[2,6,3,3,3,1]=>[[],[[]],[[],[]]]=>3
[3,1,2,3,3,6]=>[[[]],[[],[[]]]]=>2
[3,1,2,3,6,3]=>[[[[],[[[]]]]]]=>1
[3,1,2,6,3,3]=>[[],[[[]],[[]]]]=>2
[3,1,3,2,3,6]=>[[[[[[[]]]]]]]=>1
[3,1,3,2,6,3]=>[[[[],[[[]]]]]]=>1
[3,1,3,3,2,6]=>[[[]],[[[[]]]]]=>2
[3,1,3,3,6,2]=>[[[]],[[],[[]]]]=>2
[3,1,3,6,2,3]=>[[[[[]],[[]]]]]=>1
[3,1,3,6,3,2]=>[[[[[[[]]]]]]]=>1
[3,1,6,2,3,3]=>[[],[[[[],[]]]]]=>2
[3,1,6,3,2,3]=>[[[],[[[[]]]]]]=>1
[3,1,6,3,3,2]=>[[[]],[[[],[]]]]=>2
[3,2,1,3,3,6]=>[[[]],[[[],[]]]]=>2
[3,2,1,3,6,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,3,3]=>[[[[]]],[[],[]]]=>2
[3,2,3,1,3,6]=>[[[[[[[]]]]]]]=>1
[3,2,3,1,6,3]=>[[[[[],[[]]]]]]=>1
[3,2,3,3,1,6]=>[[[]],[[],[[]]]]=>2
[3,2,3,3,6,1]=>[[[]],[[[[]]]]]=>2
[3,2,3,6,1,3]=>[[[[],[[[]]]]]]=>1
[3,2,3,6,3,1]=>[[[[[[[]]]]]]]=>1
[3,2,6,1,3,3]=>[[[]],[[],[[]]]]=>2
[3,2,6,3,1,3]=>[[[[[[],[]]]]]]=>1
[3,2,6,3,3,1]=>[[[[]]],[[],[]]]=>2
[3,3,1,2,3,6]=>[[],[[[],[[]]]]]=>2
[3,3,1,2,6,3]=>[[],[[[],[[]]]]]=>2
[3,3,1,3,2,6]=>[[],[[[[[]]]]]]=>2
[3,3,1,3,6,2]=>[[],[[[],[[]]]]]=>2
[3,3,1,6,2,3]=>[[],[[],[[[]]]]]=>2
[3,3,1,6,3,2]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,3,6]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,6,3]=>[[],[[],[[[]]]]]=>2
[3,3,2,3,1,6]=>[[],[[[],[[]]]]]=>2
[3,3,2,3,6,1]=>[[],[[[[[]]]]]]=>2
[3,3,2,6,1,3]=>[[],[[[],[[]]]]]=>2
[3,3,2,6,3,1]=>[[],[[[[],[]]]]]=>2
[3,3,3,1,2,6]=>[[],[],[[[[]]]]]=>3
[3,3,3,1,6,2]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,1,6]=>[[],[],[[],[[]]]]=>3
[3,3,3,2,6,1]=>[[],[],[[[[]]]]]=>3
[3,3,3,6,1,2]=>[[],[],[[[[]]]]]=>3
[3,3,3,6,2,1]=>[[],[],[[],[[]]]]=>3
[3,3,6,1,2,3]=>[[],[[[[],[]]]]]=>2
[3,3,6,1,3,2]=>[[],[[[],[[]]]]]=>2
[3,3,6,2,1,3]=>[[],[[],[[[]]]]]=>2
[3,3,6,2,3,1]=>[[],[[],[[[]]]]]=>2
[3,3,6,3,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,6,3,2,1]=>[[],[[[],[[]]]]]=>2
[3,6,1,2,3,3]=>[[],[[],[[[]]]]]=>2
[3,6,1,3,2,3]=>[[[[],[[[]]]]]]=>1
[3,6,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[3,6,2,1,3,3]=>[[[]],[[[],[]]]]=>2
[3,6,2,3,1,3]=>[[[],[[[[]]]]]]=>1
[3,6,2,3,3,1]=>[[[[],[]]],[[]]]=>2
[3,6,3,1,2,3]=>[[[[[],[[]]]]]]=>1
[3,6,3,1,3,2]=>[[[[[[[]]]]]]]=>1
[3,6,3,2,1,3]=>[[[[[]],[[]]]]]=>1
[3,6,3,2,3,1]=>[[[[[[[]]]]]]]=>1
[3,6,3,3,1,2]=>[[[[]]],[[[]]]]=>2
[3,6,3,3,2,1]=>[[[]],[[],[[]]]]=>2
[6,1,2,3,3,3]=>[[],[],[[],[[]]]]=>3
[6,1,3,2,3,3]=>[[[]],[[[],[]]]]=>2
[6,1,3,3,2,3]=>[[[[]]],[[],[]]]=>2
[6,1,3,3,3,2]=>[[],[[]],[[],[]]]=>3
[6,2,1,3,3,3]=>[[],[[]],[[[]]]]=>3
[6,2,3,1,3,3]=>[[],[[[[[]]]]]]=>2
[6,2,3,3,1,3]=>[[[[]]],[[[]]]]=>2
[6,2,3,3,3,1]=>[[],[[[]]],[[]]]=>3
[6,3,1,2,3,3]=>[[],[[[]],[[]]]]=>2
[6,3,1,3,2,3]=>[[[[[[[]]]]]]]=>1
[6,3,1,3,3,2]=>[[[[]]],[[[]]]]=>2
[6,3,2,1,3,3]=>[[[]],[[],[[]]]]=>2
[6,3,2,3,1,3]=>[[[[[[[]]]]]]]=>1
[6,3,2,3,3,1]=>[[[[]]],[[[]]]]=>2
[6,3,3,1,2,3]=>[[],[[[],[[]]]]]=>2
[6,3,3,1,3,2]=>[[],[[[[[]]]]]]=>2
[6,3,3,2,1,3]=>[[],[[[]],[[]]]]=>2
[6,3,3,2,3,1]=>[[],[[[[[]]]]]]=>2
[6,3,3,3,1,2]=>[[],[[]],[[[]]]]=>3
[6,3,3,3,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,3,3,4,4]=>[[],[],[[],[],[]]]=>3
[1,2,3,4,3,4]=>[[[],[],[],[[]]]]=>1
[1,2,3,4,4,3]=>[[[]],[[],[],[]]]=>2
[1,2,4,3,3,4]=>[[],[[],[[[]]]]]=>2
[1,2,4,3,4,3]=>[[[],[[],[[]]]]]=>1
[1,2,4,4,3,3]=>[[],[[[]]],[[]]]=>3
[1,3,2,3,4,4]=>[[[[]]],[[],[]]]=>2
[1,3,2,4,3,4]=>[[[],[[],[[]]]]]=>1
[1,3,2,4,4,3]=>[[[],[]],[[],[]]]=>2
[1,3,3,2,4,4]=>[[],[[]],[[],[]]]=>3
[1,3,3,4,2,4]=>[[],[[[[],[]]]]]=>2
[1,3,3,4,4,2]=>[[[]],[[]],[[]]]=>3
[1,3,4,2,3,4]=>[[[[],[],[[]]]]]=>1
[1,3,4,2,4,3]=>[[[],[[[[]]]]]]=>1
[1,3,4,3,2,4]=>[[[],[[],[[]]]]]=>1
[1,3,4,3,4,2]=>[[[[],[[[]]]]]]=>1
[1,3,4,4,2,3]=>[[],[[[],[[]]]]]=>2
[1,3,4,4,3,2]=>[[[[]]],[[],[]]]=>2
[1,4,2,3,3,4]=>[[[[]]],[[],[]]]=>2
[1,4,2,3,4,3]=>[[[[],[[[]]]]]]=>1
[1,4,2,4,3,3]=>[[[[]]],[[[]]]]=>2
[1,4,3,2,3,4]=>[[[[],[[],[]]]]]=>1
[1,4,3,2,4,3]=>[[[[],[],[[]]]]]=>1
[1,4,3,3,2,4]=>[[],[[[]],[[]]]]=>2
[1,4,3,3,4,2]=>[[],[[[[[]]]]]]=>2
[1,4,3,4,2,3]=>[[[[[]],[[]]]]]=>1
[1,4,3,4,3,2]=>[[[[[],[],[]]]]]=>1
[1,4,4,2,3,3]=>[[],[[[]]],[[]]]=>3
[1,4,4,3,2,3]=>[[[]],[[],[[]]]]=>2
[1,4,4,3,3,2]=>[[],[],[[],[[]]]]=>3
[2,1,3,3,4,4]=>[[[]],[[]],[[]]]=>3
[2,1,3,4,3,4]=>[[[],[[],[[]]]]]=>1
[2,1,3,4,4,3]=>[[[[]]],[[],[]]]=>2
[2,1,4,3,3,4]=>[[],[[[],[[]]]]]=>2
[2,1,4,3,4,3]=>[[[],[[]],[[]]]]=>1
[2,1,4,4,3,3]=>[[],[[]],[[],[]]]=>3
[2,3,1,3,4,4]=>[[],[[],[[[]]]]]=>2
[2,3,1,4,3,4]=>[[[[]],[[[]]]]]=>1
[2,3,1,4,4,3]=>[[[]],[[[[]]]]]=>2
[2,3,3,1,4,4]=>[[],[[]],[[[]]]]=>3
[2,3,3,4,1,4]=>[[],[[],[[[]]]]]=>2
[2,3,3,4,4,1]=>[[],[[]],[[],[]]]=>3
[2,3,4,1,3,4]=>[[[],[],[[[]]]]]=>1
[2,3,4,1,4,3]=>[[[],[[[[]]]]]]=>1
[2,3,4,3,1,4]=>[[[],[[[[]]]]]]=>1
[2,3,4,3,4,1]=>[[[],[],[[[]]]]]=>1
[2,3,4,4,1,3]=>[[[[]]],[[],[]]]=>2
[2,3,4,4,3,1]=>[[[[]]],[[],[]]]=>2
[2,4,1,3,3,4]=>[[[]],[[],[[]]]]=>2
[2,4,1,3,4,3]=>[[[[[]]],[[]]]]=>1
[2,4,1,4,3,3]=>[[],[[[[[]]]]]]=>2
[2,4,3,1,3,4]=>[[[[[]]],[[]]]]=>1
[2,4,3,1,4,3]=>[[[[[],[[]]]]]]=>1
[2,4,3,3,1,4]=>[[],[[[[[]]]]]]=>2
[2,4,3,3,4,1]=>[[],[[[[[]]]]]]=>2
[2,4,3,4,1,3]=>[[[[[]]],[[]]]]=>1
[2,4,3,4,3,1]=>[[[[[]],[[]]]]]=>1
[2,4,4,1,3,3]=>[[],[],[[],[[]]]]=>3
[2,4,4,3,1,3]=>[[],[[[],[[]]]]]=>2
[2,4,4,3,3,1]=>[[],[[]],[[[]]]]=>3
[3,1,2,3,4,4]=>[[],[[],[],[[]]]]=>2
[3,1,2,4,3,4]=>[[[[],[[[]]]]]]=>1
[3,1,2,4,4,3]=>[[[[]]],[[[]]]]=>2
[3,1,3,2,4,4]=>[[[]],[[],[[]]]]=>2
[3,1,3,4,2,4]=>[[[[]],[[],[]]]]=>1
[3,1,3,4,4,2]=>[[[[]]],[[],[]]]=>2
[3,1,4,2,3,4]=>[[[[]],[[],[]]]]=>1
[3,1,4,2,4,3]=>[[[[]],[[[]]]]]=>1
[3,1,4,3,2,4]=>[[[[[],[[]]]]]]=>1
[3,1,4,3,4,2]=>[[[[]],[[[]]]]]=>1
[3,1,4,4,2,3]=>[[[]],[[],[[]]]]=>2
[3,1,4,4,3,2]=>[[[]],[[],[[]]]]=>2
[3,2,1,3,4,4]=>[[[[]]],[[],[]]]=>2
[3,2,1,4,3,4]=>[[[],[[]],[[]]]]=>1
[3,2,1,4,4,3]=>[[[]],[[],[],[]]]=>2
[3,2,3,1,4,4]=>[[[[[]]]],[[]]]=>2
[3,2,3,4,1,4]=>[[[[[[],[]]]]]]=>1
[3,2,3,4,4,1]=>[[[[]]],[[],[]]]=>2
[3,2,4,1,3,4]=>[[[[[],[[]]]]]]=>1
[3,2,4,1,4,3]=>[[[],[[[[]]]]]]=>1
[3,2,4,3,1,4]=>[[[[]],[[[]]]]]=>1
[3,2,4,3,4,1]=>[[[[]],[[[]]]]]=>1
[3,2,4,4,1,3]=>[[],[[[],[[]]]]]=>2
[3,2,4,4,3,1]=>[[[]],[[],[[]]]]=>2
[3,3,1,2,4,4]=>[[],[],[[[[]]]]]=>3
[3,3,1,4,2,4]=>[[],[[[]],[[]]]]=>2
[3,3,1,4,4,2]=>[[],[[]],[[],[]]]=>3
[3,3,2,1,4,4]=>[[],[[]],[[],[]]]=>3
[3,3,2,4,1,4]=>[[],[[[[[]]]]]]=>2
[3,3,2,4,4,1]=>[[],[[]],[[[]]]]=>3
[3,3,4,1,2,4]=>[[],[[[]],[[]]]]=>2
[3,3,4,1,4,2]=>[[],[[[[[]]]]]]=>2
[3,3,4,2,1,4]=>[[],[[[[[]]]]]]=>2
[3,3,4,2,4,1]=>[[],[[[[[]]]]]]=>2
[3,3,4,4,1,2]=>[[],[],[[[],[]]]]=>3
[3,3,4,4,2,1]=>[[],[[]],[[[]]]]=>3
[3,4,1,2,3,4]=>[[[],[],[],[[]]]]=>1
[3,4,1,2,4,3]=>[[[[[]]],[[]]]]=>1
[3,4,1,3,2,4]=>[[[[[[],[]]]]]]=>1
[3,4,1,3,4,2]=>[[[[[]]],[[]]]]=>1
[3,4,1,4,2,3]=>[[[],[[[[]]]]]]=>1
[3,4,1,4,3,2]=>[[[[[],[[]]]]]]=>1
[3,4,2,1,3,4]=>[[[[[]]],[[]]]]=>1
[3,4,2,1,4,3]=>[[[[[],[[]]]]]]=>1
[3,4,2,3,1,4]=>[[[],[[],[[]]]]]=>1
[3,4,2,3,4,1]=>[[[],[[]],[[]]]]=>1
[3,4,2,4,1,3]=>[[[[[[],[]]]]]]=>1
[3,4,2,4,3,1]=>[[[[],[[[]]]]]]=>1
[3,4,3,1,2,4]=>[[[[[]]],[[]]]]=>1
[3,4,3,1,4,2]=>[[[[[],[[]]]]]]=>1
[3,4,3,2,1,4]=>[[[[],[],[[]]]]]=>1
[3,4,3,2,4,1]=>[[[[],[[[]]]]]]=>1
[3,4,3,4,1,2]=>[[[],[[]],[[]]]]=>1
[3,4,3,4,2,1]=>[[[],[[[],[]]]]]=>1
[3,4,4,1,2,3]=>[[],[[[],[],[]]]]=>2
[3,4,4,1,3,2]=>[[[]],[[[[]]]]]=>2
[3,4,4,2,1,3]=>[[[]],[[[[]]]]]=>2
[3,4,4,2,3,1]=>[[],[[],[[],[]]]]=>2
[3,4,4,3,1,2]=>[[],[[[],[[]]]]]=>2
[3,4,4,3,2,1]=>[[[]],[[],[],[]]]=>2
[4,1,2,3,3,4]=>[[],[[],[],[[]]]]=>2
[4,1,2,3,4,3]=>[[[[],[],[[]]]]]=>1
[4,1,2,4,3,3]=>[[],[[[[[]]]]]]=>2
[4,1,3,2,3,4]=>[[[[],[[[]]]]]]=>1
[4,1,3,2,4,3]=>[[[[],[[],[]]]]]=>1
[4,1,3,3,2,4]=>[[[]],[[[],[]]]]=>2
[4,1,3,3,4,2]=>[[[[]]],[[[]]]]=>2
[4,1,3,4,2,3]=>[[[[[],[[]]]]]]=>1
[4,1,3,4,3,2]=>[[[[],[[[]]]]]]=>1
[4,1,4,2,3,3]=>[[],[[[[[]]]]]]=>2
[4,1,4,3,2,3]=>[[[[[]],[[]]]]]=>1
[4,1,4,3,3,2]=>[[[]],[[],[[]]]]=>2
[4,2,1,3,3,4]=>[[[[]]],[[[]]]]=>2
[4,2,1,3,4,3]=>[[[[],[[[]]]]]]=>1
[4,2,1,4,3,3]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,3,4]=>[[[],[[[],[]]]]]=>1
[4,2,3,1,4,3]=>[[[[]],[[[]]]]]=>1
[4,2,3,3,1,4]=>[[[]],[[],[[]]]]=>2
[4,2,3,3,4,1]=>[[[]],[[],[[]]]]=>2
[4,2,3,4,1,3]=>[[[[],[[[]]]]]]=>1
[4,2,3,4,3,1]=>[[[],[[[],[]]]]]=>1
[4,2,4,1,3,3]=>[[],[[],[[[]]]]]=>2
[4,2,4,3,1,3]=>[[[],[[],[[]]]]]=>1
[4,2,4,3,3,1]=>[[],[[],[[[]]]]]=>2
[4,3,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[4,3,1,2,4,3]=>[[[[[]]],[[]]]]=>1
[4,3,1,3,2,4]=>[[[],[[],[[]]]]]=>1
[4,3,1,3,4,2]=>[[[[],[[[]]]]]]=>1
[4,3,1,4,2,3]=>[[[[[],[[]]]]]]=>1
[4,3,1,4,3,2]=>[[[],[[]],[[]]]]=>1
[4,3,2,1,3,4]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,4,3]=>[[[],[],[],[[]]]]=>1
[4,3,2,3,1,4]=>[[[],[[[[]]]]]]=>1
[4,3,2,3,4,1]=>[[[],[[[],[]]]]]=>1
[4,3,2,4,1,3]=>[[[],[[],[[]]]]]=>1
[4,3,2,4,3,1]=>[[[],[[]],[[]]]]=>1
[4,3,3,1,2,4]=>[[],[[[[[]]]]]]=>2
[4,3,3,1,4,2]=>[[],[[[]],[[]]]]=>2
[4,3,3,2,1,4]=>[[],[[],[],[[]]]]=>2
[4,3,3,2,4,1]=>[[],[[],[[[]]]]]=>2
[4,3,3,4,1,2]=>[[],[[[]],[[]]]]=>2
[4,3,3,4,2,1]=>[[],[[[[],[]]]]]=>2
[4,3,4,1,2,3]=>[[[[],[],[[]]]]]=>1
[4,3,4,1,3,2]=>[[[],[[[[]]]]]]=>1
[4,3,4,2,1,3]=>[[[],[[[[]]]]]]=>1
[4,3,4,2,3,1]=>[[[[],[[],[]]]]]=>1
[4,3,4,3,1,2]=>[[[],[[],[[]]]]]=>1
[4,3,4,3,2,1]=>[[[],[],[],[[]]]]=>1
[4,4,1,2,3,3]=>[[],[],[[],[[]]]]=>3
[4,4,1,3,2,3]=>[[],[[[[[]]]]]]=>2
[4,4,1,3,3,2]=>[[],[[[]]],[[]]]=>3
[4,4,2,1,3,3]=>[[],[[[]]],[[]]]=>3
[4,4,2,3,1,3]=>[[],[[[]],[[]]]]=>2
[4,4,2,3,3,1]=>[[],[[]],[[],[]]]=>3
[4,4,3,1,2,3]=>[[],[[[],[[]]]]]=>2
[4,4,3,1,3,2]=>[[],[[[]],[[]]]]=>2
[4,4,3,2,1,3]=>[[],[[],[],[[]]]]=>2
[4,4,3,2,3,1]=>[[],[[],[[[]]]]]=>2
[4,4,3,3,1,2]=>[[],[],[[[[]]]]]=>3
[4,4,3,3,2,1]=>[[],[],[[],[],[]]]=>3
[1,2,3,3,4,5]=>[[],[[],[],[],[]]]=>2
[1,2,3,3,5,4]=>[[[[]]],[[],[]]]=>2
[1,2,3,4,3,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,5,3]=>[[[],[],[],[[]]]]=>1
[1,2,3,5,3,4]=>[[[],[],[[[]]]]]=>1
[1,2,3,5,4,3]=>[[[],[[[],[]]]]]=>1
[1,2,4,3,3,5]=>[[],[[[]],[[]]]]=>2
[1,2,4,3,5,3]=>[[[[],[[[]]]]]]=>1
[1,2,4,5,3,3]=>[[],[[[],[[]]]]]=>2
[1,2,5,3,3,4]=>[[[[]]],[[],[]]]=>2
[1,2,5,3,4,3]=>[[[],[[[[]]]]]]=>1
[1,2,5,4,3,3]=>[[],[[],[[[]]]]]=>2
[1,3,2,3,4,5]=>[[[[[],[],[]]]]]=>1
[1,3,2,3,5,4]=>[[[[]],[[],[]]]]=>1
[1,3,2,4,3,5]=>[[[],[],[[],[]]]]=>1
[1,3,2,4,5,3]=>[[[],[[[[]]]]]]=>1
[1,3,2,5,3,4]=>[[[[[[[]]]]]]]=>1
[1,3,2,5,4,3]=>[[[[[],[],[]]]]]=>1
[1,3,3,2,4,5]=>[[],[[[[],[]]]]]=>2
[1,3,3,2,5,4]=>[[[]],[[],[[]]]]=>2
[1,3,3,4,2,5]=>[[[[[]]]],[[]]]=>2
[1,3,3,4,5,2]=>[[[]],[[],[[]]]]=>2
[1,3,3,5,2,4]=>[[],[[],[],[[]]]]=>2
[1,3,3,5,4,2]=>[[],[[],[[[]]]]]=>2
[1,3,4,2,3,5]=>[[[],[[],[[]]]]]=>1
[1,3,4,2,5,3]=>[[[[[],[[]]]]]]=>1
[1,3,4,3,2,5]=>[[[[[],[[]]]]]]=>1
[1,3,4,3,5,2]=>[[[],[[[[]]]]]]=>1
[1,3,4,5,2,3]=>[[[[],[],[[]]]]]=>1
[1,3,4,5,3,2]=>[[[[],[[[]]]]]]=>1
[1,3,5,2,3,4]=>[[[],[[[],[]]]]]=>1
[1,3,5,2,4,3]=>[[[],[[]],[[]]]]=>1
[1,3,5,3,2,4]=>[[[],[[]],[[]]]]=>1
[1,3,5,3,4,2]=>[[[],[[],[[]]]]]=>1
[1,3,5,4,2,3]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,3,2]=>[[[],[[],[],[]]]]=>1
[1,4,2,3,3,5]=>[[[[[]]]],[[]]]=>2
[1,4,2,3,5,3]=>[[[[],[[[]]]]]]=>1
[1,4,2,5,3,3]=>[[],[[],[[],[]]]]=>2
[1,4,3,2,3,5]=>[[[[],[[[]]]]]]=>1
[1,4,3,2,5,3]=>[[[],[[[],[]]]]]=>1
[1,4,3,3,2,5]=>[[],[[],[[],[]]]]=>2
[1,4,3,3,5,2]=>[[],[[[[[]]]]]]=>2
[1,4,3,5,2,3]=>[[[[[[[]]]]]]]=>1
[1,4,3,5,3,2]=>[[[[[[],[]]]]]]=>1
[1,4,5,2,3,3]=>[[],[[[]],[[]]]]=>2
[1,4,5,3,2,3]=>[[[[[],[[]]]]]]=>1
[1,4,5,3,3,2]=>[[],[[[[[]]]]]]=>2
[1,5,2,3,3,4]=>[[],[[],[[],[]]]]=>2
[1,5,2,3,4,3]=>[[[],[[],[[]]]]]=>1
[1,5,2,4,3,3]=>[[],[[[[],[]]]]]=>2
[1,5,3,2,3,4]=>[[[[[]],[[]]]]]=>1
[1,5,3,2,4,3]=>[[[[[],[[]]]]]]=>1
[1,5,3,3,2,4]=>[[[]],[[[[]]]]]=>2
[1,5,3,3,4,2]=>[[[[],[]]],[[]]]=>2
[1,5,3,4,2,3]=>[[[[],[[],[]]]]]=>1
[1,5,3,4,3,2]=>[[[[[]],[[]]]]]=>1
[1,5,4,2,3,3]=>[[[[[]]]],[[]]]=>2
[1,5,4,3,2,3]=>[[[[],[],[[]]]]]=>1
[1,5,4,3,3,2]=>[[[]],[[],[],[]]]=>2
[2,1,3,3,4,5]=>[[[]],[[],[[]]]]=>2
[2,1,3,3,5,4]=>[[],[[],[[],[]]]]=>2
[2,1,3,4,3,5]=>[[[[]],[[],[]]]]=>1
[2,1,3,4,5,3]=>[[[[[],[[]]]]]]=>1
[2,1,3,5,3,4]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,4,3]=>[[[],[],[[],[]]]]=>1
[2,1,4,3,3,5]=>[[],[[[],[[]]]]]=>2
[2,1,4,3,5,3]=>[[[[]],[[[]]]]]=>1
[2,1,4,5,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,5,3,3,4]=>[[[[]]],[[[]]]]=>2
[2,1,5,3,4,3]=>[[[[[]]],[[]]]]=>1
[2,1,5,4,3,3]=>[[],[[],[],[[]]]]=>2
[2,3,1,3,4,5]=>[[[],[[]],[[]]]]=>1
[2,3,1,3,5,4]=>[[[[[[],[]]]]]]=>1
[2,3,1,4,3,5]=>[[[[[[[]]]]]]]=>1
[2,3,1,4,5,3]=>[[[[]],[[],[]]]]=>1
[2,3,1,5,3,4]=>[[[],[[],[[]]]]]=>1
[2,3,1,5,4,3]=>[[[[[],[[]]]]]]=>1
[2,3,3,1,4,5]=>[[],[[[[],[]]]]]=>2
[2,3,3,1,5,4]=>[[[]],[[[[]]]]]=>2
[2,3,3,4,1,5]=>[[],[[],[[],[]]]]=>2
[2,3,3,4,5,1]=>[[],[[],[],[[]]]]=>2
[2,3,3,5,1,4]=>[[[]],[[[],[]]]]=>2
[2,3,3,5,4,1]=>[[[]],[[[[]]]]]=>2
[2,3,4,1,3,5]=>[[[],[[[],[]]]]]=>1
[2,3,4,1,5,3]=>[[[],[[],[[]]]]]=>1
[2,3,4,3,1,5]=>[[[],[[[[]]]]]]=>1
[2,3,4,3,5,1]=>[[[],[[[[]]]]]]=>1
[2,3,4,5,1,3]=>[[[],[],[[[]]]]]=>1
[2,3,4,5,3,1]=>[[[],[],[[],[]]]]=>1
[2,3,5,1,3,4]=>[[[],[[],[[]]]]]=>1
[2,3,5,1,4,3]=>[[[[[],[[]]]]]]=>1
[2,3,5,3,1,4]=>[[[[[],[[]]]]]]=>1
[2,3,5,3,4,1]=>[[[[]],[[[]]]]]=>1
[2,3,5,4,1,3]=>[[[[[]],[[]]]]]=>1
[2,3,5,4,3,1]=>[[[[[],[[]]]]]]=>1
[2,4,1,3,3,5]=>[[],[[],[],[[]]]]=>2
[2,4,1,3,5,3]=>[[[],[[]],[[]]]]=>1
[2,4,1,5,3,3]=>[[],[[[],[[]]]]]=>2
[2,4,3,1,3,5]=>[[[],[[]],[[]]]]=>1
[2,4,3,1,5,3]=>[[[[[]],[[]]]]]=>1
[2,4,3,3,1,5]=>[[],[[[[[]]]]]]=>2
[2,4,3,3,5,1]=>[[],[[],[[[]]]]]=>2
[2,4,3,5,1,3]=>[[[],[[]],[[]]]]=>1
[2,4,3,5,3,1]=>[[[],[[],[[]]]]]=>1
[2,4,5,1,3,3]=>[[],[[],[[[]]]]]=>2
[2,4,5,3,1,3]=>[[[],[[],[[]]]]]=>1
[2,4,5,3,3,1]=>[[],[[],[[[]]]]]=>2
[2,5,1,3,3,4]=>[[[]],[[[],[]]]]=>2
[2,5,1,3,4,3]=>[[[],[[[[]]]]]]=>1
[2,5,1,4,3,3]=>[[],[[[],[],[]]]]=>2
[2,5,3,1,3,4]=>[[[[],[[[]]]]]]=>1
[2,5,3,1,4,3]=>[[[],[[[],[]]]]]=>1
[2,5,3,3,1,4]=>[[],[[],[[],[]]]]=>2
[2,5,3,3,4,1]=>[[[[]]],[[[]]]]=>2
[2,5,3,4,1,3]=>[[[[[[[]]]]]]]=>1
[2,5,3,4,3,1]=>[[[[[[],[]]]]]]=>1
[2,5,4,1,3,3]=>[[[[]]],[[[]]]]=>2
[2,5,4,3,1,3]=>[[[[],[[[]]]]]]=>1
[2,5,4,3,3,1]=>[[],[[[],[[]]]]]=>2
[3,1,2,3,4,5]=>[[[[],[],[],[]]]]=>1
[3,1,2,3,5,4]=>[[[[[[],[]]]]]]=>1
[3,1,2,4,3,5]=>[[[[[]],[[]]]]]=>1
[3,1,2,4,5,3]=>[[[],[[],[[]]]]]=>1
[3,1,2,5,3,4]=>[[[[]],[[],[]]]]=>1
[3,1,2,5,4,3]=>[[[[],[[[]]]]]]=>1
[3,1,3,2,4,5]=>[[[[],[[[]]]]]]=>1
[3,1,3,2,5,4]=>[[[[[]],[[]]]]]=>1
[3,1,3,4,2,5]=>[[[[[]]],[[]]]]=>1
[3,1,3,4,5,2]=>[[[[[]],[[]]]]]=>1
[3,1,3,5,2,4]=>[[[[[],[],[]]]]]=>1
[3,1,3,5,4,2]=>[[[],[[[],[]]]]]=>1
[3,1,4,2,3,5]=>[[[[[]]],[[]]]]=>1
[3,1,4,2,5,3]=>[[[],[],[[],[]]]]=>1
[3,1,4,3,2,5]=>[[[[],[[],[]]]]]=>1
[3,1,4,3,5,2]=>[[[[[[[]]]]]]]=>1
[3,1,4,5,2,3]=>[[[[[],[[]]]]]]=>1
[3,1,4,5,3,2]=>[[[[[]]],[[]]]]=>1
[3,1,5,2,3,4]=>[[[[],[[],[]]]]]=>1
[3,1,5,2,4,3]=>[[[[[[],[]]]]]]=>1
[3,1,5,3,2,4]=>[[[],[[[[]]]]]]=>1
[3,1,5,3,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,5,4,2,3]=>[[[[[]]],[[]]]]=>1
[3,1,5,4,3,2]=>[[[[],[],[[]]]]]=>1
[3,2,1,3,4,5]=>[[[],[[],[[]]]]]=>1
[3,2,1,3,5,4]=>[[[],[],[[],[]]]]=>1
[3,2,1,4,3,5]=>[[[],[[]],[[]]]]=>1
[3,2,1,4,5,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,3,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,4,3]=>[[[],[],[],[[]]]]=>1
[3,2,3,1,4,5]=>[[[[],[[[]]]]]]=>1
[3,2,3,1,5,4]=>[[[[]],[[[]]]]]=>1
[3,2,3,4,1,5]=>[[[[],[[],[]]]]]=>1
[3,2,3,4,5,1]=>[[[[[],[],[]]]]]=>1
[3,2,3,5,1,4]=>[[[[],[[[]]]]]]=>1
[3,2,3,5,4,1]=>[[[[[]]],[[]]]]=>1
[3,2,4,1,3,5]=>[[[[],[],[[]]]]]=>1
[3,2,4,1,5,3]=>[[[[[],[[]]]]]]=>1
[3,2,4,3,1,5]=>[[[[]],[[[]]]]]=>1
[3,2,4,3,5,1]=>[[[],[[[],[]]]]]=>1
[3,2,4,5,1,3]=>[[[[],[[[]]]]]]=>1
[3,2,4,5,3,1]=>[[[[],[[[]]]]]]=>1
[3,2,5,1,3,4]=>[[[[[[],[]]]]]]=>1
[3,2,5,1,4,3]=>[[[],[[],[],[]]]]=>1
[3,2,5,3,1,4]=>[[[[],[[],[]]]]]=>1
[3,2,5,3,4,1]=>[[[[[[[]]]]]]]=>1
[3,2,5,4,1,3]=>[[[[[]]],[[]]]]=>1
[3,2,5,4,3,1]=>[[[],[[]],[[]]]]=>1
[3,3,1,2,4,5]=>[[],[[[[],[]]]]]=>2
[3,3,1,2,5,4]=>[[],[[[[[]]]]]]=>2
[3,3,1,4,2,5]=>[[],[[],[[],[]]]]=>2
[3,3,1,4,5,2]=>[[],[[[[[]]]]]]=>2
[3,3,1,5,2,4]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,4,2]=>[[],[[[]],[[]]]]=>2
[3,3,2,1,4,5]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,5,4]=>[[],[[],[],[[]]]]=>2
[3,3,2,4,1,5]=>[[],[[[],[[]]]]]=>2
[3,3,2,4,5,1]=>[[],[[[[[]]]]]]=>2
[3,3,2,5,1,4]=>[[],[[[],[],[]]]]=>2
[3,3,2,5,4,1]=>[[],[[[]],[[]]]]=>2
[3,3,4,1,2,5]=>[[],[[[]],[[]]]]=>2
[3,3,4,1,5,2]=>[[],[[[],[],[]]]]=>2
[3,3,4,2,1,5]=>[[],[[[[[]]]]]]=>2
[3,3,4,2,5,1]=>[[],[[[[],[]]]]]=>2
[3,3,4,5,1,2]=>[[],[[],[],[[]]]]=>2
[3,3,4,5,2,1]=>[[],[[],[[[]]]]]=>2
[3,3,5,1,2,4]=>[[],[[],[[[]]]]]=>2
[3,3,5,1,4,2]=>[[],[[[],[[]]]]]=>2
[3,3,5,2,1,4]=>[[],[[[[[]]]]]]=>2
[3,3,5,2,4,1]=>[[],[[],[[],[]]]]=>2
[3,3,5,4,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,5,4,2,1]=>[[],[[[],[[]]]]]=>2
[3,4,1,2,3,5]=>[[[],[[]],[[]]]]=>1
[3,4,1,2,5,3]=>[[[[[]]],[[]]]]=>1
[3,4,1,3,2,5]=>[[[[[[[]]]]]]]=>1
[3,4,1,3,5,2]=>[[[[],[[],[]]]]]=>1
[3,4,1,5,2,3]=>[[[],[[],[],[]]]]=>1
[3,4,1,5,3,2]=>[[[[],[[[]]]]]]=>1
[3,4,2,1,3,5]=>[[[[[],[[]]]]]]=>1
[3,4,2,1,5,3]=>[[[[[]],[[]]]]]=>1
[3,4,2,3,1,5]=>[[[],[[],[[]]]]]=>1
[3,4,2,3,5,1]=>[[[[[]]],[[]]]]=>1
[3,4,2,5,1,3]=>[[[[[],[[]]]]]]=>1
[3,4,2,5,3,1]=>[[[[],[],[[]]]]]=>1
[3,4,3,1,2,5]=>[[[[[]]],[[]]]]=>1
[3,4,3,1,5,2]=>[[[[[],[[]]]]]]=>1
[3,4,3,2,1,5]=>[[[[],[],[[]]]]]=>1
[3,4,3,2,5,1]=>[[[[],[[],[]]]]]=>1
[3,4,3,5,1,2]=>[[[[[]]],[[]]]]=>1
[3,4,3,5,2,1]=>[[[[],[[[]]]]]]=>1
[3,4,5,1,2,3]=>[[[],[],[],[[]]]]=>1
[3,4,5,1,3,2]=>[[[],[[[[]]]]]]=>1
[3,4,5,2,1,3]=>[[[],[[[[]]]]]]=>1
[3,4,5,2,3,1]=>[[[],[[]],[[]]]]=>1
[3,4,5,3,1,2]=>[[[],[],[[],[]]]]=>1
[3,4,5,3,2,1]=>[[[],[[[],[]]]]]=>1
[3,5,1,2,3,4]=>[[[[[],[],[]]]]]=>1
[3,5,1,2,4,3]=>[[[[[]]],[[]]]]=>1
[3,5,1,3,2,4]=>[[[],[[]],[[]]]]=>1
[3,5,1,3,4,2]=>[[[[[]]],[[]]]]=>1
[3,5,1,4,2,3]=>[[[[],[[[]]]]]]=>1
[3,5,1,4,3,2]=>[[[[],[[],[]]]]]=>1
[3,5,2,1,3,4]=>[[[],[[[[]]]]]]=>1
[3,5,2,1,4,3]=>[[[[],[[[]]]]]]=>1
[3,5,2,3,1,4]=>[[[[[[[]]]]]]]=>1
[3,5,2,3,4,1]=>[[[[],[[],[]]]]]=>1
[3,5,2,4,1,3]=>[[[],[],[[],[]]]]=>1
[3,5,2,4,3,1]=>[[[],[[[[]]]]]]=>1
[3,5,3,1,2,4]=>[[[],[[[],[]]]]]=>1
[3,5,3,1,4,2]=>[[[[],[],[[]]]]]=>1
[3,5,3,2,1,4]=>[[[[],[[[]]]]]]=>1
[3,5,3,2,4,1]=>[[[[[]]],[[]]]]=>1
[3,5,3,4,1,2]=>[[[[[[],[]]]]]]=>1
[3,5,3,4,2,1]=>[[[[[]],[[]]]]]=>1
[3,5,4,1,2,3]=>[[[[[],[[]]]]]]=>1
[3,5,4,1,3,2]=>[[[[]],[[],[]]]]=>1
[3,5,4,2,1,3]=>[[[[]],[[],[]]]]=>1
[3,5,4,2,3,1]=>[[[[[],[[]]]]]]=>1
[3,5,4,3,1,2]=>[[[[],[[[]]]]]]=>1
[3,5,4,3,2,1]=>[[[[],[],[],[]]]]=>1
[4,1,2,3,3,5]=>[[[]],[[],[[]]]]=>2
[4,1,2,3,5,3]=>[[[[],[[[]]]]]]=>1
[4,1,2,5,3,3]=>[[],[[[[[]]]]]]=>2
[4,1,3,2,3,5]=>[[[[[],[[]]]]]]=>1
[4,1,3,2,5,3]=>[[[[[[[]]]]]]]=>1
[4,1,3,3,2,5]=>[[[[]]],[[[]]]]=>2
[4,1,3,3,5,2]=>[[],[[],[[],[]]]]=>2
[4,1,3,5,2,3]=>[[[[]],[[],[]]]]=>1
[4,1,3,5,3,2]=>[[[[[[],[]]]]]]=>1
[4,1,5,2,3,3]=>[[],[[[],[],[]]]]=>2
[4,1,5,3,2,3]=>[[[],[[[[]]]]]]=>1
[4,1,5,3,3,2]=>[[[[]]],[[],[]]]=>2
[4,2,1,3,3,5]=>[[[]],[[],[[]]]]=>2
[4,2,1,3,5,3]=>[[[[]],[[],[]]]]=>1
[4,2,1,5,3,3]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,3,5]=>[[[[]],[[],[]]]]=>1
[4,2,3,1,5,3]=>[[[],[[]],[[]]]]=>1
[4,2,3,3,1,5]=>[[[]],[[],[[]]]]=>2
[4,2,3,3,5,1]=>[[[[]]],[[[]]]]=>2
[4,2,3,5,1,3]=>[[[[[],[[]]]]]]=>1
[4,2,3,5,3,1]=>[[[],[],[[[]]]]]=>1
[4,2,5,1,3,3]=>[[],[[[],[[]]]]]=>2
[4,2,5,3,1,3]=>[[[],[[]],[[]]]]=>1
[4,2,5,3,3,1]=>[[],[[],[],[[]]]]=>2
[4,3,1,2,3,5]=>[[[[[],[[]]]]]]=>1
[4,3,1,2,5,3]=>[[[[],[[[]]]]]]=>1
[4,3,1,3,2,5]=>[[[[]],[[[]]]]]=>1
[4,3,1,3,5,2]=>[[[[[],[[]]]]]]=>1
[4,3,1,5,2,3]=>[[[[[],[[]]]]]]=>1
[4,3,1,5,3,2]=>[[[[]],[[],[]]]]=>1
[4,3,2,1,3,5]=>[[[],[],[[],[]]]]=>1
[4,3,2,1,5,3]=>[[[],[],[[[]]]]]=>1
[4,3,2,3,1,5]=>[[[],[[[[]]]]]]=>1
[4,3,2,3,5,1]=>[[[],[[[[]]]]]]=>1
[4,3,2,5,1,3]=>[[[],[[[],[]]]]]=>1
[4,3,2,5,3,1]=>[[[],[[],[[]]]]]=>1
[4,3,3,1,2,5]=>[[],[[[[[]]]]]]=>2
[4,3,3,1,5,2]=>[[],[[[],[[]]]]]=>2
[4,3,3,2,1,5]=>[[],[[],[],[[]]]]=>2
[4,3,3,2,5,1]=>[[],[[],[[],[]]]]=>2
[4,3,3,5,1,2]=>[[],[[[[[]]]]]]=>2
[4,3,3,5,2,1]=>[[],[[[[],[]]]]]=>2
[4,3,5,1,2,3]=>[[[[],[[[]]]]]]=>1
[4,3,5,1,3,2]=>[[[],[[],[[]]]]]=>1
[4,3,5,2,1,3]=>[[[[]],[[],[]]]]=>1
[4,3,5,2,3,1]=>[[[[[[[]]]]]]]=>1
[4,3,5,3,1,2]=>[[[[[],[[]]]]]]=>1
[4,3,5,3,2,1]=>[[[],[],[[[]]]]]=>1
[4,5,1,2,3,3]=>[[],[[],[],[[]]]]=>2
[4,5,1,3,2,3]=>[[[],[[[[]]]]]]=>1
[4,5,1,3,3,2]=>[[[[[]]]],[[]]]=>2
[4,5,2,1,3,3]=>[[[]],[[[[]]]]]=>2
[4,5,2,3,1,3]=>[[[[]],[[[]]]]]=>1
[4,5,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[4,5,3,1,2,3]=>[[[],[],[[],[]]]]=>1
[4,5,3,1,3,2]=>[[[[],[[[]]]]]]=>1
[4,5,3,2,1,3]=>[[[[[[],[]]]]]]=>1
[4,5,3,2,3,1]=>[[[],[[],[[]]]]]=>1
[4,5,3,3,1,2]=>[[],[[],[[],[]]]]=>2
[4,5,3,3,2,1]=>[[],[[],[[[]]]]]=>2
[5,1,2,3,3,4]=>[[],[[],[],[[]]]]=>2
[5,1,2,3,4,3]=>[[[[],[],[[]]]]]=>1
[5,1,2,4,3,3]=>[[],[[[[[]]]]]]=>2
[5,1,3,2,3,4]=>[[[[[[],[]]]]]]=>1
[5,1,3,2,4,3]=>[[[[],[[],[]]]]]=>1
[5,1,3,3,2,4]=>[[],[[[],[[]]]]]=>2
[5,1,3,3,4,2]=>[[[[]]],[[[]]]]=>2
[5,1,3,4,2,3]=>[[[[[],[[]]]]]]=>1
[5,1,3,4,3,2]=>[[[[[[],[]]]]]]=>1
[5,1,4,2,3,3]=>[[],[[[[],[]]]]]=>2
[5,1,4,3,2,3]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,3,2]=>[[],[[],[[],[]]]]=>2
[5,2,1,3,3,4]=>[[[[[]]]],[[]]]=>2
[5,2,1,3,4,3]=>[[[[[[],[]]]]]]=>1
[5,2,1,4,3,3]=>[[],[[],[[[]]]]]=>2
[5,2,3,1,3,4]=>[[[[[[],[]]]]]]=>1
[5,2,3,1,4,3]=>[[[[[[[]]]]]]]=>1
[5,2,3,3,1,4]=>[[[[]]],[[[]]]]=>2
[5,2,3,3,4,1]=>[[],[[],[[],[]]]]=>2
[5,2,3,4,1,3]=>[[[[]],[[],[]]]]=>1
[5,2,3,4,3,1]=>[[[[[[],[]]]]]]=>1
[5,2,4,1,3,3]=>[[],[[],[[],[]]]]=>2
[5,2,4,3,1,3]=>[[[[[],[[]]]]]]=>1
[5,2,4,3,3,1]=>[[[]],[[[[]]]]]=>2
[5,3,1,2,3,4]=>[[[],[[],[],[]]]]=>1
[5,3,1,2,4,3]=>[[[],[[[[]]]]]]=>1
[5,3,1,3,2,4]=>[[[],[[],[[]]]]]=>1
[5,3,1,3,4,2]=>[[[],[],[[[]]]]]=>1
[5,3,1,4,2,3]=>[[[],[[]],[[]]]]=>1
[5,3,1,4,3,2]=>[[[],[[],[[]]]]]=>1
[5,3,2,1,3,4]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,4,3]=>[[[[],[],[[]]]]]=>1
[5,3,2,3,1,4]=>[[[[]],[[[]]]]]=>1
[5,3,2,3,4,1]=>[[[[],[[[]]]]]]=>1
[5,3,2,4,1,3]=>[[[[[],[[]]]]]]=>1
[5,3,2,4,3,1]=>[[[],[[],[[]]]]]=>1
[5,3,3,1,2,4]=>[[],[[],[[[]]]]]=>2
[5,3,3,1,4,2]=>[[],[[],[],[[]]]]=>2
[5,3,3,2,1,4]=>[[],[[],[[[]]]]]=>2
[5,3,3,2,4,1]=>[[],[[[[[]]]]]]=>2
[5,3,3,4,1,2]=>[[],[[],[[[]]]]]=>2
[5,3,3,4,2,1]=>[[],[[[],[[]]]]]=>2
[5,3,4,1,2,3]=>[[[[],[],[[]]]]]=>1
[5,3,4,1,3,2]=>[[[[[[[]]]]]]]=>1
[5,3,4,2,1,3]=>[[[[]],[[[]]]]]=>1
[5,3,4,2,3,1]=>[[[],[],[[],[]]]]=>1
[5,3,4,3,1,2]=>[[[],[[],[[]]]]]=>1
[5,3,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[5,4,1,2,3,3]=>[[[]],[[],[[]]]]=>2
[5,4,1,3,2,3]=>[[[[]],[[[]]]]]=>1
[5,4,1,3,3,2]=>[[[[]]],[[],[]]]=>2
[5,4,2,1,3,3]=>[[[[]]],[[],[]]]=>2
[5,4,2,3,1,3]=>[[[[[],[[]]]]]]=>1
[5,4,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,4,3,1,2,3]=>[[[],[[],[[]]]]]=>1
[5,4,3,1,3,2]=>[[[],[[]],[[]]]]=>1
[5,4,3,2,1,3]=>[[[],[],[],[[]]]]=>1
[5,4,3,2,3,1]=>[[[],[],[[[]]]]]=>1
[5,4,3,3,1,2]=>[[],[[[[],[]]]]]=>2
[5,4,3,3,2,1]=>[[],[[],[],[],[]]]=>2
[1,2,3,3,4,6]=>[[],[[],[],[[]]]]=>2
[1,2,3,3,6,4]=>[[[[]]],[[],[]]]=>2
[1,2,3,4,3,6]=>[[[],[],[[[]]]]]=>1
[1,2,3,4,6,3]=>[[[],[],[[[]]]]]=>1
[1,2,3,6,3,4]=>[[[],[],[[[]]]]]=>1
[1,2,3,6,4,3]=>[[[],[[[[]]]]]]=>1
[1,2,4,3,3,6]=>[[],[[[[[]]]]]]=>2
[1,2,4,3,6,3]=>[[[[[[[]]]]]]]=>1
[1,2,4,6,3,3]=>[[],[[[],[[]]]]]=>2
[1,2,6,3,3,4]=>[[[],[]],[[],[]]]=>2
[1,2,6,3,4,3]=>[[[[]],[[],[]]]]=>1
[1,2,6,4,3,3]=>[[[]],[[[[]]]]]=>2
[1,3,2,3,4,6]=>[[[[]],[[],[]]]]=>1
[1,3,2,3,6,4]=>[[[[[[[]]]]]]]=>1
[1,3,2,4,3,6]=>[[[],[[],[[]]]]]=>1
[1,3,2,4,6,3]=>[[[],[],[[[]]]]]=>1
[1,3,2,6,3,4]=>[[[[[[],[]]]]]]=>1
[1,3,2,6,4,3]=>[[[[[],[[]]]]]]=>1
[1,3,3,2,4,6]=>[[],[[[],[],[]]]]=>2
[1,3,3,2,6,4]=>[[[]],[[[[]]]]]=>2
[1,3,3,4,2,6]=>[[[[[]]]],[[]]]=>2
[1,3,3,4,6,2]=>[[],[[[],[[]]]]]=>2
[1,3,3,6,2,4]=>[[],[[],[[],[]]]]=>2
[1,3,3,6,4,2]=>[[[]],[[[],[]]]]=>2
[1,3,4,2,3,6]=>[[[[[]],[[]]]]]=>1
[1,3,4,2,6,3]=>[[[[[[],[]]]]]]=>1
[1,3,4,3,2,6]=>[[[[[],[[]]]]]]=>1
[1,3,4,3,6,2]=>[[[[[[],[]]]]]]=>1
[1,3,4,6,2,3]=>[[[],[[[],[]]]]]=>1
[1,3,4,6,3,2]=>[[[[]],[[[]]]]]=>1
[1,3,6,2,3,4]=>[[[[],[[],[]]]]]=>1
[1,3,6,2,4,3]=>[[[[]],[[],[]]]]=>1
[1,3,6,3,2,4]=>[[[],[[[[]]]]]]=>1
[1,3,6,3,4,2]=>[[[[[[[]]]]]]]=>1
[1,3,6,4,2,3]=>[[[[[],[[]]]]]]=>1
[1,3,6,4,3,2]=>[[[[[],[[]]]]]]=>1
[1,4,2,3,3,6]=>[[[[]]],[[],[]]]=>2
[1,4,2,3,6,3]=>[[[[[]]],[[]]]]=>1
[1,4,2,6,3,3]=>[[],[[[]],[[]]]]=>2
[1,4,3,2,3,6]=>[[[[]],[[],[]]]]=>1
[1,4,3,2,6,3]=>[[[[],[[],[]]]]]=>1
[1,4,3,3,2,6]=>[[[]],[[],[[]]]]=>2
[1,4,3,3,6,2]=>[[],[[],[],[[]]]]=>2
[1,4,3,6,2,3]=>[[[],[],[[[]]]]]=>1
[1,4,3,6,3,2]=>[[[],[[[],[]]]]]=>1
[1,4,6,2,3,3]=>[[],[[[],[[]]]]]=>2
[1,4,6,3,2,3]=>[[[[[[[]]]]]]]=>1
[1,4,6,3,3,2]=>[[[[[]]]],[[]]]=>2
[1,6,2,3,3,4]=>[[[]],[[],[[]]]]=>2
[1,6,2,3,4,3]=>[[[[[],[[]]]]]]=>1
[1,6,2,4,3,3]=>[[[]],[[[[]]]]]=>2
[1,6,3,2,3,4]=>[[[[[]],[[]]]]]=>1
[1,6,3,2,4,3]=>[[[[],[[[]]]]]]=>1
[1,6,3,3,2,4]=>[[[]],[[[[]]]]]=>2
[1,6,3,3,4,2]=>[[[[],[]]],[[]]]=>2
[1,6,3,4,2,3]=>[[[[]],[[],[]]]]=>1
[1,6,3,4,3,2]=>[[[[[]],[[]]]]]=>1
[1,6,4,2,3,3]=>[[],[[[],[],[]]]]=>2
[1,6,4,3,2,3]=>[[[],[[[],[]]]]]=>1
[1,6,4,3,3,2]=>[[],[[],[[],[]]]]=>2
[2,1,3,3,4,6]=>[[],[[[],[[]]]]]=>2
[2,1,3,3,6,4]=>[[[]],[[[[]]]]]=>2
[2,1,3,4,3,6]=>[[[[[]]],[[]]]]=>1
[2,1,3,4,6,3]=>[[[[[],[[]]]]]]=>1
[2,1,3,6,3,4]=>[[[[[[[]]]]]]]=>1
[2,1,3,6,4,3]=>[[[],[[[[]]]]]]=>1
[2,1,4,3,3,6]=>[[],[[],[[],[]]]]=>2
[2,1,4,3,6,3]=>[[[],[[[],[]]]]]=>1
[2,1,4,6,3,3]=>[[[[[]]]],[[]]]=>2
[2,1,6,3,3,4]=>[[[[]]],[[[]]]]=>2
[2,1,6,3,4,3]=>[[[[[]]],[[]]]]=>1
[2,1,6,4,3,3]=>[[[],[]],[[],[]]]=>2
[2,3,1,3,4,6]=>[[[[]],[[],[]]]]=>1
[2,3,1,3,6,4]=>[[[[],[[[]]]]]]=>1
[2,3,1,4,3,6]=>[[[[[],[[]]]]]]=>1
[2,3,1,4,6,3]=>[[[[[[[]]]]]]]=>1
[2,3,1,6,3,4]=>[[[],[[[],[]]]]]=>1
[2,3,1,6,4,3]=>[[[[],[],[[]]]]]=>1
[2,3,3,1,4,6]=>[[[]],[[[[]]]]]=>2
[2,3,3,1,6,4]=>[[[]],[[],[],[]]]=>2
[2,3,3,4,1,6]=>[[],[[],[[[]]]]]=>2
[2,3,3,4,6,1]=>[[],[[],[[],[]]]]=>2
[2,3,3,6,1,4]=>[[[]],[[],[[]]]]=>2
[2,3,3,6,4,1]=>[[[]],[[[[]]]]]=>2
[2,3,4,1,3,6]=>[[[],[[[[]]]]]]=>1
[2,3,4,1,6,3]=>[[[],[[],[[]]]]]=>1
[2,3,4,3,1,6]=>[[[],[[[],[]]]]]=>1
[2,3,4,3,6,1]=>[[[],[[[[]]]]]]=>1
[2,3,4,6,1,3]=>[[[],[[],[],[]]]]=>1
[2,3,4,6,3,1]=>[[[],[[[[]]]]]]=>1
[2,3,6,1,3,4]=>[[[],[[],[[]]]]]=>1
[2,3,6,1,4,3]=>[[[[[]],[[]]]]]=>1
[2,3,6,3,1,4]=>[[[[],[[[]]]]]]=>1
[2,3,6,3,4,1]=>[[[],[[],[[]]]]]=>1
[2,3,6,4,1,3]=>[[[[[[[]]]]]]]=>1
[2,3,6,4,3,1]=>[[[[[[],[]]]]]]=>1
[2,4,1,3,3,6]=>[[[]],[[],[[]]]]=>2
[2,4,1,3,6,3]=>[[[],[[[],[]]]]]=>1
[2,4,1,6,3,3]=>[[],[[[]],[[]]]]=>2
[2,4,3,1,3,6]=>[[[[[]]],[[]]]]=>1
[2,4,3,1,6,3]=>[[[[],[[[]]]]]]=>1
[2,4,3,3,1,6]=>[[],[[],[[[]]]]]=>2
[2,4,3,3,6,1]=>[[],[[[],[[]]]]]=>2
[2,4,3,6,1,3]=>[[[],[[]],[[]]]]=>1
[2,4,3,6,3,1]=>[[[[[[[]]]]]]]=>1
[2,4,6,1,3,3]=>[[],[[],[],[],[]]]=>2
[2,4,6,3,1,3]=>[[[],[],[[[]]]]]=>1
[2,4,6,3,3,1]=>[[[[],[]]],[[]]]=>2
[2,6,1,3,3,4]=>[[[]],[[],[[]]]]=>2
[2,6,1,3,4,3]=>[[[[],[[[]]]]]]=>1
[2,6,1,4,3,3]=>[[],[[[[[]]]]]]=>2
[2,6,3,1,3,4]=>[[[],[[[[]]]]]]=>1
[2,6,3,1,4,3]=>[[[],[[[[]]]]]]=>1
[2,6,3,3,1,4]=>[[[[]]],[[],[]]]=>2
[2,6,3,3,4,1]=>[[],[[[],[],[]]]]=>2
[2,6,3,4,1,3]=>[[[],[[]],[[]]]]=>1
[2,6,3,4,3,1]=>[[[],[[[[]]]]]]=>1
[2,6,4,1,3,3]=>[[],[[[],[[]]]]]=>2
[2,6,4,3,1,3]=>[[[[],[[[]]]]]]=>1
[2,6,4,3,3,1]=>[[[]],[[],[[]]]]=>2
[3,1,2,3,4,6]=>[[[[],[],[[]]]]]=>1
[3,1,2,3,6,4]=>[[[],[[[],[]]]]]=>1
[3,1,2,4,3,6]=>[[[[[[[]]]]]]]=>1
[3,1,2,4,6,3]=>[[[[[]],[[]]]]]=>1
[3,1,2,6,3,4]=>[[[[],[[],[]]]]]=>1
[3,1,2,6,4,3]=>[[[],[[[[]]]]]]=>1
[3,1,3,2,4,6]=>[[[[],[],[[]]]]]=>1
[3,1,3,2,6,4]=>[[[[]],[[[]]]]]=>1
[3,1,3,4,2,6]=>[[[[[]]],[[]]]]=>1
[3,1,3,4,6,2]=>[[[[[],[[]]]]]]=>1
[3,1,3,6,2,4]=>[[[[],[[],[]]]]]=>1
[3,1,3,6,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,4,2,3,6]=>[[[],[[[],[]]]]]=>1
[3,1,4,2,6,3]=>[[[],[[],[[]]]]]=>1
[3,1,4,3,2,6]=>[[[[[],[[]]]]]]=>1
[3,1,4,3,6,2]=>[[[[],[],[[]]]]]=>1
[3,1,4,6,2,3]=>[[[[[],[[]]]]]]=>1
[3,1,4,6,3,2]=>[[[[[[[]]]]]]]=>1
[3,1,6,2,3,4]=>[[[],[[],[[]]]]]=>1
[3,1,6,2,4,3]=>[[[],[[[[]]]]]]=>1
[3,1,6,3,2,4]=>[[[],[[[[]]]]]]=>1
[3,1,6,3,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,6,4,2,3]=>[[[],[],[],[[]]]]=>1
[3,1,6,4,3,2]=>[[[],[],[[],[]]]]=>1
[3,2,1,3,4,6]=>[[[],[[],[[]]]]]=>1
[3,2,1,3,6,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,4,3,6]=>[[[],[],[[],[]]]]=>1
[3,2,1,4,6,3]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,3,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,4,3]=>[[[],[],[[],[]]]]=>1
[3,2,3,1,4,6]=>[[[[[[[]]]]]]]=>1
[3,2,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[3,2,3,4,1,6]=>[[[[[[],[]]]]]]=>1
[3,2,3,4,6,1]=>[[[[],[[],[]]]]]=>1
[3,2,3,6,1,4]=>[[[[[]],[[]]]]]=>1
[3,2,3,6,4,1]=>[[[[[[[]]]]]]]=>1
[3,2,4,1,3,6]=>[[[[[],[[]]]]]]=>1
[3,2,4,1,6,3]=>[[[[[]],[[]]]]]=>1
[3,2,4,3,1,6]=>[[[[]],[[],[]]]]=>1
[3,2,4,3,6,1]=>[[[],[[],[[]]]]]=>1
[3,2,4,6,1,3]=>[[[[],[],[],[]]]]=>1
[3,2,4,6,3,1]=>[[[[[[],[]]]]]]=>1
[3,2,6,1,3,4]=>[[[[[],[[]]]]]]=>1
[3,2,6,1,4,3]=>[[[],[[[[]]]]]]=>1
[3,2,6,3,1,4]=>[[[[[[],[]]]]]]=>1
[3,2,6,3,4,1]=>[[[[],[],[[]]]]]=>1
[3,2,6,4,1,3]=>[[[[[],[[]]]]]]=>1
[3,2,6,4,3,1]=>[[[],[[],[[]]]]]=>1
[3,3,1,2,4,6]=>[[],[[[],[[]]]]]=>2
[3,3,1,2,6,4]=>[[],[[],[[[]]]]]=>2
[3,3,1,4,2,6]=>[[],[[[]],[[]]]]=>2
[3,3,1,4,6,2]=>[[],[[[[],[]]]]]=>2
[3,3,1,6,2,4]=>[[],[[],[[[]]]]]=>2
[3,3,1,6,4,2]=>[[],[[],[],[],[]]]=>2
[3,3,2,1,4,6]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,6,4]=>[[],[[],[[],[]]]]=>2
[3,3,2,4,1,6]=>[[],[[[[[]]]]]]=>2
[3,3,2,4,6,1]=>[[],[[[],[],[]]]]=>2
[3,3,2,6,1,4]=>[[],[[[[[]]]]]]=>2
[3,3,2,6,4,1]=>[[],[[[],[[]]]]]=>2
[3,3,4,1,2,6]=>[[],[[],[[],[]]]]=>2
[3,3,4,1,6,2]=>[[],[[[[[]]]]]]=>2
[3,3,4,2,1,6]=>[[],[[[],[[]]]]]=>2
[3,3,4,2,6,1]=>[[],[[[[[]]]]]]=>2
[3,3,4,6,1,2]=>[[],[[],[[],[]]]]=>2
[3,3,4,6,2,1]=>[[],[[[[[]]]]]]=>2
[3,3,6,1,2,4]=>[[],[[[],[[]]]]]=>2
[3,3,6,1,4,2]=>[[],[[[]],[[]]]]=>2
[3,3,6,2,1,4]=>[[],[[],[],[[]]]]=>2
[3,3,6,2,4,1]=>[[],[[],[[[]]]]]=>2
[3,3,6,4,1,2]=>[[],[[[[[]]]]]]=>2
[3,3,6,4,2,1]=>[[],[[[],[[]]]]]=>2
[3,4,1,2,3,6]=>[[[],[[]],[[]]]]=>1
[3,4,1,2,6,3]=>[[[],[[],[],[]]]]=>1
[3,4,1,3,2,6]=>[[[[],[[[]]]]]]=>1
[3,4,1,3,6,2]=>[[[[[[],[]]]]]]=>1
[3,4,1,6,2,3]=>[[[],[[[[]]]]]]=>1
[3,4,1,6,3,2]=>[[[[],[[[]]]]]]=>1
[3,4,2,1,3,6]=>[[[[[[[]]]]]]]=>1
[3,4,2,1,6,3]=>[[[[],[[[]]]]]]=>1
[3,4,2,3,1,6]=>[[[],[[],[],[]]]]=>1
[3,4,2,3,6,1]=>[[[[[]]],[[]]]]=>1
[3,4,2,6,1,3]=>[[[[[],[[]]]]]]=>1
[3,4,2,6,3,1]=>[[[[],[[],[]]]]]=>1
[3,4,3,1,2,6]=>[[[[[]]],[[]]]]=>1
[3,4,3,1,6,2]=>[[[[[[],[]]]]]]=>1
[3,4,3,2,1,6]=>[[[[],[],[[]]]]]=>1
[3,4,3,2,6,1]=>[[[[],[[[]]]]]]=>1
[3,4,3,6,1,2]=>[[[[[]]],[[]]]]=>1
[3,4,3,6,2,1]=>[[[[],[[],[]]]]]=>1
[3,4,6,1,2,3]=>[[[],[],[[],[]]]]=>1
[3,4,6,1,3,2]=>[[[[],[],[[]]]]]=>1
[3,4,6,2,1,3]=>[[[[],[[[]]]]]]=>1
[3,4,6,2,3,1]=>[[[[[]]],[[]]]]=>1
[3,4,6,3,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,6,3,2,1]=>[[[[[[],[]]]]]]=>1
[3,6,1,2,3,4]=>[[[[[],[],[]]]]]=>1
[3,6,1,2,4,3]=>[[[[[]],[[]]]]]=>1
[3,6,1,3,2,4]=>[[[[],[],[[]]]]]=>1
[3,6,1,3,4,2]=>[[[[],[[[]]]]]]=>1
[3,6,1,4,2,3]=>[[[[]],[[[]]]]]=>1
[3,6,1,4,3,2]=>[[[[]],[[],[]]]]=>1
[3,6,2,1,3,4]=>[[[],[[[[]]]]]]=>1
[3,6,2,1,4,3]=>[[[],[],[[],[]]]]=>1
[3,6,2,3,1,4]=>[[[],[],[[[]]]]]=>1
[3,6,2,3,4,1]=>[[[],[[],[[]]]]]=>1
[3,6,2,4,1,3]=>[[[],[[],[[]]]]]=>1
[3,6,2,4,3,1]=>[[[],[[[[]]]]]]=>1
[3,6,3,1,2,4]=>[[[[[[[]]]]]]]=>1
[3,6,3,1,4,2]=>[[[[]],[[],[]]]]=>1
[3,6,3,2,1,4]=>[[[],[[],[[]]]]]=>1
[3,6,3,2,4,1]=>[[[[[],[[]]]]]]=>1
[3,6,3,4,1,2]=>[[[[],[[],[]]]]]=>1
[3,6,3,4,2,1]=>[[[[[[[]]]]]]]=>1
[3,6,4,1,2,3]=>[[[[[],[[]]]]]]=>1
[3,6,4,1,3,2]=>[[[[[[[]]]]]]]=>1
[3,6,4,2,1,3]=>[[[[],[[[]]]]]]=>1
[3,6,4,2,3,1]=>[[[[],[],[[]]]]]=>1
[3,6,4,3,1,2]=>[[[[[[],[]]]]]]=>1
[3,6,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[4,1,2,3,3,6]=>[[[]],[[],[[]]]]=>2
[4,1,2,3,6,3]=>[[[],[[[],[]]]]]=>1
[4,1,2,6,3,3]=>[[],[[],[],[[]]]]=>2
[4,1,3,2,3,6]=>[[[[[[[]]]]]]]=>1
[4,1,3,2,6,3]=>[[[],[],[[[]]]]]=>1
[4,1,3,3,2,6]=>[[[]],[[[],[]]]]=>2
[4,1,3,3,6,2]=>[[[[]]],[[],[]]]=>2
[4,1,3,6,2,3]=>[[[[[],[[]]]]]]=>1
[4,1,3,6,3,2]=>[[[[[]]],[[]]]]=>1
[4,1,6,2,3,3]=>[[],[[[[[]]]]]]=>2
[4,1,6,3,2,3]=>[[[],[[[[]]]]]]=>1
[4,1,6,3,3,2]=>[[[[]]],[[],[]]]=>2
[4,2,1,3,3,6]=>[[[[]]],[[[]]]]=>2
[4,2,1,3,6,3]=>[[[[[[[]]]]]]]=>1
[4,2,1,6,3,3]=>[[[[],[]]],[[]]]=>2
[4,2,3,1,3,6]=>[[[[]],[[[]]]]]=>1
[4,2,3,1,6,3]=>[[[],[[]],[[]]]]=>1
[4,2,3,3,1,6]=>[[[]],[[],[],[]]]=>2
[4,2,3,3,6,1]=>[[[[]]],[[[]]]]=>2
[4,2,3,6,1,3]=>[[[[],[[[]]]]]]=>1
[4,2,3,6,3,1]=>[[[],[[[[]]]]]]=>1
[4,2,6,1,3,3]=>[[],[[[]],[[]]]]=>2
[4,2,6,3,1,3]=>[[[[]],[[],[]]]]=>1
[4,2,6,3,3,1]=>[[[],[]],[[],[]]]=>2
[4,3,1,2,3,6]=>[[[[[],[[]]]]]]=>1
[4,3,1,2,6,3]=>[[[[[]],[[]]]]]=>1
[4,3,1,3,2,6]=>[[[[]],[[[]]]]]=>1
[4,3,1,3,6,2]=>[[[[[]],[[]]]]]=>1
[4,3,1,6,2,3]=>[[[[[[],[]]]]]]=>1
[4,3,1,6,3,2]=>[[[[]],[[],[]]]]=>1
[4,3,2,1,3,6]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,6,3]=>[[[],[],[[[]]]]]=>1
[4,3,2,3,1,6]=>[[[],[[],[[]]]]]=>1
[4,3,2,3,6,1]=>[[[],[[[[]]]]]]=>1
[4,3,2,6,1,3]=>[[[],[[],[[]]]]]=>1
[4,3,2,6,3,1]=>[[[],[[[],[]]]]]=>1
[4,3,3,1,2,6]=>[[],[[[[[]]]]]]=>2
[4,3,3,1,6,2]=>[[],[[],[[[]]]]]=>2
[4,3,3,2,1,6]=>[[],[[],[],[[]]]]=>2
[4,3,3,2,6,1]=>[[],[[],[[[]]]]]=>2
[4,3,3,6,1,2]=>[[],[[[[[]]]]]]=>2
[4,3,3,6,2,1]=>[[],[[],[[],[]]]]=>2
[4,3,6,1,2,3]=>[[[[],[[[]]]]]]=>1
[4,3,6,1,3,2]=>[[[],[[],[[]]]]]=>1
[4,3,6,2,1,3]=>[[[[]],[[],[]]]]=>1
[4,3,6,2,3,1]=>[[[[[[],[]]]]]]=>1
[4,3,6,3,1,2]=>[[[[[[[]]]]]]]=>1
[4,3,6,3,2,1]=>[[[],[[]],[[]]]]=>1
[4,6,1,2,3,3]=>[[],[[],[[],[]]]]=>2
[4,6,1,3,2,3]=>[[[],[],[[[]]]]]=>1
[4,6,1,3,3,2]=>[[[]],[[],[],[]]]=>2
[4,6,2,1,3,3]=>[[[[]]],[[],[]]]=>2
[4,6,2,3,1,3]=>[[[],[[[[]]]]]]=>1
[4,6,2,3,3,1]=>[[[[[]]]],[[]]]=>2
[4,6,3,1,2,3]=>[[[[[],[[]]]]]]=>1
[4,6,3,1,3,2]=>[[[[]],[[[]]]]]=>1
[4,6,3,2,1,3]=>[[[],[[],[[]]]]]=>1
[4,6,3,2,3,1]=>[[[[[[[]]]]]]]=>1
[4,6,3,3,1,2]=>[[[[]]],[[[]]]]=>2
[4,6,3,3,2,1]=>[[],[[],[[[]]]]]=>2
[6,1,2,3,3,4]=>[[],[[],[],[[]]]]=>2
[6,1,2,3,4,3]=>[[[[],[],[[]]]]]=>1
[6,1,2,4,3,3]=>[[],[[[],[[]]]]]=>2
[6,1,3,2,3,4]=>[[[],[[[],[]]]]]=>1
[6,1,3,2,4,3]=>[[[],[],[[],[]]]]=>1
[6,1,3,3,2,4]=>[[],[[[],[],[]]]]=>2
[6,1,3,3,4,2]=>[[[[]]],[[],[]]]=>2
[6,1,3,4,2,3]=>[[[],[[],[[]]]]]=>1
[6,1,3,4,3,2]=>[[[],[[[],[]]]]]=>1
[6,1,4,2,3,3]=>[[],[[[[[]]]]]]=>2
[6,1,4,3,2,3]=>[[[[[],[[]]]]]]=>1
[6,1,4,3,3,2]=>[[],[[],[[[]]]]]=>2
[6,2,1,3,3,4]=>[[[[[]]]],[[]]]=>2
[6,2,1,3,4,3]=>[[[[],[[[]]]]]]=>1
[6,2,1,4,3,3]=>[[],[[],[[],[]]]]=>2
[6,2,3,1,3,4]=>[[[[],[[[]]]]]]=>1
[6,2,3,1,4,3]=>[[[],[[[[]]]]]]=>1
[6,2,3,3,1,4]=>[[[]],[[[],[]]]]=>2
[6,2,3,3,4,1]=>[[],[[[]],[[]]]]=>2
[6,2,3,4,1,3]=>[[[[],[[[]]]]]]=>1
[6,2,3,4,3,1]=>[[[[],[[[]]]]]]=>1
[6,2,4,1,3,3]=>[[],[[[]],[[]]]]=>2
[6,2,4,3,1,3]=>[[[[[],[[]]]]]]=>1
[6,2,4,3,3,1]=>[[],[[[[[]]]]]]=>2
[6,3,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[6,3,1,2,4,3]=>[[[[[[[]]]]]]]=>1
[6,3,1,3,2,4]=>[[[[[],[[]]]]]]=>1
[6,3,1,3,4,2]=>[[[[[[],[]]]]]]=>1
[6,3,1,4,2,3]=>[[[[[],[[]]]]]]=>1
[6,3,1,4,3,2]=>[[[[[]],[[]]]]]=>1
[6,3,2,1,3,4]=>[[[[],[[[]]]]]]=>1
[6,3,2,1,4,3]=>[[[[[],[],[]]]]]=>1
[6,3,2,3,1,4]=>[[[[[[[]]]]]]]=>1
[6,3,2,3,4,1]=>[[[[]],[[],[]]]]=>1
[6,3,2,4,1,3]=>[[[],[[],[[]]]]]=>1
[6,3,2,4,3,1]=>[[[[[],[[]]]]]]=>1
[6,3,3,1,2,4]=>[[[]],[[[[]]]]]=>2
[6,3,3,1,4,2]=>[[],[[],[[[]]]]]=>2
[6,3,3,2,1,4]=>[[],[[[]],[[]]]]=>2
[6,3,3,2,4,1]=>[[],[[[],[[]]]]]=>2
[6,3,3,4,1,2]=>[[],[[],[[],[]]]]=>2
[6,3,3,4,2,1]=>[[],[[[[[]]]]]]=>2
[6,3,4,1,2,3]=>[[[],[[],[],[]]]]=>1
[6,3,4,1,3,2]=>[[[[]],[[[]]]]]=>1
[6,3,4,2,1,3]=>[[[[[[[]]]]]]]=>1
[6,3,4,2,3,1]=>[[[[],[[],[]]]]]=>1
[6,3,4,3,1,2]=>[[[[[],[[]]]]]]=>1
[6,3,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[6,4,1,2,3,3]=>[[],[[[]],[[]]]]=>2
[6,4,1,3,2,3]=>[[[[[[[]]]]]]]=>1
[6,4,1,3,3,2]=>[[[[]]],[[[]]]]=>2
[6,4,2,1,3,3]=>[[[[],[]]],[[]]]=>2
[6,4,2,3,1,3]=>[[[],[[]],[[]]]]=>1
[6,4,2,3,3,1]=>[[[]],[[],[],[]]]=>2
[6,4,3,1,2,3]=>[[[],[[],[[]]]]]=>1
[6,4,3,1,3,2]=>[[[],[[],[[]]]]]=>1
[6,4,3,2,1,3]=>[[[[[],[],[]]]]]=>1
[6,4,3,2,3,1]=>[[[[]],[[],[]]]]=>1
[6,4,3,3,1,2]=>[[],[[],[[[]]]]]=>2
[6,4,3,3,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,3,3,5,5]=>[[],[[]],[[],[]]]=>3
[1,2,3,5,3,5]=>[[[],[[],[[]]]]]=>1
[1,2,3,5,5,3]=>[[[[],[]]],[[]]]=>2
[1,2,5,3,3,5]=>[[[]],[[[[]]]]]=>2
[1,2,5,3,5,3]=>[[[[[],[[]]]]]]=>1
[1,2,5,5,3,3]=>[[],[[[]]],[[]]]=>3
[1,3,2,3,5,5]=>[[[]],[[],[[]]]]=>2
[1,3,2,5,3,5]=>[[[[[]]],[[]]]]=>1
[1,3,2,5,5,3]=>[[[]],[[[[]]]]]=>2
[1,3,3,2,5,5]=>[[[]],[[]],[[]]]=>3
[1,3,3,5,2,5]=>[[],[[],[[[]]]]]=>2
[1,3,3,5,5,2]=>[[],[[]],[[],[]]]=>3
[1,3,5,2,3,5]=>[[[],[],[[[]]]]]=>1
[1,3,5,2,5,3]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,2,5]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,5,2]=>[[[],[[]],[[]]]]=>1
[1,3,5,5,2,3]=>[[[[]]],[[],[]]]=>2
[1,3,5,5,3,2]=>[[[[]]],[[],[]]]=>2
[1,5,2,3,3,5]=>[[[[],[]]],[[]]]=>2
[1,5,2,3,5,3]=>[[[],[[[[]]]]]]=>1
[1,5,2,5,3,3]=>[[],[[[[],[]]]]]=>2
[1,5,3,2,3,5]=>[[[[[[[]]]]]]]=>1
[1,5,3,2,5,3]=>[[[[[],[[]]]]]]=>1
[1,5,3,3,2,5]=>[[[]],[[[[]]]]]=>2
[1,5,3,3,5,2]=>[[[[],[]]],[[]]]=>2
[1,5,3,5,2,3]=>[[[[]],[[[]]]]]=>1
[1,5,3,5,3,2]=>[[[[[],[[]]]]]]=>1
[1,5,5,2,3,3]=>[[],[],[[[],[]]]]=>3
[1,5,5,3,2,3]=>[[],[[[[[]]]]]]=>2
[1,5,5,3,3,2]=>[[],[[]],[[[]]]]=>3
[2,1,3,3,5,5]=>[[],[[]],[[],[]]]=>3
[2,1,3,5,3,5]=>[[[[],[],[[]]]]]=>1
[2,1,3,5,5,3]=>[[[[]]],[[],[]]]=>2
[2,1,5,3,3,5]=>[[[[]]],[[[]]]]=>2
[2,1,5,3,5,3]=>[[[[],[[[]]]]]]=>1
[2,1,5,5,3,3]=>[[],[[[]]],[[]]]=>3
[2,3,1,3,5,5]=>[[],[[],[[[]]]]]=>2
[2,3,1,5,3,5]=>[[[[[]],[[]]]]]=>1
[2,3,1,5,5,3]=>[[[]],[[],[[]]]]=>2
[2,3,3,1,5,5]=>[[],[[]],[[[]]]]=>3
[2,3,3,5,1,5]=>[[[]],[[[[]]]]]=>2
[2,3,3,5,5,1]=>[[[]],[[]],[[]]]=>3
[2,3,5,1,3,5]=>[[[[],[],[[]]]]]=>1
[2,3,5,1,5,3]=>[[[[[[[]]]]]]]=>1
[2,3,5,3,1,5]=>[[[[[],[[]]]]]]=>1
[2,3,5,3,5,1]=>[[[[[]],[[]]]]]=>1
[2,3,5,5,1,3]=>[[],[[[],[[]]]]]=>2
[2,3,5,5,3,1]=>[[[[]]],[[],[]]]=>2
[2,5,1,3,3,5]=>[[],[[],[[],[]]]]=>2
[2,5,1,3,5,3]=>[[[],[[],[[]]]]]=>1
[2,5,1,5,3,3]=>[[],[[[[],[]]]]]=>2
[2,5,3,1,3,5]=>[[[[],[[],[]]]]]=>1
[2,5,3,1,5,3]=>[[[[[],[],[]]]]]=>1
[2,5,3,3,1,5]=>[[[]],[[],[[]]]]=>2
[2,5,3,3,5,1]=>[[[[],[]]],[[]]]=>2
[2,5,3,5,1,3]=>[[[[]],[[],[]]]]=>1
[2,5,3,5,3,1]=>[[[[[],[],[]]]]]=>1
[2,5,5,1,3,3]=>[[],[],[[[],[]]]]=>3
[2,5,5,3,1,3]=>[[[]],[[],[[]]]]=>2
[2,5,5,3,3,1]=>[[],[],[[],[[]]]]=>3
[3,1,2,3,5,5]=>[[],[[[],[[]]]]]=>2
[3,1,2,5,3,5]=>[[[[]],[[[]]]]]=>1
[3,1,2,5,5,3]=>[[[[]]],[[],[]]]=>2
[3,1,3,2,5,5]=>[[[[]]],[[[]]]]=>2
[3,1,3,5,2,5]=>[[[[],[[[]]]]]]=>1
[3,1,3,5,5,2]=>[[[]],[[],[[]]]]=>2
[3,1,5,2,3,5]=>[[[[],[[[]]]]]]=>1
[3,1,5,2,5,3]=>[[[],[[[],[]]]]]=>1
[3,1,5,3,2,5]=>[[[],[[[[]]]]]]=>1
[3,1,5,3,5,2]=>[[[],[[[],[]]]]]=>1
[3,1,5,5,2,3]=>[[[]],[[],[[]]]]=>2
[3,1,5,5,3,2]=>[[],[[],[[[]]]]]=>2
[3,2,1,3,5,5]=>[[[],[]],[[],[]]]=>2
[3,2,1,5,3,5]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,5,3]=>[[[]],[[[],[]]]]=>2
[3,2,3,1,5,5]=>[[[[[]]]],[[]]]=>2
[3,2,3,5,1,5]=>[[[[[[[]]]]]]]=>1
[3,2,3,5,5,1]=>[[[[]]],[[[]]]]=>2
[3,2,5,1,3,5]=>[[[[],[[],[]]]]]=>1
[3,2,5,1,5,3]=>[[[[[[],[]]]]]]=>1
[3,2,5,3,1,5]=>[[[[[],[[]]]]]]=>1
[3,2,5,3,5,1]=>[[[[],[[[]]]]]]=>1
[3,2,5,5,1,3]=>[[],[[],[[[]]]]]=>2
[3,2,5,5,3,1]=>[[[]],[[],[[]]]]=>2
[3,3,1,2,5,5]=>[[],[],[[[[]]]]]=>3
[3,3,1,5,2,5]=>[[],[[[],[[]]]]]=>2
[3,3,1,5,5,2]=>[[],[[]],[[],[]]]=>3
[3,3,2,1,5,5]=>[[],[[]],[[],[]]]=>3
[3,3,2,5,1,5]=>[[],[[[[],[]]]]]=>2
[3,3,2,5,5,1]=>[[],[],[[],[[]]]]=>3
[3,3,5,1,2,5]=>[[],[[[],[[]]]]]=>2
[3,3,5,1,5,2]=>[[],[[[[],[]]]]]=>2
[3,3,5,2,1,5]=>[[],[[[],[[]]]]]=>2
[3,3,5,2,5,1]=>[[],[[[[],[]]]]]=>2
[3,3,5,5,1,2]=>[[],[[]],[[[]]]]=>3
[3,3,5,5,2,1]=>[[],[[]],[[[]]]]=>3
[3,5,1,2,3,5]=>[[[],[[],[[]]]]]=>1
[3,5,1,2,5,3]=>[[[[[]],[[]]]]]=>1
[3,5,1,3,2,5]=>[[[],[[[],[]]]]]=>1
[3,5,1,3,5,2]=>[[[],[[]],[[]]]]=>1
[3,5,1,5,2,3]=>[[[[[],[[]]]]]]=>1
[3,5,1,5,3,2]=>[[[[[[[]]]]]]]=>1
[3,5,2,1,3,5]=>[[[],[[]],[[]]]]=>1
[3,5,2,1,5,3]=>[[[[[[],[]]]]]]=>1
[3,5,2,3,1,5]=>[[[[],[[[]]]]]]=>1
[3,5,2,3,5,1]=>[[[[[]]],[[]]]]=>1
[3,5,2,5,1,3]=>[[[],[[],[[]]]]]=>1
[3,5,2,5,3,1]=>[[[[[],[[]]]]]]=>1
[3,5,3,1,2,5]=>[[[[],[[[]]]]]]=>1
[3,5,3,1,5,2]=>[[[[],[[],[]]]]]=>1
[3,5,3,2,1,5]=>[[[[],[[[]]]]]]=>1
[3,5,3,2,5,1]=>[[[[[],[[]]]]]]=>1
[3,5,3,5,1,2]=>[[[[[]]],[[]]]]=>1
[3,5,3,5,2,1]=>[[[],[[[[]]]]]]=>1
[3,5,5,1,2,3]=>[[[]],[[[],[]]]]=>2
[3,5,5,1,3,2]=>[[],[[[],[[]]]]]=>2
[3,5,5,2,1,3]=>[[],[[[[],[]]]]]=>2
[3,5,5,2,3,1]=>[[[]],[[[[]]]]]=>2
[3,5,5,3,1,2]=>[[[]],[[],[[]]]]=>2
[3,5,5,3,2,1]=>[[[]],[[[],[]]]]=>2
[5,1,2,3,3,5]=>[[[]],[[],[[]]]]=>2
[5,1,2,3,5,3]=>[[[[],[[[]]]]]]=>1
[5,1,2,5,3,3]=>[[],[[[],[[]]]]]=>2
[5,1,3,2,3,5]=>[[[[[]],[[]]]]]=>1
[5,1,3,2,5,3]=>[[[],[[[[]]]]]]=>1
[5,1,3,3,2,5]=>[[[]],[[[],[]]]]=>2
[5,1,3,3,5,2]=>[[],[[[]],[[]]]]=>2
[5,1,3,5,2,3]=>[[[[],[[[]]]]]]=>1
[5,1,3,5,3,2]=>[[[[],[[[]]]]]]=>1
[5,1,5,2,3,3]=>[[],[[[],[[]]]]]=>2
[5,1,5,3,2,3]=>[[[[[[[]]]]]]]=>1
[5,1,5,3,3,2]=>[[[]],[[[[]]]]]=>2
[5,2,1,3,3,5]=>[[],[[[]],[[]]]]=>2
[5,2,1,3,5,3]=>[[[[],[[[]]]]]]=>1
[5,2,1,5,3,3]=>[[[[],[]]],[[]]]=>2
[5,2,3,1,3,5]=>[[[[],[[[]]]]]]=>1
[5,2,3,1,5,3]=>[[[],[[],[[]]]]]=>1
[5,2,3,3,1,5]=>[[[]],[[[],[]]]]=>2
[5,2,3,3,5,1]=>[[[[]]],[[[]]]]=>2
[5,2,3,5,1,3]=>[[[[[],[[]]]]]]=>1
[5,2,3,5,3,1]=>[[[[],[[[]]]]]]=>1
[5,2,5,1,3,3]=>[[],[[[],[[]]]]]=>2
[5,2,5,3,1,3]=>[[[[[]],[[]]]]]=>1
[5,2,5,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,3,1,2,3,5]=>[[[],[[],[[]]]]]=>1
[5,3,1,2,5,3]=>[[[],[],[[[]]]]]=>1
[5,3,1,3,2,5]=>[[[],[[[[]]]]]]=>1
[5,3,1,3,5,2]=>[[[],[[],[[]]]]]=>1
[5,3,1,5,2,3]=>[[[],[[],[[]]]]]=>1
[5,3,1,5,3,2]=>[[[],[],[[[]]]]]=>1
[5,3,2,1,3,5]=>[[[[],[[],[]]]]]=>1
[5,3,2,1,5,3]=>[[[[]],[[],[]]]]=>1
[5,3,2,3,1,5]=>[[[[]],[[[]]]]]=>1
[5,3,2,3,5,1]=>[[[[[[[]]]]]]]=>1
[5,3,2,5,1,3]=>[[[[],[[[]]]]]]=>1
[5,3,2,5,3,1]=>[[[],[[]],[[]]]]=>1
[5,3,3,1,2,5]=>[[],[[],[[[]]]]]=>2
[5,3,3,1,5,2]=>[[],[[],[[],[]]]]=>2
[5,3,3,2,1,5]=>[[],[[],[[[]]]]]=>2
[5,3,3,2,5,1]=>[[],[[[],[[]]]]]=>2
[5,3,3,5,1,2]=>[[[[[]]]],[[]]]=>2
[5,3,3,5,2,1]=>[[],[[[[[]]]]]]=>2
[5,3,5,1,2,3]=>[[[[],[[[]]]]]]=>1
[5,3,5,1,3,2]=>[[[[[],[[]]]]]]=>1
[5,3,5,2,1,3]=>[[[[],[[[]]]]]]=>1
[5,3,5,2,3,1]=>[[[],[[[[]]]]]]=>1
[5,3,5,3,1,2]=>[[[],[[]],[[]]]]=>1
[5,3,5,3,2,1]=>[[[[]],[[],[]]]]=>1
[5,5,1,2,3,3]=>[[],[],[[],[[]]]]=>3
[5,5,1,3,2,3]=>[[],[[[[[]]]]]]=>2
[5,5,1,3,3,2]=>[[],[[[]]],[[]]]=>3
[5,5,2,1,3,3]=>[[],[[]],[[[]]]]=>3
[5,5,2,3,1,3]=>[[],[[[[[]]]]]]=>2
[5,5,2,3,3,1]=>[[],[[[]]],[[]]]=>3
[5,5,3,1,2,3]=>[[],[[],[[],[]]]]=>2
[5,5,3,1,3,2]=>[[],[[],[[[]]]]]=>2
[5,5,3,2,1,3]=>[[],[[[[],[]]]]]=>2
[5,5,3,2,3,1]=>[[],[[[]],[[]]]]=>2
[5,5,3,3,1,2]=>[[],[],[[],[[]]]]=>3
[5,5,3,3,2,1]=>[[],[],[[],[[]]]]=>3
[1,2,3,3,5,6]=>[[],[[[],[],[]]]]=>2
[1,2,3,3,6,5]=>[[[[]]],[[],[]]]=>2
[1,2,3,5,3,6]=>[[[],[[[[]]]]]]=>1
[1,2,3,5,6,3]=>[[[],[[]],[[]]]]=>1
[1,2,3,6,3,5]=>[[[],[[[[]]]]]]=>1
[1,2,3,6,5,3]=>[[[],[[[[]]]]]]=>1
[1,2,5,3,3,6]=>[[[]],[[],[[]]]]=>2
[1,2,5,3,6,3]=>[[[[[]],[[]]]]]=>1
[1,2,5,6,3,3]=>[[],[[[],[[]]]]]=>2
[1,2,6,3,3,5]=>[[[]],[[],[[]]]]=>2
[1,2,6,3,5,3]=>[[[[],[[[]]]]]]=>1
[1,2,6,5,3,3]=>[[[[[]]]],[[]]]=>2
[1,3,2,3,5,6]=>[[[],[[],[[]]]]]=>1
[1,3,2,3,6,5]=>[[[[],[[[]]]]]]=>1
[1,3,2,5,3,6]=>[[[[[]],[[]]]]]=>1
[1,3,2,5,6,3]=>[[[[[[[]]]]]]]=>1
[1,3,2,6,3,5]=>[[[[]],[[],[]]]]=>1
[1,3,2,6,5,3]=>[[[[[[],[]]]]]]=>1
[1,3,3,2,5,6]=>[[[]],[[[[]]]]]=>2
[1,3,3,2,6,5]=>[[[]],[[],[[]]]]=>2
[1,3,3,5,2,6]=>[[],[[],[[],[]]]]=>2
[1,3,3,5,6,2]=>[[],[[],[[[]]]]]=>2
[1,3,3,6,2,5]=>[[[]],[[],[],[]]]=>2
[1,3,3,6,5,2]=>[[[]],[[[[]]]]]=>2
[1,3,5,2,3,6]=>[[[],[[[[]]]]]]=>1
[1,3,5,2,6,3]=>[[[],[[],[],[]]]]=>1
[1,3,5,3,2,6]=>[[[],[[[[]]]]]]=>1
[1,3,5,3,6,2]=>[[[],[[[],[]]]]]=>1
[1,3,5,6,2,3]=>[[[],[[],[[]]]]]=>1
[1,3,5,6,3,2]=>[[[],[[[[]]]]]]=>1
[1,3,6,2,3,5]=>[[[],[[[],[]]]]]=>1
[1,3,6,2,5,3]=>[[[[],[],[[]]]]]=>1
[1,3,6,3,2,5]=>[[[[[[],[]]]]]]=>1
[1,3,6,3,5,2]=>[[[],[[],[[]]]]]=>1
[1,3,6,5,2,3]=>[[[[[[[]]]]]]]=>1
[1,3,6,5,3,2]=>[[[[],[[[]]]]]]=>1
[1,5,2,3,3,6]=>[[[[],[]]],[[]]]=>2
[1,5,2,3,6,3]=>[[[],[],[[[]]]]]=>1
[1,5,2,6,3,3]=>[[],[[],[],[],[]]]=>2
[1,5,3,2,3,6]=>[[[[[[[]]]]]]]=>1
[1,5,3,2,6,3]=>[[[],[[]],[[]]]]=>1
[1,5,3,3,2,6]=>[[],[[[],[[]]]]]=>2
[1,5,3,3,6,2]=>[[[]],[[],[[]]]]=>2
[1,5,3,6,2,3]=>[[[[[]],[[]]]]]=>1
[1,5,3,6,3,2]=>[[[[]],[[[]]]]]=>1
[1,5,6,2,3,3]=>[[],[[[]],[[]]]]=>2
[1,5,6,3,2,3]=>[[[],[[[],[]]]]]=>1
[1,5,6,3,3,2]=>[[[]],[[],[[]]]]=>2
[1,6,2,3,3,5]=>[[[[[]]]],[[]]]=>2
[1,6,2,3,5,3]=>[[[],[[[[]]]]]]=>1
[1,6,2,5,3,3]=>[[],[[],[[],[]]]]=>2
[1,6,3,2,3,5]=>[[[[[[[]]]]]]]=>1
[1,6,3,2,5,3]=>[[[[[]]],[[]]]]=>1
[1,6,3,3,2,5]=>[[[]],[[[[]]]]]=>2
[1,6,3,3,5,2]=>[[[[],[]]],[[]]]=>2
[1,6,3,5,2,3]=>[[[[[],[[]]]]]]=>1
[1,6,3,5,3,2]=>[[[[]],[[[]]]]]=>1
[1,6,5,2,3,3]=>[[[[[]]]],[[]]]=>2
[1,6,5,3,2,3]=>[[[],[[[],[]]]]]=>1
[1,6,5,3,3,2]=>[[],[[],[[],[]]]]=>2
[2,1,3,3,5,6]=>[[],[[],[[[]]]]]=>2
[2,1,3,3,6,5]=>[[[]],[[[],[]]]]=>2
[2,1,3,5,3,6]=>[[[[[[],[]]]]]]=>1
[2,1,3,5,6,3]=>[[[[[[],[]]]]]]=>1
[2,1,3,6,3,5]=>[[[[],[[[]]]]]]=>1
[2,1,3,6,5,3]=>[[[[[]]],[[]]]]=>1
[2,1,5,3,3,6]=>[[[[]]],[[[]]]]=>2
[2,1,5,3,6,3]=>[[[[],[[[]]]]]]=>1
[2,1,5,6,3,3]=>[[[]],[[],[[]]]]=>2
[2,1,6,3,3,5]=>[[[[]]],[[[]]]]=>2
[2,1,6,3,5,3]=>[[[[],[[[]]]]]]=>1
[2,1,6,5,3,3]=>[[[],[]],[[],[]]]=>2
[2,3,1,3,5,6]=>[[[],[[],[[]]]]]=>1
[2,3,1,3,6,5]=>[[[[[[[]]]]]]]=>1
[2,3,1,5,3,6]=>[[[[[]],[[]]]]]=>1
[2,3,1,5,6,3]=>[[[[]],[[],[]]]]=>1
[2,3,1,6,3,5]=>[[[[],[[[]]]]]]=>1
[2,3,1,6,5,3]=>[[[[],[],[[]]]]]=>1
[2,3,3,1,5,6]=>[[],[[[[],[]]]]]=>2
[2,3,3,1,6,5]=>[[[]],[[],[[]]]]=>2
[2,3,3,5,1,6]=>[[[]],[[[[]]]]]=>2
[2,3,3,5,6,1]=>[[],[[],[[],[]]]]=>2
[2,3,3,6,1,5]=>[[[]],[[[[]]]]]=>2
[2,3,3,6,5,1]=>[[[]],[[],[[]]]]=>2
[2,3,5,1,3,6]=>[[[[],[[],[]]]]]=>1
[2,3,5,1,6,3]=>[[[[[[[]]]]]]]=>1
[2,3,5,3,1,6]=>[[[[[],[],[]]]]]=>1
[2,3,5,3,6,1]=>[[[[],[[[]]]]]]=>1
[2,3,5,6,1,3]=>[[[],[[],[],[]]]]=>1
[2,3,5,6,3,1]=>[[[[]],[[[]]]]]=>1
[2,3,6,1,3,5]=>[[[[[],[],[]]]]]=>1
[2,3,6,1,5,3]=>[[[[[[[]]]]]]]=>1
[2,3,6,3,1,5]=>[[[[[[],[]]]]]]=>1
[2,3,6,3,5,1]=>[[[[],[[[]]]]]]=>1
[2,3,6,5,1,3]=>[[[[],[[[]]]]]]=>1
[2,3,6,5,3,1]=>[[[[[],[[]]]]]]=>1
[2,5,1,3,3,6]=>[[[]],[[],[],[]]]=>2
[2,5,1,3,6,3]=>[[[],[[]],[[]]]]=>1
[2,5,1,6,3,3]=>[[],[[[[],[]]]]]=>2
[2,5,3,1,3,6]=>[[[],[[[],[]]]]]=>1
[2,5,3,1,6,3]=>[[[[],[],[[]]]]]=>1
[2,5,3,3,1,6]=>[[[]],[[],[],[]]]=>2
[2,5,3,3,6,1]=>[[[]],[[],[[]]]]=>2
[2,5,3,6,1,3]=>[[[],[[],[[]]]]]=>1
[2,5,3,6,3,1]=>[[[],[[[],[]]]]]=>1
[2,5,6,1,3,3]=>[[],[[],[[[]]]]]=>2
[2,5,6,3,1,3]=>[[[[[[[]]]]]]]=>1
[2,5,6,3,3,1]=>[[[[[]]]],[[]]]=>2
[2,6,1,3,3,5]=>[[],[[],[],[[]]]]=>2
[2,6,1,3,5,3]=>[[[[],[],[[]]]]]=>1
[2,6,1,5,3,3]=>[[],[[[],[[]]]]]=>2
[2,6,3,1,3,5]=>[[[],[[],[[]]]]]=>1
[2,6,3,1,5,3]=>[[[],[],[[],[]]]]=>1
[2,6,3,3,1,5]=>[[],[[[],[],[]]]]=>2
[2,6,3,3,5,1]=>[[[[]]],[[],[]]]=>2
[2,6,3,5,1,3]=>[[[],[[],[[]]]]]=>1
[2,6,3,5,3,1]=>[[[],[[],[[]]]]]=>1
[2,6,5,1,3,3]=>[[[[]]],[[[]]]]=>2
[2,6,5,3,1,3]=>[[[[],[[[]]]]]]=>1
[2,6,5,3,3,1]=>[[[]],[[],[[]]]]=>2
[3,1,2,3,5,6]=>[[[[[],[],[]]]]]=>1
[3,1,2,3,6,5]=>[[[[[[],[]]]]]]=>1
[3,1,2,5,3,6]=>[[[],[[],[[]]]]]=>1
[3,1,2,5,6,3]=>[[[[[],[[]]]]]]=>1
[3,1,2,6,3,5]=>[[[[[]],[[]]]]]=>1
[3,1,2,6,5,3]=>[[[[[]]],[[]]]]=>1
[3,1,3,2,5,6]=>[[[[[[[]]]]]]]=>1
[3,1,3,2,6,5]=>[[[[[]],[[]]]]]=>1
[3,1,3,5,2,6]=>[[[[],[[],[]]]]]=>1
[3,1,3,5,6,2]=>[[[[],[[[]]]]]]=>1
[3,1,3,6,2,5]=>[[[[],[],[[]]]]]=>1
[3,1,3,6,5,2]=>[[[[[[[]]]]]]]=>1
[3,1,5,2,3,6]=>[[[[],[[[]]]]]]=>1
[3,1,5,2,6,3]=>[[[[],[],[],[]]]]=>1
[3,1,5,3,2,6]=>[[[],[[],[[]]]]]=>1
[3,1,5,3,6,2]=>[[[],[[],[[]]]]]=>1
[3,1,5,6,2,3]=>[[[[[],[[]]]]]]=>1
[3,1,5,6,3,2]=>[[[[[],[[]]]]]]=>1
[3,1,6,2,3,5]=>[[[],[[[[]]]]]]=>1
[3,1,6,2,5,3]=>[[[],[],[[],[]]]]=>1
[3,1,6,3,2,5]=>[[[],[[[[]]]]]]=>1
[3,1,6,3,5,2]=>[[[],[[[],[]]]]]=>1
[3,1,6,5,2,3]=>[[[],[[[[]]]]]]=>1
[3,1,6,5,3,2]=>[[[],[],[[],[]]]]=>1
[3,2,1,3,5,6]=>[[[],[[[],[]]]]]=>1
[3,2,1,3,6,5]=>[[[],[],[[[]]]]]=>1
[3,2,1,5,3,6]=>[[[],[[[[]]]]]]=>1
[3,2,1,5,6,3]=>[[[],[[],[[]]]]]=>1
[3,2,1,6,3,5]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,5,3]=>[[[],[],[[],[]]]]=>1
[3,2,3,1,5,6]=>[[[[],[[[]]]]]]=>1
[3,2,3,1,6,5]=>[[[],[[],[[]]]]]=>1
[3,2,3,5,1,6]=>[[[[[[[]]]]]]]=>1
[3,2,3,5,6,1]=>[[[[],[[],[]]]]]=>1
[3,2,3,6,1,5]=>[[[[[[[]]]]]]]=>1
[3,2,3,6,5,1]=>[[[],[[],[[]]]]]=>1
[3,2,5,1,3,6]=>[[[[],[],[[]]]]]=>1
[3,2,5,1,6,3]=>[[[[[[],[]]]]]]=>1
[3,2,5,3,1,6]=>[[[[],[],[[]]]]]=>1
[3,2,5,3,6,1]=>[[[[[],[[]]]]]]=>1
[3,2,5,6,1,3]=>[[[[],[[[]]]]]]=>1
[3,2,5,6,3,1]=>[[[[[[[]]]]]]]=>1
[3,2,6,1,3,5]=>[[[[],[],[[]]]]]=>1
[3,2,6,1,5,3]=>[[[[[],[[]]]]]]=>1
[3,2,6,3,1,5]=>[[[[],[],[[]]]]]=>1
[3,2,6,3,5,1]=>[[[[[[],[]]]]]]=>1
[3,2,6,5,1,3]=>[[[[[]]],[[]]]]=>1
[3,2,6,5,3,1]=>[[[],[[],[[]]]]]=>1
[3,3,1,2,5,6]=>[[],[[[[],[]]]]]=>2
[3,3,1,2,6,5]=>[[],[[[[[]]]]]]=>2
[3,3,1,5,2,6]=>[[],[[[],[],[]]]]=>2
[3,3,1,5,6,2]=>[[],[[[[[]]]]]]=>2
[3,3,1,6,2,5]=>[[],[[],[[],[]]]]=>2
[3,3,1,6,5,2]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,5,6]=>[[],[[],[[[]]]]]=>2
[3,3,2,1,6,5]=>[[],[[],[],[[]]]]=>2
[3,3,2,5,1,6]=>[[],[[[[],[]]]]]=>2
[3,3,2,5,6,1]=>[[],[[[[[]]]]]]=>2
[3,3,2,6,1,5]=>[[],[[[],[[]]]]]=>2
[3,3,2,6,5,1]=>[[],[[[]],[[]]]]=>2
[3,3,5,1,2,6]=>[[],[[[[[]]]]]]=>2
[3,3,5,1,6,2]=>[[],[[[],[[]]]]]=>2
[3,3,5,2,1,6]=>[[],[[[[[]]]]]]=>2
[3,3,5,2,6,1]=>[[],[[],[[],[]]]]=>2
[3,3,5,6,1,2]=>[[],[[],[[],[]]]]=>2
[3,3,5,6,2,1]=>[[],[[[[[]]]]]]=>2
[3,3,6,1,2,5]=>[[],[[],[[[]]]]]=>2
[3,3,6,1,5,2]=>[[],[[[[],[]]]]]=>2
[3,3,6,2,1,5]=>[[],[[],[[[]]]]]=>2
[3,3,6,2,5,1]=>[[],[[],[],[],[]]]=>2
[3,3,6,5,1,2]=>[[],[[],[[[]]]]]=>2
[3,3,6,5,2,1]=>[[],[[[[],[]]]]]=>2
[3,5,1,2,3,6]=>[[[[],[[],[]]]]]=>1
[3,5,1,2,6,3]=>[[[[[[],[]]]]]]=>1
[3,5,1,3,2,6]=>[[[[]],[[[]]]]]=>1
[3,5,1,3,6,2]=>[[[],[[],[],[]]]]=>1
[3,5,1,6,2,3]=>[[[[[]],[[]]]]]=>1
[3,5,1,6,3,2]=>[[[[[[[]]]]]]]=>1
[3,5,2,1,3,6]=>[[[],[[[[]]]]]]=>1
[3,5,2,1,6,3]=>[[[[[],[[]]]]]]=>1
[3,5,2,3,1,6]=>[[[[[],[[]]]]]]=>1
[3,5,2,3,6,1]=>[[[],[[[[]]]]]]=>1
[3,5,2,6,1,3]=>[[[],[],[[],[]]]]=>1
[3,5,2,6,3,1]=>[[[[],[],[[]]]]]=>1
[3,5,3,1,2,6]=>[[[[],[[[]]]]]]=>1
[3,5,3,1,6,2]=>[[[[],[],[[]]]]]=>1
[3,5,3,2,1,6]=>[[[[],[[],[]]]]]=>1
[3,5,3,2,6,1]=>[[[[[]]],[[]]]]=>1
[3,5,3,6,1,2]=>[[[[]],[[[]]]]]=>1
[3,5,3,6,2,1]=>[[[[],[[[]]]]]]=>1
[3,5,6,1,2,3]=>[[[],[[],[],[]]]]=>1
[3,5,6,1,3,2]=>[[[],[[]],[[]]]]=>1
[3,5,6,2,1,3]=>[[[],[[[[]]]]]]=>1
[3,5,6,2,3,1]=>[[[[[]],[[]]]]]=>1
[3,5,6,3,1,2]=>[[[[],[[[]]]]]]=>1
[3,5,6,3,2,1]=>[[[[[[],[]]]]]]=>1
[3,6,1,2,3,5]=>[[[[],[[],[]]]]]=>1
[3,6,1,2,5,3]=>[[[[[]]],[[]]]]=>1
[3,6,1,3,2,5]=>[[[],[[[],[]]]]]=>1
[3,6,1,3,5,2]=>[[[[],[],[[]]]]]=>1
[3,6,1,5,2,3]=>[[[[[],[[]]]]]]=>1
[3,6,1,5,3,2]=>[[[[[[[]]]]]]]=>1
[3,6,2,1,3,5]=>[[[],[[[],[]]]]]=>1
[3,6,2,1,5,3]=>[[[],[[[[]]]]]]=>1
[3,6,2,3,1,5]=>[[[],[[[[]]]]]]=>1
[3,6,2,3,5,1]=>[[[],[],[[[]]]]]=>1
[3,6,2,5,1,3]=>[[[],[],[],[[]]]]=>1
[3,6,2,5,3,1]=>[[[],[],[[],[]]]]=>1
[3,6,3,1,2,5]=>[[[],[[[[]]]]]]=>1
[3,6,3,1,5,2]=>[[[[],[],[[]]]]]=>1
[3,6,3,2,1,5]=>[[[[],[[],[]]]]]=>1
[3,6,3,2,5,1]=>[[[],[[]],[[]]]]=>1
[3,6,3,5,1,2]=>[[[[]],[[[]]]]]=>1
[3,6,3,5,2,1]=>[[[[[],[[]]]]]]=>1
[3,6,5,1,2,3]=>[[[],[[],[[]]]]]=>1
[3,6,5,1,3,2]=>[[[],[[[],[]]]]]=>1
[3,6,5,2,1,3]=>[[[[[],[[]]]]]]=>1
[3,6,5,2,3,1]=>[[[[[[[]]]]]]]=>1
[3,6,5,3,1,2]=>[[[[],[[[]]]]]]=>1
[3,6,5,3,2,1]=>[[[[],[],[[]]]]]=>1
[5,1,2,3,3,6]=>[[[],[]],[[],[]]]=>2
[5,1,2,3,6,3]=>[[[[]],[[],[]]]]=>1
[5,1,2,6,3,3]=>[[],[[],[[[]]]]]=>2
[5,1,3,2,3,6]=>[[[[]],[[[]]]]]=>1
[5,1,3,2,6,3]=>[[[[],[[[]]]]]]=>1
[5,1,3,3,2,6]=>[[[[]]],[[[]]]]=>2
[5,1,3,3,6,2]=>[[[]],[[],[],[]]]=>2
[5,1,3,6,2,3]=>[[[],[[]],[[]]]]=>1
[5,1,3,6,3,2]=>[[[[]],[[[]]]]]=>1
[5,1,6,2,3,3]=>[[],[[[],[[]]]]]=>2
[5,1,6,3,2,3]=>[[[[[[[]]]]]]]=>1
[5,1,6,3,3,2]=>[[[[]]],[[[]]]]=>2
[5,2,1,3,3,6]=>[[[]],[[[[]]]]]=>2
[5,2,1,3,6,3]=>[[[[[]]],[[]]]]=>1
[5,2,1,6,3,3]=>[[[]],[[],[[]]]]=>2
[5,2,3,1,3,6]=>[[[[[[[]]]]]]]=>1
[5,2,3,1,6,3]=>[[[],[[],[[]]]]]=>1
[5,2,3,3,1,6]=>[[[]],[[],[[]]]]=>2
[5,2,3,3,6,1]=>[[[[]]],[[[]]]]=>2
[5,2,3,6,1,3]=>[[[[[[],[]]]]]]=>1
[5,2,3,6,3,1]=>[[[[[]]],[[]]]]=>1
[5,2,6,1,3,3]=>[[],[[],[[],[]]]]=>2
[5,2,6,3,1,3]=>[[[],[],[[[]]]]]=>1
[5,2,6,3,3,1]=>[[[]],[[],[],[]]]=>2
[5,3,1,2,3,6]=>[[[],[[],[[]]]]]=>1
[5,3,1,2,6,3]=>[[[],[[],[[]]]]]=>1
[5,3,1,3,2,6]=>[[[],[[[[]]]]]]=>1
[5,3,1,3,6,2]=>[[[],[[],[[]]]]]=>1
[5,3,1,6,2,3]=>[[[],[],[[[]]]]]=>1
[5,3,1,6,3,2]=>[[[],[],[[[]]]]]=>1
[5,3,2,1,3,6]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,6,3]=>[[[],[[[],[]]]]]=>1
[5,3,2,3,1,6]=>[[[],[[]],[[]]]]=>1
[5,3,2,3,6,1]=>[[[[[[[]]]]]]]=>1
[5,3,2,6,1,3]=>[[[[[]],[[]]]]]=>1
[5,3,2,6,3,1]=>[[[[]],[[],[]]]]=>1
[5,3,3,1,2,6]=>[[],[[],[[[]]]]]=>2
[5,3,3,1,6,2]=>[[],[[],[],[[]]]]=>2
[5,3,3,2,1,6]=>[[],[[],[[],[]]]]=>2
[5,3,3,2,6,1]=>[[],[[[[[]]]]]]=>2
[5,3,3,6,1,2]=>[[[[[]]]],[[]]]=>2
[5,3,3,6,2,1]=>[[],[[],[[[]]]]]=>2
[5,3,6,1,2,3]=>[[[[],[[[]]]]]]=>1
[5,3,6,1,3,2]=>[[[[[],[[]]]]]]=>1
[5,3,6,2,1,3]=>[[[[[[],[]]]]]]=>1
[5,3,6,2,3,1]=>[[[],[[[],[]]]]]=>1
[5,3,6,3,1,2]=>[[[[]],[[[]]]]]=>1
[5,3,6,3,2,1]=>[[[[[]],[[]]]]]=>1
[5,6,1,2,3,3]=>[[],[[],[],[[]]]]=>2
[5,6,1,3,2,3]=>[[[],[[[],[]]]]]=>1
[5,6,1,3,3,2]=>[[[]],[[],[[]]]]=>2
[5,6,2,1,3,3]=>[[[]],[[[[]]]]]=>2
[5,6,2,3,1,3]=>[[[[]],[[[]]]]]=>1
[5,6,2,3,3,1]=>[[[]],[[],[[]]]]=>2
[5,6,3,1,2,3]=>[[[],[[]],[[]]]]=>1
[5,6,3,1,3,2]=>[[[[[[[]]]]]]]=>1
[5,6,3,2,1,3]=>[[[[[],[[]]]]]]=>1
[5,6,3,2,3,1]=>[[[[]],[[[]]]]]=>1
[5,6,3,3,1,2]=>[[[]],[[[],[]]]]=>2
[5,6,3,3,2,1]=>[[],[[],[[[]]]]]=>2
[6,1,2,3,3,5]=>[[[],[]],[[],[]]]=>2
[6,1,2,3,5,3]=>[[[[]],[[],[]]]]=>1
[6,1,2,5,3,3]=>[[],[[[[[]]]]]]=>2
[6,1,3,2,3,5]=>[[[],[[]],[[]]]]=>1
[6,1,3,2,5,3]=>[[[],[[[[]]]]]]=>1
[6,1,3,3,2,5]=>[[[[]]],[[],[]]]=>2
[6,1,3,3,5,2]=>[[],[[],[],[[]]]]=>2
[6,1,3,5,2,3]=>[[[],[],[[[]]]]]=>1
[6,1,3,5,3,2]=>[[[],[],[[[]]]]]=>1
[6,1,5,2,3,3]=>[[],[[[],[[]]]]]=>2
[6,1,5,3,2,3]=>[[[[[[[]]]]]]]=>1
[6,1,5,3,3,2]=>[[[[]]],[[[]]]]=>2
[6,2,1,3,3,5]=>[[],[[],[[[]]]]]=>2
[6,2,1,3,5,3]=>[[[[],[[[]]]]]]=>1
[6,2,1,5,3,3]=>[[[[[]]]],[[]]]=>2
[6,2,3,1,3,5]=>[[[[[[],[]]]]]]=>1
[6,2,3,1,5,3]=>[[[[[],[[]]]]]]=>1
[6,2,3,3,1,5]=>[[[[]]],[[[]]]]=>2
[6,2,3,3,5,1]=>[[[]],[[[],[]]]]=>2
[6,2,3,5,1,3]=>[[[],[[],[[]]]]]=>1
[6,2,3,5,3,1]=>[[[[[[],[]]]]]]=>1
[6,2,5,1,3,3]=>[[],[[[],[],[]]]]=>2
[6,2,5,3,1,3]=>[[[],[[],[[]]]]]=>1
[6,2,5,3,3,1]=>[[],[[],[[],[]]]]=>2
[6,3,1,2,3,5]=>[[[[[]],[[]]]]]=>1
[6,3,1,2,5,3]=>[[[[[[],[]]]]]]=>1
[6,3,1,3,2,5]=>[[[[[[[]]]]]]]=>1
[6,3,1,3,5,2]=>[[[],[[],[[]]]]]=>1
[6,3,1,5,2,3]=>[[[],[[]],[[]]]]=>1
[6,3,1,5,3,2]=>[[[],[[[],[]]]]]=>1
[6,3,2,1,3,5]=>[[[[],[[],[]]]]]=>1
[6,3,2,1,5,3]=>[[[],[[[],[]]]]]=>1
[6,3,2,3,1,5]=>[[[[[]]],[[]]]]=>1
[6,3,2,3,5,1]=>[[[[[[[]]]]]]]=>1
[6,3,2,5,1,3]=>[[[[],[[[]]]]]]=>1
[6,3,2,5,3,1]=>[[[[[]],[[]]]]]=>1
[6,3,3,1,2,5]=>[[[]],[[[[]]]]]=>2
[6,3,3,1,5,2]=>[[],[[[],[],[]]]]=>2
[6,3,3,2,1,5]=>[[],[[],[[],[]]]]=>2
[6,3,3,2,5,1]=>[[],[[[],[[]]]]]=>2
[6,3,3,5,1,2]=>[[[[[]]]],[[]]]=>2
[6,3,3,5,2,1]=>[[],[[[],[[]]]]]=>2
[6,3,5,1,2,3]=>[[[[[[],[]]]]]]=>1
[6,3,5,1,3,2]=>[[[[[],[[]]]]]]=>1
[6,3,5,2,1,3]=>[[[],[[[],[]]]]]=>1
[6,3,5,2,3,1]=>[[[[[]]],[[]]]]=>1
[6,3,5,3,1,2]=>[[[[[]],[[]]]]]=>1
[6,3,5,3,2,1]=>[[[[],[[[]]]]]]=>1
[6,5,1,2,3,3]=>[[[]],[[],[[]]]]=>2
[6,5,1,3,2,3]=>[[[[]],[[[]]]]]=>1
[6,5,1,3,3,2]=>[[[[]]],[[],[]]]=>2
[6,5,2,1,3,3]=>[[[]],[[],[[]]]]=>2
[6,5,2,3,1,3]=>[[[[[[[]]]]]]]=>1
[6,5,2,3,3,1]=>[[[[]]],[[[]]]]=>2
[6,5,3,1,2,3]=>[[[[],[[],[]]]]]=>1
[6,5,3,1,3,2]=>[[[[]],[[],[]]]]=>1
[6,5,3,2,1,3]=>[[[],[],[[[]]]]]=>1
[6,5,3,2,3,1]=>[[[],[[],[[]]]]]=>1
[6,5,3,3,1,2]=>[[],[[],[[[]]]]]=>2
[6,5,3,3,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,3,4,4,4]=>[[],[],[[],[],[]]]=>3
[1,2,4,3,4,4]=>[[[[]]],[[],[]]]=>2
[1,2,4,4,3,4]=>[[[]],[[[],[]]]]=>2
[1,2,4,4,4,3]=>[[],[[[]]],[[]]]=>3
[1,3,2,4,4,4]=>[[],[[]],[[],[]]]=>3
[1,3,4,2,4,4]=>[[],[[],[[[]]]]]=>2
[1,3,4,4,2,4]=>[[[]],[[[],[]]]]=>2
[1,3,4,4,4,2]=>[[],[[[]]],[[]]]=>3
[1,4,2,3,4,4]=>[[],[[],[[[]]]]]=>2
[1,4,2,4,3,4]=>[[[[[[[]]]]]]]=>1
[1,4,2,4,4,3]=>[[[]],[[[[]]]]]=>2
[1,4,3,2,4,4]=>[[[]],[[],[[]]]]=>2
[1,4,3,4,2,4]=>[[[[[[[]]]]]]]=>1
[1,4,3,4,4,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,2,3,4]=>[[[]],[[[],[]]]]=>2
[1,4,4,2,4,3]=>[[[]],[[[[]]]]]=>2
[1,4,4,3,2,4]=>[[[]],[[],[[]]]]=>2
[1,4,4,3,4,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,4,2,3]=>[[],[[]],[[[]]]]=>3
[1,4,4,4,3,2]=>[[],[[]],[[],[]]]=>3
[2,1,3,4,4,4]=>[[],[[[]]],[[]]]=>3
[2,1,4,3,4,4]=>[[[]],[[],[[]]]]=>2
[2,1,4,4,3,4]=>[[[]],[[],[[]]]]=>2
[2,1,4,4,4,3]=>[[],[[]],[[],[]]]=>3
[2,3,1,4,4,4]=>[[],[[]],[[[]]]]=>3
[2,3,4,1,4,4]=>[[],[[[[],[]]]]]=>2
[2,3,4,4,1,4]=>[[[[]]],[[],[]]]=>2
[2,3,4,4,4,1]=>[[],[[]],[[],[]]]=>3
[2,4,1,3,4,4]=>[[],[[[],[[]]]]]=>2
[2,4,1,4,3,4]=>[[[[[[[]]]]]]]=>1
[2,4,1,4,4,3]=>[[[[[]]]],[[]]]=>2
[2,4,3,1,4,4]=>[[[[]]],[[[]]]]=>2
[2,4,3,4,1,4]=>[[[[[[[]]]]]]]=>1
[2,4,3,4,4,1]=>[[[]],[[[[]]]]]=>2
[2,4,4,1,3,4]=>[[],[[[],[[]]]]]=>2
[2,4,4,1,4,3]=>[[[]],[[[[]]]]]=>2
[2,4,4,3,1,4]=>[[[]],[[[[]]]]]=>2
[2,4,4,3,4,1]=>[[[]],[[[[]]]]]=>2
[2,4,4,4,1,3]=>[[],[],[[[],[]]]]=>3
[2,4,4,4,3,1]=>[[],[[]],[[[]]]]=>3
[3,1,2,4,4,4]=>[[],[[[]]],[[]]]=>3
[3,1,4,2,4,4]=>[[],[[[],[[]]]]]=>2
[3,1,4,4,2,4]=>[[[]],[[],[[]]]]=>2
[3,1,4,4,4,2]=>[[],[[]],[[],[]]]=>3
[3,2,1,4,4,4]=>[[],[[]],[[],[]]]=>3
[3,2,4,1,4,4]=>[[[[[]]]],[[]]]=>2
[3,2,4,4,1,4]=>[[[]],[[[[]]]]]=>2
[3,2,4,4,4,1]=>[[],[[]],[[[]]]]=>3
[3,4,1,2,4,4]=>[[],[[[],[[]]]]]=>2
[3,4,1,4,2,4]=>[[[[[[[]]]]]]]=>1
[3,4,1,4,4,2]=>[[[[[]]]],[[]]]=>2
[3,4,2,1,4,4]=>[[[[[]]]],[[]]]=>2
[3,4,2,4,1,4]=>[[[[[[[]]]]]]]=>1
[3,4,2,4,4,1]=>[[[[[]]]],[[]]]=>2
[3,4,4,1,2,4]=>[[],[[[],[[]]]]]=>2
[3,4,4,1,4,2]=>[[[]],[[[[]]]]]=>2
[3,4,4,2,1,4]=>[[[]],[[[[]]]]]=>2
[3,4,4,2,4,1]=>[[[]],[[[[]]]]]=>2
[3,4,4,4,1,2]=>[[],[],[[[],[]]]]=>3
[3,4,4,4,2,1]=>[[],[[]],[[[]]]]=>3
[4,1,2,3,4,4]=>[[],[[],[],[[]]]]=>2
[4,1,2,4,3,4]=>[[[[[[],[]]]]]]=>1
[4,1,2,4,4,3]=>[[[[[]]]],[[]]]=>2
[4,1,3,2,4,4]=>[[[[]]],[[],[]]]=>2
[4,1,3,4,2,4]=>[[[[[[],[]]]]]]=>1
[4,1,3,4,4,2]=>[[[[[]]]],[[]]]=>2
[4,1,4,2,3,4]=>[[[[],[[[]]]]]]=>1
[4,1,4,2,4,3]=>[[[[[[[]]]]]]]=>1
[4,1,4,3,2,4]=>[[[[[]],[[]]]]]=>1
[4,1,4,3,4,2]=>[[[[[[[]]]]]]]=>1
[4,1,4,4,2,3]=>[[[[]]],[[[]]]]=>2
[4,1,4,4,3,2]=>[[[]],[[],[[]]]]=>2
[4,2,1,3,4,4]=>[[[[[]]]],[[]]]=>2
[4,2,1,4,3,4]=>[[[[[],[[]]]]]]=>1
[4,2,1,4,4,3]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,4,4]=>[[],[[[],[[]]]]]=>2
[4,2,3,4,1,4]=>[[[[],[[[]]]]]]=>1
[4,2,3,4,4,1]=>[[[]],[[],[[]]]]=>2
[4,2,4,1,3,4]=>[[[[[],[[]]]]]]=>1
[4,2,4,1,4,3]=>[[[[[[[]]]]]]]=>1
[4,2,4,3,1,4]=>[[[],[[[[]]]]]]=>1
[4,2,4,3,4,1]=>[[[[[[[]]]]]]]=>1
[4,2,4,4,1,3]=>[[[[],[]]],[[]]]=>2
[4,2,4,4,3,1]=>[[[]],[[[],[]]]]=>2
[4,3,1,2,4,4]=>[[[[[]]]],[[]]]=>2
[4,3,1,4,2,4]=>[[[[[],[[]]]]]]=>1
[4,3,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,4,4]=>[[[]],[[],[],[]]]=>2
[4,3,2,4,1,4]=>[[[],[[[[]]]]]]=>1
[4,3,2,4,4,1]=>[[[]],[[[],[]]]]=>2
[4,3,4,1,2,4]=>[[[[[],[[]]]]]]=>1
[4,3,4,1,4,2]=>[[[[[[[]]]]]]]=>1
[4,3,4,2,1,4]=>[[[],[[[[]]]]]]=>1
[4,3,4,2,4,1]=>[[[[[[[]]]]]]]=>1
[4,3,4,4,1,2]=>[[],[[[],[[]]]]]=>2
[4,3,4,4,2,1]=>[[[]],[[[],[]]]]=>2
[4,4,1,2,3,4]=>[[],[[[],[],[]]]]=>2
[4,4,1,2,4,3]=>[[],[[[[[]]]]]]=>2
[4,4,1,3,2,4]=>[[],[[[[],[]]]]]=>2
[4,4,1,3,4,2]=>[[],[[[[[]]]]]]=>2
[4,4,1,4,2,3]=>[[],[[[[[]]]]]]=>2
[4,4,1,4,3,2]=>[[],[[[],[[]]]]]=>2
[4,4,2,1,3,4]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,4,3]=>[[],[[[],[[]]]]]=>2
[4,4,2,3,1,4]=>[[],[[[]],[[]]]]=>2
[4,4,2,3,4,1]=>[[],[[[],[[]]]]]=>2
[4,4,2,4,1,3]=>[[],[[[[],[]]]]]=>2
[4,4,2,4,3,1]=>[[],[[],[[[]]]]]=>2
[4,4,3,1,2,4]=>[[],[[[[[]]]]]]=>2
[4,4,3,1,4,2]=>[[],[[[],[[]]]]]=>2
[4,4,3,2,1,4]=>[[],[[],[],[[]]]]=>2
[4,4,3,2,4,1]=>[[],[[],[[[]]]]]=>2
[4,4,3,4,1,2]=>[[],[[[],[[]]]]]=>2
[4,4,3,4,2,1]=>[[],[[],[[[]]]]]=>2
[4,4,4,1,2,3]=>[[],[],[[[],[]]]]=>3
[4,4,4,1,3,2]=>[[],[],[[[[]]]]]=>3
[4,4,4,2,1,3]=>[[],[],[[[[]]]]]=>3
[4,4,4,2,3,1]=>[[],[],[[],[[]]]]=>3
[4,4,4,3,1,2]=>[[],[],[[[[]]]]]=>3
[4,4,4,3,2,1]=>[[],[],[[],[],[]]]=>3
[1,2,3,4,4,5]=>[[],[[],[],[],[]]]=>2
[1,2,3,4,5,4]=>[[[],[],[],[[]]]]=>1
[1,2,3,5,4,4]=>[[],[[[[],[]]]]]=>2
[1,2,4,3,4,5]=>[[[],[],[[[]]]]]=>1
[1,2,4,3,5,4]=>[[[[],[[],[]]]]]=>1
[1,2,4,4,3,5]=>[[],[[[],[[]]]]]=>2
[1,2,4,4,5,3]=>[[[]],[[],[[]]]]=>2
[1,2,4,5,3,4]=>[[[],[[]],[[]]]]=>1
[1,2,4,5,4,3]=>[[[[]],[[],[]]]]=>1
[1,2,5,3,4,4]=>[[],[[],[[[]]]]]=>2
[1,2,5,4,3,4]=>[[[],[[],[[]]]]]=>1
[1,2,5,4,4,3]=>[[],[[],[[[]]]]]=>2
[1,3,2,4,4,5]=>[[[[]]],[[],[]]]=>2
[1,3,2,4,5,4]=>[[[],[[[],[]]]]]=>1
[1,3,2,5,4,4]=>[[],[[[]],[[]]]]=>2
[1,3,4,2,4,5]=>[[[[]],[[],[]]]]=>1
[1,3,4,2,5,4]=>[[[[[[[]]]]]]]=>1
[1,3,4,4,2,5]=>[[[[]]],[[[]]]]=>2
[1,3,4,4,5,2]=>[[],[[[]],[[]]]]=>2
[1,3,4,5,2,4]=>[[[],[[[],[]]]]]=>1
[1,3,4,5,4,2]=>[[[[],[[[]]]]]]=>1
[1,3,5,2,4,4]=>[[],[[],[],[[]]]]=>2
[1,3,5,4,2,4]=>[[[],[[]],[[]]]]=>1
[1,3,5,4,4,2]=>[[],[[[[],[]]]]]=>2
[1,4,2,3,4,5]=>[[[[],[],[[]]]]]=>1
[1,4,2,3,5,4]=>[[[[[[[]]]]]]]=>1
[1,4,2,4,3,5]=>[[[[[]],[[]]]]]=>1
[1,4,2,4,5,3]=>[[[[],[[[]]]]]]=>1
[1,4,2,5,3,4]=>[[[],[[],[[]]]]]=>1
[1,4,2,5,4,3]=>[[[],[[],[[]]]]]=>1
[1,4,3,2,4,5]=>[[[[],[[[]]]]]]=>1
[1,4,3,2,5,4]=>[[[],[[],[],[]]]]=>1
[1,4,3,4,2,5]=>[[[[[]]],[[]]]]=>1
[1,4,3,4,5,2]=>[[[[],[[[]]]]]]=>1
[1,4,3,5,2,4]=>[[[[[]],[[]]]]]=>1
[1,4,3,5,4,2]=>[[[[[],[[]]]]]]=>1
[1,4,4,2,3,5]=>[[[]],[[[[]]]]]=>2
[1,4,4,2,5,3]=>[[],[[],[[],[]]]]=>2
[1,4,4,3,2,5]=>[[],[[],[[],[]]]]=>2
[1,4,4,3,5,2]=>[[[]],[[[[]]]]]=>2
[1,4,4,5,2,3]=>[[[]],[[],[[]]]]=>2
[1,4,4,5,3,2]=>[[[[[]]]],[[]]]=>2
[1,4,5,2,3,4]=>[[[[[],[],[]]]]]=>1
[1,4,5,2,4,3]=>[[[[[[[]]]]]]]=>1
[1,4,5,3,2,4]=>[[[[[[[]]]]]]]=>1
[1,4,5,3,4,2]=>[[[[],[[],[]]]]]=>1
[1,4,5,4,2,3]=>[[[[[],[[]]]]]]=>1
[1,4,5,4,3,2]=>[[[[],[],[[]]]]]=>1
[1,5,2,3,4,4]=>[[],[[],[[],[]]]]=>2
[1,5,2,4,3,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,4,4,3]=>[[[[],[]]],[[]]]=>2
[1,5,3,2,4,4]=>[[[[]]],[[[]]]]=>2
[1,5,3,4,2,4]=>[[[[[],[[]]]]]]=>1
[1,5,3,4,4,2]=>[[[[]]],[[],[]]]=>2
[1,5,4,2,3,4]=>[[[[[]],[[]]]]]=>1
[1,5,4,2,4,3]=>[[[[[],[[]]]]]]=>1
[1,5,4,3,2,4]=>[[[[],[],[[]]]]]=>1
[1,5,4,3,4,2]=>[[[[[[],[]]]]]]=>1
[1,5,4,4,2,3]=>[[[]],[[[[]]]]]=>2
[1,5,4,4,3,2]=>[[],[[],[],[[]]]]=>2
[2,1,3,4,4,5]=>[[],[[[]],[[]]]]=>2
[2,1,3,4,5,4]=>[[[],[[],[[]]]]]=>1
[2,1,3,5,4,4]=>[[],[[],[[],[]]]]=>2
[2,1,4,3,4,5]=>[[[[]],[[],[]]]]=>1
[2,1,4,3,5,4]=>[[[],[[]],[[]]]]=>1
[2,1,4,4,3,5]=>[[[]],[[],[[]]]]=>2
[2,1,4,4,5,3]=>[[[[[]]]],[[]]]=>2
[2,1,4,5,3,4]=>[[[[[]],[[]]]]]=>1
[2,1,4,5,4,3]=>[[[],[],[[[]]]]]=>1
[2,1,5,3,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,5,4,3,4]=>[[[],[[]],[[]]]]=>1
[2,1,5,4,4,3]=>[[[]],[[],[],[]]]=>2
[2,3,1,4,4,5]=>[[[[]]],[[],[]]]=>2
[2,3,1,4,5,4]=>[[[[]],[[[]]]]]=>1
[2,3,1,5,4,4]=>[[[[]]],[[[]]]]=>2
[2,3,4,1,4,5]=>[[[],[],[[[]]]]]=>1
[2,3,4,1,5,4]=>[[[],[[],[[]]]]]=>1
[2,3,4,4,1,5]=>[[[],[]],[[],[]]]=>2
[2,3,4,4,5,1]=>[[],[[],[],[[]]]]=>2
[2,3,4,5,1,4]=>[[[],[],[[],[]]]]=>1
[2,3,4,5,4,1]=>[[[],[],[[[]]]]]=>1
[2,3,5,1,4,4]=>[[],[[],[[[]]]]]=>2
[2,3,5,4,1,4]=>[[[[[[[]]]]]]]=>1
[2,3,5,4,4,1]=>[[],[[[[[]]]]]]=>2
[2,4,1,3,4,5]=>[[[[]],[[],[]]]]=>1
[2,4,1,3,5,4]=>[[[],[[]],[[]]]]=>1
[2,4,1,4,3,5]=>[[[],[[[[]]]]]]=>1
[2,4,1,4,5,3]=>[[[[[[[]]]]]]]=>1
[2,4,1,5,3,4]=>[[[[],[[[]]]]]]=>1
[2,4,1,5,4,3]=>[[[[],[[],[]]]]]=>1
[2,4,3,1,4,5]=>[[[[[[[]]]]]]]=>1
[2,4,3,1,5,4]=>[[[[[],[[]]]]]]=>1
[2,4,3,4,1,5]=>[[[[[],[[]]]]]]=>1
[2,4,3,4,5,1]=>[[[[[[],[]]]]]]=>1
[2,4,3,5,1,4]=>[[[],[[],[[]]]]]=>1
[2,4,3,5,4,1]=>[[[],[[],[[]]]]]=>1
[2,4,4,1,3,5]=>[[],[[[],[],[]]]]=>2
[2,4,4,1,5,3]=>[[[]],[[],[[]]]]=>2
[2,4,4,3,1,5]=>[[[]],[[[[]]]]]=>2
[2,4,4,3,5,1]=>[[],[[[[],[]]]]]=>2
[2,4,4,5,1,3]=>[[],[[[[],[]]]]]=>2
[2,4,4,5,3,1]=>[[[[],[]]],[[]]]=>2
[2,4,5,1,3,4]=>[[[[]],[[],[]]]]=>1
[2,4,5,1,4,3]=>[[[[[],[[]]]]]]=>1
[2,4,5,3,1,4]=>[[[[[],[[]]]]]]=>1
[2,4,5,3,4,1]=>[[[[[]],[[]]]]]=>1
[2,4,5,4,1,3]=>[[[[]],[[[]]]]]=>1
[2,4,5,4,3,1]=>[[[[[],[[]]]]]]=>1
[2,5,1,3,4,4]=>[[],[[[[],[]]]]]=>2
[2,5,1,4,3,4]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,4,3]=>[[[]],[[],[],[]]]=>2
[2,5,3,1,4,4]=>[[],[[],[[],[]]]]=>2
[2,5,3,4,1,4]=>[[[],[[[[]]]]]]=>1
[2,5,3,4,4,1]=>[[[[[]]]],[[]]]=>2
[2,5,4,1,3,4]=>[[[[[[[]]]]]]]=>1
[2,5,4,1,4,3]=>[[[[]],[[],[]]]]=>1
[2,5,4,3,1,4]=>[[[[]],[[],[]]]]=>1
[2,5,4,3,4,1]=>[[[[],[[[]]]]]]=>1
[2,5,4,4,1,3]=>[[],[[[[[]]]]]]=>2
[2,5,4,4,3,1]=>[[[]],[[],[[]]]]=>2
[3,1,2,4,4,5]=>[[[[]]],[[],[]]]=>2
[3,1,2,4,5,4]=>[[[[[],[[]]]]]]=>1
[3,1,2,5,4,4]=>[[[]],[[[[]]]]]=>2
[3,1,4,2,4,5]=>[[[[[]]],[[]]]]=>1
[3,1,4,2,5,4]=>[[[],[[[],[]]]]]=>1
[3,1,4,4,2,5]=>[[],[[],[[],[]]]]=>2
[3,1,4,4,5,2]=>[[[[]]],[[[]]]]=>2
[3,1,4,5,2,4]=>[[[[[[[]]]]]]]=>1
[3,1,4,5,4,2]=>[[[],[[[[]]]]]]=>1
[3,1,5,2,4,4]=>[[],[[[],[[]]]]]=>2
[3,1,5,4,2,4]=>[[[[[]]],[[]]]]=>1
[3,1,5,4,4,2]=>[[[]],[[],[[]]]]=>2
[3,2,1,4,4,5]=>[[[[],[]]],[[]]]=>2
[3,2,1,4,5,4]=>[[[],[],[[[]]]]]=>1
[3,2,1,5,4,4]=>[[],[[],[],[[]]]]=>2
[3,2,4,1,4,5]=>[[[[[[[]]]]]]]=>1
[3,2,4,1,5,4]=>[[[],[[],[[]]]]]=>1
[3,2,4,4,1,5]=>[[[]],[[],[[]]]]=>2
[3,2,4,4,5,1]=>[[[[[]]]],[[]]]=>2
[3,2,4,5,1,4]=>[[[[],[[[]]]]]]=>1
[3,2,4,5,4,1]=>[[[[[]]],[[]]]]=>1
[3,2,5,1,4,4]=>[[[]],[[],[],[]]]=>2
[3,2,5,4,1,4]=>[[[],[[],[[]]]]]=>1
[3,2,5,4,4,1]=>[[],[[[],[[]]]]]=>2
[3,4,1,2,4,5]=>[[[],[[]],[[]]]]=>1
[3,4,1,2,5,4]=>[[[[[]]],[[]]]]=>1
[3,4,1,4,2,5]=>[[[[[[],[]]]]]]=>1
[3,4,1,4,5,2]=>[[[[]],[[],[]]]]=>1
[3,4,1,5,2,4]=>[[[[],[],[[]]]]]=>1
[3,4,1,5,4,2]=>[[[[],[[[]]]]]]=>1
[3,4,2,1,4,5]=>[[[[[]]],[[]]]]=>1
[3,4,2,1,5,4]=>[[[[[],[[]]]]]]=>1
[3,4,2,4,1,5]=>[[[[[],[[]]]]]]=>1
[3,4,2,4,5,1]=>[[[[[]]],[[]]]]=>1
[3,4,2,5,1,4]=>[[[[[],[],[]]]]]=>1
[3,4,2,5,4,1]=>[[[[[[[]]]]]]]=>1
[3,4,4,1,2,5]=>[[],[[[],[[]]]]]=>2
[3,4,4,1,5,2]=>[[[]],[[],[],[]]]=>2
[3,4,4,2,1,5]=>[[[]],[[[[]]]]]=>2
[3,4,4,2,5,1]=>[[[]],[[[],[]]]]=>2
[3,4,4,5,1,2]=>[[],[[],[],[[]]]]=>2
[3,4,4,5,2,1]=>[[],[[],[[[]]]]]=>2
[3,4,5,1,2,4]=>[[[],[[]],[[]]]]=>1
[3,4,5,1,4,2]=>[[[],[[],[[]]]]]=>1
[3,4,5,2,1,4]=>[[[],[[[[]]]]]]=>1
[3,4,5,2,4,1]=>[[[],[[],[[]]]]]=>1
[3,4,5,4,1,2]=>[[[],[[]],[[]]]]=>1
[3,4,5,4,2,1]=>[[[],[[],[[]]]]]=>1
[3,5,1,2,4,4]=>[[],[[],[[[]]]]]=>2
[3,5,1,4,2,4]=>[[[],[[[],[]]]]]=>1
[3,5,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[3,5,2,1,4,4]=>[[[]],[[[[]]]]]=>2
[3,5,2,4,1,4]=>[[[],[[],[[]]]]]=>1
[3,5,2,4,4,1]=>[[[],[]],[[],[]]]=>2
[3,5,4,1,2,4]=>[[[[[]]],[[]]]]=>1
[3,5,4,1,4,2]=>[[[[[[[]]]]]]]=>1
[3,5,4,2,1,4]=>[[[[[[],[]]]]]]=>1
[3,5,4,2,4,1]=>[[[[[]]],[[]]]]=>1
[3,5,4,4,1,2]=>[[],[[[[[]]]]]]=>2
[3,5,4,4,2,1]=>[[],[[[],[[]]]]]=>2
[4,1,2,3,4,5]=>[[[[],[],[],[]]]]=>1
[4,1,2,3,5,4]=>[[[[],[[[]]]]]]=>1
[4,1,2,4,3,5]=>[[[[[],[[]]]]]]=>1
[4,1,2,4,5,3]=>[[[[[],[[]]]]]]=>1
[4,1,2,5,3,4]=>[[[[[[],[]]]]]]=>1
[4,1,2,5,4,3]=>[[[[],[[[]]]]]]=>1
[4,1,3,2,4,5]=>[[[[[[],[]]]]]]=>1
[4,1,3,2,5,4]=>[[[[[],[[]]]]]]=>1
[4,1,3,4,2,5]=>[[[[[[[]]]]]]]=>1
[4,1,3,4,5,2]=>[[[],[[],[[]]]]]=>1
[4,1,3,5,2,4]=>[[[],[[],[],[]]]]=>1
[4,1,3,5,4,2]=>[[[[[[],[]]]]]]=>1
[4,1,4,2,3,5]=>[[[[[[[]]]]]]]=>1
[4,1,4,2,5,3]=>[[[[],[[],[]]]]]=>1
[4,1,4,3,2,5]=>[[[[],[[],[]]]]]=>1
[4,1,4,3,5,2]=>[[[[]],[[[]]]]]=>1
[4,1,4,5,2,3]=>[[[],[[],[[]]]]]=>1
[4,1,4,5,3,2]=>[[[[[[[]]]]]]]=>1
[4,1,5,2,3,4]=>[[[],[],[[],[]]]]=>1
[4,1,5,2,4,3]=>[[[],[],[[[]]]]]=>1
[4,1,5,3,2,4]=>[[[],[[[[]]]]]]=>1
[4,1,5,3,4,2]=>[[[],[[[],[]]]]]=>1
[4,1,5,4,2,3]=>[[[],[[[[]]]]]]=>1
[4,1,5,4,3,2]=>[[[],[[],[],[]]]]=>1
[4,2,1,3,4,5]=>[[[[[]],[[]]]]]=>1
[4,2,1,3,5,4]=>[[[[],[[],[]]]]]=>1
[4,2,1,4,3,5]=>[[[[[],[[]]]]]]=>1
[4,2,1,4,5,3]=>[[[[[]]],[[]]]]=>1
[4,2,1,5,3,4]=>[[[[[]]],[[]]]]=>1
[4,2,1,5,4,3]=>[[[[],[],[[]]]]]=>1
[4,2,3,1,4,5]=>[[[],[[[],[]]]]]=>1
[4,2,3,1,5,4]=>[[[[]],[[[]]]]]=>1
[4,2,3,4,1,5]=>[[[[],[[],[]]]]]=>1
[4,2,3,4,5,1]=>[[[[],[],[[]]]]]=>1
[4,2,3,5,1,4]=>[[[[],[[[]]]]]]=>1
[4,2,3,5,4,1]=>[[[[[[[]]]]]]]=>1
[4,2,4,1,3,5]=>[[[[],[],[[]]]]]=>1
[4,2,4,1,5,3]=>[[[],[[],[[]]]]]=>1
[4,2,4,3,1,5]=>[[[],[[[[]]]]]]=>1
[4,2,4,3,5,1]=>[[[[],[[[]]]]]]=>1
[4,2,4,5,1,3]=>[[[[[[],[]]]]]]=>1
[4,2,4,5,3,1]=>[[[],[],[[[]]]]]=>1
[4,2,5,1,3,4]=>[[[[],[[[]]]]]]=>1
[4,2,5,1,4,3]=>[[[[[],[],[]]]]]=>1
[4,2,5,3,1,4]=>[[[],[],[[],[]]]]=>1
[4,2,5,3,4,1]=>[[[[[]]],[[]]]]=>1
[4,2,5,4,1,3]=>[[[[[[[]]]]]]]=>1
[4,2,5,4,3,1]=>[[[],[[],[[]]]]]=>1
[4,3,1,2,4,5]=>[[[[],[[[]]]]]]=>1
[4,3,1,2,5,4]=>[[[[[]]],[[]]]]=>1
[4,3,1,4,2,5]=>[[[[],[[],[]]]]]=>1
[4,3,1,4,5,2]=>[[[[[[[]]]]]]]=>1
[4,3,1,5,2,4]=>[[[[[],[[]]]]]]=>1
[4,3,1,5,4,2]=>[[[],[[],[[]]]]]=>1
[4,3,2,1,4,5]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,5,4]=>[[[],[],[],[[]]]]=>1
[4,3,2,4,1,5]=>[[[],[[],[[]]]]]=>1
[4,3,2,4,5,1]=>[[[],[[[[]]]]]]=>1
[4,3,2,5,1,4]=>[[[],[[],[],[]]]]=>1
[4,3,2,5,4,1]=>[[[],[[]],[[]]]]=>1
[4,3,4,1,2,5]=>[[[[[],[[]]]]]]=>1
[4,3,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[4,3,4,2,1,5]=>[[[],[[[[]]]]]]=>1
[4,3,4,2,5,1]=>[[[[],[[[]]]]]]=>1
[4,3,4,5,1,2]=>[[[[],[],[[]]]]]=>1
[4,3,4,5,2,1]=>[[[],[[[],[]]]]]=>1
[4,3,5,1,2,4]=>[[[[],[[[]]]]]]=>1
[4,3,5,1,4,2]=>[[[[[],[[]]]]]]=>1
[4,3,5,2,1,4]=>[[[[]],[[[]]]]]=>1
[4,3,5,2,4,1]=>[[[[],[[],[]]]]]=>1
[4,3,5,4,1,2]=>[[[[[]]],[[]]]]=>1
[4,3,5,4,2,1]=>[[[],[[]],[[]]]]=>1
[4,4,1,2,3,5]=>[[],[[[],[[]]]]]=>2
[4,4,1,2,5,3]=>[[],[[[[[]]]]]]=>2
[4,4,1,3,2,5]=>[[],[[[[[]]]]]]=>2
[4,4,1,3,5,2]=>[[],[[],[[],[]]]]=>2
[4,4,1,5,2,3]=>[[],[[],[],[[]]]]=>2
[4,4,1,5,3,2]=>[[],[[],[[[]]]]]=>2
[4,4,2,1,3,5]=>[[],[[[],[[]]]]]=>2
[4,4,2,1,5,3]=>[[],[[[]],[[]]]]=>2
[4,4,2,3,1,5]=>[[],[[[]],[[]]]]=>2
[4,4,2,3,5,1]=>[[],[[[[[]]]]]]=>2
[4,4,2,5,1,3]=>[[],[[[],[[]]]]]=>2
[4,4,2,5,3,1]=>[[],[[],[],[[]]]]=>2
[4,4,3,1,2,5]=>[[],[[[[[]]]]]]=>2
[4,4,3,1,5,2]=>[[],[[[],[[]]]]]=>2
[4,4,3,2,1,5]=>[[],[[],[],[[]]]]=>2
[4,4,3,2,5,1]=>[[],[[],[[],[]]]]=>2
[4,4,3,5,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,3,5,2,1]=>[[],[[],[[[]]]]]=>2
[4,4,5,1,2,3]=>[[],[[],[],[[]]]]=>2
[4,4,5,1,3,2]=>[[],[[[[[]]]]]]=>2
[4,4,5,2,1,3]=>[[],[[[[[]]]]]]=>2
[4,4,5,2,3,1]=>[[],[[[]],[[]]]]=>2
[4,4,5,3,1,2]=>[[],[[],[[],[]]]]=>2
[4,4,5,3,2,1]=>[[],[[[[],[]]]]]=>2
[4,5,1,2,3,4]=>[[[],[],[],[[]]]]=>1
[4,5,1,2,4,3]=>[[[[[]]],[[]]]]=>1
[4,5,1,3,2,4]=>[[[[[],[[]]]]]]=>1
[4,5,1,3,4,2]=>[[[[[]]],[[]]]]=>1
[4,5,1,4,2,3]=>[[[],[[[],[]]]]]=>1
[4,5,1,4,3,2]=>[[[[],[[],[]]]]]=>1
[4,5,2,1,3,4]=>[[[[]],[[[]]]]]=>1
[4,5,2,1,4,3]=>[[[[[[],[]]]]]]=>1
[4,5,2,3,1,4]=>[[[[]],[[[]]]]]=>1
[4,5,2,3,4,1]=>[[[],[],[[],[]]]]=>1
[4,5,2,4,1,3]=>[[[[],[[],[]]]]]=>1
[4,5,2,4,3,1]=>[[[[[[[]]]]]]]=>1
[4,5,3,1,2,4]=>[[[[]],[[],[]]]]=>1
[4,5,3,1,4,2]=>[[[[],[],[[]]]]]=>1
[4,5,3,2,1,4]=>[[[[[[],[]]]]]]=>1
[4,5,3,2,4,1]=>[[[[[[[]]]]]]]=>1
[4,5,3,4,1,2]=>[[[],[],[[[]]]]]=>1
[4,5,3,4,2,1]=>[[[],[[],[[]]]]]=>1
[4,5,4,1,2,3]=>[[[],[[]],[[]]]]=>1
[4,5,4,1,3,2]=>[[[[],[[[]]]]]]=>1
[4,5,4,2,1,3]=>[[[[],[[[]]]]]]=>1
[4,5,4,2,3,1]=>[[[],[[],[[]]]]]=>1
[4,5,4,3,1,2]=>[[[[]],[[],[]]]]=>1
[4,5,4,3,2,1]=>[[[[],[],[],[]]]]=>1
[5,1,2,3,4,4]=>[[],[[],[],[[]]]]=>2
[5,1,2,4,3,4]=>[[[[],[[[]]]]]]=>1
[5,1,2,4,4,3]=>[[[[[]]]],[[]]]=>2
[5,1,3,2,4,4]=>[[[]],[[],[[]]]]=>2
[5,1,3,4,2,4]=>[[[[],[[[]]]]]]=>1
[5,1,3,4,4,2]=>[[[[[]]]],[[]]]=>2
[5,1,4,2,3,4]=>[[[],[[[],[]]]]]=>1
[5,1,4,2,4,3]=>[[[],[[[[]]]]]]=>1
[5,1,4,3,2,4]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,4,2]=>[[[],[[[[]]]]]]=>1
[5,1,4,4,2,3]=>[[[[]]],[[],[]]]=>2
[5,1,4,4,3,2]=>[[[],[]],[[],[]]]=>2
[5,2,1,3,4,4]=>[[[[]]],[[[]]]]=>2
[5,2,1,4,3,4]=>[[[[[],[[]]]]]]=>1
[5,2,1,4,4,3]=>[[[[]]],[[],[]]]=>2
[5,2,3,1,4,4]=>[[],[[[[[]]]]]]=>2
[5,2,3,4,1,4]=>[[[[]],[[],[]]]]=>1
[5,2,3,4,4,1]=>[[[],[]],[[],[]]]=>2
[5,2,4,1,3,4]=>[[[],[[],[[]]]]]=>1
[5,2,4,1,4,3]=>[[[[]],[[[]]]]]=>1
[5,2,4,3,1,4]=>[[[[[[[]]]]]]]=>1
[5,2,4,3,4,1]=>[[[[]],[[[]]]]]=>1
[5,2,4,4,1,3]=>[[],[[],[[],[]]]]=>2
[5,2,4,4,3,1]=>[[[]],[[[[]]]]]=>2
[5,3,1,2,4,4]=>[[],[[[[],[]]]]]=>2
[5,3,1,4,2,4]=>[[[],[[]],[[]]]]=>1
[5,3,1,4,4,2]=>[[[]],[[],[],[]]]=>2
[5,3,2,1,4,4]=>[[[[]]],[[],[]]]=>2
[5,3,2,4,1,4]=>[[[[[[[]]]]]]]=>1
[5,3,2,4,4,1]=>[[[[]]],[[[]]]]=>2
[5,3,4,1,2,4]=>[[[[[],[[]]]]]]=>1
[5,3,4,1,4,2]=>[[[],[[[[]]]]]]=>1
[5,3,4,2,1,4]=>[[[[]],[[[]]]]]=>1
[5,3,4,2,4,1]=>[[[[]],[[[]]]]]=>1
[5,3,4,4,1,2]=>[[[[],[]]],[[]]]=>2
[5,3,4,4,2,1]=>[[[]],[[],[[]]]]=>2
[5,4,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[5,4,1,2,4,3]=>[[[],[[[[]]]]]]=>1
[5,4,1,3,2,4]=>[[[[]],[[],[]]]]=>1
[5,4,1,3,4,2]=>[[[[[[[]]]]]]]=>1
[5,4,1,4,2,3]=>[[[[[[[]]]]]]]=>1
[5,4,1,4,3,2]=>[[[],[[]],[[]]]]=>1
[5,4,2,1,3,4]=>[[[],[[[[]]]]]]=>1
[5,4,2,1,4,3]=>[[[],[[]],[[]]]]=>1
[5,4,2,3,1,4]=>[[[[[],[[]]]]]]=>1
[5,4,2,3,4,1]=>[[[[[],[[]]]]]]=>1
[5,4,2,4,1,3]=>[[[[],[[[]]]]]]=>1
[5,4,2,4,3,1]=>[[[[]],[[],[]]]]=>1
[5,4,3,1,2,4]=>[[[],[[[[]]]]]]=>1
[5,4,3,1,4,2]=>[[[],[[],[[]]]]]=>1
[5,4,3,2,1,4]=>[[[],[],[],[[]]]]=>1
[5,4,3,2,4,1]=>[[[],[],[[[]]]]]=>1
[5,4,3,4,1,2]=>[[[],[[],[[]]]]]=>1
[5,4,3,4,2,1]=>[[[],[],[[[]]]]]=>1
[5,4,4,1,2,3]=>[[],[[[],[[]]]]]=>2
[5,4,4,1,3,2]=>[[],[[[[],[]]]]]=>2
[5,4,4,2,1,3]=>[[],[[[[],[]]]]]=>2
[5,4,4,2,3,1]=>[[],[[[]],[[]]]]=>2
[5,4,4,3,1,2]=>[[],[[],[[[]]]]]=>2
[5,4,4,3,2,1]=>[[],[[],[],[],[]]]=>2
[1,2,3,4,4,6]=>[[[]],[[],[],[]]]=>2
[1,2,3,4,6,4]=>[[[],[],[[[]]]]]=>1
[1,2,3,6,4,4]=>[[],[[[[],[]]]]]=>2
[1,2,4,3,4,6]=>[[[],[[],[[]]]]]=>1
[1,2,4,3,6,4]=>[[[[[[[]]]]]]]=>1
[1,2,4,4,3,6]=>[[[[]]],[[[]]]]=>2
[1,2,4,4,6,3]=>[[],[[[]],[[]]]]=>2
[1,2,4,6,3,4]=>[[[],[[[],[]]]]]=>1
[1,2,4,6,4,3]=>[[[[],[[[]]]]]]=>1
[1,2,6,3,4,4]=>[[],[[],[[],[]]]]=>2
[1,2,6,4,3,4]=>[[[[]],[[[]]]]]=>1
[1,2,6,4,4,3]=>[[[[]]],[[[]]]]=>2
[1,3,2,4,4,6]=>[[],[[],[],[[]]]]=>2
[1,3,2,4,6,4]=>[[[],[],[[[]]]]]=>1
[1,3,2,6,4,4]=>[[[[]]],[[[]]]]=>2
[1,3,4,2,4,6]=>[[[],[],[[[]]]]]=>1
[1,3,4,2,6,4]=>[[[[[],[[]]]]]]=>1
[1,3,4,4,2,6]=>[[[[]]],[[[]]]]=>2
[1,3,4,4,6,2]=>[[[]],[[],[[]]]]=>2
[1,3,4,6,2,4]=>[[[],[[]],[[]]]]=>1
[1,3,4,6,4,2]=>[[[[]],[[],[]]]]=>1
[1,3,6,2,4,4]=>[[],[[],[[],[]]]]=>2
[1,3,6,4,2,4]=>[[[],[[],[[]]]]]=>1
[1,3,6,4,4,2]=>[[],[[],[[[]]]]]=>2
[1,4,2,3,4,6]=>[[[[[],[[]]]]]]=>1
[1,4,2,3,6,4]=>[[[[]],[[],[]]]]=>1
[1,4,2,4,3,6]=>[[[[]],[[[]]]]]=>1
[1,4,2,4,6,3]=>[[[[[]],[[]]]]]=>1
[1,4,2,6,3,4]=>[[[[[]],[[]]]]]=>1
[1,4,2,6,4,3]=>[[[[],[[[]]]]]]=>1
[1,4,3,2,4,6]=>[[[[],[[],[]]]]]=>1
[1,4,3,2,6,4]=>[[[[[[],[]]]]]]=>1
[1,4,3,4,2,6]=>[[[[[[[]]]]]]]=>1
[1,4,3,4,6,2]=>[[[[[]]],[[]]]]=>1
[1,4,3,6,2,4]=>[[[],[],[[[]]]]]=>1
[1,4,3,6,4,2]=>[[[],[[],[[]]]]]=>1
[1,4,4,2,3,6]=>[[],[[[[],[]]]]]=>2
[1,4,4,2,6,3]=>[[],[[[],[[]]]]]=>2
[1,4,4,3,2,6]=>[[],[[[]],[[]]]]=>2
[1,4,4,3,6,2]=>[[],[[[],[],[]]]]=>2
[1,4,4,6,2,3]=>[[],[[[],[[]]]]]=>2
[1,4,4,6,3,2]=>[[[[[]]]],[[]]]=>2
[1,4,6,2,3,4]=>[[[[]],[[],[]]]]=>1
[1,4,6,2,4,3]=>[[[],[[],[[]]]]]=>1
[1,4,6,3,2,4]=>[[[[[[],[]]]]]]=>1
[1,4,6,3,4,2]=>[[[[[[[]]]]]]]=>1
[1,4,6,4,2,3]=>[[[[[],[[]]]]]]=>1
[1,4,6,4,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,2,3,4,4]=>[[],[[[]],[[]]]]=>2
[1,6,2,4,3,4]=>[[[[[[[]]]]]]]=>1
[1,6,2,4,4,3]=>[[[[]]],[[[]]]]=>2
[1,6,3,2,4,4]=>[[[[]]],[[[]]]]=>2
[1,6,3,4,2,4]=>[[[[[]]],[[]]]]=>1
[1,6,3,4,4,2]=>[[[[]]],[[],[]]]=>2
[1,6,4,2,3,4]=>[[[],[],[[],[]]]]=>1
[1,6,4,2,4,3]=>[[[],[],[[[]]]]]=>1
[1,6,4,3,2,4]=>[[[],[[[],[]]]]]=>1
[1,6,4,3,4,2]=>[[[],[[]],[[]]]]=>1
[1,6,4,4,2,3]=>[[],[[],[],[[]]]]=>2
[1,6,4,4,3,2]=>[[],[[],[[],[]]]]=>2
[2,1,3,4,4,6]=>[[[]],[[],[[]]]]=>2
[2,1,3,4,6,4]=>[[[[[],[[]]]]]]=>1
[2,1,3,6,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,4,3,4,6]=>[[[[[]]],[[]]]]=>1
[2,1,4,3,6,4]=>[[[],[[[],[]]]]]=>1
[2,1,4,4,3,6]=>[[],[[],[[],[]]]]=>2
[2,1,4,4,6,3]=>[[[[[]]]],[[]]]=>2
[2,1,4,6,3,4]=>[[[[[[[]]]]]]]=>1
[2,1,4,6,4,3]=>[[[],[[[[]]]]]]=>1
[2,1,6,3,4,4]=>[[[[[]]]],[[]]]=>2
[2,1,6,4,3,4]=>[[[],[[[],[]]]]]=>1
[2,1,6,4,4,3]=>[[],[[],[[],[]]]]=>2
[2,3,1,4,4,6]=>[[[]],[[[[]]]]]=>2
[2,3,1,4,6,4]=>[[[[],[[[]]]]]]=>1
[2,3,1,6,4,4]=>[[],[[],[],[[]]]]=>2
[2,3,4,1,4,6]=>[[[],[[[[]]]]]]=>1
[2,3,4,1,6,4]=>[[[],[[[],[]]]]]=>1
[2,3,4,4,1,6]=>[[[[]]],[[],[]]]=>2
[2,3,4,4,6,1]=>[[[],[]],[[],[]]]=>2
[2,3,4,6,1,4]=>[[[],[[],[[]]]]]=>1
[2,3,4,6,4,1]=>[[[],[[[[]]]]]]=>1
[2,3,6,1,4,4]=>[[],[[[]],[[]]]]=>2
[2,3,6,4,1,4]=>[[[[],[[[]]]]]]=>1
[2,3,6,4,4,1]=>[[[]],[[[[]]]]]=>2
[2,4,1,3,4,6]=>[[[],[[]],[[]]]]=>1
[2,4,1,3,6,4]=>[[[[[]]],[[]]]]=>1
[2,4,1,4,3,6]=>[[[[],[[[]]]]]]=>1
[2,4,1,4,6,3]=>[[[[]],[[],[]]]]=>1
[2,4,1,6,3,4]=>[[[[[]],[[]]]]]=>1
[2,4,1,6,4,3]=>[[[[],[[[]]]]]]=>1
[2,4,3,1,4,6]=>[[[[[]]],[[]]]]=>1
[2,4,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[2,4,3,4,1,6]=>[[[[[[[]]]]]]]=>1
[2,4,3,4,6,1]=>[[[],[[]],[[]]]]=>1
[2,4,3,6,1,4]=>[[[],[[],[[]]]]]=>1
[2,4,3,6,4,1]=>[[[[[[[]]]]]]]=>1
[2,4,4,1,3,6]=>[[],[[[],[[]]]]]=>2
[2,4,4,1,6,3]=>[[[]],[[],[[]]]]=>2
[2,4,4,3,1,6]=>[[[]],[[[],[]]]]=>2
[2,4,4,3,6,1]=>[[],[[[],[[]]]]]=>2
[2,4,4,6,1,3]=>[[],[[],[],[],[]]]=>2
[2,4,4,6,3,1]=>[[],[[],[[[]]]]]=>2
[2,4,6,1,3,4]=>[[[],[],[],[[]]]]=>1
[2,4,6,1,4,3]=>[[[],[],[[[]]]]]=>1
[2,4,6,3,1,4]=>[[[],[[[[]]]]]]=>1
[2,4,6,3,4,1]=>[[[],[[],[[]]]]]=>1
[2,4,6,4,1,3]=>[[[],[],[[[]]]]]=>1
[2,4,6,4,3,1]=>[[[],[[],[[]]]]]=>1
[2,6,1,3,4,4]=>[[],[[[],[[]]]]]=>2
[2,6,1,4,3,4]=>[[[[[[[]]]]]]]=>1
[2,6,1,4,4,3]=>[[[[[]]]],[[]]]=>2
[2,6,3,1,4,4]=>[[],[[[[],[]]]]]=>2
[2,6,3,4,1,4]=>[[[],[[]],[[]]]]=>1
[2,6,3,4,4,1]=>[[[]],[[],[],[]]]=>2
[2,6,4,1,3,4]=>[[[[[]]],[[]]]]=>1
[2,6,4,1,4,3]=>[[[],[[[[]]]]]]=>1
[2,6,4,3,1,4]=>[[[[],[[[]]]]]]=>1
[2,6,4,3,4,1]=>[[[[[]]],[[]]]]=>1
[2,6,4,4,1,3]=>[[[]],[[],[[]]]]=>2
[2,6,4,4,3,1]=>[[],[[[],[[]]]]]=>2
[3,1,2,4,4,6]=>[[[]],[[],[[]]]]=>2
[3,1,2,4,6,4]=>[[[],[[],[[]]]]]=>1
[3,1,2,6,4,4]=>[[],[[],[[[]]]]]=>2
[3,1,4,2,4,6]=>[[[[]],[[],[]]]]=>1
[3,1,4,2,6,4]=>[[[],[],[[[]]]]]=>1
[3,1,4,4,2,6]=>[[[]],[[],[[]]]]=>2
[3,1,4,4,6,2]=>[[[[],[]]],[[]]]=>2
[3,1,4,6,2,4]=>[[[[],[[],[]]]]]=>1
[3,1,4,6,4,2]=>[[[],[],[[[]]]]]=>1
[3,1,6,2,4,4]=>[[],[[[[],[]]]]]=>2
[3,1,6,4,2,4]=>[[[],[],[],[[]]]]=>1
[3,1,6,4,4,2]=>[[],[[],[],[],[]]]=>2
[3,2,1,4,4,6]=>[[[[],[]]],[[]]]=>2
[3,2,1,4,6,4]=>[[[],[[[[]]]]]]=>1
[3,2,1,6,4,4]=>[[[],[]],[[],[]]]=>2
[3,2,4,1,4,6]=>[[[[],[[[]]]]]]=>1
[3,2,4,1,6,4]=>[[[[],[[[]]]]]]=>1
[3,2,4,4,1,6]=>[[[]],[[[[]]]]]=>2
[3,2,4,4,6,1]=>[[],[[],[],[[]]]]=>2
[3,2,4,6,1,4]=>[[[[[],[],[]]]]]=>1
[3,2,4,6,4,1]=>[[[[[[],[]]]]]]=>1
[3,2,6,1,4,4]=>[[[[[]]]],[[]]]=>2
[3,2,6,4,1,4]=>[[[[[],[[]]]]]]=>1
[3,2,6,4,4,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,2,4,6]=>[[[[]],[[],[]]]]=>1
[3,4,1,2,6,4]=>[[[],[[],[[]]]]]=>1
[3,4,1,4,2,6]=>[[[[],[[[]]]]]]=>1
[3,4,1,4,6,2]=>[[[[[],[[]]]]]]=>1
[3,4,1,6,2,4]=>[[[[[[[]]]]]]]=>1
[3,4,1,6,4,2]=>[[[[[],[],[]]]]]=>1
[3,4,2,1,4,6]=>[[[[[[[]]]]]]]=>1
[3,4,2,1,6,4]=>[[[[],[],[[]]]]]=>1
[3,4,2,4,1,6]=>[[[[],[[[]]]]]]=>1
[3,4,2,4,6,1]=>[[[[[],[],[]]]]]=>1
[3,4,2,6,1,4]=>[[[[[[[]]]]]]]=>1
[3,4,2,6,4,1]=>[[[[],[[],[]]]]]=>1
[3,4,4,1,2,6]=>[[],[[],[[],[]]]]=>2
[3,4,4,1,6,2]=>[[[]],[[[[]]]]]=>2
[3,4,4,2,1,6]=>[[[]],[[],[[]]]]=>2
[3,4,4,2,6,1]=>[[[]],[[[[]]]]]=>2
[3,4,4,6,1,2]=>[[],[[],[[],[]]]]=>2
[3,4,4,6,2,1]=>[[[]],[[[[]]]]]=>2
[3,4,6,1,2,4]=>[[[],[[],[],[]]]]=>1
[3,4,6,1,4,2]=>[[[[],[[[]]]]]]=>1
[3,4,6,2,1,4]=>[[[[[],[[]]]]]]=>1
[3,4,6,2,4,1]=>[[[[[]],[[]]]]]=>1
[3,4,6,4,1,2]=>[[[],[[[[]]]]]]=>1
[3,4,6,4,2,1]=>[[[[[],[[]]]]]]=>1
[3,6,1,2,4,4]=>[[],[[[]],[[]]]]=>2
[3,6,1,4,2,4]=>[[[],[[[],[]]]]]=>1
[3,6,1,4,4,2]=>[[[]],[[],[[]]]]=>2
[3,6,2,1,4,4]=>[[[]],[[],[],[]]]=>2
[3,6,2,4,1,4]=>[[[],[],[[[]]]]]=>1
[3,6,2,4,4,1]=>[[[[],[]]],[[]]]=>2
[3,6,4,1,2,4]=>[[[[[[[]]]]]]]=>1
[3,6,4,1,4,2]=>[[[[]],[[],[]]]]=>1
[3,6,4,2,1,4]=>[[[[]],[[],[]]]]=>1
[3,6,4,2,4,1]=>[[[[],[[[]]]]]]=>1
[3,6,4,4,1,2]=>[[[[]]],[[[]]]]=>2
[3,6,4,4,2,1]=>[[[]],[[],[[]]]]=>2
[4,1,2,3,4,6]=>[[[[],[],[[]]]]]=>1
[4,1,2,3,6,4]=>[[[[],[[[]]]]]]=>1
[4,1,2,4,3,6]=>[[[[[[[]]]]]]]=>1
[4,1,2,4,6,3]=>[[[],[[],[[]]]]]=>1
[4,1,2,6,3,4]=>[[[],[],[[],[]]]]=>1
[4,1,2,6,4,3]=>[[[[]],[[[]]]]]=>1
[4,1,3,2,4,6]=>[[[[],[],[[]]]]]=>1
[4,1,3,2,6,4]=>[[[],[[[[]]]]]]=>1
[4,1,3,4,2,6]=>[[[],[[[[]]]]]]=>1
[4,1,3,4,6,2]=>[[[[[]],[[]]]]]=>1
[4,1,3,6,2,4]=>[[[[],[[],[]]]]]=>1
[4,1,3,6,4,2]=>[[[[],[[[]]]]]]=>1
[4,1,4,2,3,6]=>[[[[[[],[]]]]]]=>1
[4,1,4,2,6,3]=>[[[],[[]],[[]]]]=>1
[4,1,4,3,2,6]=>[[[],[[],[[]]]]]=>1
[4,1,4,3,6,2]=>[[[[],[],[[]]]]]=>1
[4,1,4,6,2,3]=>[[[[[]],[[]]]]]=>1
[4,1,4,6,3,2]=>[[[[[]]],[[]]]]=>1
[4,1,6,2,3,4]=>[[[[[],[[]]]]]]=>1
[4,1,6,2,4,3]=>[[[[[[[]]]]]]]=>1
[4,1,6,3,2,4]=>[[[],[[[[]]]]]]=>1
[4,1,6,3,4,2]=>[[[],[[[],[]]]]]=>1
[4,1,6,4,2,3]=>[[[[],[],[[]]]]]=>1
[4,1,6,4,3,2]=>[[[[],[[],[]]]]]=>1
[4,2,1,3,4,6]=>[[[[[],[[]]]]]]=>1
[4,2,1,3,6,4]=>[[[[[]]],[[]]]]=>1
[4,2,1,4,3,6]=>[[[[],[[],[]]]]]=>1
[4,2,1,4,6,3]=>[[[[[[[]]]]]]]=>1
[4,2,1,6,3,4]=>[[[],[[[[]]]]]]=>1
[4,2,1,6,4,3]=>[[[],[],[[],[]]]]=>1
[4,2,3,1,4,6]=>[[[[]],[[[]]]]]=>1
[4,2,3,1,6,4]=>[[[],[],[],[[]]]]=>1
[4,2,3,4,1,6]=>[[[],[[[],[]]]]]=>1
[4,2,3,4,6,1]=>[[[[],[[],[]]]]]=>1
[4,2,3,6,1,4]=>[[[[[],[[]]]]]]=>1
[4,2,3,6,4,1]=>[[[[[]]],[[]]]]=>1
[4,2,4,1,3,6]=>[[[[[],[[]]]]]]=>1
[4,2,4,1,6,3]=>[[[],[[],[[]]]]]=>1
[4,2,4,3,1,6]=>[[[],[],[[[]]]]]=>1
[4,2,4,3,6,1]=>[[[[[],[[]]]]]]=>1
[4,2,4,6,1,3]=>[[[[],[],[],[]]]]=>1
[4,2,4,6,3,1]=>[[[],[[[],[]]]]]=>1
[4,2,6,1,3,4]=>[[[[[]],[[]]]]]=>1
[4,2,6,1,4,3]=>[[[[[[[]]]]]]]=>1
[4,2,6,3,1,4]=>[[[[]],[[],[]]]]=>1
[4,2,6,3,4,1]=>[[[[[],[],[]]]]]=>1
[4,2,6,4,1,3]=>[[[],[[],[[]]]]]=>1
[4,2,6,4,3,1]=>[[[],[[]],[[]]]]=>1
[4,3,1,2,4,6]=>[[[[[]],[[]]]]]=>1
[4,3,1,2,6,4]=>[[[[],[[[]]]]]]=>1
[4,3,1,4,2,6]=>[[[[[],[[]]]]]]=>1
[4,3,1,4,6,2]=>[[[[],[[[]]]]]]=>1
[4,3,1,6,2,4]=>[[[[[[],[]]]]]]=>1
[4,3,1,6,4,2]=>[[[[],[],[],[]]]]=>1
[4,3,2,1,4,6]=>[[[],[],[[[]]]]]=>1
[4,3,2,1,6,4]=>[[[],[],[[],[]]]]=>1
[4,3,2,4,1,6]=>[[[],[[[[]]]]]]=>1
[4,3,2,4,6,1]=>[[[],[[],[],[]]]]=>1
[4,3,2,6,1,4]=>[[[],[[[[]]]]]]=>1
[4,3,2,6,4,1]=>[[[],[[],[[]]]]]=>1
[4,3,4,1,2,6]=>[[[[],[[],[]]]]]=>1
[4,3,4,1,6,2]=>[[[[[[[]]]]]]]=>1
[4,3,4,2,1,6]=>[[[],[[],[[]]]]]=>1
[4,3,4,2,6,1]=>[[[[[[[]]]]]]]=>1
[4,3,4,6,1,2]=>[[[[],[[],[]]]]]=>1
[4,3,4,6,2,1]=>[[[],[[[[]]]]]]=>1
[4,3,6,1,2,4]=>[[[[[]],[[]]]]]=>1
[4,3,6,1,4,2]=>[[[[[],[[]]]]]]=>1
[4,3,6,2,1,4]=>[[[],[[],[],[]]]]=>1
[4,3,6,2,4,1]=>[[[[[[],[]]]]]]=>1
[4,3,6,4,1,2]=>[[[[[[[]]]]]]]=>1
[4,3,6,4,2,1]=>[[[],[[],[[]]]]]=>1
[4,4,1,2,3,6]=>[[],[[[],[[]]]]]=>2
[4,4,1,2,6,3]=>[[],[[],[],[[]]]]=>2
[4,4,1,3,2,6]=>[[],[[],[[[]]]]]=>2
[4,4,1,3,6,2]=>[[],[[[[],[]]]]]=>2
[4,4,1,6,2,3]=>[[],[[[[[]]]]]]=>2
[4,4,1,6,3,2]=>[[],[[],[[[]]]]]=>2
[4,4,2,1,3,6]=>[[],[[[[[]]]]]]=>2
[4,4,2,1,6,3]=>[[],[[],[[[]]]]]=>2
[4,4,2,3,1,6]=>[[],[[],[],[[]]]]=>2
[4,4,2,3,6,1]=>[[],[[[[[]]]]]]=>2
[4,4,2,6,1,3]=>[[],[[[],[[]]]]]=>2
[4,4,2,6,3,1]=>[[],[[],[[],[]]]]=>2
[4,4,3,1,2,6]=>[[],[[[[[]]]]]]=>2
[4,4,3,1,6,2]=>[[],[[[[],[]]]]]=>2
[4,4,3,2,1,6]=>[[],[[],[],[[]]]]=>2
[4,4,3,2,6,1]=>[[],[[],[[[]]]]]=>2
[4,4,3,6,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,3,6,2,1]=>[[],[[],[[],[]]]]=>2
[4,4,6,1,2,3]=>[[],[[],[[],[]]]]=>2
[4,4,6,1,3,2]=>[[],[[],[],[[]]]]=>2
[4,4,6,2,1,3]=>[[],[[],[[[]]]]]=>2
[4,4,6,2,3,1]=>[[],[[[[[]]]]]]=>2
[4,4,6,3,1,2]=>[[],[[[[[]]]]]]=>2
[4,4,6,3,2,1]=>[[],[[[[],[]]]]]=>2
[4,6,1,2,3,4]=>[[[],[[],[],[]]]]=>1
[4,6,1,2,4,3]=>[[[],[[]],[[]]]]=>1
[4,6,1,3,2,4]=>[[[],[],[],[[]]]]=>1
[4,6,1,3,4,2]=>[[[],[],[[[]]]]]=>1
[4,6,1,4,2,3]=>[[[],[[[[]]]]]]=>1
[4,6,1,4,3,2]=>[[[],[[[],[]]]]]=>1
[4,6,2,1,3,4]=>[[[],[[[[]]]]]]=>1
[4,6,2,1,4,3]=>[[[[],[[],[]]]]]=>1
[4,6,2,3,1,4]=>[[[[],[[[]]]]]]=>1
[4,6,2,3,4,1]=>[[[[[],[[]]]]]]=>1
[4,6,2,4,1,3]=>[[[],[[]],[[]]]]=>1
[4,6,2,4,3,1]=>[[[[]],[[[]]]]]=>1
[4,6,3,1,2,4]=>[[[],[[[[]]]]]]=>1
[4,6,3,1,4,2]=>[[[[],[[[]]]]]]=>1
[4,6,3,2,1,4]=>[[[[[]],[[]]]]]=>1
[4,6,3,2,4,1]=>[[[],[[],[[]]]]]=>1
[4,6,3,4,1,2]=>[[[[],[[],[]]]]]=>1
[4,6,3,4,2,1]=>[[[[[[[]]]]]]]=>1
[4,6,4,1,2,3]=>[[[[[],[[]]]]]]=>1
[4,6,4,1,3,2]=>[[[[]],[[[]]]]]=>1
[4,6,4,2,1,3]=>[[[[]],[[],[]]]]=>1
[4,6,4,2,3,1]=>[[[[],[],[[]]]]]=>1
[4,6,4,3,1,2]=>[[[[],[[[]]]]]]=>1
[4,6,4,3,2,1]=>[[[[],[],[[]]]]]=>1
[6,1,2,3,4,4]=>[[],[[],[],[[]]]]=>2
[6,1,2,4,3,4]=>[[[],[[[],[]]]]]=>1
[6,1,2,4,4,3]=>[[[]],[[],[[]]]]=>2
[6,1,3,2,4,4]=>[[[]],[[],[],[]]]=>2
[6,1,3,4,2,4]=>[[[],[],[[[]]]]]=>1
[6,1,3,4,4,2]=>[[[[],[]]],[[]]]=>2
[6,1,4,2,3,4]=>[[[[[[],[]]]]]]=>1
[6,1,4,2,4,3]=>[[[],[[[[]]]]]]=>1
[6,1,4,3,2,4]=>[[[],[[],[[]]]]]=>1
[6,1,4,3,4,2]=>[[[[[[[]]]]]]]=>1
[6,1,4,4,2,3]=>[[[[]]],[[[]]]]=>2
[6,1,4,4,3,2]=>[[[[]]],[[],[]]]=>2
[6,2,1,3,4,4]=>[[[[]]],[[[]]]]=>2
[6,2,1,4,3,4]=>[[[],[[],[[]]]]]=>1
[6,2,1,4,4,3]=>[[[],[]],[[],[]]]=>2
[6,2,3,1,4,4]=>[[],[[],[[[]]]]]=>2
[6,2,3,4,1,4]=>[[[],[[[],[]]]]]=>1
[6,2,3,4,4,1]=>[[[]],[[],[[]]]]=>2
[6,2,4,1,3,4]=>[[[[[]],[[]]]]]=>1
[6,2,4,1,4,3]=>[[[[[]]],[[]]]]=>1
[6,2,4,3,1,4]=>[[[[]],[[[]]]]]=>1
[6,2,4,3,4,1]=>[[[[[[[]]]]]]]=>1
[6,2,4,4,1,3]=>[[],[[[],[[]]]]]=>2
[6,2,4,4,3,1]=>[[[[]]],[[[]]]]=>2
[6,3,1,2,4,4]=>[[],[[[[[]]]]]]=>2
[6,3,1,4,2,4]=>[[[[[],[[]]]]]]=>1
[6,3,1,4,4,2]=>[[[[]]],[[],[]]]=>2
[6,3,2,1,4,4]=>[[[]],[[],[[]]]]=>2
[6,3,2,4,1,4]=>[[[[]],[[[]]]]]=>1
[6,3,2,4,4,1]=>[[[]],[[],[[]]]]=>2
[6,3,4,1,2,4]=>[[[],[[],[[]]]]]=>1
[6,3,4,1,4,2]=>[[[[]],[[[]]]]]=>1
[6,3,4,2,1,4]=>[[[[[[[]]]]]]]=>1
[6,3,4,2,4,1]=>[[[],[[[[]]]]]]=>1
[6,3,4,4,1,2]=>[[],[[],[[],[]]]]=>2
[6,3,4,4,2,1]=>[[[]],[[[[]]]]]=>2
[6,4,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[6,4,1,2,4,3]=>[[[[[[[]]]]]]]=>1
[6,4,1,3,2,4]=>[[[[],[[[]]]]]]=>1
[6,4,1,3,4,2]=>[[[],[[[[]]]]]]=>1
[6,4,1,4,2,3]=>[[[[]],[[[]]]]]=>1
[6,4,1,4,3,2]=>[[[[[]],[[]]]]]=>1
[6,4,2,1,3,4]=>[[[],[[[[]]]]]]=>1
[6,4,2,1,4,3]=>[[[],[[],[[]]]]]=>1
[6,4,2,3,1,4]=>[[[],[[]],[[]]]]=>1
[6,4,2,3,4,1]=>[[[],[[],[[]]]]]=>1
[6,4,2,4,1,3]=>[[[],[[[],[]]]]]=>1
[6,4,2,4,3,1]=>[[[],[],[[[]]]]]=>1
[6,4,3,1,2,4]=>[[[],[[[[]]]]]]=>1
[6,4,3,1,4,2]=>[[[],[[]],[[]]]]=>1
[6,4,3,2,1,4]=>[[[[[],[],[]]]]]=>1
[6,4,3,2,4,1]=>[[[[[[],[]]]]]]=>1
[6,4,3,4,1,2]=>[[[[[],[[]]]]]]=>1
[6,4,3,4,2,1]=>[[[[]],[[],[]]]]=>1
[6,4,4,1,2,3]=>[[],[[[],[[]]]]]=>2
[6,4,4,1,3,2]=>[[],[[[[[]]]]]]=>2
[6,4,4,2,1,3]=>[[],[[],[[[]]]]]=>2
[6,4,4,2,3,1]=>[[],[[],[],[[]]]]=>2
[6,4,4,3,1,2]=>[[],[[[[],[]]]]]=>2
[6,4,4,3,2,1]=>[[],[[],[],[[]]]]=>2
[1,2,3,4,5,5]=>[[],[[],[],[],[]]]=>2
[1,2,3,5,4,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,5,5,4]=>[[[[],[]]],[[]]]=>2
[1,2,4,3,5,5]=>[[[]],[[],[[]]]]=>2
[1,2,4,5,3,5]=>[[[],[[[],[]]]]]=>1
[1,2,4,5,5,3]=>[[[]],[[],[[]]]]=>2
[1,2,5,3,4,5]=>[[[],[],[[[]]]]]=>1
[1,2,5,3,5,4]=>[[[[[[[]]]]]]]=>1
[1,2,5,4,3,5]=>[[[[[],[[]]]]]]=>1
[1,2,5,4,5,3]=>[[[],[[[[]]]]]]=>1
[1,2,5,5,3,4]=>[[[]],[[[],[]]]]=>2
[1,2,5,5,4,3]=>[[[[]]],[[],[]]]=>2
[1,3,2,4,5,5]=>[[[[],[]]],[[]]]=>2
[1,3,2,5,4,5]=>[[[[[]],[[]]]]]=>1
[1,3,2,5,5,4]=>[[[]],[[],[[]]]]=>2
[1,3,4,2,5,5]=>[[],[[[[[]]]]]]=>2
[1,3,4,5,2,5]=>[[[[],[[[]]]]]]=>1
[1,3,4,5,5,2]=>[[[]],[[],[[]]]]=>2
[1,3,5,2,4,5]=>[[[],[[]],[[]]]]=>1
[1,3,5,2,5,4]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,2,5]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,5,2]=>[[[],[[[[]]]]]]=>1
[1,3,5,5,2,4]=>[[],[[[],[],[]]]]=>2
[1,3,5,5,4,2]=>[[[[]]],[[],[]]]=>2
[1,4,2,3,5,5]=>[[],[[[[[]]]]]]=>2
[1,4,2,5,3,5]=>[[[],[[],[[]]]]]=>1
[1,4,2,5,5,3]=>[[[],[]],[[],[]]]=>2
[1,4,3,2,5,5]=>[[[],[]],[[],[]]]=>2
[1,4,3,5,2,5]=>[[[[[]]],[[]]]]=>1
[1,4,3,5,5,2]=>[[[]],[[[[]]]]]=>2
[1,4,5,2,3,5]=>[[[[[]],[[]]]]]=>1
[1,4,5,2,5,3]=>[[[[[]]],[[]]]]=>1
[1,4,5,3,2,5]=>[[[[[]]],[[]]]]=>1
[1,4,5,3,5,2]=>[[[[[[[]]]]]]]=>1
[1,4,5,5,2,3]=>[[],[[[],[[]]]]]=>2
[1,4,5,5,3,2]=>[[[[]]],[[[]]]]=>2
[1,5,2,3,4,5]=>[[[],[[],[],[]]]]=>1
[1,5,2,3,5,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,4,3,5]=>[[[],[[[],[]]]]]=>1
[1,5,2,4,5,3]=>[[[],[[[[]]]]]]=>1
[1,5,2,5,3,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,5,4,3]=>[[[],[[],[[]]]]]=>1
[1,5,3,2,4,5]=>[[[[[[[]]]]]]]=>1
[1,5,3,2,5,4]=>[[[[[],[[]]]]]]=>1
[1,5,3,4,2,5]=>[[[[[],[[]]]]]]=>1
[1,5,3,4,5,2]=>[[[],[[],[[]]]]]=>1
[1,5,3,5,2,4]=>[[[[]],[[],[]]]]=>1
[1,5,3,5,4,2]=>[[[[],[[[]]]]]]=>1
[1,5,4,2,3,5]=>[[[[[[[]]]]]]]=>1
[1,5,4,2,5,3]=>[[[[[],[[]]]]]]=>1
[1,5,4,3,2,5]=>[[[[],[],[[]]]]]=>1
[1,5,4,3,5,2]=>[[[[]],[[],[]]]]=>1
[1,5,4,5,2,3]=>[[[],[[],[[]]]]]=>1
[1,5,4,5,3,2]=>[[[[],[[[]]]]]]=>1
[1,5,5,2,3,4]=>[[],[[],[[],[]]]]=>2
[1,5,5,2,4,3]=>[[],[[],[[[]]]]]=>2
[1,5,5,3,2,4]=>[[],[[[[[]]]]]]=>2
[1,5,5,3,4,2]=>[[],[[],[[[]]]]]=>2
[1,5,5,4,2,3]=>[[],[[[[[]]]]]]=>2
[1,5,5,4,3,2]=>[[],[[],[],[[]]]]=>2
[2,1,3,4,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,3,5,4,5]=>[[[[]],[[],[]]]]=>1
[2,1,3,5,5,4]=>[[[],[]],[[],[]]]=>2
[2,1,4,3,5,5]=>[[[]],[[],[[]]]]=>2
[2,1,4,5,3,5]=>[[[[[[[]]]]]]]=>1
[2,1,4,5,5,3]=>[[[[]]],[[[]]]]=>2
[2,1,5,3,4,5]=>[[[[[]],[[]]]]]=>1
[2,1,5,3,5,4]=>[[[[[]]],[[]]]]=>1
[2,1,5,4,3,5]=>[[[],[[]],[[]]]]=>1
[2,1,5,4,5,3]=>[[[],[[[[]]]]]]=>1
[2,1,5,5,3,4]=>[[[]],[[[[]]]]]=>2
[2,1,5,5,4,3]=>[[],[[],[],[[]]]]=>2
[2,3,1,4,5,5]=>[[],[[],[[[]]]]]=>2
[2,3,1,5,4,5]=>[[[[]],[[[]]]]]=>1
[2,3,1,5,5,4]=>[[[]],[[[[]]]]]=>2
[2,3,4,1,5,5]=>[[],[[],[[],[]]]]=>2
[2,3,4,5,1,5]=>[[[],[],[[[]]]]]=>1
[2,3,4,5,5,1]=>[[[]],[[],[],[]]]=>2
[2,3,5,1,4,5]=>[[[],[[],[[]]]]]=>1
[2,3,5,1,5,4]=>[[[[[[[]]]]]]]=>1
[2,3,5,4,1,5]=>[[[[[[],[]]]]]]=>1
[2,3,5,4,5,1]=>[[[],[[[[]]]]]]=>1
[2,3,5,5,1,4]=>[[[[]]],[[],[]]]=>2
[2,3,5,5,4,1]=>[[[[]]],[[[]]]]=>2
[2,4,1,3,5,5]=>[[],[[],[],[[]]]]=>2
[2,4,1,5,3,5]=>[[[],[[[],[]]]]]=>1
[2,4,1,5,5,3]=>[[[]],[[],[[]]]]=>2
[2,4,3,1,5,5]=>[[[[]]],[[[]]]]=>2
[2,4,3,5,1,5]=>[[[],[[[[]]]]]]=>1
[2,4,3,5,5,1]=>[[[[]]],[[],[]]]=>2
[2,4,5,1,3,5]=>[[[],[],[[[]]]]]=>1
[2,4,5,1,5,3]=>[[[[[[[]]]]]]]=>1
[2,4,5,3,1,5]=>[[[[[],[[]]]]]]=>1
[2,4,5,3,5,1]=>[[[[]],[[[]]]]]=>1
[2,4,5,5,1,3]=>[[[]],[[[],[]]]]=>2
[2,4,5,5,3,1]=>[[[[]]],[[],[]]]=>2
[2,5,1,3,4,5]=>[[[],[[[],[]]]]]=>1
[2,5,1,3,5,4]=>[[[],[[],[[]]]]]=>1
[2,5,1,4,3,5]=>[[[],[],[[[]]]]]=>1
[2,5,1,4,5,3]=>[[[],[],[[[]]]]]=>1
[2,5,1,5,3,4]=>[[[],[[[[]]]]]]=>1
[2,5,1,5,4,3]=>[[[],[[],[[]]]]]=>1
[2,5,3,1,4,5]=>[[[[]],[[],[]]]]=>1
[2,5,3,1,5,4]=>[[[[[[],[]]]]]]=>1
[2,5,3,4,1,5]=>[[[[[],[[]]]]]]=>1
[2,5,3,4,5,1]=>[[[],[[],[[]]]]]=>1
[2,5,3,5,1,4]=>[[[],[[]],[[]]]]=>1
[2,5,3,5,4,1]=>[[[[[[[]]]]]]]=>1
[2,5,4,1,3,5]=>[[[[[],[[]]]]]]=>1
[2,5,4,1,5,3]=>[[[[],[[[]]]]]]=>1
[2,5,4,3,1,5]=>[[[[[[],[]]]]]]=>1
[2,5,4,3,5,1]=>[[[[]],[[],[]]]]=>1
[2,5,4,5,1,3]=>[[[[]],[[[]]]]]=>1
[2,5,4,5,3,1]=>[[[[[],[[]]]]]]=>1
[2,5,5,1,3,4]=>[[],[[],[[[]]]]]=>2
[2,5,5,1,4,3]=>[[],[[],[],[[]]]]=>2
[2,5,5,3,1,4]=>[[],[[],[[],[]]]]=>2
[2,5,5,3,4,1]=>[[[]],[[[[]]]]]=>2
[2,5,5,4,1,3]=>[[[]],[[[[]]]]]=>2
[2,5,5,4,3,1]=>[[],[[[]],[[]]]]=>2
[3,1,2,4,5,5]=>[[],[[],[[[]]]]]=>2
[3,1,2,5,4,5]=>[[[[],[[[]]]]]]=>1
[3,1,2,5,5,4]=>[[[[]]],[[[]]]]=>2
[3,1,4,2,5,5]=>[[],[[],[[],[]]]]=>2
[3,1,4,5,2,5]=>[[[[[[],[]]]]]]=>1
[3,1,4,5,5,2]=>[[[[[]]]],[[]]]=>2
[3,1,5,2,4,5]=>[[[[],[[[]]]]]]=>1
[3,1,5,2,5,4]=>[[[[[[],[]]]]]]=>1
[3,1,5,4,2,5]=>[[[[[]]],[[]]]]=>1
[3,1,5,4,5,2]=>[[[[[],[[]]]]]]=>1
[3,1,5,5,2,4]=>[[[]],[[],[[]]]]=>2
[3,1,5,5,4,2]=>[[],[[[],[[]]]]]=>2
[3,2,1,4,5,5]=>[[[[]]],[[],[]]]=>2
[3,2,1,5,4,5]=>[[[],[[]],[[]]]]=>1
[3,2,1,5,5,4]=>[[[]],[[],[],[]]]=>2
[3,2,4,1,5,5]=>[[[]],[[],[[]]]]=>2
[3,2,4,5,1,5]=>[[[[[[[]]]]]]]=>1
[3,2,4,5,5,1]=>[[[[]]],[[[]]]]=>2
[3,2,5,1,4,5]=>[[[[[],[],[]]]]]=>1
[3,2,5,1,5,4]=>[[[],[[[],[]]]]]=>1
[3,2,5,4,1,5]=>[[[],[[],[[]]]]]=>1
[3,2,5,4,5,1]=>[[[],[[],[[]]]]]=>1
[3,2,5,5,1,4]=>[[],[[],[],[[]]]]=>2
[3,2,5,5,4,1]=>[[[]],[[],[[]]]]=>2
[3,4,1,2,5,5]=>[[],[[[],[[]]]]]=>2
[3,4,1,5,2,5]=>[[[[],[],[[]]]]]=>1
[3,4,1,5,5,2]=>[[],[[],[],[[]]]]=>2
[3,4,2,1,5,5]=>[[[[[]]]],[[]]]=>2
[3,4,2,5,1,5]=>[[[[[],[[]]]]]]=>1
[3,4,2,5,5,1]=>[[[[]]],[[],[]]]=>2
[3,4,5,1,2,5]=>[[[],[],[[],[]]]]=>1
[3,4,5,1,5,2]=>[[[],[[[],[]]]]]=>1
[3,4,5,2,1,5]=>[[[],[[],[[]]]]]=>1
[3,4,5,2,5,1]=>[[[],[[[],[]]]]]=>1
[3,4,5,5,1,2]=>[[],[[[],[],[]]]]=>2
[3,4,5,5,2,1]=>[[[[]]],[[],[]]]=>2
[3,5,1,2,4,5]=>[[[],[[],[[]]]]]=>1
[3,5,1,2,5,4]=>[[[[[]],[[]]]]]=>1
[3,5,1,4,2,5]=>[[[[],[],[[]]]]]=>1
[3,5,1,4,5,2]=>[[[[],[[[]]]]]]=>1
[3,5,1,5,2,4]=>[[[],[[],[[]]]]]=>1
[3,5,1,5,4,2]=>[[[[[[[]]]]]]]=>1
[3,5,2,1,4,5]=>[[[[[[[]]]]]]]=>1
[3,5,2,1,5,4]=>[[[[],[[],[]]]]]=>1
[3,5,2,4,1,5]=>[[[],[[],[],[]]]]=>1
[3,5,2,4,5,1]=>[[[[[]]],[[]]]]=>1
[3,5,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[3,5,2,5,4,1]=>[[[[[[],[]]]]]]=>1
[3,5,4,1,2,5]=>[[[[[[[]]]]]]]=>1
[3,5,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[3,5,4,2,1,5]=>[[[[[[],[]]]]]]=>1
[3,5,4,2,5,1]=>[[[[[],[[]]]]]]=>1
[3,5,4,5,1,2]=>[[[[[],[[]]]]]]=>1
[3,5,4,5,2,1]=>[[[[],[[[]]]]]]=>1
[3,5,5,1,2,4]=>[[],[[[[],[]]]]]=>2
[3,5,5,1,4,2]=>[[[]],[[],[[]]]]=>2
[3,5,5,2,1,4]=>[[[]],[[[[]]]]]=>2
[3,5,5,2,4,1]=>[[],[[],[[],[]]]]=>2
[3,5,5,4,1,2]=>[[[]],[[[[]]]]]=>2
[3,5,5,4,2,1]=>[[[]],[[],[[]]]]=>2
[4,1,2,3,5,5]=>[[],[[[],[[]]]]]=>2
[4,1,2,5,3,5]=>[[[[[[[]]]]]]]=>1
[4,1,2,5,5,3]=>[[[[[]]]],[[]]]=>2
[4,1,3,2,5,5]=>[[[]],[[[[]]]]]=>2
[4,1,3,5,2,5]=>[[[[]],[[],[]]]]=>1
[4,1,3,5,5,2]=>[[[],[]],[[],[]]]=>2
[4,1,5,2,3,5]=>[[[],[],[[[]]]]]=>1
[4,1,5,2,5,3]=>[[[],[],[[[]]]]]=>1
[4,1,5,3,2,5]=>[[[],[[[[]]]]]]=>1
[4,1,5,3,5,2]=>[[[],[],[[[]]]]]=>1
[4,1,5,5,2,3]=>[[],[[],[],[[]]]]=>2
[4,1,5,5,3,2]=>[[],[[[[],[]]]]]=>2
[4,2,1,3,5,5]=>[[[]],[[],[[]]]]=>2
[4,2,1,5,3,5]=>[[[[[]]],[[]]]]=>1
[4,2,1,5,5,3]=>[[[]],[[],[[]]]]=>2
[4,2,3,1,5,5]=>[[],[[[],[[]]]]]=>2
[4,2,3,5,1,5]=>[[[[[[[]]]]]]]=>1
[4,2,3,5,5,1]=>[[[[[]]]],[[]]]=>2
[4,2,5,1,3,5]=>[[[[],[[],[]]]]]=>1
[4,2,5,1,5,3]=>[[[],[[[],[]]]]]=>1
[4,2,5,3,1,5]=>[[[],[[]],[[]]]]=>1
[4,2,5,3,5,1]=>[[[],[[[],[]]]]]=>1
[4,2,5,5,1,3]=>[[[]],[[],[[]]]]=>2
[4,2,5,5,3,1]=>[[[]],[[],[],[]]]=>2
[4,3,1,2,5,5]=>[[[[[]]]],[[]]]=>2
[4,3,1,5,2,5]=>[[[[[],[[]]]]]]=>1
[4,3,1,5,5,2]=>[[[]],[[],[[]]]]=>2
[4,3,2,1,5,5]=>[[[]],[[],[],[]]]=>2
[4,3,2,5,1,5]=>[[[],[[[],[]]]]]=>1
[4,3,2,5,5,1]=>[[],[[],[[],[]]]]=>2
[4,3,5,1,2,5]=>[[[[[]],[[]]]]]=>1
[4,3,5,1,5,2]=>[[[[],[[[]]]]]]=>1
[4,3,5,2,1,5]=>[[[],[[],[[]]]]]=>1
[4,3,5,2,5,1]=>[[[[],[[[]]]]]]=>1
[4,3,5,5,1,2]=>[[[]],[[[[]]]]]=>2
[4,3,5,5,2,1]=>[[[]],[[[],[]]]]=>2
[4,5,1,2,3,5]=>[[[],[[]],[[]]]]=>1
[4,5,1,2,5,3]=>[[[],[[],[[]]]]]=>1
[4,5,1,3,2,5]=>[[[[],[[[]]]]]]=>1
[4,5,1,3,5,2]=>[[[[[],[[]]]]]]=>1
[4,5,1,5,2,3]=>[[[],[[],[[]]]]]=>1
[4,5,1,5,3,2]=>[[[[[[[]]]]]]]=>1
[4,5,2,1,3,5]=>[[[[[],[[]]]]]]=>1
[4,5,2,1,5,3]=>[[[[],[[[]]]]]]=>1
[4,5,2,3,1,5]=>[[[],[[[],[]]]]]=>1
[4,5,2,3,5,1]=>[[[[[]]],[[]]]]=>1
[4,5,2,5,1,3]=>[[[[[],[[]]]]]]=>1
[4,5,2,5,3,1]=>[[[[[],[[]]]]]]=>1
[4,5,3,1,2,5]=>[[[[]],[[],[]]]]=>1
[4,5,3,1,5,2]=>[[[[],[[],[]]]]]=>1
[4,5,3,2,1,5]=>[[[[[[],[]]]]]]=>1
[4,5,3,2,5,1]=>[[[[[],[[]]]]]]=>1
[4,5,3,5,1,2]=>[[[],[[[[]]]]]]=>1
[4,5,3,5,2,1]=>[[[[[[[]]]]]]]=>1
[4,5,5,1,2,3]=>[[],[[[],[],[]]]]=>2
[4,5,5,1,3,2]=>[[[]],[[[[]]]]]=>2
[4,5,5,2,1,3]=>[[[]],[[[[]]]]]=>2
[4,5,5,2,3,1]=>[[],[[[],[[]]]]]=>2
[4,5,5,3,1,2]=>[[],[[],[[],[]]]]=>2
[4,5,5,3,2,1]=>[[[]],[[[],[]]]]=>2
[5,1,2,3,4,5]=>[[[[],[],[],[]]]]=>1
[5,1,2,3,5,4]=>[[[[],[[[]]]]]]=>1
[5,1,2,4,3,5]=>[[[[[],[[]]]]]]=>1
[5,1,2,4,5,3]=>[[[[[]],[[]]]]]=>1
[5,1,2,5,3,4]=>[[[],[[[],[]]]]]=>1
[5,1,2,5,4,3]=>[[[[]],[[],[]]]]=>1
[5,1,3,2,4,5]=>[[[[],[[[]]]]]]=>1
[5,1,3,2,5,4]=>[[[],[[],[[]]]]]=>1
[5,1,3,4,2,5]=>[[[],[[[[]]]]]]=>1
[5,1,3,4,5,2]=>[[[[[],[[]]]]]]=>1
[5,1,3,5,2,4]=>[[[[],[],[[]]]]]=>1
[5,1,3,5,4,2]=>[[[[],[[[]]]]]]=>1
[5,1,4,2,3,5]=>[[[],[[[[]]]]]]=>1
[5,1,4,2,5,3]=>[[[],[],[[],[]]]]=>1
[5,1,4,3,2,5]=>[[[],[],[[],[]]]]=>1
[5,1,4,3,5,2]=>[[[],[[[[]]]]]]=>1
[5,1,4,5,2,3]=>[[[],[[],[[]]]]]=>1
[5,1,4,5,3,2]=>[[[],[[[[]]]]]]=>1
[5,1,5,2,3,4]=>[[[[],[[],[]]]]]=>1
[5,1,5,2,4,3]=>[[[[],[[[]]]]]]=>1
[5,1,5,3,2,4]=>[[[[[[[]]]]]]]=>1
[5,1,5,3,4,2]=>[[[[],[[[]]]]]]=>1
[5,1,5,4,2,3]=>[[[[[[[]]]]]]]=>1
[5,1,5,4,3,2]=>[[[[],[],[[]]]]]=>1
[5,2,1,3,4,5]=>[[[[[],[[]]]]]]=>1
[5,2,1,3,5,4]=>[[[[],[[],[]]]]]=>1
[5,2,1,4,3,5]=>[[[[[],[[]]]]]]=>1
[5,2,1,4,5,3]=>[[[[[[[]]]]]]]=>1
[5,2,1,5,3,4]=>[[[],[[[[]]]]]]=>1
[5,2,1,5,4,3]=>[[[],[[],[],[]]]]=>1
[5,2,3,1,4,5]=>[[[[[[],[]]]]]]=>1
[5,2,3,1,5,4]=>[[[],[[[[]]]]]]=>1
[5,2,3,4,1,5]=>[[[],[],[[],[]]]]=>1
[5,2,3,4,5,1]=>[[[[],[],[[]]]]]=>1
[5,2,3,5,1,4]=>[[[[[[],[]]]]]]=>1
[5,2,3,5,4,1]=>[[[],[[[[]]]]]]=>1
[5,2,4,1,3,5]=>[[[],[[],[],[]]]]=>1
[5,2,4,1,5,3]=>[[[],[[]],[[]]]]=>1
[5,2,4,3,1,5]=>[[[[]],[[[]]]]]=>1
[5,2,4,3,5,1]=>[[[[[[],[]]]]]]=>1
[5,2,4,5,1,3]=>[[[[],[[[]]]]]]=>1
[5,2,4,5,3,1]=>[[[[],[[[]]]]]]=>1
[5,2,5,1,3,4]=>[[[[],[[[]]]]]]=>1
[5,2,5,1,4,3]=>[[[[],[],[[]]]]]=>1
[5,2,5,3,1,4]=>[[[[],[[],[]]]]]=>1
[5,2,5,3,4,1]=>[[[],[[[[]]]]]]=>1
[5,2,5,4,1,3]=>[[[],[[[[]]]]]]=>1
[5,2,5,4,3,1]=>[[[[[],[[]]]]]]=>1
[5,3,1,2,4,5]=>[[[],[[[],[]]]]]=>1
[5,3,1,2,5,4]=>[[[],[[[[]]]]]]=>1
[5,3,1,4,2,5]=>[[[],[],[[],[]]]]=>1
[5,3,1,4,5,2]=>[[[],[[[[]]]]]]=>1
[5,3,1,5,2,4]=>[[[],[[],[[]]]]]=>1
[5,3,1,5,4,2]=>[[[],[[]],[[]]]]=>1
[5,3,2,1,4,5]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,5,4]=>[[[[],[],[[]]]]]=>1
[5,3,2,4,1,5]=>[[[[[]],[[]]]]]=>1
[5,3,2,4,5,1]=>[[[[[[[]]]]]]]=>1
[5,3,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[5,3,2,5,4,1]=>[[[[[],[[]]]]]]=>1
[5,3,4,1,2,5]=>[[[[[],[[]]]]]]=>1
[5,3,4,1,5,2]=>[[[[],[],[[]]]]]=>1
[5,3,4,2,1,5]=>[[[[]],[[[]]]]]=>1
[5,3,4,2,5,1]=>[[[[]],[[],[]]]]=>1
[5,3,4,5,1,2]=>[[[[[],[],[]]]]]=>1
[5,3,4,5,2,1]=>[[[[[[],[]]]]]]=>1
[5,3,5,1,2,4]=>[[[[[[],[]]]]]]=>1
[5,3,5,1,4,2]=>[[[],[[],[[]]]]]=>1
[5,3,5,2,1,4]=>[[[[[[[]]]]]]]=>1
[5,3,5,2,4,1]=>[[[[],[[],[]]]]]=>1
[5,3,5,4,1,2]=>[[[[[[[]]]]]]]=>1
[5,3,5,4,2,1]=>[[[],[[],[[]]]]]=>1
[5,4,1,2,3,5]=>[[[[[],[[]]]]]]=>1
[5,4,1,2,5,3]=>[[[[[[[]]]]]]]=>1
[5,4,1,3,2,5]=>[[[[[]]],[[]]]]=>1
[5,4,1,3,5,2]=>[[[[],[[],[]]]]]=>1
[5,4,1,5,2,3]=>[[[[[],[],[]]]]]=>1
[5,4,1,5,3,2]=>[[[[]],[[],[]]]]=>1
[5,4,2,1,3,5]=>[[[],[[],[[]]]]]=>1
[5,4,2,1,5,3]=>[[[],[[],[[]]]]]=>1
[5,4,2,3,1,5]=>[[[[[],[[]]]]]]=>1
[5,4,2,3,5,1]=>[[[[[[[]]]]]]]=>1
[5,4,2,5,1,3]=>[[[[[],[[]]]]]]=>1
[5,4,2,5,3,1]=>[[[[],[],[[]]]]]=>1
[5,4,3,1,2,5]=>[[[],[[[[]]]]]]=>1
[5,4,3,1,5,2]=>[[[],[[],[[]]]]]=>1
[5,4,3,2,1,5]=>[[[],[],[],[[]]]]=>1
[5,4,3,2,5,1]=>[[[],[],[[],[]]]]=>1
[5,4,3,5,1,2]=>[[[],[[[[]]]]]]=>1
[5,4,3,5,2,1]=>[[[],[],[[[]]]]]=>1
[5,4,5,1,2,3]=>[[[[],[],[[]]]]]=>1
[5,4,5,1,3,2]=>[[[],[[[[]]]]]]=>1
[5,4,5,2,1,3]=>[[[[]],[[[]]]]]=>1
[5,4,5,2,3,1]=>[[[[[],[[]]]]]]=>1
[5,4,5,3,1,2]=>[[[[],[[],[]]]]]=>1
[5,4,5,3,2,1]=>[[[],[],[[[]]]]]=>1
[5,5,1,2,3,4]=>[[],[[[],[],[]]]]=>2
[5,5,1,2,4,3]=>[[],[[[[[]]]]]]=>2
[5,5,1,3,2,4]=>[[],[[[],[[]]]]]=>2
[5,5,1,3,4,2]=>[[],[[[[[]]]]]]=>2
[5,5,1,4,2,3]=>[[],[[],[[[]]]]]=>2
[5,5,1,4,3,2]=>[[],[[],[[],[]]]]=>2
[5,5,2,1,3,4]=>[[],[[[[[]]]]]]=>2
[5,5,2,1,4,3]=>[[],[[[[],[]]]]]=>2
[5,5,2,3,1,4]=>[[],[[[[[]]]]]]=>2
[5,5,2,3,4,1]=>[[],[[],[[],[]]]]=>2
[5,5,2,4,1,3]=>[[],[[],[[],[]]]]=>2
[5,5,2,4,3,1]=>[[],[[[[[]]]]]]=>2
[5,5,3,1,2,4]=>[[],[[],[[[]]]]]=>2
[5,5,3,1,4,2]=>[[],[[],[],[[]]]]=>2
[5,5,3,2,1,4]=>[[],[[[[],[]]]]]=>2
[5,5,3,2,4,1]=>[[],[[[[[]]]]]]=>2
[5,5,3,4,1,2]=>[[],[[[[],[]]]]]=>2
[5,5,3,4,2,1]=>[[],[[[]],[[]]]]=>2
[5,5,4,1,2,3]=>[[],[[[],[[]]]]]=>2
[5,5,4,1,3,2]=>[[],[[],[[[]]]]]=>2
[5,5,4,2,1,3]=>[[],[[],[[[]]]]]=>2
[5,5,4,2,3,1]=>[[],[[[],[[]]]]]=>2
[5,5,4,3,1,2]=>[[],[[],[[[]]]]]=>2
[5,5,4,3,2,1]=>[[],[[],[],[],[]]]=>2
[1,2,3,4,5,6]=>[[[],[],[],[],[]]]=>1
[1,2,3,4,6,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,5,4,6]=>[[[],[[],[[]]]]]=>1
[1,2,3,5,6,4]=>[[[],[[]],[[]]]]=>1
[1,2,3,6,4,5]=>[[[],[],[[[]]]]]=>1
[1,2,3,6,5,4]=>[[[],[[[],[]]]]]=>1
[1,2,4,3,5,6]=>[[[[]],[[],[]]]]=>1
[1,2,4,3,6,5]=>[[[[[],[[]]]]]]=>1
[1,2,4,5,3,6]=>[[[[]],[[[]]]]]=>1
[1,2,4,5,6,3]=>[[[],[[]],[[]]]]=>1
[1,2,4,6,3,5]=>[[[[],[],[[]]]]]=>1
[1,2,4,6,5,3]=>[[[[],[[[]]]]]]=>1
[1,2,5,3,4,6]=>[[[[]],[[[]]]]]=>1
[1,2,5,3,6,4]=>[[[[],[[],[]]]]]=>1
[1,2,5,4,3,6]=>[[[[],[[],[]]]]]=>1
[1,2,5,4,6,3]=>[[[[[[[]]]]]]]=>1
[1,2,5,6,3,4]=>[[[],[[]],[[]]]]=>1
[1,2,5,6,4,3]=>[[[[]],[[[]]]]]=>1
[1,2,6,3,4,5]=>[[[],[],[[],[]]]]=>1
[1,2,6,3,5,4]=>[[[[],[[[]]]]]]=>1
[1,2,6,4,3,5]=>[[[[[[[]]]]]]]=>1
[1,2,6,4,5,3]=>[[[[]],[[],[]]]]=>1
[1,2,6,5,3,4]=>[[[[[]]],[[]]]]=>1
[1,2,6,5,4,3]=>[[[[[],[],[]]]]]=>1
[1,3,2,4,5,6]=>[[[],[[],[[]]]]]=>1
[1,3,2,4,6,5]=>[[[],[],[[],[]]]]=>1
[1,3,2,5,4,6]=>[[[],[[],[[]]]]]=>1
[1,3,2,5,6,4]=>[[[[[[[]]]]]]]=>1
[1,3,2,6,4,5]=>[[[[[[[]]]]]]]=>1
[1,3,2,6,5,4]=>[[[[[],[],[]]]]]=>1
[1,3,4,2,5,6]=>[[[[],[[[]]]]]]=>1
[1,3,4,2,6,5]=>[[[[[[[]]]]]]]=>1
[1,3,4,5,2,6]=>[[[[],[[],[]]]]]=>1
[1,3,4,5,6,2]=>[[[[],[],[[]]]]]=>1
[1,3,4,6,2,5]=>[[[[]],[[],[]]]]=>1
[1,3,4,6,5,2]=>[[[[]],[[[]]]]]=>1
[1,3,5,2,4,6]=>[[[],[],[],[[]]]]=>1
[1,3,5,2,6,4]=>[[[],[[],[[]]]]]=>1
[1,3,5,4,2,6]=>[[[],[[[[]]]]]]=>1
[1,3,5,4,6,2]=>[[[],[],[[[]]]]]=>1
[1,3,5,6,2,4]=>[[[],[],[[[]]]]]=>1
[1,3,5,6,4,2]=>[[[],[[[],[]]]]]=>1
[1,3,6,2,4,5]=>[[[[]],[[],[]]]]=>1
[1,3,6,2,5,4]=>[[[[],[],[[]]]]]=>1
[1,3,6,4,2,5]=>[[[[],[[],[]]]]]=>1
[1,3,6,4,5,2]=>[[[[[[[]]]]]]]=>1
[1,3,6,5,2,4]=>[[[[]],[[[]]]]]=>1
[1,3,6,5,4,2]=>[[[[[]],[[]]]]]=>1
[1,4,2,3,5,6]=>[[[[[[],[]]]]]]=>1
[1,4,2,3,6,5]=>[[[[]],[[[]]]]]=>1
[1,4,2,5,3,6]=>[[[],[],[[],[]]]]=>1
[1,4,2,5,6,3]=>[[[[[]]],[[]]]]=>1
[1,4,2,6,3,5]=>[[[[[]],[[]]]]]=>1
[1,4,2,6,5,3]=>[[[[[],[[]]]]]]=>1
[1,4,3,2,5,6]=>[[[],[[[],[]]]]]=>1
[1,4,3,2,6,5]=>[[[[[],[],[]]]]]=>1
[1,4,3,5,2,6]=>[[[[[],[[]]]]]]=>1
[1,4,3,5,6,2]=>[[[[[]]],[[]]]]=>1
[1,4,3,6,2,5]=>[[[],[],[],[[]]]]=>1
[1,4,3,6,5,2]=>[[[],[[],[[]]]]]=>1
[1,4,5,2,3,6]=>[[[],[[],[[]]]]]=>1
[1,4,5,2,6,3]=>[[[[],[],[[]]]]]=>1
[1,4,5,3,2,6]=>[[[[[[[]]]]]]]=>1
[1,4,5,3,6,2]=>[[[],[],[[[]]]]]=>1
[1,4,5,6,2,3]=>[[[],[[],[],[]]]]=>1
[1,4,5,6,3,2]=>[[[[],[[[]]]]]]=>1
[1,4,6,2,3,5]=>[[[],[[[],[]]]]]=>1
[1,4,6,2,5,3]=>[[[],[[]],[[]]]]=>1
[1,4,6,3,2,5]=>[[[],[[[[]]]]]]=>1
[1,4,6,3,5,2]=>[[[[],[[],[]]]]]=>1
[1,4,6,5,2,3]=>[[[[[[[]]]]]]]=>1
[1,4,6,5,3,2]=>[[[[[],[[]]]]]]=>1
[1,5,2,3,4,6]=>[[[],[[],[[]]]]]=>1
[1,5,2,3,6,4]=>[[[],[[[[]]]]]]=>1
[1,5,2,4,3,6]=>[[[],[[[[]]]]]]=>1
[1,5,2,4,6,3]=>[[[],[],[[],[]]]]=>1
[1,5,2,6,3,4]=>[[[],[],[],[[]]]]=>1
[1,5,2,6,4,3]=>[[[],[],[[[]]]]]=>1
[1,5,3,2,4,6]=>[[[[[]],[[]]]]]=>1
[1,5,3,2,6,4]=>[[[],[[],[[]]]]]=>1
[1,5,3,4,2,6]=>[[[],[[],[[]]]]]=>1
[1,5,3,4,6,2]=>[[[[[[[]]]]]]]=>1
[1,5,3,6,2,4]=>[[[[[]],[[]]]]]=>1
[1,5,3,6,4,2]=>[[[[],[],[[]]]]]=>1
[1,5,4,2,3,6]=>[[[[[[[]]]]]]]=>1
[1,5,4,2,6,3]=>[[[],[[]],[[]]]]=>1
[1,5,4,3,2,6]=>[[[],[[],[],[]]]]=>1
[1,5,4,3,6,2]=>[[[[],[[],[]]]]]=>1
[1,5,4,6,2,3]=>[[[[[[[]]]]]]]=>1
[1,5,4,6,3,2]=>[[[[]],[[],[]]]]=>1
[1,5,6,2,3,4]=>[[[[[],[],[]]]]]=>1
[1,5,6,2,4,3]=>[[[[[[[]]]]]]]=>1
[1,5,6,3,2,4]=>[[[[]],[[[]]]]]=>1
[1,5,6,3,4,2]=>[[[],[[],[[]]]]]=>1
[1,5,6,4,2,3]=>[[[[],[[],[]]]]]=>1
[1,5,6,4,3,2]=>[[[[],[[[]]]]]]=>1
[1,6,2,3,4,5]=>[[[[],[],[[]]]]]=>1
[1,6,2,3,5,4]=>[[[[[[[]]]]]]]=>1
[1,6,2,4,3,5]=>[[[[[]],[[]]]]]=>1
[1,6,2,4,5,3]=>[[[],[[[[]]]]]]=>1
[1,6,2,5,3,4]=>[[[[]],[[],[]]]]=>1
[1,6,2,5,4,3]=>[[[[],[[],[]]]]]=>1
[1,6,3,2,4,5]=>[[[[[[[]]]]]]]=>1
[1,6,3,2,5,4]=>[[[[],[[[]]]]]]=>1
[1,6,3,4,2,5]=>[[[[[]]],[[]]]]=>1
[1,6,3,4,5,2]=>[[[[],[[],[]]]]]=>1
[1,6,3,5,2,4]=>[[[[],[[],[]]]]]=>1
[1,6,3,5,4,2]=>[[[[]],[[[]]]]]=>1
[1,6,4,2,3,5]=>[[[],[],[[[]]]]]=>1
[1,6,4,2,5,3]=>[[[],[],[],[[]]]]=>1
[1,6,4,3,2,5]=>[[[],[[[],[]]]]]=>1
[1,6,4,3,5,2]=>[[[],[[[[]]]]]]=>1
[1,6,4,5,2,3]=>[[[],[[[],[]]]]]=>1
[1,6,4,5,3,2]=>[[[],[[]],[[]]]]=>1
[1,6,5,2,3,4]=>[[[[[]],[[]]]]]=>1
[1,6,5,2,4,3]=>[[[[],[[[]]]]]]=>1
[1,6,5,3,2,4]=>[[[],[[[],[]]]]]=>1
[1,6,5,3,4,2]=>[[[],[[]],[[]]]]=>1
[1,6,5,4,2,3]=>[[[],[[[],[]]]]]=>1
[1,6,5,4,3,2]=>[[[[],[],[],[]]]]=>1
[2,1,3,4,5,6]=>[[[[],[],[[]]]]]=>1
[2,1,3,4,6,5]=>[[[],[[],[[]]]]]=>1
[2,1,3,5,4,6]=>[[[],[[],[],[]]]]=>1
[2,1,3,5,6,4]=>[[[[[[],[]]]]]]=>1
[2,1,3,6,4,5]=>[[[[[[[]]]]]]]=>1
[2,1,3,6,5,4]=>[[[],[],[[[]]]]]=>1
[2,1,4,3,5,6]=>[[[[[]]],[[]]]]=>1
[2,1,4,3,6,5]=>[[[],[],[[],[]]]]=>1
[2,1,4,5,3,6]=>[[[[],[[[]]]]]]=>1
[2,1,4,5,6,3]=>[[[[[],[[]]]]]]=>1
[2,1,4,6,3,5]=>[[[[[]],[[]]]]]=>1
[2,1,4,6,5,3]=>[[[[[]]],[[]]]]=>1
[2,1,5,3,4,6]=>[[[[[[[]]]]]]]=>1
[2,1,5,3,6,4]=>[[[[],[[[]]]]]]=>1
[2,1,5,4,3,6]=>[[[],[[]],[[]]]]=>1
[2,1,5,4,6,3]=>[[[],[[],[[]]]]]=>1
[2,1,5,6,3,4]=>[[[[],[[],[]]]]]=>1
[2,1,5,6,4,3]=>[[[[]],[[[]]]]]=>1
[2,1,6,3,4,5]=>[[[[[]],[[]]]]]=>1
[2,1,6,3,5,4]=>[[[[[]]],[[]]]]=>1
[2,1,6,4,3,5]=>[[[],[[[],[]]]]]=>1
[2,1,6,4,5,3]=>[[[[],[],[[]]]]]=>1
[2,1,6,5,3,4]=>[[[],[[[],[]]]]]=>1
[2,1,6,5,4,3]=>[[[],[],[],[[]]]]=>1
[2,3,1,4,5,6]=>[[[],[[]],[[]]]]=>1
[2,3,1,4,6,5]=>[[[[[[[]]]]]]]=>1
[2,3,1,5,4,6]=>[[[[[[[]]]]]]]=>1
[2,3,1,5,6,4]=>[[[[]],[[],[]]]]=>1
[2,3,1,6,4,5]=>[[[],[[],[],[]]]]=>1
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[4,6,1,3,5,2]=>[[[],[],[],[[]]]]=>1
[4,6,1,5,2,3]=>[[[],[[],[[]]]]]=>1
[4,6,1,5,3,2]=>[[[],[[[[]]]]]]=>1
[4,6,2,1,3,5]=>[[[],[],[[[]]]]]=>1
[4,6,2,1,5,3]=>[[[[[[[]]]]]]]=>1
[4,6,2,3,1,5]=>[[[[[[[]]]]]]]=>1
[4,6,2,3,5,1]=>[[[[]],[[],[]]]]=>1
[4,6,2,5,1,3]=>[[[],[[],[],[]]]]=>1
[4,6,2,5,3,1]=>[[[[],[[],[]]]]]=>1
[4,6,3,1,2,5]=>[[[[[[[]]]]]]]=>1
[4,6,3,1,5,2]=>[[[[[],[],[]]]]]=>1
[4,6,3,2,1,5]=>[[[[],[[],[]]]]]=>1
[4,6,3,2,5,1]=>[[[[[],[[]]]]]]=>1
[4,6,3,5,1,2]=>[[[[[]]],[[]]]]=>1
[4,6,3,5,2,1]=>[[[],[[],[[]]]]]=>1
[4,6,5,1,2,3]=>[[[[[],[[]]]]]]=>1
[4,6,5,1,3,2]=>[[[[]],[[],[]]]]=>1
[4,6,5,2,1,3]=>[[[],[[],[[]]]]]=>1
[4,6,5,2,3,1]=>[[[[[[[]]]]]]]=>1
[4,6,5,3,1,2]=>[[[[[[],[]]]]]]=>1
[4,6,5,3,2,1]=>[[[[[],[],[]]]]]=>1
[5,1,2,3,4,6]=>[[[[],[],[[]]]]]=>1
[5,1,2,3,6,4]=>[[[[]],[[],[]]]]=>1
[5,1,2,4,3,6]=>[[[],[[[[]]]]]]=>1
[5,1,2,4,6,3]=>[[[[[],[[]]]]]]=>1
[5,1,2,6,3,4]=>[[[[],[[],[]]]]]=>1
[5,1,2,6,4,3]=>[[[[[[[]]]]]]]=>1
[5,1,3,2,4,6]=>[[[[[],[],[]]]]]=>1
[5,1,3,2,6,4]=>[[[[[[[]]]]]]]=>1
[5,1,3,4,2,6]=>[[[[[[[]]]]]]]=>1
[5,1,3,4,6,2]=>[[[],[[],[[]]]]]=>1
[5,1,3,6,2,4]=>[[[],[],[[],[]]]]=>1
[5,1,3,6,4,2]=>[[[[]],[[],[]]]]=>1
[5,1,4,2,3,6]=>[[[],[],[[[]]]]]=>1
[5,1,4,2,6,3]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,2,6]=>[[[],[[],[[]]]]]=>1
[5,1,4,3,6,2]=>[[[],[],[],[[]]]]=>1
[5,1,4,6,2,3]=>[[[],[[]],[[]]]]=>1
[5,1,4,6,3,2]=>[[[],[[[[]]]]]]=>1
[5,1,6,2,3,4]=>[[[],[[],[[]]]]]=>1
[5,1,6,2,4,3]=>[[[],[[[[]]]]]]=>1
[5,1,6,3,2,4]=>[[[[[[[]]]]]]]=>1
[5,1,6,3,4,2]=>[[[[[[],[]]]]]]=>1
[5,1,6,4,2,3]=>[[[[],[],[[]]]]]=>1
[5,1,6,4,3,2]=>[[[[],[[],[]]]]]=>1
[5,2,1,3,4,6]=>[[[[[]],[[]]]]]=>1
[5,2,1,3,6,4]=>[[[[[[[]]]]]]]=>1
[5,2,1,4,3,6]=>[[[[],[[],[]]]]]=>1
[5,2,1,4,6,3]=>[[[[[]]],[[]]]]=>1
[5,2,1,6,3,4]=>[[[[[]]],[[]]]]=>1
[5,2,1,6,4,3]=>[[[[],[[],[]]]]]=>1
[5,2,3,1,4,6]=>[[[[[[[]]]]]]]=>1
[5,2,3,1,6,4]=>[[[[],[],[[]]]]]=>1
[5,2,3,4,1,6]=>[[[[]],[[],[]]]]=>1
[5,2,3,4,6,1]=>[[[[],[[],[]]]]]=>1
[5,2,3,6,1,4]=>[[[[[],[[]]]]]]=>1
[5,2,3,6,4,1]=>[[[],[[[[]]]]]]=>1
[5,2,4,1,3,6]=>[[[],[[],[[]]]]]=>1
[5,2,4,1,6,3]=>[[[],[[]],[[]]]]=>1
[5,2,4,3,1,6]=>[[[[],[[[]]]]]]=>1
[5,2,4,3,6,1]=>[[[[[],[[]]]]]]=>1
[5,2,4,6,1,3]=>[[[[],[],[],[]]]]=>1
[5,2,4,6,3,1]=>[[[[]],[[],[]]]]=>1
[5,2,6,1,3,4]=>[[[],[[],[[]]]]]=>1
[5,2,6,1,4,3]=>[[[],[[[[]]]]]]=>1
[5,2,6,3,1,4]=>[[[],[],[[[]]]]]=>1
[5,2,6,3,4,1]=>[[[],[],[],[[]]]]=>1
[5,2,6,4,1,3]=>[[[],[[]],[[]]]]=>1
[5,2,6,4,3,1]=>[[[],[[],[[]]]]]=>1
[5,3,1,2,4,6]=>[[[],[[],[[]]]]]=>1
[5,3,1,2,6,4]=>[[[],[],[[[]]]]]=>1
[5,3,1,4,2,6]=>[[[],[[]],[[]]]]=>1
[5,3,1,4,6,2]=>[[[],[[[],[]]]]]=>1
[5,3,1,6,2,4]=>[[[],[],[[[]]]]]=>1
[5,3,1,6,4,2]=>[[[],[],[],[],[]]]=>1
[5,3,2,1,4,6]=>[[[[[[],[]]]]]]=>1
[5,3,2,1,6,4]=>[[[],[],[[],[]]]]=>1
[5,3,2,4,1,6]=>[[[[[]]],[[]]]]=>1
[5,3,2,4,6,1]=>[[[[],[],[[]]]]]=>1
[5,3,2,6,1,4]=>[[[[[[[]]]]]]]=>1
[5,3,2,6,4,1]=>[[[],[[],[[]]]]]=>1
[5,3,4,1,2,6]=>[[[[],[[],[]]]]]=>1
[5,3,4,1,6,2]=>[[[[]],[[[]]]]]=>1
[5,3,4,2,1,6]=>[[[],[[]],[[]]]]=>1
[5,3,4,2,6,1]=>[[[[]],[[[]]]]]=>1
[5,3,4,6,1,2]=>[[[[],[[],[]]]]]=>1
[5,3,4,6,2,1]=>[[[[[[[]]]]]]]=>1
[5,3,6,1,2,4]=>[[[[[],[[]]]]]]=>1
[5,3,6,1,4,2]=>[[[],[[],[[]]]]]=>1
[5,3,6,2,1,4]=>[[[[],[],[[]]]]]=>1
[5,3,6,2,4,1]=>[[[[],[[[]]]]]]=>1
[5,3,6,4,1,2]=>[[[[]],[[[]]]]]=>1
[5,3,6,4,2,1]=>[[[],[[]],[[]]]]=>1
[5,4,1,2,3,6]=>[[[[[],[[]]]]]]=>1
[5,4,1,2,6,3]=>[[[[],[],[[]]]]]=>1
[5,4,1,3,2,6]=>[[[[]],[[],[]]]]=>1
[5,4,1,3,6,2]=>[[[[],[[[]]]]]]=>1
[5,4,1,6,2,3]=>[[[[[[[]]]]]]]=>1
[5,4,1,6,3,2]=>[[[[]],[[],[]]]]=>1
[5,4,2,1,3,6]=>[[[],[[[[]]]]]]=>1
[5,4,2,1,6,3]=>[[[],[[[],[]]]]]=>1
[5,4,2,3,1,6]=>[[[[],[],[[]]]]]=>1
[5,4,2,3,6,1]=>[[[[[[[]]]]]]]=>1
[5,4,2,6,1,3]=>[[[[[]],[[]]]]]=>1
[5,4,2,6,3,1]=>[[[[],[[],[]]]]]=>1
[5,4,3,1,2,6]=>[[[],[[[[]]]]]]=>1
[5,4,3,1,6,2]=>[[[],[[[],[]]]]]=>1
[5,4,3,2,1,6]=>[[[],[],[],[[]]]]=>1
[5,4,3,2,6,1]=>[[[],[],[[[]]]]]=>1
[5,4,3,6,1,2]=>[[[],[[[[]]]]]]=>1
[5,4,3,6,2,1]=>[[[],[],[[],[]]]]=>1
[5,4,6,1,2,3]=>[[[[],[[],[]]]]]=>1
[5,4,6,1,3,2]=>[[[],[[],[],[]]]]=>1
[5,4,6,2,1,3]=>[[[[]],[[],[]]]]=>1
[5,4,6,2,3,1]=>[[[[[[[]]]]]]]=>1
[5,4,6,3,1,2]=>[[[[[[[]]]]]]]=>1
[5,4,6,3,2,1]=>[[[],[],[[[]]]]]=>1
[5,6,1,2,3,4]=>[[[],[],[],[[]]]]=>1
[5,6,1,2,4,3]=>[[[],[[],[[]]]]]=>1
[5,6,1,3,2,4]=>[[[[],[],[[]]]]]=>1
[5,6,1,3,4,2]=>[[[[]],[[],[]]]]=>1
[5,6,1,4,2,3]=>[[[],[[[[]]]]]]=>1
[5,6,1,4,3,2]=>[[[[[[],[]]]]]]=>1
[5,6,2,1,3,4]=>[[[[]],[[[]]]]]=>1
[5,6,2,1,4,3]=>[[[[],[[],[]]]]]=>1
[5,6,2,3,1,4]=>[[[],[[[],[]]]]]=>1
[5,6,2,3,4,1]=>[[[],[[]],[[]]]]=>1
[5,6,2,4,1,3]=>[[[[[],[[]]]]]]=>1
[5,6,2,4,3,1]=>[[[[[[[]]]]]]]=>1
[5,6,3,1,2,4]=>[[[[]],[[[]]]]]=>1
[5,6,3,1,4,2]=>[[[[[[],[]]]]]]=>1
[5,6,3,2,1,4]=>[[[[[],[[]]]]]]=>1
[5,6,3,2,4,1]=>[[[[[]],[[]]]]]=>1
[5,6,3,4,1,2]=>[[[],[],[[],[]]]]=>1
[5,6,3,4,2,1]=>[[[],[[[[]]]]]]=>1
[5,6,4,1,2,3]=>[[[],[[]],[[]]]]=>1
[5,6,4,1,3,2]=>[[[[[[[]]]]]]]=>1
[5,6,4,2,1,3]=>[[[[],[[[]]]]]]=>1
[5,6,4,2,3,1]=>[[[],[[],[],[]]]]=>1
[5,6,4,3,1,2]=>[[[[]],[[],[]]]]=>1
[5,6,4,3,2,1]=>[[[[[],[],[]]]]]=>1
[6,1,2,3,4,5]=>[[[[],[],[],[]]]]=>1
[6,1,2,3,5,4]=>[[[[]],[[],[]]]]=>1
[6,1,2,4,3,5]=>[[[],[[]],[[]]]]=>1
[6,1,2,4,5,3]=>[[[],[[],[[]]]]]=>1
[6,1,2,5,3,4]=>[[[[],[[[]]]]]]=>1
[6,1,2,5,4,3]=>[[[[[[],[]]]]]]=>1
[6,1,3,2,4,5]=>[[[],[],[[[]]]]]=>1
[6,1,3,2,5,4]=>[[[],[[],[[]]]]]=>1
[6,1,3,4,2,5]=>[[[],[[[[]]]]]]=>1
[6,1,3,4,5,2]=>[[[],[[],[[]]]]]=>1
[6,1,3,5,2,4]=>[[[],[],[],[[]]]]=>1
[6,1,3,5,4,2]=>[[[],[],[[[]]]]]=>1
[6,1,4,2,3,5]=>[[[],[[[[]]]]]]=>1
[6,1,4,2,5,3]=>[[[[],[[],[]]]]]=>1
[6,1,4,3,2,5]=>[[[[],[[],[]]]]]=>1
[6,1,4,3,5,2]=>[[[],[[[[]]]]]]=>1
[6,1,4,5,2,3]=>[[[[[],[[]]]]]]=>1
[6,1,4,5,3,2]=>[[[[[[[]]]]]]]=>1
[6,1,5,2,3,4]=>[[[[],[[],[]]]]]=>1
[6,1,5,2,4,3]=>[[[[]],[[],[]]]]=>1
[6,1,5,3,2,4]=>[[[[]],[[[]]]]]=>1
[6,1,5,3,4,2]=>[[[[[[],[]]]]]]=>1
[6,1,5,4,2,3]=>[[[[[[[]]]]]]]=>1
[6,1,5,4,3,2]=>[[[[],[],[[]]]]]=>1
[6,2,1,3,4,5]=>[[[[[],[[]]]]]]=>1
[6,2,1,3,5,4]=>[[[[],[[],[]]]]]=>1
[6,2,1,4,3,5]=>[[[],[[],[[]]]]]=>1
[6,2,1,4,5,3]=>[[[],[[[[]]]]]]=>1
[6,2,1,5,3,4]=>[[[[[[[]]]]]]]=>1
[6,2,1,5,4,3]=>[[[[],[],[[]]]]]=>1
[6,2,3,1,4,5]=>[[[[]],[[],[]]]]=>1
[6,2,3,1,5,4]=>[[[[[[[]]]]]]]=>1
[6,2,3,4,1,5]=>[[[[],[[],[]]]]]=>1
[6,2,3,4,5,1]=>[[[],[[],[],[]]]]=>1
[6,2,3,5,1,4]=>[[[],[],[[[]]]]]=>1
[6,2,3,5,4,1]=>[[[[[[[]]]]]]]=>1
[6,2,4,1,3,5]=>[[[[[],[],[]]]]]=>1
[6,2,4,1,5,3]=>[[[[[]],[[]]]]]=>1
[6,2,4,3,1,5]=>[[[[[[[]]]]]]]=>1
[6,2,4,3,5,1]=>[[[[]],[[],[]]]]=>1
[6,2,4,5,1,3]=>[[[[]],[[],[]]]]=>1
[6,2,4,5,3,1]=>[[[[[[],[]]]]]]=>1
[6,2,5,1,3,4]=>[[[],[],[[[]]]]]=>1
[6,2,5,1,4,3]=>[[[],[],[],[[]]]]=>1
[6,2,5,3,1,4]=>[[[],[],[[],[]]]]=>1
[6,2,5,3,4,1]=>[[[],[[[[]]]]]]=>1
[6,2,5,4,1,3]=>[[[],[[[[]]]]]]=>1
[6,2,5,4,3,1]=>[[[],[[],[[]]]]]=>1
[6,3,1,2,4,5]=>[[[[],[[[]]]]]]=>1
[6,3,1,2,5,4]=>[[[[[[[]]]]]]]=>1
[6,3,1,4,2,5]=>[[[[],[[],[]]]]]=>1
[6,3,1,4,5,2]=>[[[],[[[[]]]]]]=>1
[6,3,1,5,2,4]=>[[[],[[]],[[]]]]=>1
[6,3,1,5,4,2]=>[[[],[[],[[]]]]]=>1
[6,3,2,1,4,5]=>[[[[],[[[]]]]]]=>1
[6,3,2,1,5,4]=>[[[],[[],[],[]]]]=>1
[6,3,2,4,1,5]=>[[[],[[]],[[]]]]=>1
[6,3,2,4,5,1]=>[[[[[[[]]]]]]]=>1
[6,3,2,5,1,4]=>[[[[],[],[[]]]]]=>1
[6,3,2,5,4,1]=>[[[],[[],[[]]]]]=>1
[6,3,4,1,2,5]=>[[[],[[],[[]]]]]=>1
[6,3,4,1,5,2]=>[[[],[],[],[[]]]]=>1
[6,3,4,2,1,5]=>[[[[[]]],[[]]]]=>1
[6,3,4,2,5,1]=>[[[[],[[[]]]]]]=>1
[6,3,4,5,1,2]=>[[[[],[],[[]]]]]=>1
[6,3,4,5,2,1]=>[[[[]],[[],[]]]]=>1
[6,3,5,1,2,4]=>[[[[],[[[]]]]]]=>1
[6,3,5,1,4,2]=>[[[[[]],[[]]]]]=>1
[6,3,5,2,1,4]=>[[[[]],[[[]]]]]=>1
[6,3,5,2,4,1]=>[[[],[],[[],[]]]]=>1
[6,3,5,4,1,2]=>[[[],[[[[]]]]]]=>1
[6,3,5,4,2,1]=>[[[[[]],[[]]]]]=>1
[6,4,1,2,3,5]=>[[[[[]],[[]]]]]=>1
[6,4,1,2,5,3]=>[[[],[[[[]]]]]]=>1
[6,4,1,3,2,5]=>[[[[[[[]]]]]]]=>1
[6,4,1,3,5,2]=>[[[[],[[],[]]]]]=>1
[6,4,1,5,2,3]=>[[[[],[],[[]]]]]=>1
[6,4,1,5,3,2]=>[[[],[[[],[]]]]]=>1
[6,4,2,1,3,5]=>[[[],[[],[[]]]]]=>1
[6,4,2,1,5,3]=>[[[],[[]],[[]]]]=>1
[6,4,2,3,1,5]=>[[[],[[]],[[]]]]=>1
[6,4,2,3,5,1]=>[[[],[[[[]]]]]]=>1
[6,4,2,5,1,3]=>[[[],[[],[[]]]]]=>1
[6,4,2,5,3,1]=>[[[],[],[],[[]]]]=>1
[6,4,3,1,2,5]=>[[[],[[[[]]]]]]=>1
[6,4,3,1,5,2]=>[[[],[[],[[]]]]]=>1
[6,4,3,2,1,5]=>[[[[[],[],[]]]]]=>1
[6,4,3,2,5,1]=>[[[[],[[],[]]]]]=>1
[6,4,3,5,1,2]=>[[[[[[[]]]]]]]=>1
[6,4,3,5,2,1]=>[[[[],[[[]]]]]]=>1
[6,4,5,1,2,3]=>[[[[],[],[[]]]]]=>1
[6,4,5,1,3,2]=>[[[[[[[]]]]]]]=>1
[6,4,5,2,1,3]=>[[[[[[[]]]]]]]=>1
[6,4,5,2,3,1]=>[[[],[[],[[]]]]]=>1
[6,4,5,3,1,2]=>[[[],[],[[],[]]]]=>1
[6,4,5,3,2,1]=>[[[[]],[[],[]]]]=>1
[6,5,1,2,3,4]=>[[[[],[],[[]]]]]=>1
[6,5,1,2,4,3]=>[[[],[[[[]]]]]]=>1
[6,5,1,3,2,4]=>[[[],[[],[[]]]]]=>1
[6,5,1,3,4,2]=>[[[[[[[]]]]]]]=>1
[6,5,1,4,2,3]=>[[[[[[],[]]]]]]=>1
[6,5,1,4,3,2]=>[[[],[],[[],[]]]]=>1
[6,5,2,1,3,4]=>[[[[[]]],[[]]]]=>1
[6,5,2,1,4,3]=>[[[],[],[[[]]]]]=>1
[6,5,2,3,1,4]=>[[[[[[[]]]]]]]=>1
[6,5,2,3,4,1]=>[[[[],[[],[]]]]]=>1
[6,5,2,4,1,3]=>[[[[],[[],[]]]]]=>1
[6,5,2,4,3,1]=>[[[[]],[[[]]]]]=>1
[6,5,3,1,2,4]=>[[[[[[],[]]]]]]=>1
[6,5,3,1,4,2]=>[[[[],[],[[]]]]]=>1
[6,5,3,2,1,4]=>[[[],[],[[[]]]]]=>1
[6,5,3,2,4,1]=>[[[],[[[[]]]]]]=>1
[6,5,3,4,1,2]=>[[[[],[[[]]]]]]=>1
[6,5,3,4,2,1]=>[[[],[[],[[]]]]]=>1
[6,5,4,1,2,3]=>[[[],[[],[[]]]]]=>1
[6,5,4,1,3,2]=>[[[],[],[[[]]]]]=>1
[6,5,4,2,1,3]=>[[[],[],[[[]]]]]=>1
[6,5,4,2,3,1]=>[[[],[[],[[]]]]]=>1
[6,5,4,3,1,2]=>[[[],[],[[[]]]]]=>1
[6,5,4,3,2,1]=>[[[],[],[],[],[]]]=>1
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The number of subtrees.
Map
ordered tree
Description
The ordered tree associated with the parking function by Pollak.
Let $(p_1,\dots,p_n)$ be a parking function. Set $c_i = p_{i+1}-p_i \mod (n+1)$ to obtain a Prüfer code, and return the underlying ordered tree rooted at $0$.
Let $(p_1,\dots,p_n)$ be a parking function. Set $c_i = p_{i+1}-p_i \mod (n+1)$ to obtain a Prüfer code, and return the underlying ordered tree rooted at $0$.
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