Identifier
Mp00161:
Signed permutations
—reverse⟶
Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00267: Signed permutations —signs⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Images
=>
[1]=>[1]=>0=>[1]
[-1]=>[-1]=>1=>[1]
[1,2]=>[2,1]=>00=>[2]
[1,-2]=>[-2,1]=>10=>[1,1]
[-1,2]=>[2,-1]=>01=>[1,1]
[-1,-2]=>[-2,-1]=>11=>[2]
[2,1]=>[1,2]=>00=>[2]
[2,-1]=>[-1,2]=>10=>[1,1]
[-2,1]=>[1,-2]=>01=>[1,1]
[-2,-1]=>[-1,-2]=>11=>[2]
[1,2,3]=>[3,2,1]=>000=>[3]
[1,2,-3]=>[-3,2,1]=>100=>[1,2]
[1,-2,3]=>[3,-2,1]=>010=>[1,1,1]
[1,-2,-3]=>[-3,-2,1]=>110=>[2,1]
[-1,2,3]=>[3,2,-1]=>001=>[2,1]
[-1,2,-3]=>[-3,2,-1]=>101=>[1,1,1]
[-1,-2,3]=>[3,-2,-1]=>011=>[1,2]
[-1,-2,-3]=>[-3,-2,-1]=>111=>[3]
[1,3,2]=>[2,3,1]=>000=>[3]
[1,3,-2]=>[-2,3,1]=>100=>[1,2]
[1,-3,2]=>[2,-3,1]=>010=>[1,1,1]
[1,-3,-2]=>[-2,-3,1]=>110=>[2,1]
[-1,3,2]=>[2,3,-1]=>001=>[2,1]
[-1,3,-2]=>[-2,3,-1]=>101=>[1,1,1]
[-1,-3,2]=>[2,-3,-1]=>011=>[1,2]
[-1,-3,-2]=>[-2,-3,-1]=>111=>[3]
[2,1,3]=>[3,1,2]=>000=>[3]
[2,1,-3]=>[-3,1,2]=>100=>[1,2]
[2,-1,3]=>[3,-1,2]=>010=>[1,1,1]
[2,-1,-3]=>[-3,-1,2]=>110=>[2,1]
[-2,1,3]=>[3,1,-2]=>001=>[2,1]
[-2,1,-3]=>[-3,1,-2]=>101=>[1,1,1]
[-2,-1,3]=>[3,-1,-2]=>011=>[1,2]
[-2,-1,-3]=>[-3,-1,-2]=>111=>[3]
[2,3,1]=>[1,3,2]=>000=>[3]
[2,3,-1]=>[-1,3,2]=>100=>[1,2]
[2,-3,1]=>[1,-3,2]=>010=>[1,1,1]
[2,-3,-1]=>[-1,-3,2]=>110=>[2,1]
[-2,3,1]=>[1,3,-2]=>001=>[2,1]
[-2,3,-1]=>[-1,3,-2]=>101=>[1,1,1]
[-2,-3,1]=>[1,-3,-2]=>011=>[1,2]
[-2,-3,-1]=>[-1,-3,-2]=>111=>[3]
[3,1,2]=>[2,1,3]=>000=>[3]
[3,1,-2]=>[-2,1,3]=>100=>[1,2]
[3,-1,2]=>[2,-1,3]=>010=>[1,1,1]
[3,-1,-2]=>[-2,-1,3]=>110=>[2,1]
[-3,1,2]=>[2,1,-3]=>001=>[2,1]
[-3,1,-2]=>[-2,1,-3]=>101=>[1,1,1]
[-3,-1,2]=>[2,-1,-3]=>011=>[1,2]
[-3,-1,-2]=>[-2,-1,-3]=>111=>[3]
[3,2,1]=>[1,2,3]=>000=>[3]
[3,2,-1]=>[-1,2,3]=>100=>[1,2]
[3,-2,1]=>[1,-2,3]=>010=>[1,1,1]
[3,-2,-1]=>[-1,-2,3]=>110=>[2,1]
[-3,2,1]=>[1,2,-3]=>001=>[2,1]
[-3,2,-1]=>[-1,2,-3]=>101=>[1,1,1]
[-3,-2,1]=>[1,-2,-3]=>011=>[1,2]
[-3,-2,-1]=>[-1,-2,-3]=>111=>[3]
[1,2,3,4]=>[4,3,2,1]=>0000=>[4]
[1,2,3,-4]=>[-4,3,2,1]=>1000=>[1,3]
[1,2,-3,4]=>[4,-3,2,1]=>0100=>[1,1,2]
[1,2,-3,-4]=>[-4,-3,2,1]=>1100=>[2,2]
[1,-2,3,4]=>[4,3,-2,1]=>0010=>[2,1,1]
[1,-2,3,-4]=>[-4,3,-2,1]=>1010=>[1,1,1,1]
[1,-2,-3,4]=>[4,-3,-2,1]=>0110=>[1,2,1]
[1,-2,-3,-4]=>[-4,-3,-2,1]=>1110=>[3,1]
[-1,2,3,4]=>[4,3,2,-1]=>0001=>[3,1]
[-1,2,3,-4]=>[-4,3,2,-1]=>1001=>[1,2,1]
[-1,2,-3,4]=>[4,-3,2,-1]=>0101=>[1,1,1,1]
[-1,2,-3,-4]=>[-4,-3,2,-1]=>1101=>[2,1,1]
[-1,-2,3,4]=>[4,3,-2,-1]=>0011=>[2,2]
[-1,-2,3,-4]=>[-4,3,-2,-1]=>1011=>[1,1,2]
[-1,-2,-3,4]=>[4,-3,-2,-1]=>0111=>[1,3]
[-1,-2,-3,-4]=>[-4,-3,-2,-1]=>1111=>[4]
[1,2,4,3]=>[3,4,2,1]=>0000=>[4]
[1,2,4,-3]=>[-3,4,2,1]=>1000=>[1,3]
[1,2,-4,3]=>[3,-4,2,1]=>0100=>[1,1,2]
[1,2,-4,-3]=>[-3,-4,2,1]=>1100=>[2,2]
[1,-2,4,3]=>[3,4,-2,1]=>0010=>[2,1,1]
[1,-2,4,-3]=>[-3,4,-2,1]=>1010=>[1,1,1,1]
[1,-2,-4,3]=>[3,-4,-2,1]=>0110=>[1,2,1]
[1,-2,-4,-3]=>[-3,-4,-2,1]=>1110=>[3,1]
[-1,2,4,3]=>[3,4,2,-1]=>0001=>[3,1]
[-1,2,4,-3]=>[-3,4,2,-1]=>1001=>[1,2,1]
[-1,2,-4,3]=>[3,-4,2,-1]=>0101=>[1,1,1,1]
[-1,2,-4,-3]=>[-3,-4,2,-1]=>1101=>[2,1,1]
[-1,-2,4,3]=>[3,4,-2,-1]=>0011=>[2,2]
[-1,-2,4,-3]=>[-3,4,-2,-1]=>1011=>[1,1,2]
[-1,-2,-4,3]=>[3,-4,-2,-1]=>0111=>[1,3]
[-1,-2,-4,-3]=>[-3,-4,-2,-1]=>1111=>[4]
[1,3,2,4]=>[4,2,3,1]=>0000=>[4]
[1,3,2,-4]=>[-4,2,3,1]=>1000=>[1,3]
[1,3,-2,4]=>[4,-2,3,1]=>0100=>[1,1,2]
[1,3,-2,-4]=>[-4,-2,3,1]=>1100=>[2,2]
[1,-3,2,4]=>[4,2,-3,1]=>0010=>[2,1,1]
[1,-3,2,-4]=>[-4,2,-3,1]=>1010=>[1,1,1,1]
[1,-3,-2,4]=>[4,-2,-3,1]=>0110=>[1,2,1]
[1,-3,-2,-4]=>[-4,-2,-3,1]=>1110=>[3,1]
[-1,3,2,4]=>[4,2,3,-1]=>0001=>[3,1]
[-1,3,2,-4]=>[-4,2,3,-1]=>1001=>[1,2,1]
[-1,3,-2,4]=>[4,-2,3,-1]=>0101=>[1,1,1,1]
[-1,3,-2,-4]=>[-4,-2,3,-1]=>1101=>[2,1,1]
[-1,-3,2,4]=>[4,2,-3,-1]=>0011=>[2,2]
[-1,-3,2,-4]=>[-4,2,-3,-1]=>1011=>[1,1,2]
[-1,-3,-2,4]=>[4,-2,-3,-1]=>0111=>[1,3]
[-1,-3,-2,-4]=>[-4,-2,-3,-1]=>1111=>[4]
[1,3,4,2]=>[2,4,3,1]=>0000=>[4]
[1,3,4,-2]=>[-2,4,3,1]=>1000=>[1,3]
[1,3,-4,2]=>[2,-4,3,1]=>0100=>[1,1,2]
[1,3,-4,-2]=>[-2,-4,3,1]=>1100=>[2,2]
[1,-3,4,2]=>[2,4,-3,1]=>0010=>[2,1,1]
[1,-3,4,-2]=>[-2,4,-3,1]=>1010=>[1,1,1,1]
[1,-3,-4,2]=>[2,-4,-3,1]=>0110=>[1,2,1]
[1,-3,-4,-2]=>[-2,-4,-3,1]=>1110=>[3,1]
[-1,3,4,2]=>[2,4,3,-1]=>0001=>[3,1]
[-1,3,4,-2]=>[-2,4,3,-1]=>1001=>[1,2,1]
[-1,3,-4,2]=>[2,-4,3,-1]=>0101=>[1,1,1,1]
[-1,3,-4,-2]=>[-2,-4,3,-1]=>1101=>[2,1,1]
[-1,-3,4,2]=>[2,4,-3,-1]=>0011=>[2,2]
[-1,-3,4,-2]=>[-2,4,-3,-1]=>1011=>[1,1,2]
[-1,-3,-4,2]=>[2,-4,-3,-1]=>0111=>[1,3]
[-1,-3,-4,-2]=>[-2,-4,-3,-1]=>1111=>[4]
[1,4,2,3]=>[3,2,4,1]=>0000=>[4]
[1,4,2,-3]=>[-3,2,4,1]=>1000=>[1,3]
[1,4,-2,3]=>[3,-2,4,1]=>0100=>[1,1,2]
[1,4,-2,-3]=>[-3,-2,4,1]=>1100=>[2,2]
[1,-4,2,3]=>[3,2,-4,1]=>0010=>[2,1,1]
[1,-4,2,-3]=>[-3,2,-4,1]=>1010=>[1,1,1,1]
[1,-4,-2,3]=>[3,-2,-4,1]=>0110=>[1,2,1]
[1,-4,-2,-3]=>[-3,-2,-4,1]=>1110=>[3,1]
[-1,4,2,3]=>[3,2,4,-1]=>0001=>[3,1]
[-1,4,2,-3]=>[-3,2,4,-1]=>1001=>[1,2,1]
[-1,4,-2,3]=>[3,-2,4,-1]=>0101=>[1,1,1,1]
[-1,4,-2,-3]=>[-3,-2,4,-1]=>1101=>[2,1,1]
[-1,-4,2,3]=>[3,2,-4,-1]=>0011=>[2,2]
[-1,-4,2,-3]=>[-3,2,-4,-1]=>1011=>[1,1,2]
[-1,-4,-2,3]=>[3,-2,-4,-1]=>0111=>[1,3]
[-1,-4,-2,-3]=>[-3,-2,-4,-1]=>1111=>[4]
[1,4,3,2]=>[2,3,4,1]=>0000=>[4]
[1,4,3,-2]=>[-2,3,4,1]=>1000=>[1,3]
[1,4,-3,2]=>[2,-3,4,1]=>0100=>[1,1,2]
[1,4,-3,-2]=>[-2,-3,4,1]=>1100=>[2,2]
[1,-4,3,2]=>[2,3,-4,1]=>0010=>[2,1,1]
[1,-4,3,-2]=>[-2,3,-4,1]=>1010=>[1,1,1,1]
[1,-4,-3,2]=>[2,-3,-4,1]=>0110=>[1,2,1]
[1,-4,-3,-2]=>[-2,-3,-4,1]=>1110=>[3,1]
[-1,4,3,2]=>[2,3,4,-1]=>0001=>[3,1]
[-1,4,3,-2]=>[-2,3,4,-1]=>1001=>[1,2,1]
[-1,4,-3,2]=>[2,-3,4,-1]=>0101=>[1,1,1,1]
[-1,4,-3,-2]=>[-2,-3,4,-1]=>1101=>[2,1,1]
[-1,-4,3,2]=>[2,3,-4,-1]=>0011=>[2,2]
[-1,-4,3,-2]=>[-2,3,-4,-1]=>1011=>[1,1,2]
[-1,-4,-3,2]=>[2,-3,-4,-1]=>0111=>[1,3]
[-1,-4,-3,-2]=>[-2,-3,-4,-1]=>1111=>[4]
[2,1,3,4]=>[4,3,1,2]=>0000=>[4]
[2,1,3,-4]=>[-4,3,1,2]=>1000=>[1,3]
[2,1,-3,4]=>[4,-3,1,2]=>0100=>[1,1,2]
[2,1,-3,-4]=>[-4,-3,1,2]=>1100=>[2,2]
[2,-1,3,4]=>[4,3,-1,2]=>0010=>[2,1,1]
[2,-1,3,-4]=>[-4,3,-1,2]=>1010=>[1,1,1,1]
[2,-1,-3,4]=>[4,-3,-1,2]=>0110=>[1,2,1]
[2,-1,-3,-4]=>[-4,-3,-1,2]=>1110=>[3,1]
[-2,1,3,4]=>[4,3,1,-2]=>0001=>[3,1]
[-2,1,3,-4]=>[-4,3,1,-2]=>1001=>[1,2,1]
[-2,1,-3,4]=>[4,-3,1,-2]=>0101=>[1,1,1,1]
[-2,1,-3,-4]=>[-4,-3,1,-2]=>1101=>[2,1,1]
[-2,-1,3,4]=>[4,3,-1,-2]=>0011=>[2,2]
[-2,-1,3,-4]=>[-4,3,-1,-2]=>1011=>[1,1,2]
[-2,-1,-3,4]=>[4,-3,-1,-2]=>0111=>[1,3]
[-2,-1,-3,-4]=>[-4,-3,-1,-2]=>1111=>[4]
[2,1,4,3]=>[3,4,1,2]=>0000=>[4]
[2,1,4,-3]=>[-3,4,1,2]=>1000=>[1,3]
[2,1,-4,3]=>[3,-4,1,2]=>0100=>[1,1,2]
[2,1,-4,-3]=>[-3,-4,1,2]=>1100=>[2,2]
[2,-1,4,3]=>[3,4,-1,2]=>0010=>[2,1,1]
[2,-1,4,-3]=>[-3,4,-1,2]=>1010=>[1,1,1,1]
[2,-1,-4,3]=>[3,-4,-1,2]=>0110=>[1,2,1]
[2,-1,-4,-3]=>[-3,-4,-1,2]=>1110=>[3,1]
[-2,1,4,3]=>[3,4,1,-2]=>0001=>[3,1]
[-2,1,4,-3]=>[-3,4,1,-2]=>1001=>[1,2,1]
[-2,1,-4,3]=>[3,-4,1,-2]=>0101=>[1,1,1,1]
[-2,1,-4,-3]=>[-3,-4,1,-2]=>1101=>[2,1,1]
[-2,-1,4,3]=>[3,4,-1,-2]=>0011=>[2,2]
[-2,-1,4,-3]=>[-3,4,-1,-2]=>1011=>[1,1,2]
[-2,-1,-4,3]=>[3,-4,-1,-2]=>0111=>[1,3]
[-2,-1,-4,-3]=>[-3,-4,-1,-2]=>1111=>[4]
[2,3,1,4]=>[4,1,3,2]=>0000=>[4]
[2,3,1,-4]=>[-4,1,3,2]=>1000=>[1,3]
[2,3,-1,4]=>[4,-1,3,2]=>0100=>[1,1,2]
[2,3,-1,-4]=>[-4,-1,3,2]=>1100=>[2,2]
[2,-3,1,4]=>[4,1,-3,2]=>0010=>[2,1,1]
[2,-3,1,-4]=>[-4,1,-3,2]=>1010=>[1,1,1,1]
[2,-3,-1,4]=>[4,-1,-3,2]=>0110=>[1,2,1]
[2,-3,-1,-4]=>[-4,-1,-3,2]=>1110=>[3,1]
[-2,3,1,4]=>[4,1,3,-2]=>0001=>[3,1]
[-2,3,1,-4]=>[-4,1,3,-2]=>1001=>[1,2,1]
[-2,3,-1,4]=>[4,-1,3,-2]=>0101=>[1,1,1,1]
[-2,3,-1,-4]=>[-4,-1,3,-2]=>1101=>[2,1,1]
[-2,-3,1,4]=>[4,1,-3,-2]=>0011=>[2,2]
[-2,-3,1,-4]=>[-4,1,-3,-2]=>1011=>[1,1,2]
[-2,-3,-1,4]=>[4,-1,-3,-2]=>0111=>[1,3]
[-2,-3,-1,-4]=>[-4,-1,-3,-2]=>1111=>[4]
[2,3,4,1]=>[1,4,3,2]=>0000=>[4]
[2,3,4,-1]=>[-1,4,3,2]=>1000=>[1,3]
[2,3,-4,1]=>[1,-4,3,2]=>0100=>[1,1,2]
[2,3,-4,-1]=>[-1,-4,3,2]=>1100=>[2,2]
[2,-3,4,1]=>[1,4,-3,2]=>0010=>[2,1,1]
[2,-3,4,-1]=>[-1,4,-3,2]=>1010=>[1,1,1,1]
[2,-3,-4,1]=>[1,-4,-3,2]=>0110=>[1,2,1]
[2,-3,-4,-1]=>[-1,-4,-3,2]=>1110=>[3,1]
[-2,3,4,1]=>[1,4,3,-2]=>0001=>[3,1]
[-2,3,4,-1]=>[-1,4,3,-2]=>1001=>[1,2,1]
[-2,3,-4,1]=>[1,-4,3,-2]=>0101=>[1,1,1,1]
[-2,3,-4,-1]=>[-1,-4,3,-2]=>1101=>[2,1,1]
[-2,-3,4,1]=>[1,4,-3,-2]=>0011=>[2,2]
[-2,-3,4,-1]=>[-1,4,-3,-2]=>1011=>[1,1,2]
[-2,-3,-4,1]=>[1,-4,-3,-2]=>0111=>[1,3]
[-2,-3,-4,-1]=>[-1,-4,-3,-2]=>1111=>[4]
[2,4,1,3]=>[3,1,4,2]=>0000=>[4]
[2,4,1,-3]=>[-3,1,4,2]=>1000=>[1,3]
[2,4,-1,3]=>[3,-1,4,2]=>0100=>[1,1,2]
[2,4,-1,-3]=>[-3,-1,4,2]=>1100=>[2,2]
[2,-4,1,3]=>[3,1,-4,2]=>0010=>[2,1,1]
[2,-4,1,-3]=>[-3,1,-4,2]=>1010=>[1,1,1,1]
[2,-4,-1,3]=>[3,-1,-4,2]=>0110=>[1,2,1]
[2,-4,-1,-3]=>[-3,-1,-4,2]=>1110=>[3,1]
[-2,4,1,3]=>[3,1,4,-2]=>0001=>[3,1]
[-2,4,1,-3]=>[-3,1,4,-2]=>1001=>[1,2,1]
[-2,4,-1,3]=>[3,-1,4,-2]=>0101=>[1,1,1,1]
[-2,4,-1,-3]=>[-3,-1,4,-2]=>1101=>[2,1,1]
[-2,-4,1,3]=>[3,1,-4,-2]=>0011=>[2,2]
[-2,-4,1,-3]=>[-3,1,-4,-2]=>1011=>[1,1,2]
[-2,-4,-1,3]=>[3,-1,-4,-2]=>0111=>[1,3]
[-2,-4,-1,-3]=>[-3,-1,-4,-2]=>1111=>[4]
[2,4,3,1]=>[1,3,4,2]=>0000=>[4]
[2,4,3,-1]=>[-1,3,4,2]=>1000=>[1,3]
[2,4,-3,1]=>[1,-3,4,2]=>0100=>[1,1,2]
[2,4,-3,-1]=>[-1,-3,4,2]=>1100=>[2,2]
[2,-4,3,1]=>[1,3,-4,2]=>0010=>[2,1,1]
[2,-4,3,-1]=>[-1,3,-4,2]=>1010=>[1,1,1,1]
[2,-4,-3,1]=>[1,-3,-4,2]=>0110=>[1,2,1]
[2,-4,-3,-1]=>[-1,-3,-4,2]=>1110=>[3,1]
[-2,4,3,1]=>[1,3,4,-2]=>0001=>[3,1]
[-2,4,3,-1]=>[-1,3,4,-2]=>1001=>[1,2,1]
[-2,4,-3,1]=>[1,-3,4,-2]=>0101=>[1,1,1,1]
[-2,4,-3,-1]=>[-1,-3,4,-2]=>1101=>[2,1,1]
[-2,-4,3,1]=>[1,3,-4,-2]=>0011=>[2,2]
[-2,-4,3,-1]=>[-1,3,-4,-2]=>1011=>[1,1,2]
[-2,-4,-3,1]=>[1,-3,-4,-2]=>0111=>[1,3]
[-2,-4,-3,-1]=>[-1,-3,-4,-2]=>1111=>[4]
[3,1,2,4]=>[4,2,1,3]=>0000=>[4]
[3,1,2,-4]=>[-4,2,1,3]=>1000=>[1,3]
[3,1,-2,4]=>[4,-2,1,3]=>0100=>[1,1,2]
[3,1,-2,-4]=>[-4,-2,1,3]=>1100=>[2,2]
[3,-1,2,4]=>[4,2,-1,3]=>0010=>[2,1,1]
[3,-1,2,-4]=>[-4,2,-1,3]=>1010=>[1,1,1,1]
[3,-1,-2,4]=>[4,-2,-1,3]=>0110=>[1,2,1]
[3,-1,-2,-4]=>[-4,-2,-1,3]=>1110=>[3,1]
[-3,1,2,4]=>[4,2,1,-3]=>0001=>[3,1]
[-3,1,2,-4]=>[-4,2,1,-3]=>1001=>[1,2,1]
[-3,1,-2,4]=>[4,-2,1,-3]=>0101=>[1,1,1,1]
[-3,1,-2,-4]=>[-4,-2,1,-3]=>1101=>[2,1,1]
[-3,-1,2,4]=>[4,2,-1,-3]=>0011=>[2,2]
[-3,-1,2,-4]=>[-4,2,-1,-3]=>1011=>[1,1,2]
[-3,-1,-2,4]=>[4,-2,-1,-3]=>0111=>[1,3]
[-3,-1,-2,-4]=>[-4,-2,-1,-3]=>1111=>[4]
[3,1,4,2]=>[2,4,1,3]=>0000=>[4]
[3,1,4,-2]=>[-2,4,1,3]=>1000=>[1,3]
[3,1,-4,2]=>[2,-4,1,3]=>0100=>[1,1,2]
[3,1,-4,-2]=>[-2,-4,1,3]=>1100=>[2,2]
[3,-1,4,2]=>[2,4,-1,3]=>0010=>[2,1,1]
[3,-1,4,-2]=>[-2,4,-1,3]=>1010=>[1,1,1,1]
[3,-1,-4,2]=>[2,-4,-1,3]=>0110=>[1,2,1]
[3,-1,-4,-2]=>[-2,-4,-1,3]=>1110=>[3,1]
[-3,1,4,2]=>[2,4,1,-3]=>0001=>[3,1]
[-3,1,4,-2]=>[-2,4,1,-3]=>1001=>[1,2,1]
[-3,1,-4,2]=>[2,-4,1,-3]=>0101=>[1,1,1,1]
[-3,1,-4,-2]=>[-2,-4,1,-3]=>1101=>[2,1,1]
[-3,-1,4,2]=>[2,4,-1,-3]=>0011=>[2,2]
[-3,-1,4,-2]=>[-2,4,-1,-3]=>1011=>[1,1,2]
[-3,-1,-4,2]=>[2,-4,-1,-3]=>0111=>[1,3]
[-3,-1,-4,-2]=>[-2,-4,-1,-3]=>1111=>[4]
[3,2,1,4]=>[4,1,2,3]=>0000=>[4]
[3,2,1,-4]=>[-4,1,2,3]=>1000=>[1,3]
[3,2,-1,4]=>[4,-1,2,3]=>0100=>[1,1,2]
[3,2,-1,-4]=>[-4,-1,2,3]=>1100=>[2,2]
[3,-2,1,4]=>[4,1,-2,3]=>0010=>[2,1,1]
[3,-2,1,-4]=>[-4,1,-2,3]=>1010=>[1,1,1,1]
[3,-2,-1,4]=>[4,-1,-2,3]=>0110=>[1,2,1]
[3,-2,-1,-4]=>[-4,-1,-2,3]=>1110=>[3,1]
[-3,2,1,4]=>[4,1,2,-3]=>0001=>[3,1]
[-3,2,1,-4]=>[-4,1,2,-3]=>1001=>[1,2,1]
[-3,2,-1,4]=>[4,-1,2,-3]=>0101=>[1,1,1,1]
[-3,2,-1,-4]=>[-4,-1,2,-3]=>1101=>[2,1,1]
[-3,-2,1,4]=>[4,1,-2,-3]=>0011=>[2,2]
[-3,-2,1,-4]=>[-4,1,-2,-3]=>1011=>[1,1,2]
[-3,-2,-1,4]=>[4,-1,-2,-3]=>0111=>[1,3]
[-3,-2,-1,-4]=>[-4,-1,-2,-3]=>1111=>[4]
[3,2,4,1]=>[1,4,2,3]=>0000=>[4]
[3,2,4,-1]=>[-1,4,2,3]=>1000=>[1,3]
[3,2,-4,1]=>[1,-4,2,3]=>0100=>[1,1,2]
[3,2,-4,-1]=>[-1,-4,2,3]=>1100=>[2,2]
[3,-2,4,1]=>[1,4,-2,3]=>0010=>[2,1,1]
[3,-2,4,-1]=>[-1,4,-2,3]=>1010=>[1,1,1,1]
[3,-2,-4,1]=>[1,-4,-2,3]=>0110=>[1,2,1]
[3,-2,-4,-1]=>[-1,-4,-2,3]=>1110=>[3,1]
[-3,2,4,1]=>[1,4,2,-3]=>0001=>[3,1]
[-3,2,4,-1]=>[-1,4,2,-3]=>1001=>[1,2,1]
[-3,2,-4,1]=>[1,-4,2,-3]=>0101=>[1,1,1,1]
[-3,2,-4,-1]=>[-1,-4,2,-3]=>1101=>[2,1,1]
[-3,-2,4,1]=>[1,4,-2,-3]=>0011=>[2,2]
[-3,-2,4,-1]=>[-1,4,-2,-3]=>1011=>[1,1,2]
[-3,-2,-4,1]=>[1,-4,-2,-3]=>0111=>[1,3]
[-3,-2,-4,-1]=>[-1,-4,-2,-3]=>1111=>[4]
[3,4,1,2]=>[2,1,4,3]=>0000=>[4]
[3,4,1,-2]=>[-2,1,4,3]=>1000=>[1,3]
[3,4,-1,2]=>[2,-1,4,3]=>0100=>[1,1,2]
[3,4,-1,-2]=>[-2,-1,4,3]=>1100=>[2,2]
[3,-4,1,2]=>[2,1,-4,3]=>0010=>[2,1,1]
[3,-4,1,-2]=>[-2,1,-4,3]=>1010=>[1,1,1,1]
[3,-4,-1,2]=>[2,-1,-4,3]=>0110=>[1,2,1]
[3,-4,-1,-2]=>[-2,-1,-4,3]=>1110=>[3,1]
[-3,4,1,2]=>[2,1,4,-3]=>0001=>[3,1]
[-3,4,1,-2]=>[-2,1,4,-3]=>1001=>[1,2,1]
[-3,4,-1,2]=>[2,-1,4,-3]=>0101=>[1,1,1,1]
[-3,4,-1,-2]=>[-2,-1,4,-3]=>1101=>[2,1,1]
[-3,-4,1,2]=>[2,1,-4,-3]=>0011=>[2,2]
[-3,-4,1,-2]=>[-2,1,-4,-3]=>1011=>[1,1,2]
[-3,-4,-1,2]=>[2,-1,-4,-3]=>0111=>[1,3]
[-3,-4,-1,-2]=>[-2,-1,-4,-3]=>1111=>[4]
[3,4,2,1]=>[1,2,4,3]=>0000=>[4]
[3,4,2,-1]=>[-1,2,4,3]=>1000=>[1,3]
[3,4,-2,1]=>[1,-2,4,3]=>0100=>[1,1,2]
[3,4,-2,-1]=>[-1,-2,4,3]=>1100=>[2,2]
[3,-4,2,1]=>[1,2,-4,3]=>0010=>[2,1,1]
[3,-4,2,-1]=>[-1,2,-4,3]=>1010=>[1,1,1,1]
[3,-4,-2,1]=>[1,-2,-4,3]=>0110=>[1,2,1]
[3,-4,-2,-1]=>[-1,-2,-4,3]=>1110=>[3,1]
[-3,4,2,1]=>[1,2,4,-3]=>0001=>[3,1]
[-3,4,2,-1]=>[-1,2,4,-3]=>1001=>[1,2,1]
[-3,4,-2,1]=>[1,-2,4,-3]=>0101=>[1,1,1,1]
[-3,4,-2,-1]=>[-1,-2,4,-3]=>1101=>[2,1,1]
[-3,-4,2,1]=>[1,2,-4,-3]=>0011=>[2,2]
[-3,-4,2,-1]=>[-1,2,-4,-3]=>1011=>[1,1,2]
[-3,-4,-2,1]=>[1,-2,-4,-3]=>0111=>[1,3]
[-3,-4,-2,-1]=>[-1,-2,-4,-3]=>1111=>[4]
[4,1,2,3]=>[3,2,1,4]=>0000=>[4]
[4,1,2,-3]=>[-3,2,1,4]=>1000=>[1,3]
[4,1,-2,3]=>[3,-2,1,4]=>0100=>[1,1,2]
[4,1,-2,-3]=>[-3,-2,1,4]=>1100=>[2,2]
[4,-1,2,3]=>[3,2,-1,4]=>0010=>[2,1,1]
[4,-1,2,-3]=>[-3,2,-1,4]=>1010=>[1,1,1,1]
[4,-1,-2,3]=>[3,-2,-1,4]=>0110=>[1,2,1]
[4,-1,-2,-3]=>[-3,-2,-1,4]=>1110=>[3,1]
[-4,1,2,3]=>[3,2,1,-4]=>0001=>[3,1]
[-4,1,2,-3]=>[-3,2,1,-4]=>1001=>[1,2,1]
[-4,1,-2,3]=>[3,-2,1,-4]=>0101=>[1,1,1,1]
[-4,1,-2,-3]=>[-3,-2,1,-4]=>1101=>[2,1,1]
[-4,-1,2,3]=>[3,2,-1,-4]=>0011=>[2,2]
[-4,-1,2,-3]=>[-3,2,-1,-4]=>1011=>[1,1,2]
[-4,-1,-2,3]=>[3,-2,-1,-4]=>0111=>[1,3]
[-4,-1,-2,-3]=>[-3,-2,-1,-4]=>1111=>[4]
[4,1,3,2]=>[2,3,1,4]=>0000=>[4]
[4,1,3,-2]=>[-2,3,1,4]=>1000=>[1,3]
[4,1,-3,2]=>[2,-3,1,4]=>0100=>[1,1,2]
[4,1,-3,-2]=>[-2,-3,1,4]=>1100=>[2,2]
[4,-1,3,2]=>[2,3,-1,4]=>0010=>[2,1,1]
[4,-1,3,-2]=>[-2,3,-1,4]=>1010=>[1,1,1,1]
[4,-1,-3,2]=>[2,-3,-1,4]=>0110=>[1,2,1]
[4,-1,-3,-2]=>[-2,-3,-1,4]=>1110=>[3,1]
[-4,1,3,2]=>[2,3,1,-4]=>0001=>[3,1]
[-4,1,3,-2]=>[-2,3,1,-4]=>1001=>[1,2,1]
[-4,1,-3,2]=>[2,-3,1,-4]=>0101=>[1,1,1,1]
[-4,1,-3,-2]=>[-2,-3,1,-4]=>1101=>[2,1,1]
[-4,-1,3,2]=>[2,3,-1,-4]=>0011=>[2,2]
[-4,-1,3,-2]=>[-2,3,-1,-4]=>1011=>[1,1,2]
[-4,-1,-3,2]=>[2,-3,-1,-4]=>0111=>[1,3]
[-4,-1,-3,-2]=>[-2,-3,-1,-4]=>1111=>[4]
[4,2,1,3]=>[3,1,2,4]=>0000=>[4]
[4,2,1,-3]=>[-3,1,2,4]=>1000=>[1,3]
[4,2,-1,3]=>[3,-1,2,4]=>0100=>[1,1,2]
[4,2,-1,-3]=>[-3,-1,2,4]=>1100=>[2,2]
[4,-2,1,3]=>[3,1,-2,4]=>0010=>[2,1,1]
[4,-2,1,-3]=>[-3,1,-2,4]=>1010=>[1,1,1,1]
[4,-2,-1,3]=>[3,-1,-2,4]=>0110=>[1,2,1]
[4,-2,-1,-3]=>[-3,-1,-2,4]=>1110=>[3,1]
[-4,2,1,3]=>[3,1,2,-4]=>0001=>[3,1]
[-4,2,1,-3]=>[-3,1,2,-4]=>1001=>[1,2,1]
[-4,2,-1,3]=>[3,-1,2,-4]=>0101=>[1,1,1,1]
[-4,2,-1,-3]=>[-3,-1,2,-4]=>1101=>[2,1,1]
[-4,-2,1,3]=>[3,1,-2,-4]=>0011=>[2,2]
[-4,-2,1,-3]=>[-3,1,-2,-4]=>1011=>[1,1,2]
[-4,-2,-1,3]=>[3,-1,-2,-4]=>0111=>[1,3]
[-4,-2,-1,-3]=>[-3,-1,-2,-4]=>1111=>[4]
[4,2,3,1]=>[1,3,2,4]=>0000=>[4]
[4,2,3,-1]=>[-1,3,2,4]=>1000=>[1,3]
[4,2,-3,1]=>[1,-3,2,4]=>0100=>[1,1,2]
[4,2,-3,-1]=>[-1,-3,2,4]=>1100=>[2,2]
[4,-2,3,1]=>[1,3,-2,4]=>0010=>[2,1,1]
[4,-2,3,-1]=>[-1,3,-2,4]=>1010=>[1,1,1,1]
[4,-2,-3,1]=>[1,-3,-2,4]=>0110=>[1,2,1]
[4,-2,-3,-1]=>[-1,-3,-2,4]=>1110=>[3,1]
[-4,2,3,1]=>[1,3,2,-4]=>0001=>[3,1]
[-4,2,3,-1]=>[-1,3,2,-4]=>1001=>[1,2,1]
[-4,2,-3,1]=>[1,-3,2,-4]=>0101=>[1,1,1,1]
[-4,2,-3,-1]=>[-1,-3,2,-4]=>1101=>[2,1,1]
[-4,-2,3,1]=>[1,3,-2,-4]=>0011=>[2,2]
[-4,-2,3,-1]=>[-1,3,-2,-4]=>1011=>[1,1,2]
[-4,-2,-3,1]=>[1,-3,-2,-4]=>0111=>[1,3]
[-4,-2,-3,-1]=>[-1,-3,-2,-4]=>1111=>[4]
[4,3,1,2]=>[2,1,3,4]=>0000=>[4]
[4,3,1,-2]=>[-2,1,3,4]=>1000=>[1,3]
[4,3,-1,2]=>[2,-1,3,4]=>0100=>[1,1,2]
[4,3,-1,-2]=>[-2,-1,3,4]=>1100=>[2,2]
[4,-3,1,2]=>[2,1,-3,4]=>0010=>[2,1,1]
[4,-3,1,-2]=>[-2,1,-3,4]=>1010=>[1,1,1,1]
[4,-3,-1,2]=>[2,-1,-3,4]=>0110=>[1,2,1]
[4,-3,-1,-2]=>[-2,-1,-3,4]=>1110=>[3,1]
[-4,3,1,2]=>[2,1,3,-4]=>0001=>[3,1]
[-4,3,1,-2]=>[-2,1,3,-4]=>1001=>[1,2,1]
[-4,3,-1,2]=>[2,-1,3,-4]=>0101=>[1,1,1,1]
[-4,3,-1,-2]=>[-2,-1,3,-4]=>1101=>[2,1,1]
[-4,-3,1,2]=>[2,1,-3,-4]=>0011=>[2,2]
[-4,-3,1,-2]=>[-2,1,-3,-4]=>1011=>[1,1,2]
[-4,-3,-1,2]=>[2,-1,-3,-4]=>0111=>[1,3]
[-4,-3,-1,-2]=>[-2,-1,-3,-4]=>1111=>[4]
[4,3,2,1]=>[1,2,3,4]=>0000=>[4]
[4,3,2,-1]=>[-1,2,3,4]=>1000=>[1,3]
[4,3,-2,1]=>[1,-2,3,4]=>0100=>[1,1,2]
[4,3,-2,-1]=>[-1,-2,3,4]=>1100=>[2,2]
[4,-3,2,1]=>[1,2,-3,4]=>0010=>[2,1,1]
[4,-3,2,-1]=>[-1,2,-3,4]=>1010=>[1,1,1,1]
[4,-3,-2,1]=>[1,-2,-3,4]=>0110=>[1,2,1]
[4,-3,-2,-1]=>[-1,-2,-3,4]=>1110=>[3,1]
[-4,3,2,1]=>[1,2,3,-4]=>0001=>[3,1]
[-4,3,2,-1]=>[-1,2,3,-4]=>1001=>[1,2,1]
[-4,3,-2,1]=>[1,-2,3,-4]=>0101=>[1,1,1,1]
[-4,3,-2,-1]=>[-1,-2,3,-4]=>1101=>[2,1,1]
[-4,-3,2,1]=>[1,2,-3,-4]=>0011=>[2,2]
[-4,-3,2,-1]=>[-1,2,-3,-4]=>1011=>[1,1,2]
[-4,-3,-2,1]=>[1,-2,-3,-4]=>0111=>[1,3]
[-4,-3,-2,-1]=>[-1,-2,-3,-4]=>1111=>[4]
[1,2,3,4,5]=>[5,4,3,2,1]=>00000=>[5]
[1,2,3,4,-5]=>[-5,4,3,2,1]=>10000=>[1,4]
[1,2,3,-4,5]=>[5,-4,3,2,1]=>01000=>[1,1,3]
[1,2,3,-4,-5]=>[-5,-4,3,2,1]=>11000=>[2,3]
[1,2,-3,4,5]=>[5,4,-3,2,1]=>00100=>[2,1,2]
[1,2,-3,4,-5]=>[-5,4,-3,2,1]=>10100=>[1,1,1,2]
[1,2,-3,-4,5]=>[5,-4,-3,2,1]=>01100=>[1,2,2]
[1,2,-3,-4,-5]=>[-5,-4,-3,2,1]=>11100=>[3,2]
[1,-2,3,4,5]=>[5,4,3,-2,1]=>00010=>[3,1,1]
[1,-2,3,4,-5]=>[-5,4,3,-2,1]=>10010=>[1,2,1,1]
[1,-2,3,-4,5]=>[5,-4,3,-2,1]=>01010=>[1,1,1,1,1]
[1,-2,3,-4,-5]=>[-5,-4,3,-2,1]=>11010=>[2,1,1,1]
[1,-2,-3,4,5]=>[5,4,-3,-2,1]=>00110=>[2,2,1]
[1,-2,-3,4,-5]=>[-5,4,-3,-2,1]=>10110=>[1,1,2,1]
[1,-2,-3,-4,5]=>[5,-4,-3,-2,1]=>01110=>[1,3,1]
[1,-2,-3,-4,-5]=>[-5,-4,-3,-2,1]=>11110=>[4,1]
[-1,2,3,4,5]=>[5,4,3,2,-1]=>00001=>[4,1]
[-1,2,3,4,-5]=>[-5,4,3,2,-1]=>10001=>[1,3,1]
[-1,2,3,-4,5]=>[5,-4,3,2,-1]=>01001=>[1,1,2,1]
[-1,2,3,-4,-5]=>[-5,-4,3,2,-1]=>11001=>[2,2,1]
[-1,2,-3,4,5]=>[5,4,-3,2,-1]=>00101=>[2,1,1,1]
[-1,2,-3,4,-5]=>[-5,4,-3,2,-1]=>10101=>[1,1,1,1,1]
[-1,2,-3,-4,5]=>[5,-4,-3,2,-1]=>01101=>[1,2,1,1]
[-1,2,-3,-4,-5]=>[-5,-4,-3,2,-1]=>11101=>[3,1,1]
[-1,-2,3,4,5]=>[5,4,3,-2,-1]=>00011=>[3,2]
[-1,-2,3,4,-5]=>[-5,4,3,-2,-1]=>10011=>[1,2,2]
[-1,-2,3,-4,5]=>[5,-4,3,-2,-1]=>01011=>[1,1,1,2]
[-1,-2,3,-4,-5]=>[-5,-4,3,-2,-1]=>11011=>[2,1,2]
[-1,-2,-3,4,5]=>[5,4,-3,-2,-1]=>00111=>[2,3]
[-1,-2,-3,4,-5]=>[-5,4,-3,-2,-1]=>10111=>[1,1,3]
[-1,-2,-3,-4,5]=>[5,-4,-3,-2,-1]=>01111=>[1,4]
[-1,-2,-3,-4,-5]=>[-5,-4,-3,-2,-1]=>11111=>[5]
[1,2,3,5,4]=>[4,5,3,2,1]=>00000=>[5]
[1,2,3,5,-4]=>[-4,5,3,2,1]=>10000=>[1,4]
[1,2,3,-5,4]=>[4,-5,3,2,1]=>01000=>[1,1,3]
[1,2,3,-5,-4]=>[-4,-5,3,2,1]=>11000=>[2,3]
[1,2,-3,5,4]=>[4,5,-3,2,1]=>00100=>[2,1,2]
[1,2,-3,5,-4]=>[-4,5,-3,2,1]=>10100=>[1,1,1,2]
[1,2,-3,-5,4]=>[4,-5,-3,2,1]=>01100=>[1,2,2]
[1,2,-3,-5,-4]=>[-4,-5,-3,2,1]=>11100=>[3,2]
[1,-2,3,5,4]=>[4,5,3,-2,1]=>00010=>[3,1,1]
[1,-2,3,5,-4]=>[-4,5,3,-2,1]=>10010=>[1,2,1,1]
[1,-2,3,-5,4]=>[4,-5,3,-2,1]=>01010=>[1,1,1,1,1]
[1,-2,3,-5,-4]=>[-4,-5,3,-2,1]=>11010=>[2,1,1,1]
[1,-2,-3,5,4]=>[4,5,-3,-2,1]=>00110=>[2,2,1]
[1,-2,-3,5,-4]=>[-4,5,-3,-2,1]=>10110=>[1,1,2,1]
[1,-2,-3,-5,4]=>[4,-5,-3,-2,1]=>01110=>[1,3,1]
[1,-2,-3,-5,-4]=>[-4,-5,-3,-2,1]=>11110=>[4,1]
[-1,2,3,5,4]=>[4,5,3,2,-1]=>00001=>[4,1]
[-1,2,3,5,-4]=>[-4,5,3,2,-1]=>10001=>[1,3,1]
[-1,2,3,-5,4]=>[4,-5,3,2,-1]=>01001=>[1,1,2,1]
[-1,2,3,-5,-4]=>[-4,-5,3,2,-1]=>11001=>[2,2,1]
[-1,2,-3,5,4]=>[4,5,-3,2,-1]=>00101=>[2,1,1,1]
[-1,2,-3,5,-4]=>[-4,5,-3,2,-1]=>10101=>[1,1,1,1,1]
[-1,2,-3,-5,4]=>[4,-5,-3,2,-1]=>01101=>[1,2,1,1]
[-1,2,-3,-5,-4]=>[-4,-5,-3,2,-1]=>11101=>[3,1,1]
[-1,-2,3,5,4]=>[4,5,3,-2,-1]=>00011=>[3,2]
[-1,-2,3,5,-4]=>[-4,5,3,-2,-1]=>10011=>[1,2,2]
[-1,-2,3,-5,4]=>[4,-5,3,-2,-1]=>01011=>[1,1,1,2]
[-1,-2,3,-5,-4]=>[-4,-5,3,-2,-1]=>11011=>[2,1,2]
[-1,-2,-3,5,4]=>[4,5,-3,-2,-1]=>00111=>[2,3]
[-1,-2,-3,5,-4]=>[-4,5,-3,-2,-1]=>10111=>[1,1,3]
[-1,-2,-3,-5,4]=>[4,-5,-3,-2,-1]=>01111=>[1,4]
[-1,-2,-3,-5,-4]=>[-4,-5,-3,-2,-1]=>11111=>[5]
[1,2,4,3,5]=>[5,3,4,2,1]=>00000=>[5]
[1,2,4,3,-5]=>[-5,3,4,2,1]=>10000=>[1,4]
[1,2,4,-3,5]=>[5,-3,4,2,1]=>01000=>[1,1,3]
[1,2,4,-3,-5]=>[-5,-3,4,2,1]=>11000=>[2,3]
[1,2,-4,3,5]=>[5,3,-4,2,1]=>00100=>[2,1,2]
[1,2,-4,3,-5]=>[-5,3,-4,2,1]=>10100=>[1,1,1,2]
[1,2,-4,-3,5]=>[5,-3,-4,2,1]=>01100=>[1,2,2]
[1,2,-4,-3,-5]=>[-5,-3,-4,2,1]=>11100=>[3,2]
[1,-2,4,3,5]=>[5,3,4,-2,1]=>00010=>[3,1,1]
[1,-2,4,3,-5]=>[-5,3,4,-2,1]=>10010=>[1,2,1,1]
[1,-2,4,-3,5]=>[5,-3,4,-2,1]=>01010=>[1,1,1,1,1]
[1,-2,4,-3,-5]=>[-5,-3,4,-2,1]=>11010=>[2,1,1,1]
[1,-2,-4,3,5]=>[5,3,-4,-2,1]=>00110=>[2,2,1]
[1,-2,-4,3,-5]=>[-5,3,-4,-2,1]=>10110=>[1,1,2,1]
[1,-2,-4,-3,5]=>[5,-3,-4,-2,1]=>01110=>[1,3,1]
[1,-2,-4,-3,-5]=>[-5,-3,-4,-2,1]=>11110=>[4,1]
[-1,2,4,3,5]=>[5,3,4,2,-1]=>00001=>[4,1]
[-1,2,4,3,-5]=>[-5,3,4,2,-1]=>10001=>[1,3,1]
[-1,2,4,-3,5]=>[5,-3,4,2,-1]=>01001=>[1,1,2,1]
[-1,2,4,-3,-5]=>[-5,-3,4,2,-1]=>11001=>[2,2,1]
[-1,2,-4,3,5]=>[5,3,-4,2,-1]=>00101=>[2,1,1,1]
[-1,2,-4,3,-5]=>[-5,3,-4,2,-1]=>10101=>[1,1,1,1,1]
[-1,2,-4,-3,5]=>[5,-3,-4,2,-1]=>01101=>[1,2,1,1]
[-1,2,-4,-3,-5]=>[-5,-3,-4,2,-1]=>11101=>[3,1,1]
[-1,-2,4,3,5]=>[5,3,4,-2,-1]=>00011=>[3,2]
[-1,-2,4,3,-5]=>[-5,3,4,-2,-1]=>10011=>[1,2,2]
[-1,-2,4,-3,5]=>[5,-3,4,-2,-1]=>01011=>[1,1,1,2]
[-1,-2,4,-3,-5]=>[-5,-3,4,-2,-1]=>11011=>[2,1,2]
[-1,-2,-4,3,5]=>[5,3,-4,-2,-1]=>00111=>[2,3]
[-1,-2,-4,3,-5]=>[-5,3,-4,-2,-1]=>10111=>[1,1,3]
[-1,-2,-4,-3,5]=>[5,-3,-4,-2,-1]=>01111=>[1,4]
[-1,-2,-4,-3,-5]=>[-5,-3,-4,-2,-1]=>11111=>[5]
[1,2,4,5,3]=>[3,5,4,2,1]=>00000=>[5]
[1,2,4,5,-3]=>[-3,5,4,2,1]=>10000=>[1,4]
[1,2,4,-5,3]=>[3,-5,4,2,1]=>01000=>[1,1,3]
[1,2,4,-5,-3]=>[-3,-5,4,2,1]=>11000=>[2,3]
[1,2,-4,5,3]=>[3,5,-4,2,1]=>00100=>[2,1,2]
[1,2,-4,5,-3]=>[-3,5,-4,2,1]=>10100=>[1,1,1,2]
[1,2,-4,-5,3]=>[3,-5,-4,2,1]=>01100=>[1,2,2]
[1,2,-4,-5,-3]=>[-3,-5,-4,2,1]=>11100=>[3,2]
[1,-2,4,5,3]=>[3,5,4,-2,1]=>00010=>[3,1,1]
[1,-2,4,5,-3]=>[-3,5,4,-2,1]=>10010=>[1,2,1,1]
[1,-2,4,-5,3]=>[3,-5,4,-2,1]=>01010=>[1,1,1,1,1]
[1,-2,4,-5,-3]=>[-3,-5,4,-2,1]=>11010=>[2,1,1,1]
[1,-2,-4,5,3]=>[3,5,-4,-2,1]=>00110=>[2,2,1]
[1,-2,-4,5,-3]=>[-3,5,-4,-2,1]=>10110=>[1,1,2,1]
[1,-2,-4,-5,3]=>[3,-5,-4,-2,1]=>01110=>[1,3,1]
[1,-2,-4,-5,-3]=>[-3,-5,-4,-2,1]=>11110=>[4,1]
[-1,2,4,5,3]=>[3,5,4,2,-1]=>00001=>[4,1]
[-1,2,4,5,-3]=>[-3,5,4,2,-1]=>10001=>[1,3,1]
[-1,2,4,-5,3]=>[3,-5,4,2,-1]=>01001=>[1,1,2,1]
[-1,2,4,-5,-3]=>[-3,-5,4,2,-1]=>11001=>[2,2,1]
[-1,2,-4,5,3]=>[3,5,-4,2,-1]=>00101=>[2,1,1,1]
[-1,2,-4,5,-3]=>[-3,5,-4,2,-1]=>10101=>[1,1,1,1,1]
[-1,2,-4,-5,3]=>[3,-5,-4,2,-1]=>01101=>[1,2,1,1]
[-1,2,-4,-5,-3]=>[-3,-5,-4,2,-1]=>11101=>[3,1,1]
[-1,-2,4,5,3]=>[3,5,4,-2,-1]=>00011=>[3,2]
[-1,-2,4,5,-3]=>[-3,5,4,-2,-1]=>10011=>[1,2,2]
[-1,-2,4,-5,3]=>[3,-5,4,-2,-1]=>01011=>[1,1,1,2]
[-1,-2,4,-5,-3]=>[-3,-5,4,-2,-1]=>11011=>[2,1,2]
[-1,-2,-4,5,3]=>[3,5,-4,-2,-1]=>00111=>[2,3]
[-1,-2,-4,5,-3]=>[-3,5,-4,-2,-1]=>10111=>[1,1,3]
[-1,-2,-4,-5,3]=>[3,-5,-4,-2,-1]=>01111=>[1,4]
[-1,-2,-4,-5,-3]=>[-3,-5,-4,-2,-1]=>11111=>[5]
[1,2,5,3,4]=>[4,3,5,2,1]=>00000=>[5]
[1,2,5,3,-4]=>[-4,3,5,2,1]=>10000=>[1,4]
[1,2,5,-3,4]=>[4,-3,5,2,1]=>01000=>[1,1,3]
[1,2,5,-3,-4]=>[-4,-3,5,2,1]=>11000=>[2,3]
[1,2,-5,3,4]=>[4,3,-5,2,1]=>00100=>[2,1,2]
[1,2,-5,3,-4]=>[-4,3,-5,2,1]=>10100=>[1,1,1,2]
[1,2,-5,-3,4]=>[4,-3,-5,2,1]=>01100=>[1,2,2]
[1,2,-5,-3,-4]=>[-4,-3,-5,2,1]=>11100=>[3,2]
[1,-2,5,3,4]=>[4,3,5,-2,1]=>00010=>[3,1,1]
[1,-2,5,3,-4]=>[-4,3,5,-2,1]=>10010=>[1,2,1,1]
[1,-2,5,-3,4]=>[4,-3,5,-2,1]=>01010=>[1,1,1,1,1]
[1,-2,5,-3,-4]=>[-4,-3,5,-2,1]=>11010=>[2,1,1,1]
[1,-2,-5,3,4]=>[4,3,-5,-2,1]=>00110=>[2,2,1]
[1,-2,-5,3,-4]=>[-4,3,-5,-2,1]=>10110=>[1,1,2,1]
[1,-2,-5,-3,4]=>[4,-3,-5,-2,1]=>01110=>[1,3,1]
[1,-2,-5,-3,-4]=>[-4,-3,-5,-2,1]=>11110=>[4,1]
[-1,2,5,3,4]=>[4,3,5,2,-1]=>00001=>[4,1]
[-1,2,5,3,-4]=>[-4,3,5,2,-1]=>10001=>[1,3,1]
[-1,2,5,-3,4]=>[4,-3,5,2,-1]=>01001=>[1,1,2,1]
[-1,2,5,-3,-4]=>[-4,-3,5,2,-1]=>11001=>[2,2,1]
[-1,2,-5,3,4]=>[4,3,-5,2,-1]=>00101=>[2,1,1,1]
[-1,2,-5,3,-4]=>[-4,3,-5,2,-1]=>10101=>[1,1,1,1,1]
[-1,2,-5,-3,4]=>[4,-3,-5,2,-1]=>01101=>[1,2,1,1]
[-1,2,-5,-3,-4]=>[-4,-3,-5,2,-1]=>11101=>[3,1,1]
[-1,-2,5,3,4]=>[4,3,5,-2,-1]=>00011=>[3,2]
[-1,-2,5,3,-4]=>[-4,3,5,-2,-1]=>10011=>[1,2,2]
[-1,-2,5,-3,4]=>[4,-3,5,-2,-1]=>01011=>[1,1,1,2]
[-1,-2,5,-3,-4]=>[-4,-3,5,-2,-1]=>11011=>[2,1,2]
[-1,-2,-5,3,4]=>[4,3,-5,-2,-1]=>00111=>[2,3]
[-1,-2,-5,3,-4]=>[-4,3,-5,-2,-1]=>10111=>[1,1,3]
[-1,-2,-5,-3,4]=>[4,-3,-5,-2,-1]=>01111=>[1,4]
[-1,-2,-5,-3,-4]=>[-4,-3,-5,-2,-1]=>11111=>[5]
[1,2,5,4,3]=>[3,4,5,2,1]=>00000=>[5]
[1,2,5,4,-3]=>[-3,4,5,2,1]=>10000=>[1,4]
[1,2,5,-4,3]=>[3,-4,5,2,1]=>01000=>[1,1,3]
[1,2,5,-4,-3]=>[-3,-4,5,2,1]=>11000=>[2,3]
[1,2,-5,4,3]=>[3,4,-5,2,1]=>00100=>[2,1,2]
[1,2,-5,4,-3]=>[-3,4,-5,2,1]=>10100=>[1,1,1,2]
[1,2,-5,-4,3]=>[3,-4,-5,2,1]=>01100=>[1,2,2]
[1,2,-5,-4,-3]=>[-3,-4,-5,2,1]=>11100=>[3,2]
[1,-2,5,4,3]=>[3,4,5,-2,1]=>00010=>[3,1,1]
[1,-2,5,4,-3]=>[-3,4,5,-2,1]=>10010=>[1,2,1,1]
[1,-2,5,-4,3]=>[3,-4,5,-2,1]=>01010=>[1,1,1,1,1]
[1,-2,5,-4,-3]=>[-3,-4,5,-2,1]=>11010=>[2,1,1,1]
[1,-2,-5,4,3]=>[3,4,-5,-2,1]=>00110=>[2,2,1]
[1,-2,-5,4,-3]=>[-3,4,-5,-2,1]=>10110=>[1,1,2,1]
[1,-2,-5,-4,3]=>[3,-4,-5,-2,1]=>01110=>[1,3,1]
[1,-2,-5,-4,-3]=>[-3,-4,-5,-2,1]=>11110=>[4,1]
[-1,2,5,4,3]=>[3,4,5,2,-1]=>00001=>[4,1]
[-1,2,5,4,-3]=>[-3,4,5,2,-1]=>10001=>[1,3,1]
[-1,2,5,-4,3]=>[3,-4,5,2,-1]=>01001=>[1,1,2,1]
[-1,2,5,-4,-3]=>[-3,-4,5,2,-1]=>11001=>[2,2,1]
[-1,2,-5,4,3]=>[3,4,-5,2,-1]=>00101=>[2,1,1,1]
[-1,2,-5,4,-3]=>[-3,4,-5,2,-1]=>10101=>[1,1,1,1,1]
[-1,2,-5,-4,3]=>[3,-4,-5,2,-1]=>01101=>[1,2,1,1]
[-1,2,-5,-4,-3]=>[-3,-4,-5,2,-1]=>11101=>[3,1,1]
[-1,-2,5,4,3]=>[3,4,5,-2,-1]=>00011=>[3,2]
[-1,-2,5,4,-3]=>[-3,4,5,-2,-1]=>10011=>[1,2,2]
[-1,-2,5,-4,3]=>[3,-4,5,-2,-1]=>01011=>[1,1,1,2]
[-1,-2,5,-4,-3]=>[-3,-4,5,-2,-1]=>11011=>[2,1,2]
[-1,-2,-5,4,3]=>[3,4,-5,-2,-1]=>00111=>[2,3]
[-1,-2,-5,4,-3]=>[-3,4,-5,-2,-1]=>10111=>[1,1,3]
[-1,-2,-5,-4,3]=>[3,-4,-5,-2,-1]=>01111=>[1,4]
[-1,-2,-5,-4,-3]=>[-3,-4,-5,-2,-1]=>11111=>[5]
[1,3,2,4,5]=>[5,4,2,3,1]=>00000=>[5]
[1,3,2,4,-5]=>[-5,4,2,3,1]=>10000=>[1,4]
[1,3,2,-4,5]=>[5,-4,2,3,1]=>01000=>[1,1,3]
[1,3,2,-4,-5]=>[-5,-4,2,3,1]=>11000=>[2,3]
[1,3,-2,4,5]=>[5,4,-2,3,1]=>00100=>[2,1,2]
[1,3,-2,4,-5]=>[-5,4,-2,3,1]=>10100=>[1,1,1,2]
[1,3,-2,-4,5]=>[5,-4,-2,3,1]=>01100=>[1,2,2]
[1,3,-2,-4,-5]=>[-5,-4,-2,3,1]=>11100=>[3,2]
[1,-3,2,4,5]=>[5,4,2,-3,1]=>00010=>[3,1,1]
[1,-3,2,4,-5]=>[-5,4,2,-3,1]=>10010=>[1,2,1,1]
[1,-3,2,-4,5]=>[5,-4,2,-3,1]=>01010=>[1,1,1,1,1]
[1,-3,2,-4,-5]=>[-5,-4,2,-3,1]=>11010=>[2,1,1,1]
[1,-3,-2,4,5]=>[5,4,-2,-3,1]=>00110=>[2,2,1]
[1,-3,-2,4,-5]=>[-5,4,-2,-3,1]=>10110=>[1,1,2,1]
[1,-3,-2,-4,5]=>[5,-4,-2,-3,1]=>01110=>[1,3,1]
[1,-3,-2,-4,-5]=>[-5,-4,-2,-3,1]=>11110=>[4,1]
[-1,3,2,4,5]=>[5,4,2,3,-1]=>00001=>[4,1]
[-1,3,2,4,-5]=>[-5,4,2,3,-1]=>10001=>[1,3,1]
[-1,3,2,-4,5]=>[5,-4,2,3,-1]=>01001=>[1,1,2,1]
[-1,3,2,-4,-5]=>[-5,-4,2,3,-1]=>11001=>[2,2,1]
[-1,3,-2,4,5]=>[5,4,-2,3,-1]=>00101=>[2,1,1,1]
[-1,3,-2,4,-5]=>[-5,4,-2,3,-1]=>10101=>[1,1,1,1,1]
[-1,3,-2,-4,5]=>[5,-4,-2,3,-1]=>01101=>[1,2,1,1]
[-1,3,-2,-4,-5]=>[-5,-4,-2,3,-1]=>11101=>[3,1,1]
[-1,-3,2,4,5]=>[5,4,2,-3,-1]=>00011=>[3,2]
[-1,-3,2,4,-5]=>[-5,4,2,-3,-1]=>10011=>[1,2,2]
[-1,-3,2,-4,5]=>[5,-4,2,-3,-1]=>01011=>[1,1,1,2]
[-1,-3,2,-4,-5]=>[-5,-4,2,-3,-1]=>11011=>[2,1,2]
[-1,-3,-2,4,5]=>[5,4,-2,-3,-1]=>00111=>[2,3]
[-1,-3,-2,4,-5]=>[-5,4,-2,-3,-1]=>10111=>[1,1,3]
[-1,-3,-2,-4,5]=>[5,-4,-2,-3,-1]=>01111=>[1,4]
[-1,-3,-2,-4,-5]=>[-5,-4,-2,-3,-1]=>11111=>[5]
[1,3,2,5,4]=>[4,5,2,3,1]=>00000=>[5]
[1,3,2,5,-4]=>[-4,5,2,3,1]=>10000=>[1,4]
[1,3,2,-5,4]=>[4,-5,2,3,1]=>01000=>[1,1,3]
[1,3,2,-5,-4]=>[-4,-5,2,3,1]=>11000=>[2,3]
[1,3,-2,5,4]=>[4,5,-2,3,1]=>00100=>[2,1,2]
[1,3,-2,5,-4]=>[-4,5,-2,3,1]=>10100=>[1,1,1,2]
[1,3,-2,-5,4]=>[4,-5,-2,3,1]=>01100=>[1,2,2]
[1,3,-2,-5,-4]=>[-4,-5,-2,3,1]=>11100=>[3,2]
[1,-3,2,5,4]=>[4,5,2,-3,1]=>00010=>[3,1,1]
[1,-3,2,5,-4]=>[-4,5,2,-3,1]=>10010=>[1,2,1,1]
[1,-3,2,-5,4]=>[4,-5,2,-3,1]=>01010=>[1,1,1,1,1]
[1,-3,2,-5,-4]=>[-4,-5,2,-3,1]=>11010=>[2,1,1,1]
[1,-3,-2,5,4]=>[4,5,-2,-3,1]=>00110=>[2,2,1]
[1,-3,-2,5,-4]=>[-4,5,-2,-3,1]=>10110=>[1,1,2,1]
[1,-3,-2,-5,4]=>[4,-5,-2,-3,1]=>01110=>[1,3,1]
[1,-3,-2,-5,-4]=>[-4,-5,-2,-3,1]=>11110=>[4,1]
[-1,3,2,5,4]=>[4,5,2,3,-1]=>00001=>[4,1]
[-1,3,2,5,-4]=>[-4,5,2,3,-1]=>10001=>[1,3,1]
[-1,3,2,-5,4]=>[4,-5,2,3,-1]=>01001=>[1,1,2,1]
[-1,3,2,-5,-4]=>[-4,-5,2,3,-1]=>11001=>[2,2,1]
[-1,3,-2,5,4]=>[4,5,-2,3,-1]=>00101=>[2,1,1,1]
[-1,3,-2,5,-4]=>[-4,5,-2,3,-1]=>10101=>[1,1,1,1,1]
[-1,3,-2,-5,4]=>[4,-5,-2,3,-1]=>01101=>[1,2,1,1]
[-1,3,-2,-5,-4]=>[-4,-5,-2,3,-1]=>11101=>[3,1,1]
[-1,-3,2,5,4]=>[4,5,2,-3,-1]=>00011=>[3,2]
[-1,-3,2,5,-4]=>[-4,5,2,-3,-1]=>10011=>[1,2,2]
[-1,-3,2,-5,4]=>[4,-5,2,-3,-1]=>01011=>[1,1,1,2]
[-1,-3,2,-5,-4]=>[-4,-5,2,-3,-1]=>11011=>[2,1,2]
[-1,-3,-2,5,4]=>[4,5,-2,-3,-1]=>00111=>[2,3]
[-1,-3,-2,5,-4]=>[-4,5,-2,-3,-1]=>10111=>[1,1,3]
[-1,-3,-2,-5,4]=>[4,-5,-2,-3,-1]=>01111=>[1,4]
[-1,-3,-2,-5,-4]=>[-4,-5,-2,-3,-1]=>11111=>[5]
[1,3,4,2,5]=>[5,2,4,3,1]=>00000=>[5]
[1,3,4,2,-5]=>[-5,2,4,3,1]=>10000=>[1,4]
[1,3,4,-2,5]=>[5,-2,4,3,1]=>01000=>[1,1,3]
[1,3,4,-2,-5]=>[-5,-2,4,3,1]=>11000=>[2,3]
[1,3,-4,2,5]=>[5,2,-4,3,1]=>00100=>[2,1,2]
[1,3,-4,2,-5]=>[-5,2,-4,3,1]=>10100=>[1,1,1,2]
[1,3,-4,-2,5]=>[5,-2,-4,3,1]=>01100=>[1,2,2]
[1,3,-4,-2,-5]=>[-5,-2,-4,3,1]=>11100=>[3,2]
[1,-3,4,2,5]=>[5,2,4,-3,1]=>00010=>[3,1,1]
[1,-3,4,2,-5]=>[-5,2,4,-3,1]=>10010=>[1,2,1,1]
[1,-3,4,-2,5]=>[5,-2,4,-3,1]=>01010=>[1,1,1,1,1]
[1,-3,4,-2,-5]=>[-5,-2,4,-3,1]=>11010=>[2,1,1,1]
[1,-3,-4,2,5]=>[5,2,-4,-3,1]=>00110=>[2,2,1]
[1,-3,-4,2,-5]=>[-5,2,-4,-3,1]=>10110=>[1,1,2,1]
[1,-3,-4,-2,5]=>[5,-2,-4,-3,1]=>01110=>[1,3,1]
[1,-3,-4,-2,-5]=>[-5,-2,-4,-3,1]=>11110=>[4,1]
[-1,3,4,2,5]=>[5,2,4,3,-1]=>00001=>[4,1]
[-1,3,4,2,-5]=>[-5,2,4,3,-1]=>10001=>[1,3,1]
[-1,3,4,-2,5]=>[5,-2,4,3,-1]=>01001=>[1,1,2,1]
[-1,3,4,-2,-5]=>[-5,-2,4,3,-1]=>11001=>[2,2,1]
[-1,3,-4,2,5]=>[5,2,-4,3,-1]=>00101=>[2,1,1,1]
[-1,3,-4,2,-5]=>[-5,2,-4,3,-1]=>10101=>[1,1,1,1,1]
[-1,3,-4,-2,5]=>[5,-2,-4,3,-1]=>01101=>[1,2,1,1]
[-1,3,-4,-2,-5]=>[-5,-2,-4,3,-1]=>11101=>[3,1,1]
[-1,-3,4,2,5]=>[5,2,4,-3,-1]=>00011=>[3,2]
[-1,-3,4,2,-5]=>[-5,2,4,-3,-1]=>10011=>[1,2,2]
[-1,-3,4,-2,5]=>[5,-2,4,-3,-1]=>01011=>[1,1,1,2]
[-1,-3,4,-2,-5]=>[-5,-2,4,-3,-1]=>11011=>[2,1,2]
[-1,-3,-4,2,5]=>[5,2,-4,-3,-1]=>00111=>[2,3]
[-1,-3,-4,2,-5]=>[-5,2,-4,-3,-1]=>10111=>[1,1,3]
[-1,-3,-4,-2,5]=>[5,-2,-4,-3,-1]=>01111=>[1,4]
[-1,-3,-4,-2,-5]=>[-5,-2,-4,-3,-1]=>11111=>[5]
[1,3,4,5,2]=>[2,5,4,3,1]=>00000=>[5]
[1,3,4,5,-2]=>[-2,5,4,3,1]=>10000=>[1,4]
[1,3,4,-5,2]=>[2,-5,4,3,1]=>01000=>[1,1,3]
[1,3,4,-5,-2]=>[-2,-5,4,3,1]=>11000=>[2,3]
[1,3,-4,5,2]=>[2,5,-4,3,1]=>00100=>[2,1,2]
[1,3,-4,5,-2]=>[-2,5,-4,3,1]=>10100=>[1,1,1,2]
[1,3,-4,-5,2]=>[2,-5,-4,3,1]=>01100=>[1,2,2]
[1,3,-4,-5,-2]=>[-2,-5,-4,3,1]=>11100=>[3,2]
[1,-3,4,5,2]=>[2,5,4,-3,1]=>00010=>[3,1,1]
[1,-3,4,5,-2]=>[-2,5,4,-3,1]=>10010=>[1,2,1,1]
[1,-3,4,-5,2]=>[2,-5,4,-3,1]=>01010=>[1,1,1,1,1]
[1,-3,4,-5,-2]=>[-2,-5,4,-3,1]=>11010=>[2,1,1,1]
[1,-3,-4,5,2]=>[2,5,-4,-3,1]=>00110=>[2,2,1]
[1,-3,-4,5,-2]=>[-2,5,-4,-3,1]=>10110=>[1,1,2,1]
[1,-3,-4,-5,2]=>[2,-5,-4,-3,1]=>01110=>[1,3,1]
[1,-3,-4,-5,-2]=>[-2,-5,-4,-3,1]=>11110=>[4,1]
[-1,3,4,5,2]=>[2,5,4,3,-1]=>00001=>[4,1]
[-1,3,4,5,-2]=>[-2,5,4,3,-1]=>10001=>[1,3,1]
[-1,3,4,-5,2]=>[2,-5,4,3,-1]=>01001=>[1,1,2,1]
[-1,3,4,-5,-2]=>[-2,-5,4,3,-1]=>11001=>[2,2,1]
[-1,3,-4,5,2]=>[2,5,-4,3,-1]=>00101=>[2,1,1,1]
[-1,3,-4,5,-2]=>[-2,5,-4,3,-1]=>10101=>[1,1,1,1,1]
[-1,3,-4,-5,2]=>[2,-5,-4,3,-1]=>01101=>[1,2,1,1]
[-1,3,-4,-5,-2]=>[-2,-5,-4,3,-1]=>11101=>[3,1,1]
[-1,-3,4,5,2]=>[2,5,4,-3,-1]=>00011=>[3,2]
[-1,-3,4,5,-2]=>[-2,5,4,-3,-1]=>10011=>[1,2,2]
[-1,-3,4,-5,2]=>[2,-5,4,-3,-1]=>01011=>[1,1,1,2]
[-1,-3,4,-5,-2]=>[-2,-5,4,-3,-1]=>11011=>[2,1,2]
[-1,-3,-4,5,2]=>[2,5,-4,-3,-1]=>00111=>[2,3]
[-1,-3,-4,5,-2]=>[-2,5,-4,-3,-1]=>10111=>[1,1,3]
[-1,-3,-4,-5,2]=>[2,-5,-4,-3,-1]=>01111=>[1,4]
[-1,-3,-4,-5,-2]=>[-2,-5,-4,-3,-1]=>11111=>[5]
[1,3,5,2,4]=>[4,2,5,3,1]=>00000=>[5]
[1,3,5,2,-4]=>[-4,2,5,3,1]=>10000=>[1,4]
[1,3,5,-2,4]=>[4,-2,5,3,1]=>01000=>[1,1,3]
[1,3,5,-2,-4]=>[-4,-2,5,3,1]=>11000=>[2,3]
[1,3,-5,2,4]=>[4,2,-5,3,1]=>00100=>[2,1,2]
[1,3,-5,2,-4]=>[-4,2,-5,3,1]=>10100=>[1,1,1,2]
[1,3,-5,-2,4]=>[4,-2,-5,3,1]=>01100=>[1,2,2]
[1,3,-5,-2,-4]=>[-4,-2,-5,3,1]=>11100=>[3,2]
[1,-3,5,2,4]=>[4,2,5,-3,1]=>00010=>[3,1,1]
[1,-3,5,2,-4]=>[-4,2,5,-3,1]=>10010=>[1,2,1,1]
[1,-3,5,-2,4]=>[4,-2,5,-3,1]=>01010=>[1,1,1,1,1]
[1,-3,5,-2,-4]=>[-4,-2,5,-3,1]=>11010=>[2,1,1,1]
[1,-3,-5,2,4]=>[4,2,-5,-3,1]=>00110=>[2,2,1]
[1,-3,-5,2,-4]=>[-4,2,-5,-3,1]=>10110=>[1,1,2,1]
[1,-3,-5,-2,4]=>[4,-2,-5,-3,1]=>01110=>[1,3,1]
[1,-3,-5,-2,-4]=>[-4,-2,-5,-3,1]=>11110=>[4,1]
[-1,3,5,2,4]=>[4,2,5,3,-1]=>00001=>[4,1]
[-1,3,5,2,-4]=>[-4,2,5,3,-1]=>10001=>[1,3,1]
[-1,3,5,-2,4]=>[4,-2,5,3,-1]=>01001=>[1,1,2,1]
[-1,3,5,-2,-4]=>[-4,-2,5,3,-1]=>11001=>[2,2,1]
[-1,3,-5,2,4]=>[4,2,-5,3,-1]=>00101=>[2,1,1,1]
[-1,3,-5,2,-4]=>[-4,2,-5,3,-1]=>10101=>[1,1,1,1,1]
[-1,3,-5,-2,4]=>[4,-2,-5,3,-1]=>01101=>[1,2,1,1]
[-1,3,-5,-2,-4]=>[-4,-2,-5,3,-1]=>11101=>[3,1,1]
[-1,-3,5,2,4]=>[4,2,5,-3,-1]=>00011=>[3,2]
[-1,-3,5,2,-4]=>[-4,2,5,-3,-1]=>10011=>[1,2,2]
[-1,-3,5,-2,4]=>[4,-2,5,-3,-1]=>01011=>[1,1,1,2]
[-1,-3,5,-2,-4]=>[-4,-2,5,-3,-1]=>11011=>[2,1,2]
[-1,-3,-5,2,4]=>[4,2,-5,-3,-1]=>00111=>[2,3]
[-1,-3,-5,2,-4]=>[-4,2,-5,-3,-1]=>10111=>[1,1,3]
[-1,-3,-5,-2,4]=>[4,-2,-5,-3,-1]=>01111=>[1,4]
[-1,-3,-5,-2,-4]=>[-4,-2,-5,-3,-1]=>11111=>[5]
[1,3,5,4,2]=>[2,4,5,3,1]=>00000=>[5]
[1,3,5,4,-2]=>[-2,4,5,3,1]=>10000=>[1,4]
[1,3,5,-4,2]=>[2,-4,5,3,1]=>01000=>[1,1,3]
[1,3,5,-4,-2]=>[-2,-4,5,3,1]=>11000=>[2,3]
[1,3,-5,4,2]=>[2,4,-5,3,1]=>00100=>[2,1,2]
[1,3,-5,4,-2]=>[-2,4,-5,3,1]=>10100=>[1,1,1,2]
[1,3,-5,-4,2]=>[2,-4,-5,3,1]=>01100=>[1,2,2]
[1,3,-5,-4,-2]=>[-2,-4,-5,3,1]=>11100=>[3,2]
[1,-3,5,4,2]=>[2,4,5,-3,1]=>00010=>[3,1,1]
[1,-3,5,4,-2]=>[-2,4,5,-3,1]=>10010=>[1,2,1,1]
[1,-3,5,-4,2]=>[2,-4,5,-3,1]=>01010=>[1,1,1,1,1]
[1,-3,5,-4,-2]=>[-2,-4,5,-3,1]=>11010=>[2,1,1,1]
[1,-3,-5,4,2]=>[2,4,-5,-3,1]=>00110=>[2,2,1]
[1,-3,-5,4,-2]=>[-2,4,-5,-3,1]=>10110=>[1,1,2,1]
[1,-3,-5,-4,2]=>[2,-4,-5,-3,1]=>01110=>[1,3,1]
[1,-3,-5,-4,-2]=>[-2,-4,-5,-3,1]=>11110=>[4,1]
[-1,3,5,4,2]=>[2,4,5,3,-1]=>00001=>[4,1]
[-1,3,5,4,-2]=>[-2,4,5,3,-1]=>10001=>[1,3,1]
[-1,3,5,-4,2]=>[2,-4,5,3,-1]=>01001=>[1,1,2,1]
[-1,3,5,-4,-2]=>[-2,-4,5,3,-1]=>11001=>[2,2,1]
[-1,3,-5,4,2]=>[2,4,-5,3,-1]=>00101=>[2,1,1,1]
[-1,3,-5,4,-2]=>[-2,4,-5,3,-1]=>10101=>[1,1,1,1,1]
[-1,3,-5,-4,2]=>[2,-4,-5,3,-1]=>01101=>[1,2,1,1]
[-1,3,-5,-4,-2]=>[-2,-4,-5,3,-1]=>11101=>[3,1,1]
[-1,-3,5,4,2]=>[2,4,5,-3,-1]=>00011=>[3,2]
[-1,-3,5,4,-2]=>[-2,4,5,-3,-1]=>10011=>[1,2,2]
[-1,-3,5,-4,2]=>[2,-4,5,-3,-1]=>01011=>[1,1,1,2]
[-1,-3,5,-4,-2]=>[-2,-4,5,-3,-1]=>11011=>[2,1,2]
[-1,-3,-5,4,2]=>[2,4,-5,-3,-1]=>00111=>[2,3]
[-1,-3,-5,4,-2]=>[-2,4,-5,-3,-1]=>10111=>[1,1,3]
[-1,-3,-5,-4,2]=>[2,-4,-5,-3,-1]=>01111=>[1,4]
[-1,-3,-5,-4,-2]=>[-2,-4,-5,-3,-1]=>11111=>[5]
[1,4,2,3,5]=>[5,3,2,4,1]=>00000=>[5]
[1,4,2,3,-5]=>[-5,3,2,4,1]=>10000=>[1,4]
[1,4,2,-3,5]=>[5,-3,2,4,1]=>01000=>[1,1,3]
[1,4,2,-3,-5]=>[-5,-3,2,4,1]=>11000=>[2,3]
[1,4,-2,3,5]=>[5,3,-2,4,1]=>00100=>[2,1,2]
[1,4,-2,3,-5]=>[-5,3,-2,4,1]=>10100=>[1,1,1,2]
[1,4,-2,-3,5]=>[5,-3,-2,4,1]=>01100=>[1,2,2]
[1,4,-2,-3,-5]=>[-5,-3,-2,4,1]=>11100=>[3,2]
[1,-4,2,3,5]=>[5,3,2,-4,1]=>00010=>[3,1,1]
[1,-4,2,3,-5]=>[-5,3,2,-4,1]=>10010=>[1,2,1,1]
[1,-4,2,-3,5]=>[5,-3,2,-4,1]=>01010=>[1,1,1,1,1]
[1,-4,2,-3,-5]=>[-5,-3,2,-4,1]=>11010=>[2,1,1,1]
[1,-4,-2,3,5]=>[5,3,-2,-4,1]=>00110=>[2,2,1]
[1,-4,-2,3,-5]=>[-5,3,-2,-4,1]=>10110=>[1,1,2,1]
[1,-4,-2,-3,5]=>[5,-3,-2,-4,1]=>01110=>[1,3,1]
[1,-4,-2,-3,-5]=>[-5,-3,-2,-4,1]=>11110=>[4,1]
[-1,4,2,3,5]=>[5,3,2,4,-1]=>00001=>[4,1]
[-1,4,2,3,-5]=>[-5,3,2,4,-1]=>10001=>[1,3,1]
[-1,4,2,-3,5]=>[5,-3,2,4,-1]=>01001=>[1,1,2,1]
[-1,4,2,-3,-5]=>[-5,-3,2,4,-1]=>11001=>[2,2,1]
[-1,4,-2,3,5]=>[5,3,-2,4,-1]=>00101=>[2,1,1,1]
[-1,4,-2,3,-5]=>[-5,3,-2,4,-1]=>10101=>[1,1,1,1,1]
[-1,4,-2,-3,5]=>[5,-3,-2,4,-1]=>01101=>[1,2,1,1]
[-1,4,-2,-3,-5]=>[-5,-3,-2,4,-1]=>11101=>[3,1,1]
[-1,-4,2,3,5]=>[5,3,2,-4,-1]=>00011=>[3,2]
[-1,-4,2,3,-5]=>[-5,3,2,-4,-1]=>10011=>[1,2,2]
[-1,-4,2,-3,5]=>[5,-3,2,-4,-1]=>01011=>[1,1,1,2]
[-1,-4,2,-3,-5]=>[-5,-3,2,-4,-1]=>11011=>[2,1,2]
[-1,-4,-2,3,5]=>[5,3,-2,-4,-1]=>00111=>[2,3]
[-1,-4,-2,3,-5]=>[-5,3,-2,-4,-1]=>10111=>[1,1,3]
[-1,-4,-2,-3,5]=>[5,-3,-2,-4,-1]=>01111=>[1,4]
[-1,-4,-2,-3,-5]=>[-5,-3,-2,-4,-1]=>11111=>[5]
[1,4,2,5,3]=>[3,5,2,4,1]=>00000=>[5]
[1,4,2,5,-3]=>[-3,5,2,4,1]=>10000=>[1,4]
[1,4,2,-5,3]=>[3,-5,2,4,1]=>01000=>[1,1,3]
[1,4,2,-5,-3]=>[-3,-5,2,4,1]=>11000=>[2,3]
[1,4,-2,5,3]=>[3,5,-2,4,1]=>00100=>[2,1,2]
[1,4,-2,5,-3]=>[-3,5,-2,4,1]=>10100=>[1,1,1,2]
[1,4,-2,-5,3]=>[3,-5,-2,4,1]=>01100=>[1,2,2]
[1,4,-2,-5,-3]=>[-3,-5,-2,4,1]=>11100=>[3,2]
[1,-4,2,5,3]=>[3,5,2,-4,1]=>00010=>[3,1,1]
[1,-4,2,5,-3]=>[-3,5,2,-4,1]=>10010=>[1,2,1,1]
[1,-4,2,-5,3]=>[3,-5,2,-4,1]=>01010=>[1,1,1,1,1]
[1,-4,2,-5,-3]=>[-3,-5,2,-4,1]=>11010=>[2,1,1,1]
[1,-4,-2,5,3]=>[3,5,-2,-4,1]=>00110=>[2,2,1]
[1,-4,-2,5,-3]=>[-3,5,-2,-4,1]=>10110=>[1,1,2,1]
[1,-4,-2,-5,3]=>[3,-5,-2,-4,1]=>01110=>[1,3,1]
[1,-4,-2,-5,-3]=>[-3,-5,-2,-4,1]=>11110=>[4,1]
[-1,4,2,5,3]=>[3,5,2,4,-1]=>00001=>[4,1]
[-1,4,2,5,-3]=>[-3,5,2,4,-1]=>10001=>[1,3,1]
[-1,4,2,-5,3]=>[3,-5,2,4,-1]=>01001=>[1,1,2,1]
[-1,4,2,-5,-3]=>[-3,-5,2,4,-1]=>11001=>[2,2,1]
[-1,4,-2,5,3]=>[3,5,-2,4,-1]=>00101=>[2,1,1,1]
[-1,4,-2,5,-3]=>[-3,5,-2,4,-1]=>10101=>[1,1,1,1,1]
[-1,4,-2,-5,3]=>[3,-5,-2,4,-1]=>01101=>[1,2,1,1]
[-1,4,-2,-5,-3]=>[-3,-5,-2,4,-1]=>11101=>[3,1,1]
[-1,-4,2,5,3]=>[3,5,2,-4,-1]=>00011=>[3,2]
[-1,-4,2,5,-3]=>[-3,5,2,-4,-1]=>10011=>[1,2,2]
[-1,-4,2,-5,3]=>[3,-5,2,-4,-1]=>01011=>[1,1,1,2]
[-1,-4,2,-5,-3]=>[-3,-5,2,-4,-1]=>11011=>[2,1,2]
[-1,-4,-2,5,3]=>[3,5,-2,-4,-1]=>00111=>[2,3]
[-1,-4,-2,5,-3]=>[-3,5,-2,-4,-1]=>10111=>[1,1,3]
[-1,-4,-2,-5,3]=>[3,-5,-2,-4,-1]=>01111=>[1,4]
[-1,-4,-2,-5,-3]=>[-3,-5,-2,-4,-1]=>11111=>[5]
[1,4,3,2,5]=>[5,2,3,4,1]=>00000=>[5]
[1,4,3,2,-5]=>[-5,2,3,4,1]=>10000=>[1,4]
[1,4,3,-2,5]=>[5,-2,3,4,1]=>01000=>[1,1,3]
[1,4,3,-2,-5]=>[-5,-2,3,4,1]=>11000=>[2,3]
[1,4,-3,2,5]=>[5,2,-3,4,1]=>00100=>[2,1,2]
[1,4,-3,2,-5]=>[-5,2,-3,4,1]=>10100=>[1,1,1,2]
[1,4,-3,-2,5]=>[5,-2,-3,4,1]=>01100=>[1,2,2]
[1,4,-3,-2,-5]=>[-5,-2,-3,4,1]=>11100=>[3,2]
[1,-4,3,2,5]=>[5,2,3,-4,1]=>00010=>[3,1,1]
[1,-4,3,2,-5]=>[-5,2,3,-4,1]=>10010=>[1,2,1,1]
[1,-4,3,-2,5]=>[5,-2,3,-4,1]=>01010=>[1,1,1,1,1]
[1,-4,3,-2,-5]=>[-5,-2,3,-4,1]=>11010=>[2,1,1,1]
[1,-4,-3,2,5]=>[5,2,-3,-4,1]=>00110=>[2,2,1]
[1,-4,-3,2,-5]=>[-5,2,-3,-4,1]=>10110=>[1,1,2,1]
[1,-4,-3,-2,5]=>[5,-2,-3,-4,1]=>01110=>[1,3,1]
[1,-4,-3,-2,-5]=>[-5,-2,-3,-4,1]=>11110=>[4,1]
[-1,4,3,2,5]=>[5,2,3,4,-1]=>00001=>[4,1]
[-1,4,3,2,-5]=>[-5,2,3,4,-1]=>10001=>[1,3,1]
[-1,4,3,-2,5]=>[5,-2,3,4,-1]=>01001=>[1,1,2,1]
[-1,4,3,-2,-5]=>[-5,-2,3,4,-1]=>11001=>[2,2,1]
[-1,4,-3,2,5]=>[5,2,-3,4,-1]=>00101=>[2,1,1,1]
[-1,4,-3,2,-5]=>[-5,2,-3,4,-1]=>10101=>[1,1,1,1,1]
[-1,4,-3,-2,5]=>[5,-2,-3,4,-1]=>01101=>[1,2,1,1]
[-1,4,-3,-2,-5]=>[-5,-2,-3,4,-1]=>11101=>[3,1,1]
[-1,-4,3,2,5]=>[5,2,3,-4,-1]=>00011=>[3,2]
[-1,-4,3,2,-5]=>[-5,2,3,-4,-1]=>10011=>[1,2,2]
[-1,-4,3,-2,5]=>[5,-2,3,-4,-1]=>01011=>[1,1,1,2]
[-1,-4,3,-2,-5]=>[-5,-2,3,-4,-1]=>11011=>[2,1,2]
[-1,-4,-3,2,5]=>[5,2,-3,-4,-1]=>00111=>[2,3]
[-1,-4,-3,2,-5]=>[-5,2,-3,-4,-1]=>10111=>[1,1,3]
[-1,-4,-3,-2,5]=>[5,-2,-3,-4,-1]=>01111=>[1,4]
[-1,-4,-3,-2,-5]=>[-5,-2,-3,-4,-1]=>11111=>[5]
[1,4,3,5,2]=>[2,5,3,4,1]=>00000=>[5]
[1,4,3,5,-2]=>[-2,5,3,4,1]=>10000=>[1,4]
[1,4,3,-5,2]=>[2,-5,3,4,1]=>01000=>[1,1,3]
[1,4,3,-5,-2]=>[-2,-5,3,4,1]=>11000=>[2,3]
[1,4,-3,5,2]=>[2,5,-3,4,1]=>00100=>[2,1,2]
[1,4,-3,5,-2]=>[-2,5,-3,4,1]=>10100=>[1,1,1,2]
[1,4,-3,-5,2]=>[2,-5,-3,4,1]=>01100=>[1,2,2]
[1,4,-3,-5,-2]=>[-2,-5,-3,4,1]=>11100=>[3,2]
[1,-4,3,5,2]=>[2,5,3,-4,1]=>00010=>[3,1,1]
[1,-4,3,5,-2]=>[-2,5,3,-4,1]=>10010=>[1,2,1,1]
[1,-4,3,-5,2]=>[2,-5,3,-4,1]=>01010=>[1,1,1,1,1]
[1,-4,3,-5,-2]=>[-2,-5,3,-4,1]=>11010=>[2,1,1,1]
[1,-4,-3,5,2]=>[2,5,-3,-4,1]=>00110=>[2,2,1]
[1,-4,-3,5,-2]=>[-2,5,-3,-4,1]=>10110=>[1,1,2,1]
[1,-4,-3,-5,2]=>[2,-5,-3,-4,1]=>01110=>[1,3,1]
[1,-4,-3,-5,-2]=>[-2,-5,-3,-4,1]=>11110=>[4,1]
[-1,4,3,5,2]=>[2,5,3,4,-1]=>00001=>[4,1]
[-1,4,3,5,-2]=>[-2,5,3,4,-1]=>10001=>[1,3,1]
[-1,4,3,-5,2]=>[2,-5,3,4,-1]=>01001=>[1,1,2,1]
[-1,4,3,-5,-2]=>[-2,-5,3,4,-1]=>11001=>[2,2,1]
[-1,4,-3,5,2]=>[2,5,-3,4,-1]=>00101=>[2,1,1,1]
[-1,4,-3,5,-2]=>[-2,5,-3,4,-1]=>10101=>[1,1,1,1,1]
[-1,4,-3,-5,2]=>[2,-5,-3,4,-1]=>01101=>[1,2,1,1]
[-1,4,-3,-5,-2]=>[-2,-5,-3,4,-1]=>11101=>[3,1,1]
[-1,-4,3,5,2]=>[2,5,3,-4,-1]=>00011=>[3,2]
[-1,-4,3,5,-2]=>[-2,5,3,-4,-1]=>10011=>[1,2,2]
[-1,-4,3,-5,2]=>[2,-5,3,-4,-1]=>01011=>[1,1,1,2]
[-1,-4,3,-5,-2]=>[-2,-5,3,-4,-1]=>11011=>[2,1,2]
[-1,-4,-3,5,2]=>[2,5,-3,-4,-1]=>00111=>[2,3]
[-1,-4,-3,5,-2]=>[-2,5,-3,-4,-1]=>10111=>[1,1,3]
[-1,-4,-3,-5,2]=>[2,-5,-3,-4,-1]=>01111=>[1,4]
[-1,-4,-3,-5,-2]=>[-2,-5,-3,-4,-1]=>11111=>[5]
[1,4,5,2,3]=>[3,2,5,4,1]=>00000=>[5]
[1,4,5,2,-3]=>[-3,2,5,4,1]=>10000=>[1,4]
[1,4,5,-2,3]=>[3,-2,5,4,1]=>01000=>[1,1,3]
[1,4,5,-2,-3]=>[-3,-2,5,4,1]=>11000=>[2,3]
[1,4,-5,2,3]=>[3,2,-5,4,1]=>00100=>[2,1,2]
[1,4,-5,2,-3]=>[-3,2,-5,4,1]=>10100=>[1,1,1,2]
[1,4,-5,-2,3]=>[3,-2,-5,4,1]=>01100=>[1,2,2]
[1,4,-5,-2,-3]=>[-3,-2,-5,4,1]=>11100=>[3,2]
[1,-4,5,2,3]=>[3,2,5,-4,1]=>00010=>[3,1,1]
[1,-4,5,2,-3]=>[-3,2,5,-4,1]=>10010=>[1,2,1,1]
[1,-4,5,-2,3]=>[3,-2,5,-4,1]=>01010=>[1,1,1,1,1]
[1,-4,5,-2,-3]=>[-3,-2,5,-4,1]=>11010=>[2,1,1,1]
[1,-4,-5,2,3]=>[3,2,-5,-4,1]=>00110=>[2,2,1]
[1,-4,-5,2,-3]=>[-3,2,-5,-4,1]=>10110=>[1,1,2,1]
[1,-4,-5,-2,3]=>[3,-2,-5,-4,1]=>01110=>[1,3,1]
[1,-4,-5,-2,-3]=>[-3,-2,-5,-4,1]=>11110=>[4,1]
[-1,4,5,2,3]=>[3,2,5,4,-1]=>00001=>[4,1]
[-1,4,5,2,-3]=>[-3,2,5,4,-1]=>10001=>[1,3,1]
[-1,4,5,-2,3]=>[3,-2,5,4,-1]=>01001=>[1,1,2,1]
[-1,4,5,-2,-3]=>[-3,-2,5,4,-1]=>11001=>[2,2,1]
[-1,4,-5,2,3]=>[3,2,-5,4,-1]=>00101=>[2,1,1,1]
[-1,4,-5,2,-3]=>[-3,2,-5,4,-1]=>10101=>[1,1,1,1,1]
[-1,4,-5,-2,3]=>[3,-2,-5,4,-1]=>01101=>[1,2,1,1]
[-1,4,-5,-2,-3]=>[-3,-2,-5,4,-1]=>11101=>[3,1,1]
[-1,-4,5,2,3]=>[3,2,5,-4,-1]=>00011=>[3,2]
[-1,-4,5,2,-3]=>[-3,2,5,-4,-1]=>10011=>[1,2,2]
[-1,-4,5,-2,3]=>[3,-2,5,-4,-1]=>01011=>[1,1,1,2]
[-1,-4,5,-2,-3]=>[-3,-2,5,-4,-1]=>11011=>[2,1,2]
[-1,-4,-5,2,3]=>[3,2,-5,-4,-1]=>00111=>[2,3]
[-1,-4,-5,2,-3]=>[-3,2,-5,-4,-1]=>10111=>[1,1,3]
[-1,-4,-5,-2,3]=>[3,-2,-5,-4,-1]=>01111=>[1,4]
[-1,-4,-5,-2,-3]=>[-3,-2,-5,-4,-1]=>11111=>[5]
[1,4,5,3,2]=>[2,3,5,4,1]=>00000=>[5]
[1,4,5,3,-2]=>[-2,3,5,4,1]=>10000=>[1,4]
[1,4,5,-3,2]=>[2,-3,5,4,1]=>01000=>[1,1,3]
[1,4,5,-3,-2]=>[-2,-3,5,4,1]=>11000=>[2,3]
[1,4,-5,3,2]=>[2,3,-5,4,1]=>00100=>[2,1,2]
[1,4,-5,3,-2]=>[-2,3,-5,4,1]=>10100=>[1,1,1,2]
[1,4,-5,-3,2]=>[2,-3,-5,4,1]=>01100=>[1,2,2]
[1,4,-5,-3,-2]=>[-2,-3,-5,4,1]=>11100=>[3,2]
[1,-4,5,3,2]=>[2,3,5,-4,1]=>00010=>[3,1,1]
[1,-4,5,3,-2]=>[-2,3,5,-4,1]=>10010=>[1,2,1,1]
[1,-4,5,-3,2]=>[2,-3,5,-4,1]=>01010=>[1,1,1,1,1]
[1,-4,5,-3,-2]=>[-2,-3,5,-4,1]=>11010=>[2,1,1,1]
[1,-4,-5,3,2]=>[2,3,-5,-4,1]=>00110=>[2,2,1]
[1,-4,-5,3,-2]=>[-2,3,-5,-4,1]=>10110=>[1,1,2,1]
[1,-4,-5,-3,2]=>[2,-3,-5,-4,1]=>01110=>[1,3,1]
[1,-4,-5,-3,-2]=>[-2,-3,-5,-4,1]=>11110=>[4,1]
[-1,4,5,3,2]=>[2,3,5,4,-1]=>00001=>[4,1]
[-1,4,5,3,-2]=>[-2,3,5,4,-1]=>10001=>[1,3,1]
[-1,4,5,-3,2]=>[2,-3,5,4,-1]=>01001=>[1,1,2,1]
[-1,4,5,-3,-2]=>[-2,-3,5,4,-1]=>11001=>[2,2,1]
[-1,4,-5,3,2]=>[2,3,-5,4,-1]=>00101=>[2,1,1,1]
[-1,4,-5,3,-2]=>[-2,3,-5,4,-1]=>10101=>[1,1,1,1,1]
[-1,4,-5,-3,2]=>[2,-3,-5,4,-1]=>01101=>[1,2,1,1]
[-1,4,-5,-3,-2]=>[-2,-3,-5,4,-1]=>11101=>[3,1,1]
[-1,-4,5,3,2]=>[2,3,5,-4,-1]=>00011=>[3,2]
[-1,-4,5,3,-2]=>[-2,3,5,-4,-1]=>10011=>[1,2,2]
[-1,-4,5,-3,2]=>[2,-3,5,-4,-1]=>01011=>[1,1,1,2]
[-1,-4,5,-3,-2]=>[-2,-3,5,-4,-1]=>11011=>[2,1,2]
[-1,-4,-5,3,2]=>[2,3,-5,-4,-1]=>00111=>[2,3]
[-1,-4,-5,3,-2]=>[-2,3,-5,-4,-1]=>10111=>[1,1,3]
[-1,-4,-5,-3,2]=>[2,-3,-5,-4,-1]=>01111=>[1,4]
[-1,-4,-5,-3,-2]=>[-2,-3,-5,-4,-1]=>11111=>[5]
[1,5,2,3,4]=>[4,3,2,5,1]=>00000=>[5]
[1,5,2,3,-4]=>[-4,3,2,5,1]=>10000=>[1,4]
[1,5,2,-3,4]=>[4,-3,2,5,1]=>01000=>[1,1,3]
[1,5,2,-3,-4]=>[-4,-3,2,5,1]=>11000=>[2,3]
[1,5,-2,3,4]=>[4,3,-2,5,1]=>00100=>[2,1,2]
[1,5,-2,3,-4]=>[-4,3,-2,5,1]=>10100=>[1,1,1,2]
[1,5,-2,-3,4]=>[4,-3,-2,5,1]=>01100=>[1,2,2]
[1,5,-2,-3,-4]=>[-4,-3,-2,5,1]=>11100=>[3,2]
[1,-5,2,3,4]=>[4,3,2,-5,1]=>00010=>[3,1,1]
[1,-5,2,3,-4]=>[-4,3,2,-5,1]=>10010=>[1,2,1,1]
[1,-5,2,-3,4]=>[4,-3,2,-5,1]=>01010=>[1,1,1,1,1]
[1,-5,2,-3,-4]=>[-4,-3,2,-5,1]=>11010=>[2,1,1,1]
[1,-5,-2,3,4]=>[4,3,-2,-5,1]=>00110=>[2,2,1]
[1,-5,-2,3,-4]=>[-4,3,-2,-5,1]=>10110=>[1,1,2,1]
[1,-5,-2,-3,4]=>[4,-3,-2,-5,1]=>01110=>[1,3,1]
[1,-5,-2,-3,-4]=>[-4,-3,-2,-5,1]=>11110=>[4,1]
[-1,5,2,3,4]=>[4,3,2,5,-1]=>00001=>[4,1]
[-1,5,2,3,-4]=>[-4,3,2,5,-1]=>10001=>[1,3,1]
[-1,5,2,-3,4]=>[4,-3,2,5,-1]=>01001=>[1,1,2,1]
[-1,5,2,-3,-4]=>[-4,-3,2,5,-1]=>11001=>[2,2,1]
[-1,5,-2,3,4]=>[4,3,-2,5,-1]=>00101=>[2,1,1,1]
[-1,5,-2,3,-4]=>[-4,3,-2,5,-1]=>10101=>[1,1,1,1,1]
[-1,5,-2,-3,4]=>[4,-3,-2,5,-1]=>01101=>[1,2,1,1]
[-1,5,-2,-3,-4]=>[-4,-3,-2,5,-1]=>11101=>[3,1,1]
[-1,-5,2,3,4]=>[4,3,2,-5,-1]=>00011=>[3,2]
[-1,-5,2,3,-4]=>[-4,3,2,-5,-1]=>10011=>[1,2,2]
[-1,-5,2,-3,4]=>[4,-3,2,-5,-1]=>01011=>[1,1,1,2]
[-1,-5,2,-3,-4]=>[-4,-3,2,-5,-1]=>11011=>[2,1,2]
[-1,-5,-2,3,4]=>[4,3,-2,-5,-1]=>00111=>[2,3]
[-1,-5,-2,3,-4]=>[-4,3,-2,-5,-1]=>10111=>[1,1,3]
[-1,-5,-2,-3,4]=>[4,-3,-2,-5,-1]=>01111=>[1,4]
[-1,-5,-2,-3,-4]=>[-4,-3,-2,-5,-1]=>11111=>[5]
[1,5,2,4,3]=>[3,4,2,5,1]=>00000=>[5]
[1,5,2,4,-3]=>[-3,4,2,5,1]=>10000=>[1,4]
[1,5,2,-4,3]=>[3,-4,2,5,1]=>01000=>[1,1,3]
[1,5,2,-4,-3]=>[-3,-4,2,5,1]=>11000=>[2,3]
[1,5,-2,4,3]=>[3,4,-2,5,1]=>00100=>[2,1,2]
[1,5,-2,4,-3]=>[-3,4,-2,5,1]=>10100=>[1,1,1,2]
[1,5,-2,-4,3]=>[3,-4,-2,5,1]=>01100=>[1,2,2]
[1,5,-2,-4,-3]=>[-3,-4,-2,5,1]=>11100=>[3,2]
[1,-5,2,4,3]=>[3,4,2,-5,1]=>00010=>[3,1,1]
[1,-5,2,4,-3]=>[-3,4,2,-5,1]=>10010=>[1,2,1,1]
[1,-5,2,-4,3]=>[3,-4,2,-5,1]=>01010=>[1,1,1,1,1]
[1,-5,2,-4,-3]=>[-3,-4,2,-5,1]=>11010=>[2,1,1,1]
[1,-5,-2,4,3]=>[3,4,-2,-5,1]=>00110=>[2,2,1]
[1,-5,-2,4,-3]=>[-3,4,-2,-5,1]=>10110=>[1,1,2,1]
[1,-5,-2,-4,3]=>[3,-4,-2,-5,1]=>01110=>[1,3,1]
[1,-5,-2,-4,-3]=>[-3,-4,-2,-5,1]=>11110=>[4,1]
[-1,5,2,4,3]=>[3,4,2,5,-1]=>00001=>[4,1]
[-1,5,2,4,-3]=>[-3,4,2,5,-1]=>10001=>[1,3,1]
[-1,5,2,-4,3]=>[3,-4,2,5,-1]=>01001=>[1,1,2,1]
[-1,5,2,-4,-3]=>[-3,-4,2,5,-1]=>11001=>[2,2,1]
[-1,5,-2,4,3]=>[3,4,-2,5,-1]=>00101=>[2,1,1,1]
[-1,5,-2,4,-3]=>[-3,4,-2,5,-1]=>10101=>[1,1,1,1,1]
[-1,5,-2,-4,3]=>[3,-4,-2,5,-1]=>01101=>[1,2,1,1]
[-1,5,-2,-4,-3]=>[-3,-4,-2,5,-1]=>11101=>[3,1,1]
[-1,-5,2,4,3]=>[3,4,2,-5,-1]=>00011=>[3,2]
[-1,-5,2,4,-3]=>[-3,4,2,-5,-1]=>10011=>[1,2,2]
[-1,-5,2,-4,3]=>[3,-4,2,-5,-1]=>01011=>[1,1,1,2]
[-1,-5,2,-4,-3]=>[-3,-4,2,-5,-1]=>11011=>[2,1,2]
[-1,-5,-2,4,3]=>[3,4,-2,-5,-1]=>00111=>[2,3]
[-1,-5,-2,4,-3]=>[-3,4,-2,-5,-1]=>10111=>[1,1,3]
[-1,-5,-2,-4,3]=>[3,-4,-2,-5,-1]=>01111=>[1,4]
[-1,-5,-2,-4,-3]=>[-3,-4,-2,-5,-1]=>11111=>[5]
[1,5,3,2,4]=>[4,2,3,5,1]=>00000=>[5]
[1,5,3,2,-4]=>[-4,2,3,5,1]=>10000=>[1,4]
[1,5,3,-2,4]=>[4,-2,3,5,1]=>01000=>[1,1,3]
[1,5,3,-2,-4]=>[-4,-2,3,5,1]=>11000=>[2,3]
[1,5,-3,2,4]=>[4,2,-3,5,1]=>00100=>[2,1,2]
[1,5,-3,2,-4]=>[-4,2,-3,5,1]=>10100=>[1,1,1,2]
[1,5,-3,-2,4]=>[4,-2,-3,5,1]=>01100=>[1,2,2]
[1,5,-3,-2,-4]=>[-4,-2,-3,5,1]=>11100=>[3,2]
[1,-5,3,2,4]=>[4,2,3,-5,1]=>00010=>[3,1,1]
[1,-5,3,2,-4]=>[-4,2,3,-5,1]=>10010=>[1,2,1,1]
[1,-5,3,-2,4]=>[4,-2,3,-5,1]=>01010=>[1,1,1,1,1]
[1,-5,3,-2,-4]=>[-4,-2,3,-5,1]=>11010=>[2,1,1,1]
[1,-5,-3,2,4]=>[4,2,-3,-5,1]=>00110=>[2,2,1]
[1,-5,-3,2,-4]=>[-4,2,-3,-5,1]=>10110=>[1,1,2,1]
[1,-5,-3,-2,4]=>[4,-2,-3,-5,1]=>01110=>[1,3,1]
[1,-5,-3,-2,-4]=>[-4,-2,-3,-5,1]=>11110=>[4,1]
[-1,5,3,2,4]=>[4,2,3,5,-1]=>00001=>[4,1]
[-1,5,3,2,-4]=>[-4,2,3,5,-1]=>10001=>[1,3,1]
[-1,5,3,-2,4]=>[4,-2,3,5,-1]=>01001=>[1,1,2,1]
[-1,5,3,-2,-4]=>[-4,-2,3,5,-1]=>11001=>[2,2,1]
[-1,5,-3,2,4]=>[4,2,-3,5,-1]=>00101=>[2,1,1,1]
[-1,5,-3,2,-4]=>[-4,2,-3,5,-1]=>10101=>[1,1,1,1,1]
[-1,5,-3,-2,4]=>[4,-2,-3,5,-1]=>01101=>[1,2,1,1]
[-1,5,-3,-2,-4]=>[-4,-2,-3,5,-1]=>11101=>[3,1,1]
[-1,-5,3,2,4]=>[4,2,3,-5,-1]=>00011=>[3,2]
[-1,-5,3,2,-4]=>[-4,2,3,-5,-1]=>10011=>[1,2,2]
[-1,-5,3,-2,4]=>[4,-2,3,-5,-1]=>01011=>[1,1,1,2]
[-1,-5,3,-2,-4]=>[-4,-2,3,-5,-1]=>11011=>[2,1,2]
[-1,-5,-3,2,4]=>[4,2,-3,-5,-1]=>00111=>[2,3]
[-1,-5,-3,2,-4]=>[-4,2,-3,-5,-1]=>10111=>[1,1,3]
[-1,-5,-3,-2,4]=>[4,-2,-3,-5,-1]=>01111=>[1,4]
[-1,-5,-3,-2,-4]=>[-4,-2,-3,-5,-1]=>11111=>[5]
[1,5,3,4,2]=>[2,4,3,5,1]=>00000=>[5]
[1,5,3,4,-2]=>[-2,4,3,5,1]=>10000=>[1,4]
[1,5,3,-4,2]=>[2,-4,3,5,1]=>01000=>[1,1,3]
[1,5,3,-4,-2]=>[-2,-4,3,5,1]=>11000=>[2,3]
[1,5,-3,4,2]=>[2,4,-3,5,1]=>00100=>[2,1,2]
[1,5,-3,4,-2]=>[-2,4,-3,5,1]=>10100=>[1,1,1,2]
[1,5,-3,-4,2]=>[2,-4,-3,5,1]=>01100=>[1,2,2]
[1,5,-3,-4,-2]=>[-2,-4,-3,5,1]=>11100=>[3,2]
[1,-5,3,4,2]=>[2,4,3,-5,1]=>00010=>[3,1,1]
[1,-5,3,4,-2]=>[-2,4,3,-5,1]=>10010=>[1,2,1,1]
[1,-5,3,-4,2]=>[2,-4,3,-5,1]=>01010=>[1,1,1,1,1]
[1,-5,3,-4,-2]=>[-2,-4,3,-5,1]=>11010=>[2,1,1,1]
[1,-5,-3,4,2]=>[2,4,-3,-5,1]=>00110=>[2,2,1]
[1,-5,-3,4,-2]=>[-2,4,-3,-5,1]=>10110=>[1,1,2,1]
[1,-5,-3,-4,2]=>[2,-4,-3,-5,1]=>01110=>[1,3,1]
[1,-5,-3,-4,-2]=>[-2,-4,-3,-5,1]=>11110=>[4,1]
[-1,5,3,4,2]=>[2,4,3,5,-1]=>00001=>[4,1]
[-1,5,3,4,-2]=>[-2,4,3,5,-1]=>10001=>[1,3,1]
[-1,5,3,-4,2]=>[2,-4,3,5,-1]=>01001=>[1,1,2,1]
[-1,5,3,-4,-2]=>[-2,-4,3,5,-1]=>11001=>[2,2,1]
[-1,5,-3,4,2]=>[2,4,-3,5,-1]=>00101=>[2,1,1,1]
[-1,5,-3,4,-2]=>[-2,4,-3,5,-1]=>10101=>[1,1,1,1,1]
[-1,5,-3,-4,2]=>[2,-4,-3,5,-1]=>01101=>[1,2,1,1]
[-1,5,-3,-4,-2]=>[-2,-4,-3,5,-1]=>11101=>[3,1,1]
[-1,-5,3,4,2]=>[2,4,3,-5,-1]=>00011=>[3,2]
[-1,-5,3,4,-2]=>[-2,4,3,-5,-1]=>10011=>[1,2,2]
[-1,-5,3,-4,2]=>[2,-4,3,-5,-1]=>01011=>[1,1,1,2]
[-1,-5,3,-4,-2]=>[-2,-4,3,-5,-1]=>11011=>[2,1,2]
[-1,-5,-3,4,2]=>[2,4,-3,-5,-1]=>00111=>[2,3]
[-1,-5,-3,4,-2]=>[-2,4,-3,-5,-1]=>10111=>[1,1,3]
[-1,-5,-3,-4,2]=>[2,-4,-3,-5,-1]=>01111=>[1,4]
[-1,-5,-3,-4,-2]=>[-2,-4,-3,-5,-1]=>11111=>[5]
[1,5,4,2,3]=>[3,2,4,5,1]=>00000=>[5]
[1,5,4,2,-3]=>[-3,2,4,5,1]=>10000=>[1,4]
[1,5,4,-2,3]=>[3,-2,4,5,1]=>01000=>[1,1,3]
[1,5,4,-2,-3]=>[-3,-2,4,5,1]=>11000=>[2,3]
[1,5,-4,2,3]=>[3,2,-4,5,1]=>00100=>[2,1,2]
[1,5,-4,2,-3]=>[-3,2,-4,5,1]=>10100=>[1,1,1,2]
[1,5,-4,-2,3]=>[3,-2,-4,5,1]=>01100=>[1,2,2]
[1,5,-4,-2,-3]=>[-3,-2,-4,5,1]=>11100=>[3,2]
[1,-5,4,2,3]=>[3,2,4,-5,1]=>00010=>[3,1,1]
[1,-5,4,2,-3]=>[-3,2,4,-5,1]=>10010=>[1,2,1,1]
[1,-5,4,-2,3]=>[3,-2,4,-5,1]=>01010=>[1,1,1,1,1]
[1,-5,4,-2,-3]=>[-3,-2,4,-5,1]=>11010=>[2,1,1,1]
[1,-5,-4,2,3]=>[3,2,-4,-5,1]=>00110=>[2,2,1]
[1,-5,-4,2,-3]=>[-3,2,-4,-5,1]=>10110=>[1,1,2,1]
[1,-5,-4,-2,3]=>[3,-2,-4,-5,1]=>01110=>[1,3,1]
[1,-5,-4,-2,-3]=>[-3,-2,-4,-5,1]=>11110=>[4,1]
[-1,5,4,2,3]=>[3,2,4,5,-1]=>00001=>[4,1]
[-1,5,4,2,-3]=>[-3,2,4,5,-1]=>10001=>[1,3,1]
[-1,5,4,-2,3]=>[3,-2,4,5,-1]=>01001=>[1,1,2,1]
[-1,5,4,-2,-3]=>[-3,-2,4,5,-1]=>11001=>[2,2,1]
[-1,5,-4,2,3]=>[3,2,-4,5,-1]=>00101=>[2,1,1,1]
[-1,5,-4,2,-3]=>[-3,2,-4,5,-1]=>10101=>[1,1,1,1,1]
[-1,5,-4,-2,3]=>[3,-2,-4,5,-1]=>01101=>[1,2,1,1]
[-1,5,-4,-2,-3]=>[-3,-2,-4,5,-1]=>11101=>[3,1,1]
[-1,-5,4,2,3]=>[3,2,4,-5,-1]=>00011=>[3,2]
[-1,-5,4,2,-3]=>[-3,2,4,-5,-1]=>10011=>[1,2,2]
[-1,-5,4,-2,3]=>[3,-2,4,-5,-1]=>01011=>[1,1,1,2]
[-1,-5,4,-2,-3]=>[-3,-2,4,-5,-1]=>11011=>[2,1,2]
[-1,-5,-4,2,3]=>[3,2,-4,-5,-1]=>00111=>[2,3]
[-1,-5,-4,2,-3]=>[-3,2,-4,-5,-1]=>10111=>[1,1,3]
[-1,-5,-4,-2,3]=>[3,-2,-4,-5,-1]=>01111=>[1,4]
[-1,-5,-4,-2,-3]=>[-3,-2,-4,-5,-1]=>11111=>[5]
[1,5,4,3,2]=>[2,3,4,5,1]=>00000=>[5]
[1,5,4,3,-2]=>[-2,3,4,5,1]=>10000=>[1,4]
[1,5,4,-3,2]=>[2,-3,4,5,1]=>01000=>[1,1,3]
[1,5,4,-3,-2]=>[-2,-3,4,5,1]=>11000=>[2,3]
[1,5,-4,3,2]=>[2,3,-4,5,1]=>00100=>[2,1,2]
[1,5,-4,3,-2]=>[-2,3,-4,5,1]=>10100=>[1,1,1,2]
[1,5,-4,-3,2]=>[2,-3,-4,5,1]=>01100=>[1,2,2]
[1,5,-4,-3,-2]=>[-2,-3,-4,5,1]=>11100=>[3,2]
[1,-5,4,3,2]=>[2,3,4,-5,1]=>00010=>[3,1,1]
[1,-5,4,3,-2]=>[-2,3,4,-5,1]=>10010=>[1,2,1,1]
[1,-5,4,-3,2]=>[2,-3,4,-5,1]=>01010=>[1,1,1,1,1]
[1,-5,4,-3,-2]=>[-2,-3,4,-5,1]=>11010=>[2,1,1,1]
[1,-5,-4,3,2]=>[2,3,-4,-5,1]=>00110=>[2,2,1]
[1,-5,-4,3,-2]=>[-2,3,-4,-5,1]=>10110=>[1,1,2,1]
[1,-5,-4,-3,2]=>[2,-3,-4,-5,1]=>01110=>[1,3,1]
[1,-5,-4,-3,-2]=>[-2,-3,-4,-5,1]=>11110=>[4,1]
[-1,5,4,3,2]=>[2,3,4,5,-1]=>00001=>[4,1]
[-1,5,4,3,-2]=>[-2,3,4,5,-1]=>10001=>[1,3,1]
[-1,5,4,-3,2]=>[2,-3,4,5,-1]=>01001=>[1,1,2,1]
[-1,5,4,-3,-2]=>[-2,-3,4,5,-1]=>11001=>[2,2,1]
[-1,5,-4,3,2]=>[2,3,-4,5,-1]=>00101=>[2,1,1,1]
[-1,5,-4,3,-2]=>[-2,3,-4,5,-1]=>10101=>[1,1,1,1,1]
[-1,5,-4,-3,2]=>[2,-3,-4,5,-1]=>01101=>[1,2,1,1]
[-1,5,-4,-3,-2]=>[-2,-3,-4,5,-1]=>11101=>[3,1,1]
[-1,-5,4,3,2]=>[2,3,4,-5,-1]=>00011=>[3,2]
[-1,-5,4,3,-2]=>[-2,3,4,-5,-1]=>10011=>[1,2,2]
[-1,-5,4,-3,2]=>[2,-3,4,-5,-1]=>01011=>[1,1,1,2]
[-1,-5,4,-3,-2]=>[-2,-3,4,-5,-1]=>11011=>[2,1,2]
[-1,-5,-4,3,2]=>[2,3,-4,-5,-1]=>00111=>[2,3]
[-1,-5,-4,3,-2]=>[-2,3,-4,-5,-1]=>10111=>[1,1,3]
[-1,-5,-4,-3,2]=>[2,-3,-4,-5,-1]=>01111=>[1,4]
[-1,-5,-4,-3,-2]=>[-2,-3,-4,-5,-1]=>11111=>[5]
[2,1,3,4,5]=>[5,4,3,1,2]=>00000=>[5]
[2,1,3,4,-5]=>[-5,4,3,1,2]=>10000=>[1,4]
[2,1,3,-4,5]=>[5,-4,3,1,2]=>01000=>[1,1,3]
[2,1,3,-4,-5]=>[-5,-4,3,1,2]=>11000=>[2,3]
[2,1,-3,4,5]=>[5,4,-3,1,2]=>00100=>[2,1,2]
[2,1,-3,4,-5]=>[-5,4,-3,1,2]=>10100=>[1,1,1,2]
[2,1,-3,-4,5]=>[5,-4,-3,1,2]=>01100=>[1,2,2]
[2,1,-3,-4,-5]=>[-5,-4,-3,1,2]=>11100=>[3,2]
[2,-1,3,4,5]=>[5,4,3,-1,2]=>00010=>[3,1,1]
[2,-1,3,4,-5]=>[-5,4,3,-1,2]=>10010=>[1,2,1,1]
[2,-1,3,-4,5]=>[5,-4,3,-1,2]=>01010=>[1,1,1,1,1]
[2,-1,3,-4,-5]=>[-5,-4,3,-1,2]=>11010=>[2,1,1,1]
[2,-1,-3,4,5]=>[5,4,-3,-1,2]=>00110=>[2,2,1]
[2,-1,-3,4,-5]=>[-5,4,-3,-1,2]=>10110=>[1,1,2,1]
[2,-1,-3,-4,5]=>[5,-4,-3,-1,2]=>01110=>[1,3,1]
[2,-1,-3,-4,-5]=>[-5,-4,-3,-1,2]=>11110=>[4,1]
[-2,1,3,4,5]=>[5,4,3,1,-2]=>00001=>[4,1]
[-2,1,3,4,-5]=>[-5,4,3,1,-2]=>10001=>[1,3,1]
[-2,1,3,-4,5]=>[5,-4,3,1,-2]=>01001=>[1,1,2,1]
[-2,1,3,-4,-5]=>[-5,-4,3,1,-2]=>11001=>[2,2,1]
[-2,1,-3,4,5]=>[5,4,-3,1,-2]=>00101=>[2,1,1,1]
[-2,1,-3,4,-5]=>[-5,4,-3,1,-2]=>10101=>[1,1,1,1,1]
[-2,1,-3,-4,5]=>[5,-4,-3,1,-2]=>01101=>[1,2,1,1]
[-2,1,-3,-4,-5]=>[-5,-4,-3,1,-2]=>11101=>[3,1,1]
[-2,-1,3,4,5]=>[5,4,3,-1,-2]=>00011=>[3,2]
[-2,-1,3,4,-5]=>[-5,4,3,-1,-2]=>10011=>[1,2,2]
[-2,-1,3,-4,5]=>[5,-4,3,-1,-2]=>01011=>[1,1,1,2]
[-2,-1,3,-4,-5]=>[-5,-4,3,-1,-2]=>11011=>[2,1,2]
[-2,-1,-3,4,5]=>[5,4,-3,-1,-2]=>00111=>[2,3]
[-2,-1,-3,4,-5]=>[-5,4,-3,-1,-2]=>10111=>[1,1,3]
[-2,-1,-3,-4,5]=>[5,-4,-3,-1,-2]=>01111=>[1,4]
[-2,-1,-3,-4,-5]=>[-5,-4,-3,-1,-2]=>11111=>[5]
[2,1,3,5,4]=>[4,5,3,1,2]=>00000=>[5]
[2,1,3,5,-4]=>[-4,5,3,1,2]=>10000=>[1,4]
[2,1,3,-5,4]=>[4,-5,3,1,2]=>01000=>[1,1,3]
[2,1,3,-5,-4]=>[-4,-5,3,1,2]=>11000=>[2,3]
[2,1,-3,5,4]=>[4,5,-3,1,2]=>00100=>[2,1,2]
[2,1,-3,5,-4]=>[-4,5,-3,1,2]=>10100=>[1,1,1,2]
[2,1,-3,-5,4]=>[4,-5,-3,1,2]=>01100=>[1,2,2]
[2,1,-3,-5,-4]=>[-4,-5,-3,1,2]=>11100=>[3,2]
[2,-1,3,5,4]=>[4,5,3,-1,2]=>00010=>[3,1,1]
[2,-1,3,5,-4]=>[-4,5,3,-1,2]=>10010=>[1,2,1,1]
[2,-1,3,-5,4]=>[4,-5,3,-1,2]=>01010=>[1,1,1,1,1]
[2,-1,3,-5,-4]=>[-4,-5,3,-1,2]=>11010=>[2,1,1,1]
[2,-1,-3,5,4]=>[4,5,-3,-1,2]=>00110=>[2,2,1]
[2,-1,-3,5,-4]=>[-4,5,-3,-1,2]=>10110=>[1,1,2,1]
[2,-1,-3,-5,4]=>[4,-5,-3,-1,2]=>01110=>[1,3,1]
[2,-1,-3,-5,-4]=>[-4,-5,-3,-1,2]=>11110=>[4,1]
[-2,1,3,5,4]=>[4,5,3,1,-2]=>00001=>[4,1]
[-2,1,3,5,-4]=>[-4,5,3,1,-2]=>10001=>[1,3,1]
[-2,1,3,-5,4]=>[4,-5,3,1,-2]=>01001=>[1,1,2,1]
[-2,1,3,-5,-4]=>[-4,-5,3,1,-2]=>11001=>[2,2,1]
[-2,1,-3,5,4]=>[4,5,-3,1,-2]=>00101=>[2,1,1,1]
[-2,1,-3,5,-4]=>[-4,5,-3,1,-2]=>10101=>[1,1,1,1,1]
[-2,1,-3,-5,4]=>[4,-5,-3,1,-2]=>01101=>[1,2,1,1]
[-2,1,-3,-5,-4]=>[-4,-5,-3,1,-2]=>11101=>[3,1,1]
[-2,-1,3,5,4]=>[4,5,3,-1,-2]=>00011=>[3,2]
[-2,-1,3,5,-4]=>[-4,5,3,-1,-2]=>10011=>[1,2,2]
[-2,-1,3,-5,4]=>[4,-5,3,-1,-2]=>01011=>[1,1,1,2]
[-2,-1,3,-5,-4]=>[-4,-5,3,-1,-2]=>11011=>[2,1,2]
[-2,-1,-3,5,4]=>[4,5,-3,-1,-2]=>00111=>[2,3]
[-2,-1,-3,5,-4]=>[-4,5,-3,-1,-2]=>10111=>[1,1,3]
[-2,-1,-3,-5,4]=>[4,-5,-3,-1,-2]=>01111=>[1,4]
[-2,-1,-3,-5,-4]=>[-4,-5,-3,-1,-2]=>11111=>[5]
[2,1,4,3,5]=>[5,3,4,1,2]=>00000=>[5]
[2,1,4,3,-5]=>[-5,3,4,1,2]=>10000=>[1,4]
[2,1,4,-3,5]=>[5,-3,4,1,2]=>01000=>[1,1,3]
[2,1,4,-3,-5]=>[-5,-3,4,1,2]=>11000=>[2,3]
[2,1,-4,3,5]=>[5,3,-4,1,2]=>00100=>[2,1,2]
[2,1,-4,3,-5]=>[-5,3,-4,1,2]=>10100=>[1,1,1,2]
[2,1,-4,-3,5]=>[5,-3,-4,1,2]=>01100=>[1,2,2]
[2,1,-4,-3,-5]=>[-5,-3,-4,1,2]=>11100=>[3,2]
[2,-1,4,3,5]=>[5,3,4,-1,2]=>00010=>[3,1,1]
[2,-1,4,3,-5]=>[-5,3,4,-1,2]=>10010=>[1,2,1,1]
[2,-1,4,-3,5]=>[5,-3,4,-1,2]=>01010=>[1,1,1,1,1]
[2,-1,4,-3,-5]=>[-5,-3,4,-1,2]=>11010=>[2,1,1,1]
[2,-1,-4,3,5]=>[5,3,-4,-1,2]=>00110=>[2,2,1]
[2,-1,-4,3,-5]=>[-5,3,-4,-1,2]=>10110=>[1,1,2,1]
[2,-1,-4,-3,5]=>[5,-3,-4,-1,2]=>01110=>[1,3,1]
[2,-1,-4,-3,-5]=>[-5,-3,-4,-1,2]=>11110=>[4,1]
[-2,1,4,3,5]=>[5,3,4,1,-2]=>00001=>[4,1]
[-2,1,4,3,-5]=>[-5,3,4,1,-2]=>10001=>[1,3,1]
[-2,1,4,-3,5]=>[5,-3,4,1,-2]=>01001=>[1,1,2,1]
[-2,1,4,-3,-5]=>[-5,-3,4,1,-2]=>11001=>[2,2,1]
[-2,1,-4,3,5]=>[5,3,-4,1,-2]=>00101=>[2,1,1,1]
[-2,1,-4,3,-5]=>[-5,3,-4,1,-2]=>10101=>[1,1,1,1,1]
[-2,1,-4,-3,5]=>[5,-3,-4,1,-2]=>01101=>[1,2,1,1]
[-2,1,-4,-3,-5]=>[-5,-3,-4,1,-2]=>11101=>[3,1,1]
[-2,-1,4,3,5]=>[5,3,4,-1,-2]=>00011=>[3,2]
[-2,-1,4,3,-5]=>[-5,3,4,-1,-2]=>10011=>[1,2,2]
[-2,-1,4,-3,5]=>[5,-3,4,-1,-2]=>01011=>[1,1,1,2]
[-2,-1,4,-3,-5]=>[-5,-3,4,-1,-2]=>11011=>[2,1,2]
[-2,-1,-4,3,5]=>[5,3,-4,-1,-2]=>00111=>[2,3]
[-2,-1,-4,3,-5]=>[-5,3,-4,-1,-2]=>10111=>[1,1,3]
[-2,-1,-4,-3,5]=>[5,-3,-4,-1,-2]=>01111=>[1,4]
[-2,-1,-4,-3,-5]=>[-5,-3,-4,-1,-2]=>11111=>[5]
[2,1,4,5,3]=>[3,5,4,1,2]=>00000=>[5]
[2,1,4,5,-3]=>[-3,5,4,1,2]=>10000=>[1,4]
[2,1,4,-5,3]=>[3,-5,4,1,2]=>01000=>[1,1,3]
[2,1,4,-5,-3]=>[-3,-5,4,1,2]=>11000=>[2,3]
[2,1,-4,5,3]=>[3,5,-4,1,2]=>00100=>[2,1,2]
[2,1,-4,5,-3]=>[-3,5,-4,1,2]=>10100=>[1,1,1,2]
[2,1,-4,-5,3]=>[3,-5,-4,1,2]=>01100=>[1,2,2]
[2,1,-4,-5,-3]=>[-3,-5,-4,1,2]=>11100=>[3,2]
[2,-1,4,5,3]=>[3,5,4,-1,2]=>00010=>[3,1,1]
[2,-1,4,5,-3]=>[-3,5,4,-1,2]=>10010=>[1,2,1,1]
[2,-1,4,-5,3]=>[3,-5,4,-1,2]=>01010=>[1,1,1,1,1]
[2,-1,4,-5,-3]=>[-3,-5,4,-1,2]=>11010=>[2,1,1,1]
[2,-1,-4,5,3]=>[3,5,-4,-1,2]=>00110=>[2,2,1]
[2,-1,-4,5,-3]=>[-3,5,-4,-1,2]=>10110=>[1,1,2,1]
[2,-1,-4,-5,3]=>[3,-5,-4,-1,2]=>01110=>[1,3,1]
[2,-1,-4,-5,-3]=>[-3,-5,-4,-1,2]=>11110=>[4,1]
[-2,1,4,5,3]=>[3,5,4,1,-2]=>00001=>[4,1]
[-2,1,4,5,-3]=>[-3,5,4,1,-2]=>10001=>[1,3,1]
[-2,1,4,-5,3]=>[3,-5,4,1,-2]=>01001=>[1,1,2,1]
[-2,1,4,-5,-3]=>[-3,-5,4,1,-2]=>11001=>[2,2,1]
[-2,1,-4,5,3]=>[3,5,-4,1,-2]=>00101=>[2,1,1,1]
[-2,1,-4,5,-3]=>[-3,5,-4,1,-2]=>10101=>[1,1,1,1,1]
[-2,1,-4,-5,3]=>[3,-5,-4,1,-2]=>01101=>[1,2,1,1]
[-2,1,-4,-5,-3]=>[-3,-5,-4,1,-2]=>11101=>[3,1,1]
[-2,-1,4,5,3]=>[3,5,4,-1,-2]=>00011=>[3,2]
[-2,-1,4,5,-3]=>[-3,5,4,-1,-2]=>10011=>[1,2,2]
[-2,-1,4,-5,3]=>[3,-5,4,-1,-2]=>01011=>[1,1,1,2]
[-2,-1,4,-5,-3]=>[-3,-5,4,-1,-2]=>11011=>[2,1,2]
[-2,-1,-4,5,3]=>[3,5,-4,-1,-2]=>00111=>[2,3]
[-2,-1,-4,5,-3]=>[-3,5,-4,-1,-2]=>10111=>[1,1,3]
[-2,-1,-4,-5,3]=>[3,-5,-4,-1,-2]=>01111=>[1,4]
[-2,-1,-4,-5,-3]=>[-3,-5,-4,-1,-2]=>11111=>[5]
[2,1,5,3,4]=>[4,3,5,1,2]=>00000=>[5]
[2,1,5,3,-4]=>[-4,3,5,1,2]=>10000=>[1,4]
[2,1,5,-3,4]=>[4,-3,5,1,2]=>01000=>[1,1,3]
[2,1,5,-3,-4]=>[-4,-3,5,1,2]=>11000=>[2,3]
[2,1,-5,3,4]=>[4,3,-5,1,2]=>00100=>[2,1,2]
[2,1,-5,3,-4]=>[-4,3,-5,1,2]=>10100=>[1,1,1,2]
[2,1,-5,-3,4]=>[4,-3,-5,1,2]=>01100=>[1,2,2]
[2,1,-5,-3,-4]=>[-4,-3,-5,1,2]=>11100=>[3,2]
[2,-1,5,3,4]=>[4,3,5,-1,2]=>00010=>[3,1,1]
[2,-1,5,3,-4]=>[-4,3,5,-1,2]=>10010=>[1,2,1,1]
[2,-1,5,-3,4]=>[4,-3,5,-1,2]=>01010=>[1,1,1,1,1]
[2,-1,5,-3,-4]=>[-4,-3,5,-1,2]=>11010=>[2,1,1,1]
[2,-1,-5,3,4]=>[4,3,-5,-1,2]=>00110=>[2,2,1]
[2,-1,-5,3,-4]=>[-4,3,-5,-1,2]=>10110=>[1,1,2,1]
[2,-1,-5,-3,4]=>[4,-3,-5,-1,2]=>01110=>[1,3,1]
[2,-1,-5,-3,-4]=>[-4,-3,-5,-1,2]=>11110=>[4,1]
[-2,1,5,3,4]=>[4,3,5,1,-2]=>00001=>[4,1]
[-2,1,5,3,-4]=>[-4,3,5,1,-2]=>10001=>[1,3,1]
[-2,1,5,-3,4]=>[4,-3,5,1,-2]=>01001=>[1,1,2,1]
[-2,1,5,-3,-4]=>[-4,-3,5,1,-2]=>11001=>[2,2,1]
[-2,1,-5,3,4]=>[4,3,-5,1,-2]=>00101=>[2,1,1,1]
[-2,1,-5,3,-4]=>[-4,3,-5,1,-2]=>10101=>[1,1,1,1,1]
[-2,1,-5,-3,4]=>[4,-3,-5,1,-2]=>01101=>[1,2,1,1]
[-2,1,-5,-3,-4]=>[-4,-3,-5,1,-2]=>11101=>[3,1,1]
[-2,-1,5,3,4]=>[4,3,5,-1,-2]=>00011=>[3,2]
[-2,-1,5,3,-4]=>[-4,3,5,-1,-2]=>10011=>[1,2,2]
[-2,-1,5,-3,4]=>[4,-3,5,-1,-2]=>01011=>[1,1,1,2]
[-2,-1,5,-3,-4]=>[-4,-3,5,-1,-2]=>11011=>[2,1,2]
[-2,-1,-5,3,4]=>[4,3,-5,-1,-2]=>00111=>[2,3]
[-2,-1,-5,3,-4]=>[-4,3,-5,-1,-2]=>10111=>[1,1,3]
[-2,-1,-5,-3,4]=>[4,-3,-5,-1,-2]=>01111=>[1,4]
[-2,-1,-5,-3,-4]=>[-4,-3,-5,-1,-2]=>11111=>[5]
[2,1,5,4,3]=>[3,4,5,1,2]=>00000=>[5]
[2,1,5,4,-3]=>[-3,4,5,1,2]=>10000=>[1,4]
[2,1,5,-4,3]=>[3,-4,5,1,2]=>01000=>[1,1,3]
[2,1,5,-4,-3]=>[-3,-4,5,1,2]=>11000=>[2,3]
[2,1,-5,4,3]=>[3,4,-5,1,2]=>00100=>[2,1,2]
[2,1,-5,4,-3]=>[-3,4,-5,1,2]=>10100=>[1,1,1,2]
[2,1,-5,-4,3]=>[3,-4,-5,1,2]=>01100=>[1,2,2]
[2,1,-5,-4,-3]=>[-3,-4,-5,1,2]=>11100=>[3,2]
[2,-1,5,4,3]=>[3,4,5,-1,2]=>00010=>[3,1,1]
[2,-1,5,4,-3]=>[-3,4,5,-1,2]=>10010=>[1,2,1,1]
[2,-1,5,-4,3]=>[3,-4,5,-1,2]=>01010=>[1,1,1,1,1]
[2,-1,5,-4,-3]=>[-3,-4,5,-1,2]=>11010=>[2,1,1,1]
[2,-1,-5,4,3]=>[3,4,-5,-1,2]=>00110=>[2,2,1]
[2,-1,-5,4,-3]=>[-3,4,-5,-1,2]=>10110=>[1,1,2,1]
[2,-1,-5,-4,3]=>[3,-4,-5,-1,2]=>01110=>[1,3,1]
[2,-1,-5,-4,-3]=>[-3,-4,-5,-1,2]=>11110=>[4,1]
[-2,1,5,4,3]=>[3,4,5,1,-2]=>00001=>[4,1]
[-2,1,5,4,-3]=>[-3,4,5,1,-2]=>10001=>[1,3,1]
[-2,1,5,-4,3]=>[3,-4,5,1,-2]=>01001=>[1,1,2,1]
[-2,1,5,-4,-3]=>[-3,-4,5,1,-2]=>11001=>[2,2,1]
[-2,1,-5,4,3]=>[3,4,-5,1,-2]=>00101=>[2,1,1,1]
[-2,1,-5,4,-3]=>[-3,4,-5,1,-2]=>10101=>[1,1,1,1,1]
[-2,1,-5,-4,3]=>[3,-4,-5,1,-2]=>01101=>[1,2,1,1]
[-2,1,-5,-4,-3]=>[-3,-4,-5,1,-2]=>11101=>[3,1,1]
[-2,-1,5,4,3]=>[3,4,5,-1,-2]=>00011=>[3,2]
[-2,-1,5,4,-3]=>[-3,4,5,-1,-2]=>10011=>[1,2,2]
[-2,-1,5,-4,3]=>[3,-4,5,-1,-2]=>01011=>[1,1,1,2]
[-2,-1,5,-4,-3]=>[-3,-4,5,-1,-2]=>11011=>[2,1,2]
[-2,-1,-5,4,3]=>[3,4,-5,-1,-2]=>00111=>[2,3]
[-2,-1,-5,4,-3]=>[-3,4,-5,-1,-2]=>10111=>[1,1,3]
[-2,-1,-5,-4,3]=>[3,-4,-5,-1,-2]=>01111=>[1,4]
[-2,-1,-5,-4,-3]=>[-3,-4,-5,-1,-2]=>11111=>[5]
[2,3,1,4,5]=>[5,4,1,3,2]=>00000=>[5]
[2,3,1,4,-5]=>[-5,4,1,3,2]=>10000=>[1,4]
[2,3,1,-4,5]=>[5,-4,1,3,2]=>01000=>[1,1,3]
[2,3,1,-4,-5]=>[-5,-4,1,3,2]=>11000=>[2,3]
[2,3,-1,4,5]=>[5,4,-1,3,2]=>00100=>[2,1,2]
[2,3,-1,4,-5]=>[-5,4,-1,3,2]=>10100=>[1,1,1,2]
[2,3,-1,-4,5]=>[5,-4,-1,3,2]=>01100=>[1,2,2]
[2,3,-1,-4,-5]=>[-5,-4,-1,3,2]=>11100=>[3,2]
[2,-3,1,4,5]=>[5,4,1,-3,2]=>00010=>[3,1,1]
[2,-3,1,4,-5]=>[-5,4,1,-3,2]=>10010=>[1,2,1,1]
[2,-3,1,-4,5]=>[5,-4,1,-3,2]=>01010=>[1,1,1,1,1]
[2,-3,1,-4,-5]=>[-5,-4,1,-3,2]=>11010=>[2,1,1,1]
[2,-3,-1,4,5]=>[5,4,-1,-3,2]=>00110=>[2,2,1]
[2,-3,-1,4,-5]=>[-5,4,-1,-3,2]=>10110=>[1,1,2,1]
[2,-3,-1,-4,5]=>[5,-4,-1,-3,2]=>01110=>[1,3,1]
[2,-3,-1,-4,-5]=>[-5,-4,-1,-3,2]=>11110=>[4,1]
[-2,3,1,4,5]=>[5,4,1,3,-2]=>00001=>[4,1]
[-2,3,1,4,-5]=>[-5,4,1,3,-2]=>10001=>[1,3,1]
[-2,3,1,-4,5]=>[5,-4,1,3,-2]=>01001=>[1,1,2,1]
[-2,3,1,-4,-5]=>[-5,-4,1,3,-2]=>11001=>[2,2,1]
[-2,3,-1,4,5]=>[5,4,-1,3,-2]=>00101=>[2,1,1,1]
[-2,3,-1,4,-5]=>[-5,4,-1,3,-2]=>10101=>[1,1,1,1,1]
[-2,3,-1,-4,5]=>[5,-4,-1,3,-2]=>01101=>[1,2,1,1]
[-2,3,-1,-4,-5]=>[-5,-4,-1,3,-2]=>11101=>[3,1,1]
[-2,-3,1,4,5]=>[5,4,1,-3,-2]=>00011=>[3,2]
[-2,-3,1,4,-5]=>[-5,4,1,-3,-2]=>10011=>[1,2,2]
[-2,-3,1,-4,5]=>[5,-4,1,-3,-2]=>01011=>[1,1,1,2]
[-2,-3,1,-4,-5]=>[-5,-4,1,-3,-2]=>11011=>[2,1,2]
[-2,-3,-1,4,5]=>[5,4,-1,-3,-2]=>00111=>[2,3]
[-2,-3,-1,4,-5]=>[-5,4,-1,-3,-2]=>10111=>[1,1,3]
[-2,-3,-1,-4,5]=>[5,-4,-1,-3,-2]=>01111=>[1,4]
[-2,-3,-1,-4,-5]=>[-5,-4,-1,-3,-2]=>11111=>[5]
[2,3,1,5,4]=>[4,5,1,3,2]=>00000=>[5]
[2,3,1,5,-4]=>[-4,5,1,3,2]=>10000=>[1,4]
[2,3,1,-5,4]=>[4,-5,1,3,2]=>01000=>[1,1,3]
[2,3,1,-5,-4]=>[-4,-5,1,3,2]=>11000=>[2,3]
[2,3,-1,5,4]=>[4,5,-1,3,2]=>00100=>[2,1,2]
[2,3,-1,5,-4]=>[-4,5,-1,3,2]=>10100=>[1,1,1,2]
[2,3,-1,-5,4]=>[4,-5,-1,3,2]=>01100=>[1,2,2]
[2,3,-1,-5,-4]=>[-4,-5,-1,3,2]=>11100=>[3,2]
[2,-3,1,5,4]=>[4,5,1,-3,2]=>00010=>[3,1,1]
[2,-3,1,5,-4]=>[-4,5,1,-3,2]=>10010=>[1,2,1,1]
[2,-3,1,-5,4]=>[4,-5,1,-3,2]=>01010=>[1,1,1,1,1]
[2,-3,1,-5,-4]=>[-4,-5,1,-3,2]=>11010=>[2,1,1,1]
[2,-3,-1,5,4]=>[4,5,-1,-3,2]=>00110=>[2,2,1]
[2,-3,-1,5,-4]=>[-4,5,-1,-3,2]=>10110=>[1,1,2,1]
[2,-3,-1,-5,4]=>[4,-5,-1,-3,2]=>01110=>[1,3,1]
[2,-3,-1,-5,-4]=>[-4,-5,-1,-3,2]=>11110=>[4,1]
[-2,3,1,5,4]=>[4,5,1,3,-2]=>00001=>[4,1]
[-2,3,1,5,-4]=>[-4,5,1,3,-2]=>10001=>[1,3,1]
[-2,3,1,-5,4]=>[4,-5,1,3,-2]=>01001=>[1,1,2,1]
[-2,3,1,-5,-4]=>[-4,-5,1,3,-2]=>11001=>[2,2,1]
[-2,3,-1,5,4]=>[4,5,-1,3,-2]=>00101=>[2,1,1,1]
[-2,3,-1,5,-4]=>[-4,5,-1,3,-2]=>10101=>[1,1,1,1,1]
[-2,3,-1,-5,4]=>[4,-5,-1,3,-2]=>01101=>[1,2,1,1]
[-2,3,-1,-5,-4]=>[-4,-5,-1,3,-2]=>11101=>[3,1,1]
[-2,-3,1,5,4]=>[4,5,1,-3,-2]=>00011=>[3,2]
[-2,-3,1,5,-4]=>[-4,5,1,-3,-2]=>10011=>[1,2,2]
[-2,-3,1,-5,4]=>[4,-5,1,-3,-2]=>01011=>[1,1,1,2]
[-2,-3,1,-5,-4]=>[-4,-5,1,-3,-2]=>11011=>[2,1,2]
[-2,-3,-1,5,4]=>[4,5,-1,-3,-2]=>00111=>[2,3]
[-2,-3,-1,5,-4]=>[-4,5,-1,-3,-2]=>10111=>[1,1,3]
[-2,-3,-1,-5,4]=>[4,-5,-1,-3,-2]=>01111=>[1,4]
[-2,-3,-1,-5,-4]=>[-4,-5,-1,-3,-2]=>11111=>[5]
[2,3,4,1,5]=>[5,1,4,3,2]=>00000=>[5]
[2,3,4,1,-5]=>[-5,1,4,3,2]=>10000=>[1,4]
[2,3,4,-1,5]=>[5,-1,4,3,2]=>01000=>[1,1,3]
[2,3,4,-1,-5]=>[-5,-1,4,3,2]=>11000=>[2,3]
[2,3,-4,1,5]=>[5,1,-4,3,2]=>00100=>[2,1,2]
[2,3,-4,1,-5]=>[-5,1,-4,3,2]=>10100=>[1,1,1,2]
[2,3,-4,-1,5]=>[5,-1,-4,3,2]=>01100=>[1,2,2]
[2,3,-4,-1,-5]=>[-5,-1,-4,3,2]=>11100=>[3,2]
[2,-3,4,1,5]=>[5,1,4,-3,2]=>00010=>[3,1,1]
[2,-3,4,1,-5]=>[-5,1,4,-3,2]=>10010=>[1,2,1,1]
[2,-3,4,-1,5]=>[5,-1,4,-3,2]=>01010=>[1,1,1,1,1]
[2,-3,4,-1,-5]=>[-5,-1,4,-3,2]=>11010=>[2,1,1,1]
[2,-3,-4,1,5]=>[5,1,-4,-3,2]=>00110=>[2,2,1]
[2,-3,-4,1,-5]=>[-5,1,-4,-3,2]=>10110=>[1,1,2,1]
[2,-3,-4,-1,5]=>[5,-1,-4,-3,2]=>01110=>[1,3,1]
[2,-3,-4,-1,-5]=>[-5,-1,-4,-3,2]=>11110=>[4,1]
[-2,3,4,1,5]=>[5,1,4,3,-2]=>00001=>[4,1]
[-2,3,4,1,-5]=>[-5,1,4,3,-2]=>10001=>[1,3,1]
[-2,3,4,-1,5]=>[5,-1,4,3,-2]=>01001=>[1,1,2,1]
[-2,3,4,-1,-5]=>[-5,-1,4,3,-2]=>11001=>[2,2,1]
[-2,3,-4,1,5]=>[5,1,-4,3,-2]=>00101=>[2,1,1,1]
[-2,3,-4,1,-5]=>[-5,1,-4,3,-2]=>10101=>[1,1,1,1,1]
[-2,3,-4,-1,5]=>[5,-1,-4,3,-2]=>01101=>[1,2,1,1]
[-2,3,-4,-1,-5]=>[-5,-1,-4,3,-2]=>11101=>[3,1,1]
[-2,-3,4,1,5]=>[5,1,4,-3,-2]=>00011=>[3,2]
[-2,-3,4,1,-5]=>[-5,1,4,-3,-2]=>10011=>[1,2,2]
[-2,-3,4,-1,5]=>[5,-1,4,-3,-2]=>01011=>[1,1,1,2]
[-2,-3,4,-1,-5]=>[-5,-1,4,-3,-2]=>11011=>[2,1,2]
[-2,-3,-4,1,5]=>[5,1,-4,-3,-2]=>00111=>[2,3]
[-2,-3,-4,1,-5]=>[-5,1,-4,-3,-2]=>10111=>[1,1,3]
[-2,-3,-4,-1,5]=>[5,-1,-4,-3,-2]=>01111=>[1,4]
[-2,-3,-4,-1,-5]=>[-5,-1,-4,-3,-2]=>11111=>[5]
[2,3,4,5,1]=>[1,5,4,3,2]=>00000=>[5]
[2,3,4,5,-1]=>[-1,5,4,3,2]=>10000=>[1,4]
[2,3,4,-5,1]=>[1,-5,4,3,2]=>01000=>[1,1,3]
[2,3,4,-5,-1]=>[-1,-5,4,3,2]=>11000=>[2,3]
[2,3,-4,5,1]=>[1,5,-4,3,2]=>00100=>[2,1,2]
[2,3,-4,5,-1]=>[-1,5,-4,3,2]=>10100=>[1,1,1,2]
[2,3,-4,-5,1]=>[1,-5,-4,3,2]=>01100=>[1,2,2]
[2,3,-4,-5,-1]=>[-1,-5,-4,3,2]=>11100=>[3,2]
[2,-3,4,5,1]=>[1,5,4,-3,2]=>00010=>[3,1,1]
[2,-3,4,5,-1]=>[-1,5,4,-3,2]=>10010=>[1,2,1,1]
[2,-3,4,-5,1]=>[1,-5,4,-3,2]=>01010=>[1,1,1,1,1]
[2,-3,4,-5,-1]=>[-1,-5,4,-3,2]=>11010=>[2,1,1,1]
[2,-3,-4,5,1]=>[1,5,-4,-3,2]=>00110=>[2,2,1]
[2,-3,-4,5,-1]=>[-1,5,-4,-3,2]=>10110=>[1,1,2,1]
[2,-3,-4,-5,1]=>[1,-5,-4,-3,2]=>01110=>[1,3,1]
[2,-3,-4,-5,-1]=>[-1,-5,-4,-3,2]=>11110=>[4,1]
[-2,3,4,5,1]=>[1,5,4,3,-2]=>00001=>[4,1]
[-2,3,4,5,-1]=>[-1,5,4,3,-2]=>10001=>[1,3,1]
[-2,3,4,-5,1]=>[1,-5,4,3,-2]=>01001=>[1,1,2,1]
[-2,3,4,-5,-1]=>[-1,-5,4,3,-2]=>11001=>[2,2,1]
[-2,3,-4,5,1]=>[1,5,-4,3,-2]=>00101=>[2,1,1,1]
[-2,3,-4,5,-1]=>[-1,5,-4,3,-2]=>10101=>[1,1,1,1,1]
[-2,3,-4,-5,1]=>[1,-5,-4,3,-2]=>01101=>[1,2,1,1]
[-2,3,-4,-5,-1]=>[-1,-5,-4,3,-2]=>11101=>[3,1,1]
[-2,-3,4,5,1]=>[1,5,4,-3,-2]=>00011=>[3,2]
[-2,-3,4,5,-1]=>[-1,5,4,-3,-2]=>10011=>[1,2,2]
[-2,-3,4,-5,1]=>[1,-5,4,-3,-2]=>01011=>[1,1,1,2]
[-2,-3,4,-5,-1]=>[-1,-5,4,-3,-2]=>11011=>[2,1,2]
[-2,-3,-4,5,1]=>[1,5,-4,-3,-2]=>00111=>[2,3]
[-2,-3,-4,5,-1]=>[-1,5,-4,-3,-2]=>10111=>[1,1,3]
[-2,-3,-4,-5,1]=>[1,-5,-4,-3,-2]=>01111=>[1,4]
[-2,-3,-4,-5,-1]=>[-1,-5,-4,-3,-2]=>11111=>[5]
[2,3,5,1,4]=>[4,1,5,3,2]=>00000=>[5]
[2,3,5,1,-4]=>[-4,1,5,3,2]=>10000=>[1,4]
[2,3,5,-1,4]=>[4,-1,5,3,2]=>01000=>[1,1,3]
[2,3,5,-1,-4]=>[-4,-1,5,3,2]=>11000=>[2,3]
[2,3,-5,1,4]=>[4,1,-5,3,2]=>00100=>[2,1,2]
[2,3,-5,1,-4]=>[-4,1,-5,3,2]=>10100=>[1,1,1,2]
[2,3,-5,-1,4]=>[4,-1,-5,3,2]=>01100=>[1,2,2]
[2,3,-5,-1,-4]=>[-4,-1,-5,3,2]=>11100=>[3,2]
[2,-3,5,1,4]=>[4,1,5,-3,2]=>00010=>[3,1,1]
[2,-3,5,1,-4]=>[-4,1,5,-3,2]=>10010=>[1,2,1,1]
[2,-3,5,-1,4]=>[4,-1,5,-3,2]=>01010=>[1,1,1,1,1]
[2,-3,5,-1,-4]=>[-4,-1,5,-3,2]=>11010=>[2,1,1,1]
[2,-3,-5,1,4]=>[4,1,-5,-3,2]=>00110=>[2,2,1]
[2,-3,-5,1,-4]=>[-4,1,-5,-3,2]=>10110=>[1,1,2,1]
[2,-3,-5,-1,4]=>[4,-1,-5,-3,2]=>01110=>[1,3,1]
[2,-3,-5,-1,-4]=>[-4,-1,-5,-3,2]=>11110=>[4,1]
[-2,3,5,1,4]=>[4,1,5,3,-2]=>00001=>[4,1]
[-2,3,5,1,-4]=>[-4,1,5,3,-2]=>10001=>[1,3,1]
[-2,3,5,-1,4]=>[4,-1,5,3,-2]=>01001=>[1,1,2,1]
[-2,3,5,-1,-4]=>[-4,-1,5,3,-2]=>11001=>[2,2,1]
[-2,3,-5,1,4]=>[4,1,-5,3,-2]=>00101=>[2,1,1,1]
[-2,3,-5,1,-4]=>[-4,1,-5,3,-2]=>10101=>[1,1,1,1,1]
[-2,3,-5,-1,4]=>[4,-1,-5,3,-2]=>01101=>[1,2,1,1]
[-2,3,-5,-1,-4]=>[-4,-1,-5,3,-2]=>11101=>[3,1,1]
[-2,-3,5,1,4]=>[4,1,5,-3,-2]=>00011=>[3,2]
[-2,-3,5,1,-4]=>[-4,1,5,-3,-2]=>10011=>[1,2,2]
[-2,-3,5,-1,4]=>[4,-1,5,-3,-2]=>01011=>[1,1,1,2]
[-2,-3,5,-1,-4]=>[-4,-1,5,-3,-2]=>11011=>[2,1,2]
[-2,-3,-5,1,4]=>[4,1,-5,-3,-2]=>00111=>[2,3]
[-2,-3,-5,1,-4]=>[-4,1,-5,-3,-2]=>10111=>[1,1,3]
[-2,-3,-5,-1,4]=>[4,-1,-5,-3,-2]=>01111=>[1,4]
[-2,-3,-5,-1,-4]=>[-4,-1,-5,-3,-2]=>11111=>[5]
[2,3,5,4,1]=>[1,4,5,3,2]=>00000=>[5]
[2,3,5,4,-1]=>[-1,4,5,3,2]=>10000=>[1,4]
[2,3,5,-4,1]=>[1,-4,5,3,2]=>01000=>[1,1,3]
[2,3,5,-4,-1]=>[-1,-4,5,3,2]=>11000=>[2,3]
[2,3,-5,4,1]=>[1,4,-5,3,2]=>00100=>[2,1,2]
[2,3,-5,4,-1]=>[-1,4,-5,3,2]=>10100=>[1,1,1,2]
[2,3,-5,-4,1]=>[1,-4,-5,3,2]=>01100=>[1,2,2]
[2,3,-5,-4,-1]=>[-1,-4,-5,3,2]=>11100=>[3,2]
[2,-3,5,4,1]=>[1,4,5,-3,2]=>00010=>[3,1,1]
[2,-3,5,4,-1]=>[-1,4,5,-3,2]=>10010=>[1,2,1,1]
[2,-3,5,-4,1]=>[1,-4,5,-3,2]=>01010=>[1,1,1,1,1]
[2,-3,5,-4,-1]=>[-1,-4,5,-3,2]=>11010=>[2,1,1,1]
[2,-3,-5,4,1]=>[1,4,-5,-3,2]=>00110=>[2,2,1]
[2,-3,-5,4,-1]=>[-1,4,-5,-3,2]=>10110=>[1,1,2,1]
[2,-3,-5,-4,1]=>[1,-4,-5,-3,2]=>01110=>[1,3,1]
[2,-3,-5,-4,-1]=>[-1,-4,-5,-3,2]=>11110=>[4,1]
[-2,3,5,4,1]=>[1,4,5,3,-2]=>00001=>[4,1]
[-2,3,5,4,-1]=>[-1,4,5,3,-2]=>10001=>[1,3,1]
[-2,3,5,-4,1]=>[1,-4,5,3,-2]=>01001=>[1,1,2,1]
[-2,3,5,-4,-1]=>[-1,-4,5,3,-2]=>11001=>[2,2,1]
[-2,3,-5,4,1]=>[1,4,-5,3,-2]=>00101=>[2,1,1,1]
[-2,3,-5,4,-1]=>[-1,4,-5,3,-2]=>10101=>[1,1,1,1,1]
[-2,3,-5,-4,1]=>[1,-4,-5,3,-2]=>01101=>[1,2,1,1]
[-2,3,-5,-4,-1]=>[-1,-4,-5,3,-2]=>11101=>[3,1,1]
[-2,-3,5,4,1]=>[1,4,5,-3,-2]=>00011=>[3,2]
[-2,-3,5,4,-1]=>[-1,4,5,-3,-2]=>10011=>[1,2,2]
[-2,-3,5,-4,1]=>[1,-4,5,-3,-2]=>01011=>[1,1,1,2]
[-2,-3,5,-4,-1]=>[-1,-4,5,-3,-2]=>11011=>[2,1,2]
[-2,-3,-5,4,1]=>[1,4,-5,-3,-2]=>00111=>[2,3]
[-2,-3,-5,4,-1]=>[-1,4,-5,-3,-2]=>10111=>[1,1,3]
[-2,-3,-5,-4,1]=>[1,-4,-5,-3,-2]=>01111=>[1,4]
[-2,-3,-5,-4,-1]=>[-1,-4,-5,-3,-2]=>11111=>[5]
[2,4,1,3,5]=>[5,3,1,4,2]=>00000=>[5]
[2,4,1,3,-5]=>[-5,3,1,4,2]=>10000=>[1,4]
[2,4,1,-3,5]=>[5,-3,1,4,2]=>01000=>[1,1,3]
[2,4,1,-3,-5]=>[-5,-3,1,4,2]=>11000=>[2,3]
[2,4,-1,3,5]=>[5,3,-1,4,2]=>00100=>[2,1,2]
[2,4,-1,3,-5]=>[-5,3,-1,4,2]=>10100=>[1,1,1,2]
[2,4,-1,-3,5]=>[5,-3,-1,4,2]=>01100=>[1,2,2]
[2,4,-1,-3,-5]=>[-5,-3,-1,4,2]=>11100=>[3,2]
[2,-4,1,3,5]=>[5,3,1,-4,2]=>00010=>[3,1,1]
[2,-4,1,3,-5]=>[-5,3,1,-4,2]=>10010=>[1,2,1,1]
[2,-4,1,-3,5]=>[5,-3,1,-4,2]=>01010=>[1,1,1,1,1]
[2,-4,1,-3,-5]=>[-5,-3,1,-4,2]=>11010=>[2,1,1,1]
[2,-4,-1,3,5]=>[5,3,-1,-4,2]=>00110=>[2,2,1]
[2,-4,-1,3,-5]=>[-5,3,-1,-4,2]=>10110=>[1,1,2,1]
[2,-4,-1,-3,5]=>[5,-3,-1,-4,2]=>01110=>[1,3,1]
[2,-4,-1,-3,-5]=>[-5,-3,-1,-4,2]=>11110=>[4,1]
[-2,4,1,3,5]=>[5,3,1,4,-2]=>00001=>[4,1]
[-2,4,1,3,-5]=>[-5,3,1,4,-2]=>10001=>[1,3,1]
[-2,4,1,-3,5]=>[5,-3,1,4,-2]=>01001=>[1,1,2,1]
[-2,4,1,-3,-5]=>[-5,-3,1,4,-2]=>11001=>[2,2,1]
[-2,4,-1,3,5]=>[5,3,-1,4,-2]=>00101=>[2,1,1,1]
[-2,4,-1,3,-5]=>[-5,3,-1,4,-2]=>10101=>[1,1,1,1,1]
[-2,4,-1,-3,5]=>[5,-3,-1,4,-2]=>01101=>[1,2,1,1]
[-2,4,-1,-3,-5]=>[-5,-3,-1,4,-2]=>11101=>[3,1,1]
[-2,-4,1,3,5]=>[5,3,1,-4,-2]=>00011=>[3,2]
[-2,-4,1,3,-5]=>[-5,3,1,-4,-2]=>10011=>[1,2,2]
[-2,-4,1,-3,5]=>[5,-3,1,-4,-2]=>01011=>[1,1,1,2]
[-2,-4,1,-3,-5]=>[-5,-3,1,-4,-2]=>11011=>[2,1,2]
[-2,-4,-1,3,5]=>[5,3,-1,-4,-2]=>00111=>[2,3]
[-2,-4,-1,3,-5]=>[-5,3,-1,-4,-2]=>10111=>[1,1,3]
[-2,-4,-1,-3,5]=>[5,-3,-1,-4,-2]=>01111=>[1,4]
[-2,-4,-1,-3,-5]=>[-5,-3,-1,-4,-2]=>11111=>[5]
[2,4,1,5,3]=>[3,5,1,4,2]=>00000=>[5]
[2,4,1,5,-3]=>[-3,5,1,4,2]=>10000=>[1,4]
[2,4,1,-5,3]=>[3,-5,1,4,2]=>01000=>[1,1,3]
[2,4,1,-5,-3]=>[-3,-5,1,4,2]=>11000=>[2,3]
[2,4,-1,5,3]=>[3,5,-1,4,2]=>00100=>[2,1,2]
[2,4,-1,5,-3]=>[-3,5,-1,4,2]=>10100=>[1,1,1,2]
[2,4,-1,-5,3]=>[3,-5,-1,4,2]=>01100=>[1,2,2]
[2,4,-1,-5,-3]=>[-3,-5,-1,4,2]=>11100=>[3,2]
[2,-4,1,5,3]=>[3,5,1,-4,2]=>00010=>[3,1,1]
[2,-4,1,5,-3]=>[-3,5,1,-4,2]=>10010=>[1,2,1,1]
[2,-4,1,-5,3]=>[3,-5,1,-4,2]=>01010=>[1,1,1,1,1]
[2,-4,1,-5,-3]=>[-3,-5,1,-4,2]=>11010=>[2,1,1,1]
[2,-4,-1,5,3]=>[3,5,-1,-4,2]=>00110=>[2,2,1]
[2,-4,-1,5,-3]=>[-3,5,-1,-4,2]=>10110=>[1,1,2,1]
[2,-4,-1,-5,3]=>[3,-5,-1,-4,2]=>01110=>[1,3,1]
[2,-4,-1,-5,-3]=>[-3,-5,-1,-4,2]=>11110=>[4,1]
[-2,4,1,5,3]=>[3,5,1,4,-2]=>00001=>[4,1]
[-2,4,1,5,-3]=>[-3,5,1,4,-2]=>10001=>[1,3,1]
[-2,4,1,-5,3]=>[3,-5,1,4,-2]=>01001=>[1,1,2,1]
[-2,4,1,-5,-3]=>[-3,-5,1,4,-2]=>11001=>[2,2,1]
[-2,4,-1,5,3]=>[3,5,-1,4,-2]=>00101=>[2,1,1,1]
[-2,4,-1,5,-3]=>[-3,5,-1,4,-2]=>10101=>[1,1,1,1,1]
[-2,4,-1,-5,3]=>[3,-5,-1,4,-2]=>01101=>[1,2,1,1]
[-2,4,-1,-5,-3]=>[-3,-5,-1,4,-2]=>11101=>[3,1,1]
[-2,-4,1,5,3]=>[3,5,1,-4,-2]=>00011=>[3,2]
[-2,-4,1,5,-3]=>[-3,5,1,-4,-2]=>10011=>[1,2,2]
[-2,-4,1,-5,3]=>[3,-5,1,-4,-2]=>01011=>[1,1,1,2]
[-2,-4,1,-5,-3]=>[-3,-5,1,-4,-2]=>11011=>[2,1,2]
[-2,-4,-1,5,3]=>[3,5,-1,-4,-2]=>00111=>[2,3]
[-2,-4,-1,5,-3]=>[-3,5,-1,-4,-2]=>10111=>[1,1,3]
[-2,-4,-1,-5,3]=>[3,-5,-1,-4,-2]=>01111=>[1,4]
[-2,-4,-1,-5,-3]=>[-3,-5,-1,-4,-2]=>11111=>[5]
[2,4,3,1,5]=>[5,1,3,4,2]=>00000=>[5]
[2,4,3,1,-5]=>[-5,1,3,4,2]=>10000=>[1,4]
[2,4,3,-1,5]=>[5,-1,3,4,2]=>01000=>[1,1,3]
[2,4,3,-1,-5]=>[-5,-1,3,4,2]=>11000=>[2,3]
[2,4,-3,1,5]=>[5,1,-3,4,2]=>00100=>[2,1,2]
[2,4,-3,1,-5]=>[-5,1,-3,4,2]=>10100=>[1,1,1,2]
[2,4,-3,-1,5]=>[5,-1,-3,4,2]=>01100=>[1,2,2]
[2,4,-3,-1,-5]=>[-5,-1,-3,4,2]=>11100=>[3,2]
[2,-4,3,1,5]=>[5,1,3,-4,2]=>00010=>[3,1,1]
[2,-4,3,1,-5]=>[-5,1,3,-4,2]=>10010=>[1,2,1,1]
[2,-4,3,-1,5]=>[5,-1,3,-4,2]=>01010=>[1,1,1,1,1]
[2,-4,3,-1,-5]=>[-5,-1,3,-4,2]=>11010=>[2,1,1,1]
[2,-4,-3,1,5]=>[5,1,-3,-4,2]=>00110=>[2,2,1]
[2,-4,-3,1,-5]=>[-5,1,-3,-4,2]=>10110=>[1,1,2,1]
[2,-4,-3,-1,5]=>[5,-1,-3,-4,2]=>01110=>[1,3,1]
[2,-4,-3,-1,-5]=>[-5,-1,-3,-4,2]=>11110=>[4,1]
[-2,4,3,1,5]=>[5,1,3,4,-2]=>00001=>[4,1]
[-2,4,3,1,-5]=>[-5,1,3,4,-2]=>10001=>[1,3,1]
[-2,4,3,-1,5]=>[5,-1,3,4,-2]=>01001=>[1,1,2,1]
[-2,4,3,-1,-5]=>[-5,-1,3,4,-2]=>11001=>[2,2,1]
[-2,4,-3,1,5]=>[5,1,-3,4,-2]=>00101=>[2,1,1,1]
[-2,4,-3,1,-5]=>[-5,1,-3,4,-2]=>10101=>[1,1,1,1,1]
[-2,4,-3,-1,5]=>[5,-1,-3,4,-2]=>01101=>[1,2,1,1]
[-2,4,-3,-1,-5]=>[-5,-1,-3,4,-2]=>11101=>[3,1,1]
[-2,-4,3,1,5]=>[5,1,3,-4,-2]=>00011=>[3,2]
[-2,-4,3,1,-5]=>[-5,1,3,-4,-2]=>10011=>[1,2,2]
[-2,-4,3,-1,5]=>[5,-1,3,-4,-2]=>01011=>[1,1,1,2]
[-2,-4,3,-1,-5]=>[-5,-1,3,-4,-2]=>11011=>[2,1,2]
[-2,-4,-3,1,5]=>[5,1,-3,-4,-2]=>00111=>[2,3]
[-2,-4,-3,1,-5]=>[-5,1,-3,-4,-2]=>10111=>[1,1,3]
[-2,-4,-3,-1,5]=>[5,-1,-3,-4,-2]=>01111=>[1,4]
[-2,-4,-3,-1,-5]=>[-5,-1,-3,-4,-2]=>11111=>[5]
[2,4,3,5,1]=>[1,5,3,4,2]=>00000=>[5]
[2,4,3,5,-1]=>[-1,5,3,4,2]=>10000=>[1,4]
[2,4,3,-5,1]=>[1,-5,3,4,2]=>01000=>[1,1,3]
[2,4,3,-5,-1]=>[-1,-5,3,4,2]=>11000=>[2,3]
[2,4,-3,5,1]=>[1,5,-3,4,2]=>00100=>[2,1,2]
[2,4,-3,5,-1]=>[-1,5,-3,4,2]=>10100=>[1,1,1,2]
[2,4,-3,-5,1]=>[1,-5,-3,4,2]=>01100=>[1,2,2]
[2,4,-3,-5,-1]=>[-1,-5,-3,4,2]=>11100=>[3,2]
[2,-4,3,5,1]=>[1,5,3,-4,2]=>00010=>[3,1,1]
[2,-4,3,5,-1]=>[-1,5,3,-4,2]=>10010=>[1,2,1,1]
[2,-4,3,-5,1]=>[1,-5,3,-4,2]=>01010=>[1,1,1,1,1]
[2,-4,3,-5,-1]=>[-1,-5,3,-4,2]=>11010=>[2,1,1,1]
[2,-4,-3,5,1]=>[1,5,-3,-4,2]=>00110=>[2,2,1]
[2,-4,-3,5,-1]=>[-1,5,-3,-4,2]=>10110=>[1,1,2,1]
[2,-4,-3,-5,1]=>[1,-5,-3,-4,2]=>01110=>[1,3,1]
[2,-4,-3,-5,-1]=>[-1,-5,-3,-4,2]=>11110=>[4,1]
[-2,4,3,5,1]=>[1,5,3,4,-2]=>00001=>[4,1]
[-2,4,3,5,-1]=>[-1,5,3,4,-2]=>10001=>[1,3,1]
[-2,4,3,-5,1]=>[1,-5,3,4,-2]=>01001=>[1,1,2,1]
[-2,4,3,-5,-1]=>[-1,-5,3,4,-2]=>11001=>[2,2,1]
[-2,4,-3,5,1]=>[1,5,-3,4,-2]=>00101=>[2,1,1,1]
[-2,4,-3,5,-1]=>[-1,5,-3,4,-2]=>10101=>[1,1,1,1,1]
[-2,4,-3,-5,1]=>[1,-5,-3,4,-2]=>01101=>[1,2,1,1]
[-2,4,-3,-5,-1]=>[-1,-5,-3,4,-2]=>11101=>[3,1,1]
[-2,-4,3,5,1]=>[1,5,3,-4,-2]=>00011=>[3,2]
[-2,-4,3,5,-1]=>[-1,5,3,-4,-2]=>10011=>[1,2,2]
[-2,-4,3,-5,1]=>[1,-5,3,-4,-2]=>01011=>[1,1,1,2]
[-2,-4,3,-5,-1]=>[-1,-5,3,-4,-2]=>11011=>[2,1,2]
[-2,-4,-3,5,1]=>[1,5,-3,-4,-2]=>00111=>[2,3]
[-2,-4,-3,5,-1]=>[-1,5,-3,-4,-2]=>10111=>[1,1,3]
[-2,-4,-3,-5,1]=>[1,-5,-3,-4,-2]=>01111=>[1,4]
[-2,-4,-3,-5,-1]=>[-1,-5,-3,-4,-2]=>11111=>[5]
[2,4,5,1,3]=>[3,1,5,4,2]=>00000=>[5]
[2,4,5,1,-3]=>[-3,1,5,4,2]=>10000=>[1,4]
[2,4,5,-1,3]=>[3,-1,5,4,2]=>01000=>[1,1,3]
[2,4,5,-1,-3]=>[-3,-1,5,4,2]=>11000=>[2,3]
[2,4,-5,1,3]=>[3,1,-5,4,2]=>00100=>[2,1,2]
[2,4,-5,1,-3]=>[-3,1,-5,4,2]=>10100=>[1,1,1,2]
[2,4,-5,-1,3]=>[3,-1,-5,4,2]=>01100=>[1,2,2]
[2,4,-5,-1,-3]=>[-3,-1,-5,4,2]=>11100=>[3,2]
[2,-4,5,1,3]=>[3,1,5,-4,2]=>00010=>[3,1,1]
[2,-4,5,1,-3]=>[-3,1,5,-4,2]=>10010=>[1,2,1,1]
[2,-4,5,-1,3]=>[3,-1,5,-4,2]=>01010=>[1,1,1,1,1]
[2,-4,5,-1,-3]=>[-3,-1,5,-4,2]=>11010=>[2,1,1,1]
[2,-4,-5,1,3]=>[3,1,-5,-4,2]=>00110=>[2,2,1]
[2,-4,-5,1,-3]=>[-3,1,-5,-4,2]=>10110=>[1,1,2,1]
[2,-4,-5,-1,3]=>[3,-1,-5,-4,2]=>01110=>[1,3,1]
[2,-4,-5,-1,-3]=>[-3,-1,-5,-4,2]=>11110=>[4,1]
[-2,4,5,1,3]=>[3,1,5,4,-2]=>00001=>[4,1]
[-2,4,5,1,-3]=>[-3,1,5,4,-2]=>10001=>[1,3,1]
[-2,4,5,-1,3]=>[3,-1,5,4,-2]=>01001=>[1,1,2,1]
[-2,4,5,-1,-3]=>[-3,-1,5,4,-2]=>11001=>[2,2,1]
[-2,4,-5,1,3]=>[3,1,-5,4,-2]=>00101=>[2,1,1,1]
[-2,4,-5,1,-3]=>[-3,1,-5,4,-2]=>10101=>[1,1,1,1,1]
[-2,4,-5,-1,3]=>[3,-1,-5,4,-2]=>01101=>[1,2,1,1]
[-2,4,-5,-1,-3]=>[-3,-1,-5,4,-2]=>11101=>[3,1,1]
[-2,-4,5,1,3]=>[3,1,5,-4,-2]=>00011=>[3,2]
[-2,-4,5,1,-3]=>[-3,1,5,-4,-2]=>10011=>[1,2,2]
[-2,-4,5,-1,3]=>[3,-1,5,-4,-2]=>01011=>[1,1,1,2]
[-2,-4,5,-1,-3]=>[-3,-1,5,-4,-2]=>11011=>[2,1,2]
[-2,-4,-5,1,3]=>[3,1,-5,-4,-2]=>00111=>[2,3]
[-2,-4,-5,1,-3]=>[-3,1,-5,-4,-2]=>10111=>[1,1,3]
[-2,-4,-5,-1,3]=>[3,-1,-5,-4,-2]=>01111=>[1,4]
[-2,-4,-5,-1,-3]=>[-3,-1,-5,-4,-2]=>11111=>[5]
[2,4,5,3,1]=>[1,3,5,4,2]=>00000=>[5]
[2,4,5,3,-1]=>[-1,3,5,4,2]=>10000=>[1,4]
[2,4,5,-3,1]=>[1,-3,5,4,2]=>01000=>[1,1,3]
[2,4,5,-3,-1]=>[-1,-3,5,4,2]=>11000=>[2,3]
[2,4,-5,3,1]=>[1,3,-5,4,2]=>00100=>[2,1,2]
[2,4,-5,3,-1]=>[-1,3,-5,4,2]=>10100=>[1,1,1,2]
[2,4,-5,-3,1]=>[1,-3,-5,4,2]=>01100=>[1,2,2]
[2,4,-5,-3,-1]=>[-1,-3,-5,4,2]=>11100=>[3,2]
[2,-4,5,3,1]=>[1,3,5,-4,2]=>00010=>[3,1,1]
[2,-4,5,3,-1]=>[-1,3,5,-4,2]=>10010=>[1,2,1,1]
[2,-4,5,-3,1]=>[1,-3,5,-4,2]=>01010=>[1,1,1,1,1]
[2,-4,5,-3,-1]=>[-1,-3,5,-4,2]=>11010=>[2,1,1,1]
[2,-4,-5,3,1]=>[1,3,-5,-4,2]=>00110=>[2,2,1]
[2,-4,-5,3,-1]=>[-1,3,-5,-4,2]=>10110=>[1,1,2,1]
[2,-4,-5,-3,1]=>[1,-3,-5,-4,2]=>01110=>[1,3,1]
[2,-4,-5,-3,-1]=>[-1,-3,-5,-4,2]=>11110=>[4,1]
[-2,4,5,3,1]=>[1,3,5,4,-2]=>00001=>[4,1]
[-2,4,5,3,-1]=>[-1,3,5,4,-2]=>10001=>[1,3,1]
[-2,4,5,-3,1]=>[1,-3,5,4,-2]=>01001=>[1,1,2,1]
[-2,4,5,-3,-1]=>[-1,-3,5,4,-2]=>11001=>[2,2,1]
[-2,4,-5,3,1]=>[1,3,-5,4,-2]=>00101=>[2,1,1,1]
[-2,4,-5,3,-1]=>[-1,3,-5,4,-2]=>10101=>[1,1,1,1,1]
[-2,4,-5,-3,1]=>[1,-3,-5,4,-2]=>01101=>[1,2,1,1]
[-2,4,-5,-3,-1]=>[-1,-3,-5,4,-2]=>11101=>[3,1,1]
[-2,-4,5,3,1]=>[1,3,5,-4,-2]=>00011=>[3,2]
[-2,-4,5,3,-1]=>[-1,3,5,-4,-2]=>10011=>[1,2,2]
[-2,-4,5,-3,1]=>[1,-3,5,-4,-2]=>01011=>[1,1,1,2]
[-2,-4,5,-3,-1]=>[-1,-3,5,-4,-2]=>11011=>[2,1,2]
[-2,-4,-5,3,1]=>[1,3,-5,-4,-2]=>00111=>[2,3]
[-2,-4,-5,3,-1]=>[-1,3,-5,-4,-2]=>10111=>[1,1,3]
[-2,-4,-5,-3,1]=>[1,-3,-5,-4,-2]=>01111=>[1,4]
[-2,-4,-5,-3,-1]=>[-1,-3,-5,-4,-2]=>11111=>[5]
[2,5,1,3,4]=>[4,3,1,5,2]=>00000=>[5]
[2,5,1,3,-4]=>[-4,3,1,5,2]=>10000=>[1,4]
[2,5,1,-3,4]=>[4,-3,1,5,2]=>01000=>[1,1,3]
[2,5,1,-3,-4]=>[-4,-3,1,5,2]=>11000=>[2,3]
[2,5,-1,3,4]=>[4,3,-1,5,2]=>00100=>[2,1,2]
[2,5,-1,3,-4]=>[-4,3,-1,5,2]=>10100=>[1,1,1,2]
[2,5,-1,-3,4]=>[4,-3,-1,5,2]=>01100=>[1,2,2]
[2,5,-1,-3,-4]=>[-4,-3,-1,5,2]=>11100=>[3,2]
[2,-5,1,3,4]=>[4,3,1,-5,2]=>00010=>[3,1,1]
[2,-5,1,3,-4]=>[-4,3,1,-5,2]=>10010=>[1,2,1,1]
[2,-5,1,-3,4]=>[4,-3,1,-5,2]=>01010=>[1,1,1,1,1]
[2,-5,1,-3,-4]=>[-4,-3,1,-5,2]=>11010=>[2,1,1,1]
[2,-5,-1,3,4]=>[4,3,-1,-5,2]=>00110=>[2,2,1]
[2,-5,-1,3,-4]=>[-4,3,-1,-5,2]=>10110=>[1,1,2,1]
[2,-5,-1,-3,4]=>[4,-3,-1,-5,2]=>01110=>[1,3,1]
[2,-5,-1,-3,-4]=>[-4,-3,-1,-5,2]=>11110=>[4,1]
[-2,5,1,3,4]=>[4,3,1,5,-2]=>00001=>[4,1]
[-2,5,1,3,-4]=>[-4,3,1,5,-2]=>10001=>[1,3,1]
[-2,5,1,-3,4]=>[4,-3,1,5,-2]=>01001=>[1,1,2,1]
[-2,5,1,-3,-4]=>[-4,-3,1,5,-2]=>11001=>[2,2,1]
[-2,5,-1,3,4]=>[4,3,-1,5,-2]=>00101=>[2,1,1,1]
[-2,5,-1,3,-4]=>[-4,3,-1,5,-2]=>10101=>[1,1,1,1,1]
[-2,5,-1,-3,4]=>[4,-3,-1,5,-2]=>01101=>[1,2,1,1]
[-2,5,-1,-3,-4]=>[-4,-3,-1,5,-2]=>11101=>[3,1,1]
[-2,-5,1,3,4]=>[4,3,1,-5,-2]=>00011=>[3,2]
[-2,-5,1,3,-4]=>[-4,3,1,-5,-2]=>10011=>[1,2,2]
[-2,-5,1,-3,4]=>[4,-3,1,-5,-2]=>01011=>[1,1,1,2]
[-2,-5,1,-3,-4]=>[-4,-3,1,-5,-2]=>11011=>[2,1,2]
[-2,-5,-1,3,4]=>[4,3,-1,-5,-2]=>00111=>[2,3]
[-2,-5,-1,3,-4]=>[-4,3,-1,-5,-2]=>10111=>[1,1,3]
[-2,-5,-1,-3,4]=>[4,-3,-1,-5,-2]=>01111=>[1,4]
[-2,-5,-1,-3,-4]=>[-4,-3,-1,-5,-2]=>11111=>[5]
[2,5,1,4,3]=>[3,4,1,5,2]=>00000=>[5]
[2,5,1,4,-3]=>[-3,4,1,5,2]=>10000=>[1,4]
[2,5,1,-4,3]=>[3,-4,1,5,2]=>01000=>[1,1,3]
[2,5,1,-4,-3]=>[-3,-4,1,5,2]=>11000=>[2,3]
[2,5,-1,4,3]=>[3,4,-1,5,2]=>00100=>[2,1,2]
[2,5,-1,4,-3]=>[-3,4,-1,5,2]=>10100=>[1,1,1,2]
[2,5,-1,-4,3]=>[3,-4,-1,5,2]=>01100=>[1,2,2]
[2,5,-1,-4,-3]=>[-3,-4,-1,5,2]=>11100=>[3,2]
[2,-5,1,4,3]=>[3,4,1,-5,2]=>00010=>[3,1,1]
[2,-5,1,4,-3]=>[-3,4,1,-5,2]=>10010=>[1,2,1,1]
[2,-5,1,-4,3]=>[3,-4,1,-5,2]=>01010=>[1,1,1,1,1]
[2,-5,1,-4,-3]=>[-3,-4,1,-5,2]=>11010=>[2,1,1,1]
[2,-5,-1,4,3]=>[3,4,-1,-5,2]=>00110=>[2,2,1]
[2,-5,-1,4,-3]=>[-3,4,-1,-5,2]=>10110=>[1,1,2,1]
[2,-5,-1,-4,3]=>[3,-4,-1,-5,2]=>01110=>[1,3,1]
[2,-5,-1,-4,-3]=>[-3,-4,-1,-5,2]=>11110=>[4,1]
[-2,5,1,4,3]=>[3,4,1,5,-2]=>00001=>[4,1]
[-2,5,1,4,-3]=>[-3,4,1,5,-2]=>10001=>[1,3,1]
[-2,5,1,-4,3]=>[3,-4,1,5,-2]=>01001=>[1,1,2,1]
[-2,5,1,-4,-3]=>[-3,-4,1,5,-2]=>11001=>[2,2,1]
[-2,5,-1,4,3]=>[3,4,-1,5,-2]=>00101=>[2,1,1,1]
[-2,5,-1,4,-3]=>[-3,4,-1,5,-2]=>10101=>[1,1,1,1,1]
[-2,5,-1,-4,3]=>[3,-4,-1,5,-2]=>01101=>[1,2,1,1]
[-2,5,-1,-4,-3]=>[-3,-4,-1,5,-2]=>11101=>[3,1,1]
[-2,-5,1,4,3]=>[3,4,1,-5,-2]=>00011=>[3,2]
[-2,-5,1,4,-3]=>[-3,4,1,-5,-2]=>10011=>[1,2,2]
[-2,-5,1,-4,3]=>[3,-4,1,-5,-2]=>01011=>[1,1,1,2]
[-2,-5,1,-4,-3]=>[-3,-4,1,-5,-2]=>11011=>[2,1,2]
[-2,-5,-1,4,3]=>[3,4,-1,-5,-2]=>00111=>[2,3]
[-2,-5,-1,4,-3]=>[-3,4,-1,-5,-2]=>10111=>[1,1,3]
[-2,-5,-1,-4,3]=>[3,-4,-1,-5,-2]=>01111=>[1,4]
[-2,-5,-1,-4,-3]=>[-3,-4,-1,-5,-2]=>11111=>[5]
[2,5,3,1,4]=>[4,1,3,5,2]=>00000=>[5]
[2,5,3,1,-4]=>[-4,1,3,5,2]=>10000=>[1,4]
[2,5,3,-1,4]=>[4,-1,3,5,2]=>01000=>[1,1,3]
[2,5,3,-1,-4]=>[-4,-1,3,5,2]=>11000=>[2,3]
[2,5,-3,1,4]=>[4,1,-3,5,2]=>00100=>[2,1,2]
[2,5,-3,1,-4]=>[-4,1,-3,5,2]=>10100=>[1,1,1,2]
[2,5,-3,-1,4]=>[4,-1,-3,5,2]=>01100=>[1,2,2]
[2,5,-3,-1,-4]=>[-4,-1,-3,5,2]=>11100=>[3,2]
[2,-5,3,1,4]=>[4,1,3,-5,2]=>00010=>[3,1,1]
[2,-5,3,1,-4]=>[-4,1,3,-5,2]=>10010=>[1,2,1,1]
[2,-5,3,-1,4]=>[4,-1,3,-5,2]=>01010=>[1,1,1,1,1]
[2,-5,3,-1,-4]=>[-4,-1,3,-5,2]=>11010=>[2,1,1,1]
[2,-5,-3,1,4]=>[4,1,-3,-5,2]=>00110=>[2,2,1]
[2,-5,-3,1,-4]=>[-4,1,-3,-5,2]=>10110=>[1,1,2,1]
[2,-5,-3,-1,4]=>[4,-1,-3,-5,2]=>01110=>[1,3,1]
[2,-5,-3,-1,-4]=>[-4,-1,-3,-5,2]=>11110=>[4,1]
[-2,5,3,1,4]=>[4,1,3,5,-2]=>00001=>[4,1]
[-2,5,3,1,-4]=>[-4,1,3,5,-2]=>10001=>[1,3,1]
[-2,5,3,-1,4]=>[4,-1,3,5,-2]=>01001=>[1,1,2,1]
[-2,5,3,-1,-4]=>[-4,-1,3,5,-2]=>11001=>[2,2,1]
[-2,5,-3,1,4]=>[4,1,-3,5,-2]=>00101=>[2,1,1,1]
[-2,5,-3,1,-4]=>[-4,1,-3,5,-2]=>10101=>[1,1,1,1,1]
[-2,5,-3,-1,4]=>[4,-1,-3,5,-2]=>01101=>[1,2,1,1]
[-2,5,-3,-1,-4]=>[-4,-1,-3,5,-2]=>11101=>[3,1,1]
[-2,-5,3,1,4]=>[4,1,3,-5,-2]=>00011=>[3,2]
[-2,-5,3,1,-4]=>[-4,1,3,-5,-2]=>10011=>[1,2,2]
[-2,-5,3,-1,4]=>[4,-1,3,-5,-2]=>01011=>[1,1,1,2]
[-2,-5,3,-1,-4]=>[-4,-1,3,-5,-2]=>11011=>[2,1,2]
[-2,-5,-3,1,4]=>[4,1,-3,-5,-2]=>00111=>[2,3]
[-2,-5,-3,1,-4]=>[-4,1,-3,-5,-2]=>10111=>[1,1,3]
[-2,-5,-3,-1,4]=>[4,-1,-3,-5,-2]=>01111=>[1,4]
[-2,-5,-3,-1,-4]=>[-4,-1,-3,-5,-2]=>11111=>[5]
[2,5,3,4,1]=>[1,4,3,5,2]=>00000=>[5]
[2,5,3,4,-1]=>[-1,4,3,5,2]=>10000=>[1,4]
[2,5,3,-4,1]=>[1,-4,3,5,2]=>01000=>[1,1,3]
[2,5,3,-4,-1]=>[-1,-4,3,5,2]=>11000=>[2,3]
[2,5,-3,4,1]=>[1,4,-3,5,2]=>00100=>[2,1,2]
[2,5,-3,4,-1]=>[-1,4,-3,5,2]=>10100=>[1,1,1,2]
[2,5,-3,-4,1]=>[1,-4,-3,5,2]=>01100=>[1,2,2]
[2,5,-3,-4,-1]=>[-1,-4,-3,5,2]=>11100=>[3,2]
[2,-5,3,4,1]=>[1,4,3,-5,2]=>00010=>[3,1,1]
[2,-5,3,4,-1]=>[-1,4,3,-5,2]=>10010=>[1,2,1,1]
[2,-5,3,-4,1]=>[1,-4,3,-5,2]=>01010=>[1,1,1,1,1]
[2,-5,3,-4,-1]=>[-1,-4,3,-5,2]=>11010=>[2,1,1,1]
[2,-5,-3,4,1]=>[1,4,-3,-5,2]=>00110=>[2,2,1]
[2,-5,-3,4,-1]=>[-1,4,-3,-5,2]=>10110=>[1,1,2,1]
[2,-5,-3,-4,1]=>[1,-4,-3,-5,2]=>01110=>[1,3,1]
[2,-5,-3,-4,-1]=>[-1,-4,-3,-5,2]=>11110=>[4,1]
[-2,5,3,4,1]=>[1,4,3,5,-2]=>00001=>[4,1]
[-2,5,3,4,-1]=>[-1,4,3,5,-2]=>10001=>[1,3,1]
[-2,5,3,-4,1]=>[1,-4,3,5,-2]=>01001=>[1,1,2,1]
[-2,5,3,-4,-1]=>[-1,-4,3,5,-2]=>11001=>[2,2,1]
[-2,5,-3,4,1]=>[1,4,-3,5,-2]=>00101=>[2,1,1,1]
[-2,5,-3,4,-1]=>[-1,4,-3,5,-2]=>10101=>[1,1,1,1,1]
[-2,5,-3,-4,1]=>[1,-4,-3,5,-2]=>01101=>[1,2,1,1]
[-2,5,-3,-4,-1]=>[-1,-4,-3,5,-2]=>11101=>[3,1,1]
[-2,-5,3,4,1]=>[1,4,3,-5,-2]=>00011=>[3,2]
[-2,-5,3,4,-1]=>[-1,4,3,-5,-2]=>10011=>[1,2,2]
[-2,-5,3,-4,1]=>[1,-4,3,-5,-2]=>01011=>[1,1,1,2]
[-2,-5,3,-4,-1]=>[-1,-4,3,-5,-2]=>11011=>[2,1,2]
[-2,-5,-3,4,1]=>[1,4,-3,-5,-2]=>00111=>[2,3]
[-2,-5,-3,4,-1]=>[-1,4,-3,-5,-2]=>10111=>[1,1,3]
[-2,-5,-3,-4,1]=>[1,-4,-3,-5,-2]=>01111=>[1,4]
[-2,-5,-3,-4,-1]=>[-1,-4,-3,-5,-2]=>11111=>[5]
[2,5,4,1,3]=>[3,1,4,5,2]=>00000=>[5]
[2,5,4,1,-3]=>[-3,1,4,5,2]=>10000=>[1,4]
[2,5,4,-1,3]=>[3,-1,4,5,2]=>01000=>[1,1,3]
[2,5,4,-1,-3]=>[-3,-1,4,5,2]=>11000=>[2,3]
[2,5,-4,1,3]=>[3,1,-4,5,2]=>00100=>[2,1,2]
[2,5,-4,1,-3]=>[-3,1,-4,5,2]=>10100=>[1,1,1,2]
[2,5,-4,-1,3]=>[3,-1,-4,5,2]=>01100=>[1,2,2]
[2,5,-4,-1,-3]=>[-3,-1,-4,5,2]=>11100=>[3,2]
[2,-5,4,1,3]=>[3,1,4,-5,2]=>00010=>[3,1,1]
[2,-5,4,1,-3]=>[-3,1,4,-5,2]=>10010=>[1,2,1,1]
[2,-5,4,-1,3]=>[3,-1,4,-5,2]=>01010=>[1,1,1,1,1]
[2,-5,4,-1,-3]=>[-3,-1,4,-5,2]=>11010=>[2,1,1,1]
[2,-5,-4,1,3]=>[3,1,-4,-5,2]=>00110=>[2,2,1]
[2,-5,-4,1,-3]=>[-3,1,-4,-5,2]=>10110=>[1,1,2,1]
[2,-5,-4,-1,3]=>[3,-1,-4,-5,2]=>01110=>[1,3,1]
[2,-5,-4,-1,-3]=>[-3,-1,-4,-5,2]=>11110=>[4,1]
[-2,5,4,1,3]=>[3,1,4,5,-2]=>00001=>[4,1]
[-2,5,4,1,-3]=>[-3,1,4,5,-2]=>10001=>[1,3,1]
[-2,5,4,-1,3]=>[3,-1,4,5,-2]=>01001=>[1,1,2,1]
[-2,5,4,-1,-3]=>[-3,-1,4,5,-2]=>11001=>[2,2,1]
[-2,5,-4,1,3]=>[3,1,-4,5,-2]=>00101=>[2,1,1,1]
[-2,5,-4,1,-3]=>[-3,1,-4,5,-2]=>10101=>[1,1,1,1,1]
[-2,5,-4,-1,3]=>[3,-1,-4,5,-2]=>01101=>[1,2,1,1]
[-2,5,-4,-1,-3]=>[-3,-1,-4,5,-2]=>11101=>[3,1,1]
[-2,-5,4,1,3]=>[3,1,4,-5,-2]=>00011=>[3,2]
[-2,-5,4,1,-3]=>[-3,1,4,-5,-2]=>10011=>[1,2,2]
[-2,-5,4,-1,3]=>[3,-1,4,-5,-2]=>01011=>[1,1,1,2]
[-2,-5,4,-1,-3]=>[-3,-1,4,-5,-2]=>11011=>[2,1,2]
[-2,-5,-4,1,3]=>[3,1,-4,-5,-2]=>00111=>[2,3]
[-2,-5,-4,1,-3]=>[-3,1,-4,-5,-2]=>10111=>[1,1,3]
[-2,-5,-4,-1,3]=>[3,-1,-4,-5,-2]=>01111=>[1,4]
[-2,-5,-4,-1,-3]=>[-3,-1,-4,-5,-2]=>11111=>[5]
[2,5,4,3,1]=>[1,3,4,5,2]=>00000=>[5]
[2,5,4,3,-1]=>[-1,3,4,5,2]=>10000=>[1,4]
[2,5,4,-3,1]=>[1,-3,4,5,2]=>01000=>[1,1,3]
[2,5,4,-3,-1]=>[-1,-3,4,5,2]=>11000=>[2,3]
[2,5,-4,3,1]=>[1,3,-4,5,2]=>00100=>[2,1,2]
[2,5,-4,3,-1]=>[-1,3,-4,5,2]=>10100=>[1,1,1,2]
[2,5,-4,-3,1]=>[1,-3,-4,5,2]=>01100=>[1,2,2]
[2,5,-4,-3,-1]=>[-1,-3,-4,5,2]=>11100=>[3,2]
[2,-5,4,3,1]=>[1,3,4,-5,2]=>00010=>[3,1,1]
[2,-5,4,3,-1]=>[-1,3,4,-5,2]=>10010=>[1,2,1,1]
[2,-5,4,-3,1]=>[1,-3,4,-5,2]=>01010=>[1,1,1,1,1]
[2,-5,4,-3,-1]=>[-1,-3,4,-5,2]=>11010=>[2,1,1,1]
[2,-5,-4,3,1]=>[1,3,-4,-5,2]=>00110=>[2,2,1]
[2,-5,-4,3,-1]=>[-1,3,-4,-5,2]=>10110=>[1,1,2,1]
[2,-5,-4,-3,1]=>[1,-3,-4,-5,2]=>01110=>[1,3,1]
[2,-5,-4,-3,-1]=>[-1,-3,-4,-5,2]=>11110=>[4,1]
[-2,5,4,3,1]=>[1,3,4,5,-2]=>00001=>[4,1]
[-2,5,4,3,-1]=>[-1,3,4,5,-2]=>10001=>[1,3,1]
[-2,5,4,-3,1]=>[1,-3,4,5,-2]=>01001=>[1,1,2,1]
[-2,5,4,-3,-1]=>[-1,-3,4,5,-2]=>11001=>[2,2,1]
[-2,5,-4,3,1]=>[1,3,-4,5,-2]=>00101=>[2,1,1,1]
[-2,5,-4,3,-1]=>[-1,3,-4,5,-2]=>10101=>[1,1,1,1,1]
[-2,5,-4,-3,1]=>[1,-3,-4,5,-2]=>01101=>[1,2,1,1]
[-2,5,-4,-3,-1]=>[-1,-3,-4,5,-2]=>11101=>[3,1,1]
[-2,-5,4,3,1]=>[1,3,4,-5,-2]=>00011=>[3,2]
[-2,-5,4,3,-1]=>[-1,3,4,-5,-2]=>10011=>[1,2,2]
[-2,-5,4,-3,1]=>[1,-3,4,-5,-2]=>01011=>[1,1,1,2]
[-2,-5,4,-3,-1]=>[-1,-3,4,-5,-2]=>11011=>[2,1,2]
[-2,-5,-4,3,1]=>[1,3,-4,-5,-2]=>00111=>[2,3]
[-2,-5,-4,3,-1]=>[-1,3,-4,-5,-2]=>10111=>[1,1,3]
[-2,-5,-4,-3,1]=>[1,-3,-4,-5,-2]=>01111=>[1,4]
[-2,-5,-4,-3,-1]=>[-1,-3,-4,-5,-2]=>11111=>[5]
[3,1,2,4,5]=>[5,4,2,1,3]=>00000=>[5]
[3,1,2,4,-5]=>[-5,4,2,1,3]=>10000=>[1,4]
[3,1,2,-4,5]=>[5,-4,2,1,3]=>01000=>[1,1,3]
[3,1,2,-4,-5]=>[-5,-4,2,1,3]=>11000=>[2,3]
[3,1,-2,4,5]=>[5,4,-2,1,3]=>00100=>[2,1,2]
[3,1,-2,4,-5]=>[-5,4,-2,1,3]=>10100=>[1,1,1,2]
[3,1,-2,-4,5]=>[5,-4,-2,1,3]=>01100=>[1,2,2]
[3,1,-2,-4,-5]=>[-5,-4,-2,1,3]=>11100=>[3,2]
[3,-1,2,4,5]=>[5,4,2,-1,3]=>00010=>[3,1,1]
[3,-1,2,4,-5]=>[-5,4,2,-1,3]=>10010=>[1,2,1,1]
[3,-1,2,-4,5]=>[5,-4,2,-1,3]=>01010=>[1,1,1,1,1]
[3,-1,2,-4,-5]=>[-5,-4,2,-1,3]=>11010=>[2,1,1,1]
[3,-1,-2,4,5]=>[5,4,-2,-1,3]=>00110=>[2,2,1]
[3,-1,-2,4,-5]=>[-5,4,-2,-1,3]=>10110=>[1,1,2,1]
[3,-1,-2,-4,5]=>[5,-4,-2,-1,3]=>01110=>[1,3,1]
[3,-1,-2,-4,-5]=>[-5,-4,-2,-1,3]=>11110=>[4,1]
[-3,1,2,4,5]=>[5,4,2,1,-3]=>00001=>[4,1]
[-3,1,2,4,-5]=>[-5,4,2,1,-3]=>10001=>[1,3,1]
[-3,1,2,-4,5]=>[5,-4,2,1,-3]=>01001=>[1,1,2,1]
[-3,1,2,-4,-5]=>[-5,-4,2,1,-3]=>11001=>[2,2,1]
[-3,1,-2,4,5]=>[5,4,-2,1,-3]=>00101=>[2,1,1,1]
[-3,1,-2,4,-5]=>[-5,4,-2,1,-3]=>10101=>[1,1,1,1,1]
[-3,1,-2,-4,5]=>[5,-4,-2,1,-3]=>01101=>[1,2,1,1]
[-3,1,-2,-4,-5]=>[-5,-4,-2,1,-3]=>11101=>[3,1,1]
[-3,-1,2,4,5]=>[5,4,2,-1,-3]=>00011=>[3,2]
[-3,-1,2,4,-5]=>[-5,4,2,-1,-3]=>10011=>[1,2,2]
[-3,-1,2,-4,5]=>[5,-4,2,-1,-3]=>01011=>[1,1,1,2]
[-3,-1,2,-4,-5]=>[-5,-4,2,-1,-3]=>11011=>[2,1,2]
[-3,-1,-2,4,5]=>[5,4,-2,-1,-3]=>00111=>[2,3]
[-3,-1,-2,4,-5]=>[-5,4,-2,-1,-3]=>10111=>[1,1,3]
[-3,-1,-2,-4,5]=>[5,-4,-2,-1,-3]=>01111=>[1,4]
[-3,-1,-2,-4,-5]=>[-5,-4,-2,-1,-3]=>11111=>[5]
[3,1,2,5,4]=>[4,5,2,1,3]=>00000=>[5]
[3,1,2,5,-4]=>[-4,5,2,1,3]=>10000=>[1,4]
[3,1,2,-5,4]=>[4,-5,2,1,3]=>01000=>[1,1,3]
[3,1,2,-5,-4]=>[-4,-5,2,1,3]=>11000=>[2,3]
[3,1,-2,5,4]=>[4,5,-2,1,3]=>00100=>[2,1,2]
[3,1,-2,5,-4]=>[-4,5,-2,1,3]=>10100=>[1,1,1,2]
[3,1,-2,-5,4]=>[4,-5,-2,1,3]=>01100=>[1,2,2]
[3,1,-2,-5,-4]=>[-4,-5,-2,1,3]=>11100=>[3,2]
[3,-1,2,5,4]=>[4,5,2,-1,3]=>00010=>[3,1,1]
[3,-1,2,5,-4]=>[-4,5,2,-1,3]=>10010=>[1,2,1,1]
[3,-1,2,-5,4]=>[4,-5,2,-1,3]=>01010=>[1,1,1,1,1]
[3,-1,2,-5,-4]=>[-4,-5,2,-1,3]=>11010=>[2,1,1,1]
[3,-1,-2,5,4]=>[4,5,-2,-1,3]=>00110=>[2,2,1]
[3,-1,-2,5,-4]=>[-4,5,-2,-1,3]=>10110=>[1,1,2,1]
[3,-1,-2,-5,4]=>[4,-5,-2,-1,3]=>01110=>[1,3,1]
[3,-1,-2,-5,-4]=>[-4,-5,-2,-1,3]=>11110=>[4,1]
[-3,1,2,5,4]=>[4,5,2,1,-3]=>00001=>[4,1]
[-3,1,2,5,-4]=>[-4,5,2,1,-3]=>10001=>[1,3,1]
[-3,1,2,-5,4]=>[4,-5,2,1,-3]=>01001=>[1,1,2,1]
[-3,1,2,-5,-4]=>[-4,-5,2,1,-3]=>11001=>[2,2,1]
[-3,1,-2,5,4]=>[4,5,-2,1,-3]=>00101=>[2,1,1,1]
[-3,1,-2,5,-4]=>[-4,5,-2,1,-3]=>10101=>[1,1,1,1,1]
[-3,1,-2,-5,4]=>[4,-5,-2,1,-3]=>01101=>[1,2,1,1]
[-3,1,-2,-5,-4]=>[-4,-5,-2,1,-3]=>11101=>[3,1,1]
[-3,-1,2,5,4]=>[4,5,2,-1,-3]=>00011=>[3,2]
[-3,-1,2,5,-4]=>[-4,5,2,-1,-3]=>10011=>[1,2,2]
[-3,-1,2,-5,4]=>[4,-5,2,-1,-3]=>01011=>[1,1,1,2]
[-3,-1,2,-5,-4]=>[-4,-5,2,-1,-3]=>11011=>[2,1,2]
[-3,-1,-2,5,4]=>[4,5,-2,-1,-3]=>00111=>[2,3]
[-3,-1,-2,5,-4]=>[-4,5,-2,-1,-3]=>10111=>[1,1,3]
[-3,-1,-2,-5,4]=>[4,-5,-2,-1,-3]=>01111=>[1,4]
[-3,-1,-2,-5,-4]=>[-4,-5,-2,-1,-3]=>11111=>[5]
[3,1,4,2,5]=>[5,2,4,1,3]=>00000=>[5]
[3,1,4,2,-5]=>[-5,2,4,1,3]=>10000=>[1,4]
[3,1,4,-2,5]=>[5,-2,4,1,3]=>01000=>[1,1,3]
[3,1,4,-2,-5]=>[-5,-2,4,1,3]=>11000=>[2,3]
[3,1,-4,2,5]=>[5,2,-4,1,3]=>00100=>[2,1,2]
[3,1,-4,2,-5]=>[-5,2,-4,1,3]=>10100=>[1,1,1,2]
[3,1,-4,-2,5]=>[5,-2,-4,1,3]=>01100=>[1,2,2]
[3,1,-4,-2,-5]=>[-5,-2,-4,1,3]=>11100=>[3,2]
[3,-1,4,2,5]=>[5,2,4,-1,3]=>00010=>[3,1,1]
[3,-1,4,2,-5]=>[-5,2,4,-1,3]=>10010=>[1,2,1,1]
[3,-1,4,-2,5]=>[5,-2,4,-1,3]=>01010=>[1,1,1,1,1]
[3,-1,4,-2,-5]=>[-5,-2,4,-1,3]=>11010=>[2,1,1,1]
[3,-1,-4,2,5]=>[5,2,-4,-1,3]=>00110=>[2,2,1]
[3,-1,-4,2,-5]=>[-5,2,-4,-1,3]=>10110=>[1,1,2,1]
[3,-1,-4,-2,5]=>[5,-2,-4,-1,3]=>01110=>[1,3,1]
[3,-1,-4,-2,-5]=>[-5,-2,-4,-1,3]=>11110=>[4,1]
[-3,1,4,2,5]=>[5,2,4,1,-3]=>00001=>[4,1]
[-3,1,4,2,-5]=>[-5,2,4,1,-3]=>10001=>[1,3,1]
[-3,1,4,-2,5]=>[5,-2,4,1,-3]=>01001=>[1,1,2,1]
[-3,1,4,-2,-5]=>[-5,-2,4,1,-3]=>11001=>[2,2,1]
[-3,1,-4,2,5]=>[5,2,-4,1,-3]=>00101=>[2,1,1,1]
[-3,1,-4,2,-5]=>[-5,2,-4,1,-3]=>10101=>[1,1,1,1,1]
[-3,1,-4,-2,5]=>[5,-2,-4,1,-3]=>01101=>[1,2,1,1]
[-3,1,-4,-2,-5]=>[-5,-2,-4,1,-3]=>11101=>[3,1,1]
[-3,-1,4,2,5]=>[5,2,4,-1,-3]=>00011=>[3,2]
[-3,-1,4,2,-5]=>[-5,2,4,-1,-3]=>10011=>[1,2,2]
[-3,-1,4,-2,5]=>[5,-2,4,-1,-3]=>01011=>[1,1,1,2]
[-3,-1,4,-2,-5]=>[-5,-2,4,-1,-3]=>11011=>[2,1,2]
[-3,-1,-4,2,5]=>[5,2,-4,-1,-3]=>00111=>[2,3]
[-3,-1,-4,2,-5]=>[-5,2,-4,-1,-3]=>10111=>[1,1,3]
[-3,-1,-4,-2,5]=>[5,-2,-4,-1,-3]=>01111=>[1,4]
[-3,-1,-4,-2,-5]=>[-5,-2,-4,-1,-3]=>11111=>[5]
[3,1,4,5,2]=>[2,5,4,1,3]=>00000=>[5]
[3,1,4,5,-2]=>[-2,5,4,1,3]=>10000=>[1,4]
[3,1,4,-5,2]=>[2,-5,4,1,3]=>01000=>[1,1,3]
[3,1,4,-5,-2]=>[-2,-5,4,1,3]=>11000=>[2,3]
[3,1,-4,5,2]=>[2,5,-4,1,3]=>00100=>[2,1,2]
[3,1,-4,5,-2]=>[-2,5,-4,1,3]=>10100=>[1,1,1,2]
[3,1,-4,-5,2]=>[2,-5,-4,1,3]=>01100=>[1,2,2]
[3,1,-4,-5,-2]=>[-2,-5,-4,1,3]=>11100=>[3,2]
[3,-1,4,5,2]=>[2,5,4,-1,3]=>00010=>[3,1,1]
[3,-1,4,5,-2]=>[-2,5,4,-1,3]=>10010=>[1,2,1,1]
[3,-1,4,-5,2]=>[2,-5,4,-1,3]=>01010=>[1,1,1,1,1]
[3,-1,4,-5,-2]=>[-2,-5,4,-1,3]=>11010=>[2,1,1,1]
[3,-1,-4,5,2]=>[2,5,-4,-1,3]=>00110=>[2,2,1]
[3,-1,-4,5,-2]=>[-2,5,-4,-1,3]=>10110=>[1,1,2,1]
[3,-1,-4,-5,2]=>[2,-5,-4,-1,3]=>01110=>[1,3,1]
[3,-1,-4,-5,-2]=>[-2,-5,-4,-1,3]=>11110=>[4,1]
[-3,1,4,5,2]=>[2,5,4,1,-3]=>00001=>[4,1]
[-3,1,4,5,-2]=>[-2,5,4,1,-3]=>10001=>[1,3,1]
[-3,1,4,-5,2]=>[2,-5,4,1,-3]=>01001=>[1,1,2,1]
[-3,1,4,-5,-2]=>[-2,-5,4,1,-3]=>11001=>[2,2,1]
[-3,1,-4,5,2]=>[2,5,-4,1,-3]=>00101=>[2,1,1,1]
[-3,1,-4,5,-2]=>[-2,5,-4,1,-3]=>10101=>[1,1,1,1,1]
[-3,1,-4,-5,2]=>[2,-5,-4,1,-3]=>01101=>[1,2,1,1]
[-3,1,-4,-5,-2]=>[-2,-5,-4,1,-3]=>11101=>[3,1,1]
[-3,-1,4,5,2]=>[2,5,4,-1,-3]=>00011=>[3,2]
[-3,-1,4,5,-2]=>[-2,5,4,-1,-3]=>10011=>[1,2,2]
[-3,-1,4,-5,2]=>[2,-5,4,-1,-3]=>01011=>[1,1,1,2]
[-3,-1,4,-5,-2]=>[-2,-5,4,-1,-3]=>11011=>[2,1,2]
[-3,-1,-4,5,2]=>[2,5,-4,-1,-3]=>00111=>[2,3]
[-3,-1,-4,5,-2]=>[-2,5,-4,-1,-3]=>10111=>[1,1,3]
[-3,-1,-4,-5,2]=>[2,-5,-4,-1,-3]=>01111=>[1,4]
[-3,-1,-4,-5,-2]=>[-2,-5,-4,-1,-3]=>11111=>[5]
[3,1,5,2,4]=>[4,2,5,1,3]=>00000=>[5]
[3,1,5,2,-4]=>[-4,2,5,1,3]=>10000=>[1,4]
[3,1,5,-2,4]=>[4,-2,5,1,3]=>01000=>[1,1,3]
[3,1,5,-2,-4]=>[-4,-2,5,1,3]=>11000=>[2,3]
[3,1,-5,2,4]=>[4,2,-5,1,3]=>00100=>[2,1,2]
[3,1,-5,2,-4]=>[-4,2,-5,1,3]=>10100=>[1,1,1,2]
[3,1,-5,-2,4]=>[4,-2,-5,1,3]=>01100=>[1,2,2]
[3,1,-5,-2,-4]=>[-4,-2,-5,1,3]=>11100=>[3,2]
[3,-1,5,2,4]=>[4,2,5,-1,3]=>00010=>[3,1,1]
[3,-1,5,2,-4]=>[-4,2,5,-1,3]=>10010=>[1,2,1,1]
[3,-1,5,-2,4]=>[4,-2,5,-1,3]=>01010=>[1,1,1,1,1]
[3,-1,5,-2,-4]=>[-4,-2,5,-1,3]=>11010=>[2,1,1,1]
[3,-1,-5,2,4]=>[4,2,-5,-1,3]=>00110=>[2,2,1]
[3,-1,-5,2,-4]=>[-4,2,-5,-1,3]=>10110=>[1,1,2,1]
[3,-1,-5,-2,4]=>[4,-2,-5,-1,3]=>01110=>[1,3,1]
[3,-1,-5,-2,-4]=>[-4,-2,-5,-1,3]=>11110=>[4,1]
[-3,1,5,2,4]=>[4,2,5,1,-3]=>00001=>[4,1]
[-3,1,5,2,-4]=>[-4,2,5,1,-3]=>10001=>[1,3,1]
[-3,1,5,-2,4]=>[4,-2,5,1,-3]=>01001=>[1,1,2,1]
[-3,1,5,-2,-4]=>[-4,-2,5,1,-3]=>11001=>[2,2,1]
[-3,1,-5,2,4]=>[4,2,-5,1,-3]=>00101=>[2,1,1,1]
[-3,1,-5,2,-4]=>[-4,2,-5,1,-3]=>10101=>[1,1,1,1,1]
[-3,1,-5,-2,4]=>[4,-2,-5,1,-3]=>01101=>[1,2,1,1]
[-3,1,-5,-2,-4]=>[-4,-2,-5,1,-3]=>11101=>[3,1,1]
[-3,-1,5,2,4]=>[4,2,5,-1,-3]=>00011=>[3,2]
[-3,-1,5,2,-4]=>[-4,2,5,-1,-3]=>10011=>[1,2,2]
[-3,-1,5,-2,4]=>[4,-2,5,-1,-3]=>01011=>[1,1,1,2]
[-3,-1,5,-2,-4]=>[-4,-2,5,-1,-3]=>11011=>[2,1,2]
[-3,-1,-5,2,4]=>[4,2,-5,-1,-3]=>00111=>[2,3]
[-3,-1,-5,2,-4]=>[-4,2,-5,-1,-3]=>10111=>[1,1,3]
[-3,-1,-5,-2,4]=>[4,-2,-5,-1,-3]=>01111=>[1,4]
[-3,-1,-5,-2,-4]=>[-4,-2,-5,-1,-3]=>11111=>[5]
[3,1,5,4,2]=>[2,4,5,1,3]=>00000=>[5]
[3,1,5,4,-2]=>[-2,4,5,1,3]=>10000=>[1,4]
[3,1,5,-4,2]=>[2,-4,5,1,3]=>01000=>[1,1,3]
[3,1,5,-4,-2]=>[-2,-4,5,1,3]=>11000=>[2,3]
[3,1,-5,4,2]=>[2,4,-5,1,3]=>00100=>[2,1,2]
[3,1,-5,4,-2]=>[-2,4,-5,1,3]=>10100=>[1,1,1,2]
[3,1,-5,-4,2]=>[2,-4,-5,1,3]=>01100=>[1,2,2]
[3,1,-5,-4,-2]=>[-2,-4,-5,1,3]=>11100=>[3,2]
[3,-1,5,4,2]=>[2,4,5,-1,3]=>00010=>[3,1,1]
[3,-1,5,4,-2]=>[-2,4,5,-1,3]=>10010=>[1,2,1,1]
[3,-1,5,-4,2]=>[2,-4,5,-1,3]=>01010=>[1,1,1,1,1]
[3,-1,5,-4,-2]=>[-2,-4,5,-1,3]=>11010=>[2,1,1,1]
[3,-1,-5,4,2]=>[2,4,-5,-1,3]=>00110=>[2,2,1]
[3,-1,-5,4,-2]=>[-2,4,-5,-1,3]=>10110=>[1,1,2,1]
[3,-1,-5,-4,2]=>[2,-4,-5,-1,3]=>01110=>[1,3,1]
[3,-1,-5,-4,-2]=>[-2,-4,-5,-1,3]=>11110=>[4,1]
[-3,1,5,4,2]=>[2,4,5,1,-3]=>00001=>[4,1]
[-3,1,5,4,-2]=>[-2,4,5,1,-3]=>10001=>[1,3,1]
[-3,1,5,-4,2]=>[2,-4,5,1,-3]=>01001=>[1,1,2,1]
[-3,1,5,-4,-2]=>[-2,-4,5,1,-3]=>11001=>[2,2,1]
[-3,1,-5,4,2]=>[2,4,-5,1,-3]=>00101=>[2,1,1,1]
[-3,1,-5,4,-2]=>[-2,4,-5,1,-3]=>10101=>[1,1,1,1,1]
[-3,1,-5,-4,2]=>[2,-4,-5,1,-3]=>01101=>[1,2,1,1]
[-3,1,-5,-4,-2]=>[-2,-4,-5,1,-3]=>11101=>[3,1,1]
[-3,-1,5,4,2]=>[2,4,5,-1,-3]=>00011=>[3,2]
[-3,-1,5,4,-2]=>[-2,4,5,-1,-3]=>10011=>[1,2,2]
[-3,-1,5,-4,2]=>[2,-4,5,-1,-3]=>01011=>[1,1,1,2]
[-3,-1,5,-4,-2]=>[-2,-4,5,-1,-3]=>11011=>[2,1,2]
[-3,-1,-5,4,2]=>[2,4,-5,-1,-3]=>00111=>[2,3]
[-3,-1,-5,4,-2]=>[-2,4,-5,-1,-3]=>10111=>[1,1,3]
[-3,-1,-5,-4,2]=>[2,-4,-5,-1,-3]=>01111=>[1,4]
[-3,-1,-5,-4,-2]=>[-2,-4,-5,-1,-3]=>11111=>[5]
[3,2,1,4,5]=>[5,4,1,2,3]=>00000=>[5]
[3,2,1,4,-5]=>[-5,4,1,2,3]=>10000=>[1,4]
[3,2,1,-4,5]=>[5,-4,1,2,3]=>01000=>[1,1,3]
[3,2,1,-4,-5]=>[-5,-4,1,2,3]=>11000=>[2,3]
[3,2,-1,4,5]=>[5,4,-1,2,3]=>00100=>[2,1,2]
[3,2,-1,4,-5]=>[-5,4,-1,2,3]=>10100=>[1,1,1,2]
[3,2,-1,-4,5]=>[5,-4,-1,2,3]=>01100=>[1,2,2]
[3,2,-1,-4,-5]=>[-5,-4,-1,2,3]=>11100=>[3,2]
[3,-2,1,4,5]=>[5,4,1,-2,3]=>00010=>[3,1,1]
[3,-2,1,4,-5]=>[-5,4,1,-2,3]=>10010=>[1,2,1,1]
[3,-2,1,-4,5]=>[5,-4,1,-2,3]=>01010=>[1,1,1,1,1]
[3,-2,1,-4,-5]=>[-5,-4,1,-2,3]=>11010=>[2,1,1,1]
[3,-2,-1,4,5]=>[5,4,-1,-2,3]=>00110=>[2,2,1]
[3,-2,-1,4,-5]=>[-5,4,-1,-2,3]=>10110=>[1,1,2,1]
[3,-2,-1,-4,5]=>[5,-4,-1,-2,3]=>01110=>[1,3,1]
[3,-2,-1,-4,-5]=>[-5,-4,-1,-2,3]=>11110=>[4,1]
[-3,2,1,4,5]=>[5,4,1,2,-3]=>00001=>[4,1]
[-3,2,1,4,-5]=>[-5,4,1,2,-3]=>10001=>[1,3,1]
[-3,2,1,-4,5]=>[5,-4,1,2,-3]=>01001=>[1,1,2,1]
[-3,2,1,-4,-5]=>[-5,-4,1,2,-3]=>11001=>[2,2,1]
[-3,2,-1,4,5]=>[5,4,-1,2,-3]=>00101=>[2,1,1,1]
[-3,2,-1,4,-5]=>[-5,4,-1,2,-3]=>10101=>[1,1,1,1,1]
[-3,2,-1,-4,5]=>[5,-4,-1,2,-3]=>01101=>[1,2,1,1]
[-3,2,-1,-4,-5]=>[-5,-4,-1,2,-3]=>11101=>[3,1,1]
[-3,-2,1,4,5]=>[5,4,1,-2,-3]=>00011=>[3,2]
[-3,-2,1,4,-5]=>[-5,4,1,-2,-3]=>10011=>[1,2,2]
[-3,-2,1,-4,5]=>[5,-4,1,-2,-3]=>01011=>[1,1,1,2]
[-3,-2,1,-4,-5]=>[-5,-4,1,-2,-3]=>11011=>[2,1,2]
[-3,-2,-1,4,5]=>[5,4,-1,-2,-3]=>00111=>[2,3]
[-3,-2,-1,4,-5]=>[-5,4,-1,-2,-3]=>10111=>[1,1,3]
[-3,-2,-1,-4,5]=>[5,-4,-1,-2,-3]=>01111=>[1,4]
[-3,-2,-1,-4,-5]=>[-5,-4,-1,-2,-3]=>11111=>[5]
[3,2,1,5,4]=>[4,5,1,2,3]=>00000=>[5]
[3,2,1,5,-4]=>[-4,5,1,2,3]=>10000=>[1,4]
[3,2,1,-5,4]=>[4,-5,1,2,3]=>01000=>[1,1,3]
[3,2,1,-5,-4]=>[-4,-5,1,2,3]=>11000=>[2,3]
[3,2,-1,5,4]=>[4,5,-1,2,3]=>00100=>[2,1,2]
[3,2,-1,5,-4]=>[-4,5,-1,2,3]=>10100=>[1,1,1,2]
[3,2,-1,-5,4]=>[4,-5,-1,2,3]=>01100=>[1,2,2]
[3,2,-1,-5,-4]=>[-4,-5,-1,2,3]=>11100=>[3,2]
[3,-2,1,5,4]=>[4,5,1,-2,3]=>00010=>[3,1,1]
[3,-2,1,5,-4]=>[-4,5,1,-2,3]=>10010=>[1,2,1,1]
[3,-2,1,-5,4]=>[4,-5,1,-2,3]=>01010=>[1,1,1,1,1]
[3,-2,1,-5,-4]=>[-4,-5,1,-2,3]=>11010=>[2,1,1,1]
[3,-2,-1,5,4]=>[4,5,-1,-2,3]=>00110=>[2,2,1]
[3,-2,-1,5,-4]=>[-4,5,-1,-2,3]=>10110=>[1,1,2,1]
[3,-2,-1,-5,4]=>[4,-5,-1,-2,3]=>01110=>[1,3,1]
[3,-2,-1,-5,-4]=>[-4,-5,-1,-2,3]=>11110=>[4,1]
[-3,2,1,5,4]=>[4,5,1,2,-3]=>00001=>[4,1]
[-3,2,1,5,-4]=>[-4,5,1,2,-3]=>10001=>[1,3,1]
[-3,2,1,-5,4]=>[4,-5,1,2,-3]=>01001=>[1,1,2,1]
[-3,2,1,-5,-4]=>[-4,-5,1,2,-3]=>11001=>[2,2,1]
[-3,2,-1,5,4]=>[4,5,-1,2,-3]=>00101=>[2,1,1,1]
[-3,2,-1,5,-4]=>[-4,5,-1,2,-3]=>10101=>[1,1,1,1,1]
[-3,2,-1,-5,4]=>[4,-5,-1,2,-3]=>01101=>[1,2,1,1]
[-3,2,-1,-5,-4]=>[-4,-5,-1,2,-3]=>11101=>[3,1,1]
[-3,-2,1,5,4]=>[4,5,1,-2,-3]=>00011=>[3,2]
[-3,-2,1,5,-4]=>[-4,5,1,-2,-3]=>10011=>[1,2,2]
[-3,-2,1,-5,4]=>[4,-5,1,-2,-3]=>01011=>[1,1,1,2]
[-3,-2,1,-5,-4]=>[-4,-5,1,-2,-3]=>11011=>[2,1,2]
[-3,-2,-1,5,4]=>[4,5,-1,-2,-3]=>00111=>[2,3]
[-3,-2,-1,5,-4]=>[-4,5,-1,-2,-3]=>10111=>[1,1,3]
[-3,-2,-1,-5,4]=>[4,-5,-1,-2,-3]=>01111=>[1,4]
[-3,-2,-1,-5,-4]=>[-4,-5,-1,-2,-3]=>11111=>[5]
[3,2,4,1,5]=>[5,1,4,2,3]=>00000=>[5]
[3,2,4,1,-5]=>[-5,1,4,2,3]=>10000=>[1,4]
[3,2,4,-1,5]=>[5,-1,4,2,3]=>01000=>[1,1,3]
[3,2,4,-1,-5]=>[-5,-1,4,2,3]=>11000=>[2,3]
[3,2,-4,1,5]=>[5,1,-4,2,3]=>00100=>[2,1,2]
[3,2,-4,1,-5]=>[-5,1,-4,2,3]=>10100=>[1,1,1,2]
[3,2,-4,-1,5]=>[5,-1,-4,2,3]=>01100=>[1,2,2]
[3,2,-4,-1,-5]=>[-5,-1,-4,2,3]=>11100=>[3,2]
[3,-2,4,1,5]=>[5,1,4,-2,3]=>00010=>[3,1,1]
[3,-2,4,1,-5]=>[-5,1,4,-2,3]=>10010=>[1,2,1,1]
[3,-2,4,-1,5]=>[5,-1,4,-2,3]=>01010=>[1,1,1,1,1]
[3,-2,4,-1,-5]=>[-5,-1,4,-2,3]=>11010=>[2,1,1,1]
[3,-2,-4,1,5]=>[5,1,-4,-2,3]=>00110=>[2,2,1]
[3,-2,-4,1,-5]=>[-5,1,-4,-2,3]=>10110=>[1,1,2,1]
[3,-2,-4,-1,5]=>[5,-1,-4,-2,3]=>01110=>[1,3,1]
[3,-2,-4,-1,-5]=>[-5,-1,-4,-2,3]=>11110=>[4,1]
[-3,2,4,1,5]=>[5,1,4,2,-3]=>00001=>[4,1]
[-3,2,4,1,-5]=>[-5,1,4,2,-3]=>10001=>[1,3,1]
[-3,2,4,-1,5]=>[5,-1,4,2,-3]=>01001=>[1,1,2,1]
[-3,2,4,-1,-5]=>[-5,-1,4,2,-3]=>11001=>[2,2,1]
[-3,2,-4,1,5]=>[5,1,-4,2,-3]=>00101=>[2,1,1,1]
[-3,2,-4,1,-5]=>[-5,1,-4,2,-3]=>10101=>[1,1,1,1,1]
[-3,2,-4,-1,5]=>[5,-1,-4,2,-3]=>01101=>[1,2,1,1]
[-3,2,-4,-1,-5]=>[-5,-1,-4,2,-3]=>11101=>[3,1,1]
[-3,-2,4,1,5]=>[5,1,4,-2,-3]=>00011=>[3,2]
[-3,-2,4,1,-5]=>[-5,1,4,-2,-3]=>10011=>[1,2,2]
[-3,-2,4,-1,5]=>[5,-1,4,-2,-3]=>01011=>[1,1,1,2]
[-3,-2,4,-1,-5]=>[-5,-1,4,-2,-3]=>11011=>[2,1,2]
[-3,-2,-4,1,5]=>[5,1,-4,-2,-3]=>00111=>[2,3]
[-3,-2,-4,1,-5]=>[-5,1,-4,-2,-3]=>10111=>[1,1,3]
[-3,-2,-4,-1,5]=>[5,-1,-4,-2,-3]=>01111=>[1,4]
[-3,-2,-4,-1,-5]=>[-5,-1,-4,-2,-3]=>11111=>[5]
[3,2,4,5,1]=>[1,5,4,2,3]=>00000=>[5]
[3,2,4,5,-1]=>[-1,5,4,2,3]=>10000=>[1,4]
[3,2,4,-5,1]=>[1,-5,4,2,3]=>01000=>[1,1,3]
[3,2,4,-5,-1]=>[-1,-5,4,2,3]=>11000=>[2,3]
[3,2,-4,5,1]=>[1,5,-4,2,3]=>00100=>[2,1,2]
[3,2,-4,5,-1]=>[-1,5,-4,2,3]=>10100=>[1,1,1,2]
[3,2,-4,-5,1]=>[1,-5,-4,2,3]=>01100=>[1,2,2]
[3,2,-4,-5,-1]=>[-1,-5,-4,2,3]=>11100=>[3,2]
[3,-2,4,5,1]=>[1,5,4,-2,3]=>00010=>[3,1,1]
[3,-2,4,5,-1]=>[-1,5,4,-2,3]=>10010=>[1,2,1,1]
[3,-2,4,-5,1]=>[1,-5,4,-2,3]=>01010=>[1,1,1,1,1]
[3,-2,4,-5,-1]=>[-1,-5,4,-2,3]=>11010=>[2,1,1,1]
[3,-2,-4,5,1]=>[1,5,-4,-2,3]=>00110=>[2,2,1]
[3,-2,-4,5,-1]=>[-1,5,-4,-2,3]=>10110=>[1,1,2,1]
[3,-2,-4,-5,1]=>[1,-5,-4,-2,3]=>01110=>[1,3,1]
[3,-2,-4,-5,-1]=>[-1,-5,-4,-2,3]=>11110=>[4,1]
[-3,2,4,5,1]=>[1,5,4,2,-3]=>00001=>[4,1]
[-3,2,4,5,-1]=>[-1,5,4,2,-3]=>10001=>[1,3,1]
[-3,2,4,-5,1]=>[1,-5,4,2,-3]=>01001=>[1,1,2,1]
[-3,2,4,-5,-1]=>[-1,-5,4,2,-3]=>11001=>[2,2,1]
[-3,2,-4,5,1]=>[1,5,-4,2,-3]=>00101=>[2,1,1,1]
[-3,2,-4,5,-1]=>[-1,5,-4,2,-3]=>10101=>[1,1,1,1,1]
[-3,2,-4,-5,1]=>[1,-5,-4,2,-3]=>01101=>[1,2,1,1]
[-3,2,-4,-5,-1]=>[-1,-5,-4,2,-3]=>11101=>[3,1,1]
[-3,-2,4,5,1]=>[1,5,4,-2,-3]=>00011=>[3,2]
[-3,-2,4,5,-1]=>[-1,5,4,-2,-3]=>10011=>[1,2,2]
[-3,-2,4,-5,1]=>[1,-5,4,-2,-3]=>01011=>[1,1,1,2]
[-3,-2,4,-5,-1]=>[-1,-5,4,-2,-3]=>11011=>[2,1,2]
[-3,-2,-4,5,1]=>[1,5,-4,-2,-3]=>00111=>[2,3]
[-3,-2,-4,5,-1]=>[-1,5,-4,-2,-3]=>10111=>[1,1,3]
[-3,-2,-4,-5,1]=>[1,-5,-4,-2,-3]=>01111=>[1,4]
[-3,-2,-4,-5,-1]=>[-1,-5,-4,-2,-3]=>11111=>[5]
[3,2,5,1,4]=>[4,1,5,2,3]=>00000=>[5]
[3,2,5,1,-4]=>[-4,1,5,2,3]=>10000=>[1,4]
[3,2,5,-1,4]=>[4,-1,5,2,3]=>01000=>[1,1,3]
[3,2,5,-1,-4]=>[-4,-1,5,2,3]=>11000=>[2,3]
[3,2,-5,1,4]=>[4,1,-5,2,3]=>00100=>[2,1,2]
[3,2,-5,1,-4]=>[-4,1,-5,2,3]=>10100=>[1,1,1,2]
[3,2,-5,-1,4]=>[4,-1,-5,2,3]=>01100=>[1,2,2]
[3,2,-5,-1,-4]=>[-4,-1,-5,2,3]=>11100=>[3,2]
[3,-2,5,1,4]=>[4,1,5,-2,3]=>00010=>[3,1,1]
[3,-2,5,1,-4]=>[-4,1,5,-2,3]=>10010=>[1,2,1,1]
[3,-2,5,-1,4]=>[4,-1,5,-2,3]=>01010=>[1,1,1,1,1]
[3,-2,5,-1,-4]=>[-4,-1,5,-2,3]=>11010=>[2,1,1,1]
[3,-2,-5,1,4]=>[4,1,-5,-2,3]=>00110=>[2,2,1]
[3,-2,-5,1,-4]=>[-4,1,-5,-2,3]=>10110=>[1,1,2,1]
[3,-2,-5,-1,4]=>[4,-1,-5,-2,3]=>01110=>[1,3,1]
[3,-2,-5,-1,-4]=>[-4,-1,-5,-2,3]=>11110=>[4,1]
[-3,2,5,1,4]=>[4,1,5,2,-3]=>00001=>[4,1]
[-3,2,5,1,-4]=>[-4,1,5,2,-3]=>10001=>[1,3,1]
[-3,2,5,-1,4]=>[4,-1,5,2,-3]=>01001=>[1,1,2,1]
[-3,2,5,-1,-4]=>[-4,-1,5,2,-3]=>11001=>[2,2,1]
[-3,2,-5,1,4]=>[4,1,-5,2,-3]=>00101=>[2,1,1,1]
[-3,2,-5,1,-4]=>[-4,1,-5,2,-3]=>10101=>[1,1,1,1,1]
[-3,2,-5,-1,4]=>[4,-1,-5,2,-3]=>01101=>[1,2,1,1]
[-3,2,-5,-1,-4]=>[-4,-1,-5,2,-3]=>11101=>[3,1,1]
[-3,-2,5,1,4]=>[4,1,5,-2,-3]=>00011=>[3,2]
[-3,-2,5,1,-4]=>[-4,1,5,-2,-3]=>10011=>[1,2,2]
[-3,-2,5,-1,4]=>[4,-1,5,-2,-3]=>01011=>[1,1,1,2]
[-3,-2,5,-1,-4]=>[-4,-1,5,-2,-3]=>11011=>[2,1,2]
[-3,-2,-5,1,4]=>[4,1,-5,-2,-3]=>00111=>[2,3]
[-3,-2,-5,1,-4]=>[-4,1,-5,-2,-3]=>10111=>[1,1,3]
[-3,-2,-5,-1,4]=>[4,-1,-5,-2,-3]=>01111=>[1,4]
[-3,-2,-5,-1,-4]=>[-4,-1,-5,-2,-3]=>11111=>[5]
[3,2,5,4,1]=>[1,4,5,2,3]=>00000=>[5]
[3,2,5,4,-1]=>[-1,4,5,2,3]=>10000=>[1,4]
[3,2,5,-4,1]=>[1,-4,5,2,3]=>01000=>[1,1,3]
[3,2,5,-4,-1]=>[-1,-4,5,2,3]=>11000=>[2,3]
[3,2,-5,4,1]=>[1,4,-5,2,3]=>00100=>[2,1,2]
[3,2,-5,4,-1]=>[-1,4,-5,2,3]=>10100=>[1,1,1,2]
[3,2,-5,-4,1]=>[1,-4,-5,2,3]=>01100=>[1,2,2]
[3,2,-5,-4,-1]=>[-1,-4,-5,2,3]=>11100=>[3,2]
[3,-2,5,4,1]=>[1,4,5,-2,3]=>00010=>[3,1,1]
[3,-2,5,4,-1]=>[-1,4,5,-2,3]=>10010=>[1,2,1,1]
[3,-2,5,-4,1]=>[1,-4,5,-2,3]=>01010=>[1,1,1,1,1]
[3,-2,5,-4,-1]=>[-1,-4,5,-2,3]=>11010=>[2,1,1,1]
[3,-2,-5,4,1]=>[1,4,-5,-2,3]=>00110=>[2,2,1]
[3,-2,-5,4,-1]=>[-1,4,-5,-2,3]=>10110=>[1,1,2,1]
[3,-2,-5,-4,1]=>[1,-4,-5,-2,3]=>01110=>[1,3,1]
[3,-2,-5,-4,-1]=>[-1,-4,-5,-2,3]=>11110=>[4,1]
[-3,2,5,4,1]=>[1,4,5,2,-3]=>00001=>[4,1]
[-3,2,5,4,-1]=>[-1,4,5,2,-3]=>10001=>[1,3,1]
[-3,2,5,-4,1]=>[1,-4,5,2,-3]=>01001=>[1,1,2,1]
[-3,2,5,-4,-1]=>[-1,-4,5,2,-3]=>11001=>[2,2,1]
[-3,2,-5,4,1]=>[1,4,-5,2,-3]=>00101=>[2,1,1,1]
[-3,2,-5,4,-1]=>[-1,4,-5,2,-3]=>10101=>[1,1,1,1,1]
[-3,2,-5,-4,1]=>[1,-4,-5,2,-3]=>01101=>[1,2,1,1]
[-3,2,-5,-4,-1]=>[-1,-4,-5,2,-3]=>11101=>[3,1,1]
[-3,-2,5,4,1]=>[1,4,5,-2,-3]=>00011=>[3,2]
[-3,-2,5,4,-1]=>[-1,4,5,-2,-3]=>10011=>[1,2,2]
[-3,-2,5,-4,1]=>[1,-4,5,-2,-3]=>01011=>[1,1,1,2]
[-3,-2,5,-4,-1]=>[-1,-4,5,-2,-3]=>11011=>[2,1,2]
[-3,-2,-5,4,1]=>[1,4,-5,-2,-3]=>00111=>[2,3]
[-3,-2,-5,4,-1]=>[-1,4,-5,-2,-3]=>10111=>[1,1,3]
[-3,-2,-5,-4,1]=>[1,-4,-5,-2,-3]=>01111=>[1,4]
[-3,-2,-5,-4,-1]=>[-1,-4,-5,-2,-3]=>11111=>[5]
[3,4,1,2,5]=>[5,2,1,4,3]=>00000=>[5]
[3,4,1,2,-5]=>[-5,2,1,4,3]=>10000=>[1,4]
[3,4,1,-2,5]=>[5,-2,1,4,3]=>01000=>[1,1,3]
[3,4,1,-2,-5]=>[-5,-2,1,4,3]=>11000=>[2,3]
[3,4,-1,2,5]=>[5,2,-1,4,3]=>00100=>[2,1,2]
[3,4,-1,2,-5]=>[-5,2,-1,4,3]=>10100=>[1,1,1,2]
[3,4,-1,-2,5]=>[5,-2,-1,4,3]=>01100=>[1,2,2]
[3,4,-1,-2,-5]=>[-5,-2,-1,4,3]=>11100=>[3,2]
[3,-4,1,2,5]=>[5,2,1,-4,3]=>00010=>[3,1,1]
[3,-4,1,2,-5]=>[-5,2,1,-4,3]=>10010=>[1,2,1,1]
[3,-4,1,-2,5]=>[5,-2,1,-4,3]=>01010=>[1,1,1,1,1]
[3,-4,1,-2,-5]=>[-5,-2,1,-4,3]=>11010=>[2,1,1,1]
[3,-4,-1,2,5]=>[5,2,-1,-4,3]=>00110=>[2,2,1]
[3,-4,-1,2,-5]=>[-5,2,-1,-4,3]=>10110=>[1,1,2,1]
[3,-4,-1,-2,5]=>[5,-2,-1,-4,3]=>01110=>[1,3,1]
[3,-4,-1,-2,-5]=>[-5,-2,-1,-4,3]=>11110=>[4,1]
[-3,4,1,2,5]=>[5,2,1,4,-3]=>00001=>[4,1]
[-3,4,1,2,-5]=>[-5,2,1,4,-3]=>10001=>[1,3,1]
[-3,4,1,-2,5]=>[5,-2,1,4,-3]=>01001=>[1,1,2,1]
[-3,4,1,-2,-5]=>[-5,-2,1,4,-3]=>11001=>[2,2,1]
[-3,4,-1,2,5]=>[5,2,-1,4,-3]=>00101=>[2,1,1,1]
[-3,4,-1,2,-5]=>[-5,2,-1,4,-3]=>10101=>[1,1,1,1,1]
[-3,4,-1,-2,5]=>[5,-2,-1,4,-3]=>01101=>[1,2,1,1]
[-3,4,-1,-2,-5]=>[-5,-2,-1,4,-3]=>11101=>[3,1,1]
[-3,-4,1,2,5]=>[5,2,1,-4,-3]=>00011=>[3,2]
[-3,-4,1,2,-5]=>[-5,2,1,-4,-3]=>10011=>[1,2,2]
[-3,-4,1,-2,5]=>[5,-2,1,-4,-3]=>01011=>[1,1,1,2]
[-3,-4,1,-2,-5]=>[-5,-2,1,-4,-3]=>11011=>[2,1,2]
[-3,-4,-1,2,5]=>[5,2,-1,-4,-3]=>00111=>[2,3]
[-3,-4,-1,2,-5]=>[-5,2,-1,-4,-3]=>10111=>[1,1,3]
[-3,-4,-1,-2,5]=>[5,-2,-1,-4,-3]=>01111=>[1,4]
[-3,-4,-1,-2,-5]=>[-5,-2,-1,-4,-3]=>11111=>[5]
[3,4,1,5,2]=>[2,5,1,4,3]=>00000=>[5]
[3,4,1,5,-2]=>[-2,5,1,4,3]=>10000=>[1,4]
[3,4,1,-5,2]=>[2,-5,1,4,3]=>01000=>[1,1,3]
[3,4,1,-5,-2]=>[-2,-5,1,4,3]=>11000=>[2,3]
[3,4,-1,5,2]=>[2,5,-1,4,3]=>00100=>[2,1,2]
[3,4,-1,5,-2]=>[-2,5,-1,4,3]=>10100=>[1,1,1,2]
[3,4,-1,-5,2]=>[2,-5,-1,4,3]=>01100=>[1,2,2]
[3,4,-1,-5,-2]=>[-2,-5,-1,4,3]=>11100=>[3,2]
[3,-4,1,5,2]=>[2,5,1,-4,3]=>00010=>[3,1,1]
[3,-4,1,5,-2]=>[-2,5,1,-4,3]=>10010=>[1,2,1,1]
[3,-4,1,-5,2]=>[2,-5,1,-4,3]=>01010=>[1,1,1,1,1]
[3,-4,1,-5,-2]=>[-2,-5,1,-4,3]=>11010=>[2,1,1,1]
[3,-4,-1,5,2]=>[2,5,-1,-4,3]=>00110=>[2,2,1]
[3,-4,-1,5,-2]=>[-2,5,-1,-4,3]=>10110=>[1,1,2,1]
[3,-4,-1,-5,2]=>[2,-5,-1,-4,3]=>01110=>[1,3,1]
[3,-4,-1,-5,-2]=>[-2,-5,-1,-4,3]=>11110=>[4,1]
[-3,4,1,5,2]=>[2,5,1,4,-3]=>00001=>[4,1]
[-3,4,1,5,-2]=>[-2,5,1,4,-3]=>10001=>[1,3,1]
[-3,4,1,-5,2]=>[2,-5,1,4,-3]=>01001=>[1,1,2,1]
[-3,4,1,-5,-2]=>[-2,-5,1,4,-3]=>11001=>[2,2,1]
[-3,4,-1,5,2]=>[2,5,-1,4,-3]=>00101=>[2,1,1,1]
[-3,4,-1,5,-2]=>[-2,5,-1,4,-3]=>10101=>[1,1,1,1,1]
[-3,4,-1,-5,2]=>[2,-5,-1,4,-3]=>01101=>[1,2,1,1]
[-3,4,-1,-5,-2]=>[-2,-5,-1,4,-3]=>11101=>[3,1,1]
[-3,-4,1,5,2]=>[2,5,1,-4,-3]=>00011=>[3,2]
[-3,-4,1,5,-2]=>[-2,5,1,-4,-3]=>10011=>[1,2,2]
[-3,-4,1,-5,2]=>[2,-5,1,-4,-3]=>01011=>[1,1,1,2]
[-3,-4,1,-5,-2]=>[-2,-5,1,-4,-3]=>11011=>[2,1,2]
[-3,-4,-1,5,2]=>[2,5,-1,-4,-3]=>00111=>[2,3]
[-3,-4,-1,5,-2]=>[-2,5,-1,-4,-3]=>10111=>[1,1,3]
[-3,-4,-1,-5,2]=>[2,-5,-1,-4,-3]=>01111=>[1,4]
[-3,-4,-1,-5,-2]=>[-2,-5,-1,-4,-3]=>11111=>[5]
[3,4,2,1,5]=>[5,1,2,4,3]=>00000=>[5]
[3,4,2,1,-5]=>[-5,1,2,4,3]=>10000=>[1,4]
[3,4,2,-1,5]=>[5,-1,2,4,3]=>01000=>[1,1,3]
[3,4,2,-1,-5]=>[-5,-1,2,4,3]=>11000=>[2,3]
[3,4,-2,1,5]=>[5,1,-2,4,3]=>00100=>[2,1,2]
[3,4,-2,1,-5]=>[-5,1,-2,4,3]=>10100=>[1,1,1,2]
[3,4,-2,-1,5]=>[5,-1,-2,4,3]=>01100=>[1,2,2]
[3,4,-2,-1,-5]=>[-5,-1,-2,4,3]=>11100=>[3,2]
[3,-4,2,1,5]=>[5,1,2,-4,3]=>00010=>[3,1,1]
[3,-4,2,1,-5]=>[-5,1,2,-4,3]=>10010=>[1,2,1,1]
[3,-4,2,-1,5]=>[5,-1,2,-4,3]=>01010=>[1,1,1,1,1]
[3,-4,2,-1,-5]=>[-5,-1,2,-4,3]=>11010=>[2,1,1,1]
[3,-4,-2,1,5]=>[5,1,-2,-4,3]=>00110=>[2,2,1]
[3,-4,-2,1,-5]=>[-5,1,-2,-4,3]=>10110=>[1,1,2,1]
[3,-4,-2,-1,5]=>[5,-1,-2,-4,3]=>01110=>[1,3,1]
[3,-4,-2,-1,-5]=>[-5,-1,-2,-4,3]=>11110=>[4,1]
[-3,4,2,1,5]=>[5,1,2,4,-3]=>00001=>[4,1]
[-3,4,2,1,-5]=>[-5,1,2,4,-3]=>10001=>[1,3,1]
[-3,4,2,-1,5]=>[5,-1,2,4,-3]=>01001=>[1,1,2,1]
[-3,4,2,-1,-5]=>[-5,-1,2,4,-3]=>11001=>[2,2,1]
[-3,4,-2,1,5]=>[5,1,-2,4,-3]=>00101=>[2,1,1,1]
[-3,4,-2,1,-5]=>[-5,1,-2,4,-3]=>10101=>[1,1,1,1,1]
[-3,4,-2,-1,5]=>[5,-1,-2,4,-3]=>01101=>[1,2,1,1]
[-3,4,-2,-1,-5]=>[-5,-1,-2,4,-3]=>11101=>[3,1,1]
[-3,-4,2,1,5]=>[5,1,2,-4,-3]=>00011=>[3,2]
[-3,-4,2,1,-5]=>[-5,1,2,-4,-3]=>10011=>[1,2,2]
[-3,-4,2,-1,5]=>[5,-1,2,-4,-3]=>01011=>[1,1,1,2]
[-3,-4,2,-1,-5]=>[-5,-1,2,-4,-3]=>11011=>[2,1,2]
[-3,-4,-2,1,5]=>[5,1,-2,-4,-3]=>00111=>[2,3]
[-3,-4,-2,1,-5]=>[-5,1,-2,-4,-3]=>10111=>[1,1,3]
[-3,-4,-2,-1,5]=>[5,-1,-2,-4,-3]=>01111=>[1,4]
[-3,-4,-2,-1,-5]=>[-5,-1,-2,-4,-3]=>11111=>[5]
[3,4,2,5,1]=>[1,5,2,4,3]=>00000=>[5]
[3,4,2,5,-1]=>[-1,5,2,4,3]=>10000=>[1,4]
[3,4,2,-5,1]=>[1,-5,2,4,3]=>01000=>[1,1,3]
[3,4,2,-5,-1]=>[-1,-5,2,4,3]=>11000=>[2,3]
[3,4,-2,5,1]=>[1,5,-2,4,3]=>00100=>[2,1,2]
[3,4,-2,5,-1]=>[-1,5,-2,4,3]=>10100=>[1,1,1,2]
[3,4,-2,-5,1]=>[1,-5,-2,4,3]=>01100=>[1,2,2]
[3,4,-2,-5,-1]=>[-1,-5,-2,4,3]=>11100=>[3,2]
[3,-4,2,5,1]=>[1,5,2,-4,3]=>00010=>[3,1,1]
[3,-4,2,5,-1]=>[-1,5,2,-4,3]=>10010=>[1,2,1,1]
[3,-4,2,-5,1]=>[1,-5,2,-4,3]=>01010=>[1,1,1,1,1]
[3,-4,2,-5,-1]=>[-1,-5,2,-4,3]=>11010=>[2,1,1,1]
[3,-4,-2,5,1]=>[1,5,-2,-4,3]=>00110=>[2,2,1]
[3,-4,-2,5,-1]=>[-1,5,-2,-4,3]=>10110=>[1,1,2,1]
[3,-4,-2,-5,1]=>[1,-5,-2,-4,3]=>01110=>[1,3,1]
[3,-4,-2,-5,-1]=>[-1,-5,-2,-4,3]=>11110=>[4,1]
[-3,4,2,5,1]=>[1,5,2,4,-3]=>00001=>[4,1]
[-3,4,2,5,-1]=>[-1,5,2,4,-3]=>10001=>[1,3,1]
[-3,4,2,-5,1]=>[1,-5,2,4,-3]=>01001=>[1,1,2,1]
[-3,4,2,-5,-1]=>[-1,-5,2,4,-3]=>11001=>[2,2,1]
[-3,4,-2,5,1]=>[1,5,-2,4,-3]=>00101=>[2,1,1,1]
[-3,4,-2,5,-1]=>[-1,5,-2,4,-3]=>10101=>[1,1,1,1,1]
[-3,4,-2,-5,1]=>[1,-5,-2,4,-3]=>01101=>[1,2,1,1]
[-3,4,-2,-5,-1]=>[-1,-5,-2,4,-3]=>11101=>[3,1,1]
[-3,-4,2,5,1]=>[1,5,2,-4,-3]=>00011=>[3,2]
[-3,-4,2,5,-1]=>[-1,5,2,-4,-3]=>10011=>[1,2,2]
[-3,-4,2,-5,1]=>[1,-5,2,-4,-3]=>01011=>[1,1,1,2]
[-3,-4,2,-5,-1]=>[-1,-5,2,-4,-3]=>11011=>[2,1,2]
[-3,-4,-2,5,1]=>[1,5,-2,-4,-3]=>00111=>[2,3]
[-3,-4,-2,5,-1]=>[-1,5,-2,-4,-3]=>10111=>[1,1,3]
[-3,-4,-2,-5,1]=>[1,-5,-2,-4,-3]=>01111=>[1,4]
[-3,-4,-2,-5,-1]=>[-1,-5,-2,-4,-3]=>11111=>[5]
[3,4,5,1,2]=>[2,1,5,4,3]=>00000=>[5]
[3,4,5,1,-2]=>[-2,1,5,4,3]=>10000=>[1,4]
[3,4,5,-1,2]=>[2,-1,5,4,3]=>01000=>[1,1,3]
[3,4,5,-1,-2]=>[-2,-1,5,4,3]=>11000=>[2,3]
[3,4,-5,1,2]=>[2,1,-5,4,3]=>00100=>[2,1,2]
[3,4,-5,1,-2]=>[-2,1,-5,4,3]=>10100=>[1,1,1,2]
[3,4,-5,-1,2]=>[2,-1,-5,4,3]=>01100=>[1,2,2]
[3,4,-5,-1,-2]=>[-2,-1,-5,4,3]=>11100=>[3,2]
[3,-4,5,1,2]=>[2,1,5,-4,3]=>00010=>[3,1,1]
[3,-4,5,1,-2]=>[-2,1,5,-4,3]=>10010=>[1,2,1,1]
[3,-4,5,-1,2]=>[2,-1,5,-4,3]=>01010=>[1,1,1,1,1]
[3,-4,5,-1,-2]=>[-2,-1,5,-4,3]=>11010=>[2,1,1,1]
[3,-4,-5,1,2]=>[2,1,-5,-4,3]=>00110=>[2,2,1]
[3,-4,-5,1,-2]=>[-2,1,-5,-4,3]=>10110=>[1,1,2,1]
[3,-4,-5,-1,2]=>[2,-1,-5,-4,3]=>01110=>[1,3,1]
[3,-4,-5,-1,-2]=>[-2,-1,-5,-4,3]=>11110=>[4,1]
[-3,4,5,1,2]=>[2,1,5,4,-3]=>00001=>[4,1]
[-3,4,5,1,-2]=>[-2,1,5,4,-3]=>10001=>[1,3,1]
[-3,4,5,-1,2]=>[2,-1,5,4,-3]=>01001=>[1,1,2,1]
[-3,4,5,-1,-2]=>[-2,-1,5,4,-3]=>11001=>[2,2,1]
[-3,4,-5,1,2]=>[2,1,-5,4,-3]=>00101=>[2,1,1,1]
[-3,4,-5,1,-2]=>[-2,1,-5,4,-3]=>10101=>[1,1,1,1,1]
[-3,4,-5,-1,2]=>[2,-1,-5,4,-3]=>01101=>[1,2,1,1]
[-3,4,-5,-1,-2]=>[-2,-1,-5,4,-3]=>11101=>[3,1,1]
[-3,-4,5,1,2]=>[2,1,5,-4,-3]=>00011=>[3,2]
[-3,-4,5,1,-2]=>[-2,1,5,-4,-3]=>10011=>[1,2,2]
[-3,-4,5,-1,2]=>[2,-1,5,-4,-3]=>01011=>[1,1,1,2]
[-3,-4,5,-1,-2]=>[-2,-1,5,-4,-3]=>11011=>[2,1,2]
[-3,-4,-5,1,2]=>[2,1,-5,-4,-3]=>00111=>[2,3]
[-3,-4,-5,1,-2]=>[-2,1,-5,-4,-3]=>10111=>[1,1,3]
[-3,-4,-5,-1,2]=>[2,-1,-5,-4,-3]=>01111=>[1,4]
[-3,-4,-5,-1,-2]=>[-2,-1,-5,-4,-3]=>11111=>[5]
[3,4,5,2,1]=>[1,2,5,4,3]=>00000=>[5]
[3,4,5,2,-1]=>[-1,2,5,4,3]=>10000=>[1,4]
[3,4,5,-2,1]=>[1,-2,5,4,3]=>01000=>[1,1,3]
[3,4,5,-2,-1]=>[-1,-2,5,4,3]=>11000=>[2,3]
[3,4,-5,2,1]=>[1,2,-5,4,3]=>00100=>[2,1,2]
[3,4,-5,2,-1]=>[-1,2,-5,4,3]=>10100=>[1,1,1,2]
[3,4,-5,-2,1]=>[1,-2,-5,4,3]=>01100=>[1,2,2]
[3,4,-5,-2,-1]=>[-1,-2,-5,4,3]=>11100=>[3,2]
[3,-4,5,2,1]=>[1,2,5,-4,3]=>00010=>[3,1,1]
[3,-4,5,2,-1]=>[-1,2,5,-4,3]=>10010=>[1,2,1,1]
[3,-4,5,-2,1]=>[1,-2,5,-4,3]=>01010=>[1,1,1,1,1]
[3,-4,5,-2,-1]=>[-1,-2,5,-4,3]=>11010=>[2,1,1,1]
[3,-4,-5,2,1]=>[1,2,-5,-4,3]=>00110=>[2,2,1]
[3,-4,-5,2,-1]=>[-1,2,-5,-4,3]=>10110=>[1,1,2,1]
[3,-4,-5,-2,1]=>[1,-2,-5,-4,3]=>01110=>[1,3,1]
[3,-4,-5,-2,-1]=>[-1,-2,-5,-4,3]=>11110=>[4,1]
[-3,4,5,2,1]=>[1,2,5,4,-3]=>00001=>[4,1]
[-3,4,5,2,-1]=>[-1,2,5,4,-3]=>10001=>[1,3,1]
[-3,4,5,-2,1]=>[1,-2,5,4,-3]=>01001=>[1,1,2,1]
[-3,4,5,-2,-1]=>[-1,-2,5,4,-3]=>11001=>[2,2,1]
[-3,4,-5,2,1]=>[1,2,-5,4,-3]=>00101=>[2,1,1,1]
[-3,4,-5,2,-1]=>[-1,2,-5,4,-3]=>10101=>[1,1,1,1,1]
[-3,4,-5,-2,1]=>[1,-2,-5,4,-3]=>01101=>[1,2,1,1]
[-3,4,-5,-2,-1]=>[-1,-2,-5,4,-3]=>11101=>[3,1,1]
[-3,-4,5,2,1]=>[1,2,5,-4,-3]=>00011=>[3,2]
[-3,-4,5,2,-1]=>[-1,2,5,-4,-3]=>10011=>[1,2,2]
[-3,-4,5,-2,1]=>[1,-2,5,-4,-3]=>01011=>[1,1,1,2]
[-3,-4,5,-2,-1]=>[-1,-2,5,-4,-3]=>11011=>[2,1,2]
[-3,-4,-5,2,1]=>[1,2,-5,-4,-3]=>00111=>[2,3]
[-3,-4,-5,2,-1]=>[-1,2,-5,-4,-3]=>10111=>[1,1,3]
[-3,-4,-5,-2,1]=>[1,-2,-5,-4,-3]=>01111=>[1,4]
[-3,-4,-5,-2,-1]=>[-1,-2,-5,-4,-3]=>11111=>[5]
[3,5,1,2,4]=>[4,2,1,5,3]=>00000=>[5]
[3,5,1,2,-4]=>[-4,2,1,5,3]=>10000=>[1,4]
[3,5,1,-2,4]=>[4,-2,1,5,3]=>01000=>[1,1,3]
[3,5,1,-2,-4]=>[-4,-2,1,5,3]=>11000=>[2,3]
[3,5,-1,2,4]=>[4,2,-1,5,3]=>00100=>[2,1,2]
[3,5,-1,2,-4]=>[-4,2,-1,5,3]=>10100=>[1,1,1,2]
[3,5,-1,-2,4]=>[4,-2,-1,5,3]=>01100=>[1,2,2]
[3,5,-1,-2,-4]=>[-4,-2,-1,5,3]=>11100=>[3,2]
[3,-5,1,2,4]=>[4,2,1,-5,3]=>00010=>[3,1,1]
[3,-5,1,2,-4]=>[-4,2,1,-5,3]=>10010=>[1,2,1,1]
[3,-5,1,-2,4]=>[4,-2,1,-5,3]=>01010=>[1,1,1,1,1]
[3,-5,1,-2,-4]=>[-4,-2,1,-5,3]=>11010=>[2,1,1,1]
[3,-5,-1,2,4]=>[4,2,-1,-5,3]=>00110=>[2,2,1]
[3,-5,-1,2,-4]=>[-4,2,-1,-5,3]=>10110=>[1,1,2,1]
[3,-5,-1,-2,4]=>[4,-2,-1,-5,3]=>01110=>[1,3,1]
[3,-5,-1,-2,-4]=>[-4,-2,-1,-5,3]=>11110=>[4,1]
[-3,5,1,2,4]=>[4,2,1,5,-3]=>00001=>[4,1]
[-3,5,1,2,-4]=>[-4,2,1,5,-3]=>10001=>[1,3,1]
[-3,5,1,-2,4]=>[4,-2,1,5,-3]=>01001=>[1,1,2,1]
[-3,5,1,-2,-4]=>[-4,-2,1,5,-3]=>11001=>[2,2,1]
[-3,5,-1,2,4]=>[4,2,-1,5,-3]=>00101=>[2,1,1,1]
[-3,5,-1,2,-4]=>[-4,2,-1,5,-3]=>10101=>[1,1,1,1,1]
[-3,5,-1,-2,4]=>[4,-2,-1,5,-3]=>01101=>[1,2,1,1]
[-3,5,-1,-2,-4]=>[-4,-2,-1,5,-3]=>11101=>[3,1,1]
[-3,-5,1,2,4]=>[4,2,1,-5,-3]=>00011=>[3,2]
[-3,-5,1,2,-4]=>[-4,2,1,-5,-3]=>10011=>[1,2,2]
[-3,-5,1,-2,4]=>[4,-2,1,-5,-3]=>01011=>[1,1,1,2]
[-3,-5,1,-2,-4]=>[-4,-2,1,-5,-3]=>11011=>[2,1,2]
[-3,-5,-1,2,4]=>[4,2,-1,-5,-3]=>00111=>[2,3]
[-3,-5,-1,2,-4]=>[-4,2,-1,-5,-3]=>10111=>[1,1,3]
[-3,-5,-1,-2,4]=>[4,-2,-1,-5,-3]=>01111=>[1,4]
[-3,-5,-1,-2,-4]=>[-4,-2,-1,-5,-3]=>11111=>[5]
[3,5,1,4,2]=>[2,4,1,5,3]=>00000=>[5]
[3,5,1,4,-2]=>[-2,4,1,5,3]=>10000=>[1,4]
[3,5,1,-4,2]=>[2,-4,1,5,3]=>01000=>[1,1,3]
[3,5,1,-4,-2]=>[-2,-4,1,5,3]=>11000=>[2,3]
[3,5,-1,4,2]=>[2,4,-1,5,3]=>00100=>[2,1,2]
[3,5,-1,4,-2]=>[-2,4,-1,5,3]=>10100=>[1,1,1,2]
[3,5,-1,-4,2]=>[2,-4,-1,5,3]=>01100=>[1,2,2]
[3,5,-1,-4,-2]=>[-2,-4,-1,5,3]=>11100=>[3,2]
[3,-5,1,4,2]=>[2,4,1,-5,3]=>00010=>[3,1,1]
[3,-5,1,4,-2]=>[-2,4,1,-5,3]=>10010=>[1,2,1,1]
[3,-5,1,-4,2]=>[2,-4,1,-5,3]=>01010=>[1,1,1,1,1]
[3,-5,1,-4,-2]=>[-2,-4,1,-5,3]=>11010=>[2,1,1,1]
[3,-5,-1,4,2]=>[2,4,-1,-5,3]=>00110=>[2,2,1]
[3,-5,-1,4,-2]=>[-2,4,-1,-5,3]=>10110=>[1,1,2,1]
[3,-5,-1,-4,2]=>[2,-4,-1,-5,3]=>01110=>[1,3,1]
[3,-5,-1,-4,-2]=>[-2,-4,-1,-5,3]=>11110=>[4,1]
[-3,5,1,4,2]=>[2,4,1,5,-3]=>00001=>[4,1]
[-3,5,1,4,-2]=>[-2,4,1,5,-3]=>10001=>[1,3,1]
[-3,5,1,-4,2]=>[2,-4,1,5,-3]=>01001=>[1,1,2,1]
[-3,5,1,-4,-2]=>[-2,-4,1,5,-3]=>11001=>[2,2,1]
[-3,5,-1,4,2]=>[2,4,-1,5,-3]=>00101=>[2,1,1,1]
[-3,5,-1,4,-2]=>[-2,4,-1,5,-3]=>10101=>[1,1,1,1,1]
[-3,5,-1,-4,2]=>[2,-4,-1,5,-3]=>01101=>[1,2,1,1]
[-3,5,-1,-4,-2]=>[-2,-4,-1,5,-3]=>11101=>[3,1,1]
[-3,-5,1,4,2]=>[2,4,1,-5,-3]=>00011=>[3,2]
[-3,-5,1,4,-2]=>[-2,4,1,-5,-3]=>10011=>[1,2,2]
[-3,-5,1,-4,2]=>[2,-4,1,-5,-3]=>01011=>[1,1,1,2]
[-3,-5,1,-4,-2]=>[-2,-4,1,-5,-3]=>11011=>[2,1,2]
[-3,-5,-1,4,2]=>[2,4,-1,-5,-3]=>00111=>[2,3]
[-3,-5,-1,4,-2]=>[-2,4,-1,-5,-3]=>10111=>[1,1,3]
[-3,-5,-1,-4,2]=>[2,-4,-1,-5,-3]=>01111=>[1,4]
[-3,-5,-1,-4,-2]=>[-2,-4,-1,-5,-3]=>11111=>[5]
[3,5,2,1,4]=>[4,1,2,5,3]=>00000=>[5]
[3,5,2,1,-4]=>[-4,1,2,5,3]=>10000=>[1,4]
[3,5,2,-1,4]=>[4,-1,2,5,3]=>01000=>[1,1,3]
[3,5,2,-1,-4]=>[-4,-1,2,5,3]=>11000=>[2,3]
[3,5,-2,1,4]=>[4,1,-2,5,3]=>00100=>[2,1,2]
[3,5,-2,1,-4]=>[-4,1,-2,5,3]=>10100=>[1,1,1,2]
[3,5,-2,-1,4]=>[4,-1,-2,5,3]=>01100=>[1,2,2]
[3,5,-2,-1,-4]=>[-4,-1,-2,5,3]=>11100=>[3,2]
[3,-5,2,1,4]=>[4,1,2,-5,3]=>00010=>[3,1,1]
[3,-5,2,1,-4]=>[-4,1,2,-5,3]=>10010=>[1,2,1,1]
[3,-5,2,-1,4]=>[4,-1,2,-5,3]=>01010=>[1,1,1,1,1]
[3,-5,2,-1,-4]=>[-4,-1,2,-5,3]=>11010=>[2,1,1,1]
[3,-5,-2,1,4]=>[4,1,-2,-5,3]=>00110=>[2,2,1]
[3,-5,-2,1,-4]=>[-4,1,-2,-5,3]=>10110=>[1,1,2,1]
[3,-5,-2,-1,4]=>[4,-1,-2,-5,3]=>01110=>[1,3,1]
[3,-5,-2,-1,-4]=>[-4,-1,-2,-5,3]=>11110=>[4,1]
[-3,5,2,1,4]=>[4,1,2,5,-3]=>00001=>[4,1]
[-3,5,2,1,-4]=>[-4,1,2,5,-3]=>10001=>[1,3,1]
[-3,5,2,-1,4]=>[4,-1,2,5,-3]=>01001=>[1,1,2,1]
[-3,5,2,-1,-4]=>[-4,-1,2,5,-3]=>11001=>[2,2,1]
[-3,5,-2,1,4]=>[4,1,-2,5,-3]=>00101=>[2,1,1,1]
[-3,5,-2,1,-4]=>[-4,1,-2,5,-3]=>10101=>[1,1,1,1,1]
[-3,5,-2,-1,4]=>[4,-1,-2,5,-3]=>01101=>[1,2,1,1]
[-3,5,-2,-1,-4]=>[-4,-1,-2,5,-3]=>11101=>[3,1,1]
[-3,-5,2,1,4]=>[4,1,2,-5,-3]=>00011=>[3,2]
[-3,-5,2,1,-4]=>[-4,1,2,-5,-3]=>10011=>[1,2,2]
[-3,-5,2,-1,4]=>[4,-1,2,-5,-3]=>01011=>[1,1,1,2]
[-3,-5,2,-1,-4]=>[-4,-1,2,-5,-3]=>11011=>[2,1,2]
[-3,-5,-2,1,4]=>[4,1,-2,-5,-3]=>00111=>[2,3]
[-3,-5,-2,1,-4]=>[-4,1,-2,-5,-3]=>10111=>[1,1,3]
[-3,-5,-2,-1,4]=>[4,-1,-2,-5,-3]=>01111=>[1,4]
[-3,-5,-2,-1,-4]=>[-4,-1,-2,-5,-3]=>11111=>[5]
[3,5,2,4,1]=>[1,4,2,5,3]=>00000=>[5]
[3,5,2,4,-1]=>[-1,4,2,5,3]=>10000=>[1,4]
[3,5,2,-4,1]=>[1,-4,2,5,3]=>01000=>[1,1,3]
[3,5,2,-4,-1]=>[-1,-4,2,5,3]=>11000=>[2,3]
[3,5,-2,4,1]=>[1,4,-2,5,3]=>00100=>[2,1,2]
[3,5,-2,4,-1]=>[-1,4,-2,5,3]=>10100=>[1,1,1,2]
[3,5,-2,-4,1]=>[1,-4,-2,5,3]=>01100=>[1,2,2]
[3,5,-2,-4,-1]=>[-1,-4,-2,5,3]=>11100=>[3,2]
[3,-5,2,4,1]=>[1,4,2,-5,3]=>00010=>[3,1,1]
[3,-5,2,4,-1]=>[-1,4,2,-5,3]=>10010=>[1,2,1,1]
[3,-5,2,-4,1]=>[1,-4,2,-5,3]=>01010=>[1,1,1,1,1]
[3,-5,2,-4,-1]=>[-1,-4,2,-5,3]=>11010=>[2,1,1,1]
[3,-5,-2,4,1]=>[1,4,-2,-5,3]=>00110=>[2,2,1]
[3,-5,-2,4,-1]=>[-1,4,-2,-5,3]=>10110=>[1,1,2,1]
[3,-5,-2,-4,1]=>[1,-4,-2,-5,3]=>01110=>[1,3,1]
[3,-5,-2,-4,-1]=>[-1,-4,-2,-5,3]=>11110=>[4,1]
[-3,5,2,4,1]=>[1,4,2,5,-3]=>00001=>[4,1]
[-3,5,2,4,-1]=>[-1,4,2,5,-3]=>10001=>[1,3,1]
[-3,5,2,-4,1]=>[1,-4,2,5,-3]=>01001=>[1,1,2,1]
[-3,5,2,-4,-1]=>[-1,-4,2,5,-3]=>11001=>[2,2,1]
[-3,5,-2,4,1]=>[1,4,-2,5,-3]=>00101=>[2,1,1,1]
[-3,5,-2,4,-1]=>[-1,4,-2,5,-3]=>10101=>[1,1,1,1,1]
[-3,5,-2,-4,1]=>[1,-4,-2,5,-3]=>01101=>[1,2,1,1]
[-3,5,-2,-4,-1]=>[-1,-4,-2,5,-3]=>11101=>[3,1,1]
[-3,-5,2,4,1]=>[1,4,2,-5,-3]=>00011=>[3,2]
[-3,-5,2,4,-1]=>[-1,4,2,-5,-3]=>10011=>[1,2,2]
[-3,-5,2,-4,1]=>[1,-4,2,-5,-3]=>01011=>[1,1,1,2]
[-3,-5,2,-4,-1]=>[-1,-4,2,-5,-3]=>11011=>[2,1,2]
[-3,-5,-2,4,1]=>[1,4,-2,-5,-3]=>00111=>[2,3]
[-3,-5,-2,4,-1]=>[-1,4,-2,-5,-3]=>10111=>[1,1,3]
[-3,-5,-2,-4,1]=>[1,-4,-2,-5,-3]=>01111=>[1,4]
[-3,-5,-2,-4,-1]=>[-1,-4,-2,-5,-3]=>11111=>[5]
[3,5,4,1,2]=>[2,1,4,5,3]=>00000=>[5]
[3,5,4,1,-2]=>[-2,1,4,5,3]=>10000=>[1,4]
[3,5,4,-1,2]=>[2,-1,4,5,3]=>01000=>[1,1,3]
[3,5,4,-1,-2]=>[-2,-1,4,5,3]=>11000=>[2,3]
[3,5,-4,1,2]=>[2,1,-4,5,3]=>00100=>[2,1,2]
[3,5,-4,1,-2]=>[-2,1,-4,5,3]=>10100=>[1,1,1,2]
[3,5,-4,-1,2]=>[2,-1,-4,5,3]=>01100=>[1,2,2]
[3,5,-4,-1,-2]=>[-2,-1,-4,5,3]=>11100=>[3,2]
[3,-5,4,1,2]=>[2,1,4,-5,3]=>00010=>[3,1,1]
[3,-5,4,1,-2]=>[-2,1,4,-5,3]=>10010=>[1,2,1,1]
[3,-5,4,-1,2]=>[2,-1,4,-5,3]=>01010=>[1,1,1,1,1]
[3,-5,4,-1,-2]=>[-2,-1,4,-5,3]=>11010=>[2,1,1,1]
[3,-5,-4,1,2]=>[2,1,-4,-5,3]=>00110=>[2,2,1]
[3,-5,-4,1,-2]=>[-2,1,-4,-5,3]=>10110=>[1,1,2,1]
[3,-5,-4,-1,2]=>[2,-1,-4,-5,3]=>01110=>[1,3,1]
[3,-5,-4,-1,-2]=>[-2,-1,-4,-5,3]=>11110=>[4,1]
[-3,5,4,1,2]=>[2,1,4,5,-3]=>00001=>[4,1]
[-3,5,4,1,-2]=>[-2,1,4,5,-3]=>10001=>[1,3,1]
[-3,5,4,-1,2]=>[2,-1,4,5,-3]=>01001=>[1,1,2,1]
[-3,5,4,-1,-2]=>[-2,-1,4,5,-3]=>11001=>[2,2,1]
[-3,5,-4,1,2]=>[2,1,-4,5,-3]=>00101=>[2,1,1,1]
[-3,5,-4,1,-2]=>[-2,1,-4,5,-3]=>10101=>[1,1,1,1,1]
[-3,5,-4,-1,2]=>[2,-1,-4,5,-3]=>01101=>[1,2,1,1]
[-3,5,-4,-1,-2]=>[-2,-1,-4,5,-3]=>11101=>[3,1,1]
[-3,-5,4,1,2]=>[2,1,4,-5,-3]=>00011=>[3,2]
[-3,-5,4,1,-2]=>[-2,1,4,-5,-3]=>10011=>[1,2,2]
[-3,-5,4,-1,2]=>[2,-1,4,-5,-3]=>01011=>[1,1,1,2]
[-3,-5,4,-1,-2]=>[-2,-1,4,-5,-3]=>11011=>[2,1,2]
[-3,-5,-4,1,2]=>[2,1,-4,-5,-3]=>00111=>[2,3]
[-3,-5,-4,1,-2]=>[-2,1,-4,-5,-3]=>10111=>[1,1,3]
[-3,-5,-4,-1,2]=>[2,-1,-4,-5,-3]=>01111=>[1,4]
[-3,-5,-4,-1,-2]=>[-2,-1,-4,-5,-3]=>11111=>[5]
[3,5,4,2,1]=>[1,2,4,5,3]=>00000=>[5]
[3,5,4,2,-1]=>[-1,2,4,5,3]=>10000=>[1,4]
[3,5,4,-2,1]=>[1,-2,4,5,3]=>01000=>[1,1,3]
[3,5,4,-2,-1]=>[-1,-2,4,5,3]=>11000=>[2,3]
[3,5,-4,2,1]=>[1,2,-4,5,3]=>00100=>[2,1,2]
[3,5,-4,2,-1]=>[-1,2,-4,5,3]=>10100=>[1,1,1,2]
[3,5,-4,-2,1]=>[1,-2,-4,5,3]=>01100=>[1,2,2]
[3,5,-4,-2,-1]=>[-1,-2,-4,5,3]=>11100=>[3,2]
[3,-5,4,2,1]=>[1,2,4,-5,3]=>00010=>[3,1,1]
[3,-5,4,2,-1]=>[-1,2,4,-5,3]=>10010=>[1,2,1,1]
[3,-5,4,-2,1]=>[1,-2,4,-5,3]=>01010=>[1,1,1,1,1]
[3,-5,4,-2,-1]=>[-1,-2,4,-5,3]=>11010=>[2,1,1,1]
[3,-5,-4,2,1]=>[1,2,-4,-5,3]=>00110=>[2,2,1]
[3,-5,-4,2,-1]=>[-1,2,-4,-5,3]=>10110=>[1,1,2,1]
[3,-5,-4,-2,1]=>[1,-2,-4,-5,3]=>01110=>[1,3,1]
[3,-5,-4,-2,-1]=>[-1,-2,-4,-5,3]=>11110=>[4,1]
[-3,5,4,2,1]=>[1,2,4,5,-3]=>00001=>[4,1]
[-3,5,4,2,-1]=>[-1,2,4,5,-3]=>10001=>[1,3,1]
[-3,5,4,-2,1]=>[1,-2,4,5,-3]=>01001=>[1,1,2,1]
[-3,5,4,-2,-1]=>[-1,-2,4,5,-3]=>11001=>[2,2,1]
[-3,5,-4,2,1]=>[1,2,-4,5,-3]=>00101=>[2,1,1,1]
[-3,5,-4,2,-1]=>[-1,2,-4,5,-3]=>10101=>[1,1,1,1,1]
[-3,5,-4,-2,1]=>[1,-2,-4,5,-3]=>01101=>[1,2,1,1]
[-3,5,-4,-2,-1]=>[-1,-2,-4,5,-3]=>11101=>[3,1,1]
[-3,-5,4,2,1]=>[1,2,4,-5,-3]=>00011=>[3,2]
[-3,-5,4,2,-1]=>[-1,2,4,-5,-3]=>10011=>[1,2,2]
[-3,-5,4,-2,1]=>[1,-2,4,-5,-3]=>01011=>[1,1,1,2]
[-3,-5,4,-2,-1]=>[-1,-2,4,-5,-3]=>11011=>[2,1,2]
[-3,-5,-4,2,1]=>[1,2,-4,-5,-3]=>00111=>[2,3]
[-3,-5,-4,2,-1]=>[-1,2,-4,-5,-3]=>10111=>[1,1,3]
[-3,-5,-4,-2,1]=>[1,-2,-4,-5,-3]=>01111=>[1,4]
[-3,-5,-4,-2,-1]=>[-1,-2,-4,-5,-3]=>11111=>[5]
[4,1,2,3,5]=>[5,3,2,1,4]=>00000=>[5]
[4,1,2,3,-5]=>[-5,3,2,1,4]=>10000=>[1,4]
[4,1,2,-3,5]=>[5,-3,2,1,4]=>01000=>[1,1,3]
[4,1,2,-3,-5]=>[-5,-3,2,1,4]=>11000=>[2,3]
[4,1,-2,3,5]=>[5,3,-2,1,4]=>00100=>[2,1,2]
[4,1,-2,3,-5]=>[-5,3,-2,1,4]=>10100=>[1,1,1,2]
[4,1,-2,-3,5]=>[5,-3,-2,1,4]=>01100=>[1,2,2]
[4,1,-2,-3,-5]=>[-5,-3,-2,1,4]=>11100=>[3,2]
[4,-1,2,3,5]=>[5,3,2,-1,4]=>00010=>[3,1,1]
[4,-1,2,3,-5]=>[-5,3,2,-1,4]=>10010=>[1,2,1,1]
[4,-1,2,-3,5]=>[5,-3,2,-1,4]=>01010=>[1,1,1,1,1]
[4,-1,2,-3,-5]=>[-5,-3,2,-1,4]=>11010=>[2,1,1,1]
[4,-1,-2,3,5]=>[5,3,-2,-1,4]=>00110=>[2,2,1]
[4,-1,-2,3,-5]=>[-5,3,-2,-1,4]=>10110=>[1,1,2,1]
[4,-1,-2,-3,5]=>[5,-3,-2,-1,4]=>01110=>[1,3,1]
[4,-1,-2,-3,-5]=>[-5,-3,-2,-1,4]=>11110=>[4,1]
[-4,1,2,3,5]=>[5,3,2,1,-4]=>00001=>[4,1]
[-4,1,2,3,-5]=>[-5,3,2,1,-4]=>10001=>[1,3,1]
[-4,1,2,-3,5]=>[5,-3,2,1,-4]=>01001=>[1,1,2,1]
[-4,1,2,-3,-5]=>[-5,-3,2,1,-4]=>11001=>[2,2,1]
[-4,1,-2,3,5]=>[5,3,-2,1,-4]=>00101=>[2,1,1,1]
[-4,1,-2,3,-5]=>[-5,3,-2,1,-4]=>10101=>[1,1,1,1,1]
[-4,1,-2,-3,5]=>[5,-3,-2,1,-4]=>01101=>[1,2,1,1]
[-4,1,-2,-3,-5]=>[-5,-3,-2,1,-4]=>11101=>[3,1,1]
[-4,-1,2,3,5]=>[5,3,2,-1,-4]=>00011=>[3,2]
[-4,-1,2,3,-5]=>[-5,3,2,-1,-4]=>10011=>[1,2,2]
[-4,-1,2,-3,5]=>[5,-3,2,-1,-4]=>01011=>[1,1,1,2]
[-4,-1,2,-3,-5]=>[-5,-3,2,-1,-4]=>11011=>[2,1,2]
[-4,-1,-2,3,5]=>[5,3,-2,-1,-4]=>00111=>[2,3]
[-4,-1,-2,3,-5]=>[-5,3,-2,-1,-4]=>10111=>[1,1,3]
[-4,-1,-2,-3,5]=>[5,-3,-2,-1,-4]=>01111=>[1,4]
[-4,-1,-2,-3,-5]=>[-5,-3,-2,-1,-4]=>11111=>[5]
[4,1,2,5,3]=>[3,5,2,1,4]=>00000=>[5]
[4,1,2,5,-3]=>[-3,5,2,1,4]=>10000=>[1,4]
[4,1,2,-5,3]=>[3,-5,2,1,4]=>01000=>[1,1,3]
[4,1,2,-5,-3]=>[-3,-5,2,1,4]=>11000=>[2,3]
[4,1,-2,5,3]=>[3,5,-2,1,4]=>00100=>[2,1,2]
[4,1,-2,5,-3]=>[-3,5,-2,1,4]=>10100=>[1,1,1,2]
[4,1,-2,-5,3]=>[3,-5,-2,1,4]=>01100=>[1,2,2]
[4,1,-2,-5,-3]=>[-3,-5,-2,1,4]=>11100=>[3,2]
[4,-1,2,5,3]=>[3,5,2,-1,4]=>00010=>[3,1,1]
[4,-1,2,5,-3]=>[-3,5,2,-1,4]=>10010=>[1,2,1,1]
[4,-1,2,-5,3]=>[3,-5,2,-1,4]=>01010=>[1,1,1,1,1]
[4,-1,2,-5,-3]=>[-3,-5,2,-1,4]=>11010=>[2,1,1,1]
[4,-1,-2,5,3]=>[3,5,-2,-1,4]=>00110=>[2,2,1]
[4,-1,-2,5,-3]=>[-3,5,-2,-1,4]=>10110=>[1,1,2,1]
[4,-1,-2,-5,3]=>[3,-5,-2,-1,4]=>01110=>[1,3,1]
[4,-1,-2,-5,-3]=>[-3,-5,-2,-1,4]=>11110=>[4,1]
[-4,1,2,5,3]=>[3,5,2,1,-4]=>00001=>[4,1]
[-4,1,2,5,-3]=>[-3,5,2,1,-4]=>10001=>[1,3,1]
[-4,1,2,-5,3]=>[3,-5,2,1,-4]=>01001=>[1,1,2,1]
[-4,1,2,-5,-3]=>[-3,-5,2,1,-4]=>11001=>[2,2,1]
[-4,1,-2,5,3]=>[3,5,-2,1,-4]=>00101=>[2,1,1,1]
[-4,1,-2,5,-3]=>[-3,5,-2,1,-4]=>10101=>[1,1,1,1,1]
[-4,1,-2,-5,3]=>[3,-5,-2,1,-4]=>01101=>[1,2,1,1]
[-4,1,-2,-5,-3]=>[-3,-5,-2,1,-4]=>11101=>[3,1,1]
[-4,-1,2,5,3]=>[3,5,2,-1,-4]=>00011=>[3,2]
[-4,-1,2,5,-3]=>[-3,5,2,-1,-4]=>10011=>[1,2,2]
[-4,-1,2,-5,3]=>[3,-5,2,-1,-4]=>01011=>[1,1,1,2]
[-4,-1,2,-5,-3]=>[-3,-5,2,-1,-4]=>11011=>[2,1,2]
[-4,-1,-2,5,3]=>[3,5,-2,-1,-4]=>00111=>[2,3]
[-4,-1,-2,5,-3]=>[-3,5,-2,-1,-4]=>10111=>[1,1,3]
[-4,-1,-2,-5,3]=>[3,-5,-2,-1,-4]=>01111=>[1,4]
[-4,-1,-2,-5,-3]=>[-3,-5,-2,-1,-4]=>11111=>[5]
[4,1,3,2,5]=>[5,2,3,1,4]=>00000=>[5]
[4,1,3,2,-5]=>[-5,2,3,1,4]=>10000=>[1,4]
[4,1,3,-2,5]=>[5,-2,3,1,4]=>01000=>[1,1,3]
[4,1,3,-2,-5]=>[-5,-2,3,1,4]=>11000=>[2,3]
[4,1,-3,2,5]=>[5,2,-3,1,4]=>00100=>[2,1,2]
[4,1,-3,2,-5]=>[-5,2,-3,1,4]=>10100=>[1,1,1,2]
[4,1,-3,-2,5]=>[5,-2,-3,1,4]=>01100=>[1,2,2]
[4,1,-3,-2,-5]=>[-5,-2,-3,1,4]=>11100=>[3,2]
[4,-1,3,2,5]=>[5,2,3,-1,4]=>00010=>[3,1,1]
[4,-1,3,2,-5]=>[-5,2,3,-1,4]=>10010=>[1,2,1,1]
[4,-1,3,-2,5]=>[5,-2,3,-1,4]=>01010=>[1,1,1,1,1]
[4,-1,3,-2,-5]=>[-5,-2,3,-1,4]=>11010=>[2,1,1,1]
[4,-1,-3,2,5]=>[5,2,-3,-1,4]=>00110=>[2,2,1]
[4,-1,-3,2,-5]=>[-5,2,-3,-1,4]=>10110=>[1,1,2,1]
[4,-1,-3,-2,5]=>[5,-2,-3,-1,4]=>01110=>[1,3,1]
[4,-1,-3,-2,-5]=>[-5,-2,-3,-1,4]=>11110=>[4,1]
[-4,1,3,2,5]=>[5,2,3,1,-4]=>00001=>[4,1]
[-4,1,3,2,-5]=>[-5,2,3,1,-4]=>10001=>[1,3,1]
[-4,1,3,-2,5]=>[5,-2,3,1,-4]=>01001=>[1,1,2,1]
[-4,1,3,-2,-5]=>[-5,-2,3,1,-4]=>11001=>[2,2,1]
[-4,1,-3,2,5]=>[5,2,-3,1,-4]=>00101=>[2,1,1,1]
[-4,1,-3,2,-5]=>[-5,2,-3,1,-4]=>10101=>[1,1,1,1,1]
[-4,1,-3,-2,5]=>[5,-2,-3,1,-4]=>01101=>[1,2,1,1]
[-4,1,-3,-2,-5]=>[-5,-2,-3,1,-4]=>11101=>[3,1,1]
[-4,-1,3,2,5]=>[5,2,3,-1,-4]=>00011=>[3,2]
[-4,-1,3,2,-5]=>[-5,2,3,-1,-4]=>10011=>[1,2,2]
[-4,-1,3,-2,5]=>[5,-2,3,-1,-4]=>01011=>[1,1,1,2]
[-4,-1,3,-2,-5]=>[-5,-2,3,-1,-4]=>11011=>[2,1,2]
[-4,-1,-3,2,5]=>[5,2,-3,-1,-4]=>00111=>[2,3]
[-4,-1,-3,2,-5]=>[-5,2,-3,-1,-4]=>10111=>[1,1,3]
[-4,-1,-3,-2,5]=>[5,-2,-3,-1,-4]=>01111=>[1,4]
[-4,-1,-3,-2,-5]=>[-5,-2,-3,-1,-4]=>11111=>[5]
[4,1,3,5,2]=>[2,5,3,1,4]=>00000=>[5]
[4,1,3,5,-2]=>[-2,5,3,1,4]=>10000=>[1,4]
[4,1,3,-5,2]=>[2,-5,3,1,4]=>01000=>[1,1,3]
[4,1,3,-5,-2]=>[-2,-5,3,1,4]=>11000=>[2,3]
[4,1,-3,5,2]=>[2,5,-3,1,4]=>00100=>[2,1,2]
[4,1,-3,5,-2]=>[-2,5,-3,1,4]=>10100=>[1,1,1,2]
[4,1,-3,-5,2]=>[2,-5,-3,1,4]=>01100=>[1,2,2]
[4,1,-3,-5,-2]=>[-2,-5,-3,1,4]=>11100=>[3,2]
[4,-1,3,5,2]=>[2,5,3,-1,4]=>00010=>[3,1,1]
[4,-1,3,5,-2]=>[-2,5,3,-1,4]=>10010=>[1,2,1,1]
[4,-1,3,-5,2]=>[2,-5,3,-1,4]=>01010=>[1,1,1,1,1]
[4,-1,3,-5,-2]=>[-2,-5,3,-1,4]=>11010=>[2,1,1,1]
[4,-1,-3,5,2]=>[2,5,-3,-1,4]=>00110=>[2,2,1]
[4,-1,-3,5,-2]=>[-2,5,-3,-1,4]=>10110=>[1,1,2,1]
[4,-1,-3,-5,2]=>[2,-5,-3,-1,4]=>01110=>[1,3,1]
[4,-1,-3,-5,-2]=>[-2,-5,-3,-1,4]=>11110=>[4,1]
[-4,1,3,5,2]=>[2,5,3,1,-4]=>00001=>[4,1]
[-4,1,3,5,-2]=>[-2,5,3,1,-4]=>10001=>[1,3,1]
[-4,1,3,-5,2]=>[2,-5,3,1,-4]=>01001=>[1,1,2,1]
[-4,1,3,-5,-2]=>[-2,-5,3,1,-4]=>11001=>[2,2,1]
[-4,1,-3,5,2]=>[2,5,-3,1,-4]=>00101=>[2,1,1,1]
[-4,1,-3,5,-2]=>[-2,5,-3,1,-4]=>10101=>[1,1,1,1,1]
[-4,1,-3,-5,2]=>[2,-5,-3,1,-4]=>01101=>[1,2,1,1]
[-4,1,-3,-5,-2]=>[-2,-5,-3,1,-4]=>11101=>[3,1,1]
[-4,-1,3,5,2]=>[2,5,3,-1,-4]=>00011=>[3,2]
[-4,-1,3,5,-2]=>[-2,5,3,-1,-4]=>10011=>[1,2,2]
[-4,-1,3,-5,2]=>[2,-5,3,-1,-4]=>01011=>[1,1,1,2]
[-4,-1,3,-5,-2]=>[-2,-5,3,-1,-4]=>11011=>[2,1,2]
[-4,-1,-3,5,2]=>[2,5,-3,-1,-4]=>00111=>[2,3]
[-4,-1,-3,5,-2]=>[-2,5,-3,-1,-4]=>10111=>[1,1,3]
[-4,-1,-3,-5,2]=>[2,-5,-3,-1,-4]=>01111=>[1,4]
[-4,-1,-3,-5,-2]=>[-2,-5,-3,-1,-4]=>11111=>[5]
[4,1,5,2,3]=>[3,2,5,1,4]=>00000=>[5]
[4,1,5,2,-3]=>[-3,2,5,1,4]=>10000=>[1,4]
[4,1,5,-2,3]=>[3,-2,5,1,4]=>01000=>[1,1,3]
[4,1,5,-2,-3]=>[-3,-2,5,1,4]=>11000=>[2,3]
[4,1,-5,2,3]=>[3,2,-5,1,4]=>00100=>[2,1,2]
[4,1,-5,2,-3]=>[-3,2,-5,1,4]=>10100=>[1,1,1,2]
[4,1,-5,-2,3]=>[3,-2,-5,1,4]=>01100=>[1,2,2]
[4,1,-5,-2,-3]=>[-3,-2,-5,1,4]=>11100=>[3,2]
[4,-1,5,2,3]=>[3,2,5,-1,4]=>00010=>[3,1,1]
[4,-1,5,2,-3]=>[-3,2,5,-1,4]=>10010=>[1,2,1,1]
[4,-1,5,-2,3]=>[3,-2,5,-1,4]=>01010=>[1,1,1,1,1]
[4,-1,5,-2,-3]=>[-3,-2,5,-1,4]=>11010=>[2,1,1,1]
[4,-1,-5,2,3]=>[3,2,-5,-1,4]=>00110=>[2,2,1]
[4,-1,-5,2,-3]=>[-3,2,-5,-1,4]=>10110=>[1,1,2,1]
[4,-1,-5,-2,3]=>[3,-2,-5,-1,4]=>01110=>[1,3,1]
[4,-1,-5,-2,-3]=>[-3,-2,-5,-1,4]=>11110=>[4,1]
[-4,1,5,2,3]=>[3,2,5,1,-4]=>00001=>[4,1]
[-4,1,5,2,-3]=>[-3,2,5,1,-4]=>10001=>[1,3,1]
[-4,1,5,-2,3]=>[3,-2,5,1,-4]=>01001=>[1,1,2,1]
[-4,1,5,-2,-3]=>[-3,-2,5,1,-4]=>11001=>[2,2,1]
[-4,1,-5,2,3]=>[3,2,-5,1,-4]=>00101=>[2,1,1,1]
[-4,1,-5,2,-3]=>[-3,2,-5,1,-4]=>10101=>[1,1,1,1,1]
[-4,1,-5,-2,3]=>[3,-2,-5,1,-4]=>01101=>[1,2,1,1]
[-4,1,-5,-2,-3]=>[-3,-2,-5,1,-4]=>11101=>[3,1,1]
[-4,-1,5,2,3]=>[3,2,5,-1,-4]=>00011=>[3,2]
[-4,-1,5,2,-3]=>[-3,2,5,-1,-4]=>10011=>[1,2,2]
[-4,-1,5,-2,3]=>[3,-2,5,-1,-4]=>01011=>[1,1,1,2]
[-4,-1,5,-2,-3]=>[-3,-2,5,-1,-4]=>11011=>[2,1,2]
[-4,-1,-5,2,3]=>[3,2,-5,-1,-4]=>00111=>[2,3]
[-4,-1,-5,2,-3]=>[-3,2,-5,-1,-4]=>10111=>[1,1,3]
[-4,-1,-5,-2,3]=>[3,-2,-5,-1,-4]=>01111=>[1,4]
[-4,-1,-5,-2,-3]=>[-3,-2,-5,-1,-4]=>11111=>[5]
[4,1,5,3,2]=>[2,3,5,1,4]=>00000=>[5]
[4,1,5,3,-2]=>[-2,3,5,1,4]=>10000=>[1,4]
[4,1,5,-3,2]=>[2,-3,5,1,4]=>01000=>[1,1,3]
[4,1,5,-3,-2]=>[-2,-3,5,1,4]=>11000=>[2,3]
[4,1,-5,3,2]=>[2,3,-5,1,4]=>00100=>[2,1,2]
[4,1,-5,3,-2]=>[-2,3,-5,1,4]=>10100=>[1,1,1,2]
[4,1,-5,-3,2]=>[2,-3,-5,1,4]=>01100=>[1,2,2]
[4,1,-5,-3,-2]=>[-2,-3,-5,1,4]=>11100=>[3,2]
[4,-1,5,3,2]=>[2,3,5,-1,4]=>00010=>[3,1,1]
[4,-1,5,3,-2]=>[-2,3,5,-1,4]=>10010=>[1,2,1,1]
[4,-1,5,-3,2]=>[2,-3,5,-1,4]=>01010=>[1,1,1,1,1]
[4,-1,5,-3,-2]=>[-2,-3,5,-1,4]=>11010=>[2,1,1,1]
[4,-1,-5,3,2]=>[2,3,-5,-1,4]=>00110=>[2,2,1]
[4,-1,-5,3,-2]=>[-2,3,-5,-1,4]=>10110=>[1,1,2,1]
[4,-1,-5,-3,2]=>[2,-3,-5,-1,4]=>01110=>[1,3,1]
[4,-1,-5,-3,-2]=>[-2,-3,-5,-1,4]=>11110=>[4,1]
[-4,1,5,3,2]=>[2,3,5,1,-4]=>00001=>[4,1]
[-4,1,5,3,-2]=>[-2,3,5,1,-4]=>10001=>[1,3,1]
[-4,1,5,-3,2]=>[2,-3,5,1,-4]=>01001=>[1,1,2,1]
[-4,1,5,-3,-2]=>[-2,-3,5,1,-4]=>11001=>[2,2,1]
[-4,1,-5,3,2]=>[2,3,-5,1,-4]=>00101=>[2,1,1,1]
[-4,1,-5,3,-2]=>[-2,3,-5,1,-4]=>10101=>[1,1,1,1,1]
[-4,1,-5,-3,2]=>[2,-3,-5,1,-4]=>01101=>[1,2,1,1]
[-4,1,-5,-3,-2]=>[-2,-3,-5,1,-4]=>11101=>[3,1,1]
[-4,-1,5,3,2]=>[2,3,5,-1,-4]=>00011=>[3,2]
[-4,-1,5,3,-2]=>[-2,3,5,-1,-4]=>10011=>[1,2,2]
[-4,-1,5,-3,2]=>[2,-3,5,-1,-4]=>01011=>[1,1,1,2]
[-4,-1,5,-3,-2]=>[-2,-3,5,-1,-4]=>11011=>[2,1,2]
[-4,-1,-5,3,2]=>[2,3,-5,-1,-4]=>00111=>[2,3]
[-4,-1,-5,3,-2]=>[-2,3,-5,-1,-4]=>10111=>[1,1,3]
[-4,-1,-5,-3,2]=>[2,-3,-5,-1,-4]=>01111=>[1,4]
[-4,-1,-5,-3,-2]=>[-2,-3,-5,-1,-4]=>11111=>[5]
[4,2,1,3,5]=>[5,3,1,2,4]=>00000=>[5]
[4,2,1,3,-5]=>[-5,3,1,2,4]=>10000=>[1,4]
[4,2,1,-3,5]=>[5,-3,1,2,4]=>01000=>[1,1,3]
[4,2,1,-3,-5]=>[-5,-3,1,2,4]=>11000=>[2,3]
[4,2,-1,3,5]=>[5,3,-1,2,4]=>00100=>[2,1,2]
[4,2,-1,3,-5]=>[-5,3,-1,2,4]=>10100=>[1,1,1,2]
[4,2,-1,-3,5]=>[5,-3,-1,2,4]=>01100=>[1,2,2]
[4,2,-1,-3,-5]=>[-5,-3,-1,2,4]=>11100=>[3,2]
[4,-2,1,3,5]=>[5,3,1,-2,4]=>00010=>[3,1,1]
[4,-2,1,3,-5]=>[-5,3,1,-2,4]=>10010=>[1,2,1,1]
[4,-2,1,-3,5]=>[5,-3,1,-2,4]=>01010=>[1,1,1,1,1]
[4,-2,1,-3,-5]=>[-5,-3,1,-2,4]=>11010=>[2,1,1,1]
[4,-2,-1,3,5]=>[5,3,-1,-2,4]=>00110=>[2,2,1]
[4,-2,-1,3,-5]=>[-5,3,-1,-2,4]=>10110=>[1,1,2,1]
[4,-2,-1,-3,5]=>[5,-3,-1,-2,4]=>01110=>[1,3,1]
[4,-2,-1,-3,-5]=>[-5,-3,-1,-2,4]=>11110=>[4,1]
[-4,2,1,3,5]=>[5,3,1,2,-4]=>00001=>[4,1]
[-4,2,1,3,-5]=>[-5,3,1,2,-4]=>10001=>[1,3,1]
[-4,2,1,-3,5]=>[5,-3,1,2,-4]=>01001=>[1,1,2,1]
[-4,2,1,-3,-5]=>[-5,-3,1,2,-4]=>11001=>[2,2,1]
[-4,2,-1,3,5]=>[5,3,-1,2,-4]=>00101=>[2,1,1,1]
[-4,2,-1,3,-5]=>[-5,3,-1,2,-4]=>10101=>[1,1,1,1,1]
[-4,2,-1,-3,5]=>[5,-3,-1,2,-4]=>01101=>[1,2,1,1]
[-4,2,-1,-3,-5]=>[-5,-3,-1,2,-4]=>11101=>[3,1,1]
[-4,-2,1,3,5]=>[5,3,1,-2,-4]=>00011=>[3,2]
[-4,-2,1,3,-5]=>[-5,3,1,-2,-4]=>10011=>[1,2,2]
[-4,-2,1,-3,5]=>[5,-3,1,-2,-4]=>01011=>[1,1,1,2]
[-4,-2,1,-3,-5]=>[-5,-3,1,-2,-4]=>11011=>[2,1,2]
[-4,-2,-1,3,5]=>[5,3,-1,-2,-4]=>00111=>[2,3]
[-4,-2,-1,3,-5]=>[-5,3,-1,-2,-4]=>10111=>[1,1,3]
[-4,-2,-1,-3,5]=>[5,-3,-1,-2,-4]=>01111=>[1,4]
[-4,-2,-1,-3,-5]=>[-5,-3,-1,-2,-4]=>11111=>[5]
[4,2,1,5,3]=>[3,5,1,2,4]=>00000=>[5]
[4,2,1,5,-3]=>[-3,5,1,2,4]=>10000=>[1,4]
[4,2,1,-5,3]=>[3,-5,1,2,4]=>01000=>[1,1,3]
[4,2,1,-5,-3]=>[-3,-5,1,2,4]=>11000=>[2,3]
[4,2,-1,5,3]=>[3,5,-1,2,4]=>00100=>[2,1,2]
[4,2,-1,5,-3]=>[-3,5,-1,2,4]=>10100=>[1,1,1,2]
[4,2,-1,-5,3]=>[3,-5,-1,2,4]=>01100=>[1,2,2]
[4,2,-1,-5,-3]=>[-3,-5,-1,2,4]=>11100=>[3,2]
[4,-2,1,5,3]=>[3,5,1,-2,4]=>00010=>[3,1,1]
[4,-2,1,5,-3]=>[-3,5,1,-2,4]=>10010=>[1,2,1,1]
[4,-2,1,-5,3]=>[3,-5,1,-2,4]=>01010=>[1,1,1,1,1]
[4,-2,1,-5,-3]=>[-3,-5,1,-2,4]=>11010=>[2,1,1,1]
[4,-2,-1,5,3]=>[3,5,-1,-2,4]=>00110=>[2,2,1]
[4,-2,-1,5,-3]=>[-3,5,-1,-2,4]=>10110=>[1,1,2,1]
[4,-2,-1,-5,3]=>[3,-5,-1,-2,4]=>01110=>[1,3,1]
[4,-2,-1,-5,-3]=>[-3,-5,-1,-2,4]=>11110=>[4,1]
[-4,2,1,5,3]=>[3,5,1,2,-4]=>00001=>[4,1]
[-4,2,1,5,-3]=>[-3,5,1,2,-4]=>10001=>[1,3,1]
[-4,2,1,-5,3]=>[3,-5,1,2,-4]=>01001=>[1,1,2,1]
[-4,2,1,-5,-3]=>[-3,-5,1,2,-4]=>11001=>[2,2,1]
[-4,2,-1,5,3]=>[3,5,-1,2,-4]=>00101=>[2,1,1,1]
[-4,2,-1,5,-3]=>[-3,5,-1,2,-4]=>10101=>[1,1,1,1,1]
[-4,2,-1,-5,3]=>[3,-5,-1,2,-4]=>01101=>[1,2,1,1]
[-4,2,-1,-5,-3]=>[-3,-5,-1,2,-4]=>11101=>[3,1,1]
[-4,-2,1,5,3]=>[3,5,1,-2,-4]=>00011=>[3,2]
[-4,-2,1,5,-3]=>[-3,5,1,-2,-4]=>10011=>[1,2,2]
[-4,-2,1,-5,3]=>[3,-5,1,-2,-4]=>01011=>[1,1,1,2]
[-4,-2,1,-5,-3]=>[-3,-5,1,-2,-4]=>11011=>[2,1,2]
[-4,-2,-1,5,3]=>[3,5,-1,-2,-4]=>00111=>[2,3]
[-4,-2,-1,5,-3]=>[-3,5,-1,-2,-4]=>10111=>[1,1,3]
[-4,-2,-1,-5,3]=>[3,-5,-1,-2,-4]=>01111=>[1,4]
[-4,-2,-1,-5,-3]=>[-3,-5,-1,-2,-4]=>11111=>[5]
[4,2,3,1,5]=>[5,1,3,2,4]=>00000=>[5]
[4,2,3,1,-5]=>[-5,1,3,2,4]=>10000=>[1,4]
[4,2,3,-1,5]=>[5,-1,3,2,4]=>01000=>[1,1,3]
[4,2,3,-1,-5]=>[-5,-1,3,2,4]=>11000=>[2,3]
[4,2,-3,1,5]=>[5,1,-3,2,4]=>00100=>[2,1,2]
[4,2,-3,1,-5]=>[-5,1,-3,2,4]=>10100=>[1,1,1,2]
[4,2,-3,-1,5]=>[5,-1,-3,2,4]=>01100=>[1,2,2]
[4,2,-3,-1,-5]=>[-5,-1,-3,2,4]=>11100=>[3,2]
[4,-2,3,1,5]=>[5,1,3,-2,4]=>00010=>[3,1,1]
[4,-2,3,1,-5]=>[-5,1,3,-2,4]=>10010=>[1,2,1,1]
[4,-2,3,-1,5]=>[5,-1,3,-2,4]=>01010=>[1,1,1,1,1]
[4,-2,3,-1,-5]=>[-5,-1,3,-2,4]=>11010=>[2,1,1,1]
[4,-2,-3,1,5]=>[5,1,-3,-2,4]=>00110=>[2,2,1]
[4,-2,-3,1,-5]=>[-5,1,-3,-2,4]=>10110=>[1,1,2,1]
[4,-2,-3,-1,5]=>[5,-1,-3,-2,4]=>01110=>[1,3,1]
[4,-2,-3,-1,-5]=>[-5,-1,-3,-2,4]=>11110=>[4,1]
[-4,2,3,1,5]=>[5,1,3,2,-4]=>00001=>[4,1]
[-4,2,3,1,-5]=>[-5,1,3,2,-4]=>10001=>[1,3,1]
[-4,2,3,-1,5]=>[5,-1,3,2,-4]=>01001=>[1,1,2,1]
[-4,2,3,-1,-5]=>[-5,-1,3,2,-4]=>11001=>[2,2,1]
[-4,2,-3,1,5]=>[5,1,-3,2,-4]=>00101=>[2,1,1,1]
[-4,2,-3,1,-5]=>[-5,1,-3,2,-4]=>10101=>[1,1,1,1,1]
[-4,2,-3,-1,5]=>[5,-1,-3,2,-4]=>01101=>[1,2,1,1]
[-4,2,-3,-1,-5]=>[-5,-1,-3,2,-4]=>11101=>[3,1,1]
[-4,-2,3,1,5]=>[5,1,3,-2,-4]=>00011=>[3,2]
[-4,-2,3,1,-5]=>[-5,1,3,-2,-4]=>10011=>[1,2,2]
[-4,-2,3,-1,5]=>[5,-1,3,-2,-4]=>01011=>[1,1,1,2]
[-4,-2,3,-1,-5]=>[-5,-1,3,-2,-4]=>11011=>[2,1,2]
[-4,-2,-3,1,5]=>[5,1,-3,-2,-4]=>00111=>[2,3]
[-4,-2,-3,1,-5]=>[-5,1,-3,-2,-4]=>10111=>[1,1,3]
[-4,-2,-3,-1,5]=>[5,-1,-3,-2,-4]=>01111=>[1,4]
[-4,-2,-3,-1,-5]=>[-5,-1,-3,-2,-4]=>11111=>[5]
[4,2,3,5,1]=>[1,5,3,2,4]=>00000=>[5]
[4,2,3,5,-1]=>[-1,5,3,2,4]=>10000=>[1,4]
[4,2,3,-5,1]=>[1,-5,3,2,4]=>01000=>[1,1,3]
[4,2,3,-5,-1]=>[-1,-5,3,2,4]=>11000=>[2,3]
[4,2,-3,5,1]=>[1,5,-3,2,4]=>00100=>[2,1,2]
[4,2,-3,5,-1]=>[-1,5,-3,2,4]=>10100=>[1,1,1,2]
[4,2,-3,-5,1]=>[1,-5,-3,2,4]=>01100=>[1,2,2]
[4,2,-3,-5,-1]=>[-1,-5,-3,2,4]=>11100=>[3,2]
[4,-2,3,5,1]=>[1,5,3,-2,4]=>00010=>[3,1,1]
[4,-2,3,5,-1]=>[-1,5,3,-2,4]=>10010=>[1,2,1,1]
[4,-2,3,-5,1]=>[1,-5,3,-2,4]=>01010=>[1,1,1,1,1]
[4,-2,3,-5,-1]=>[-1,-5,3,-2,4]=>11010=>[2,1,1,1]
[4,-2,-3,5,1]=>[1,5,-3,-2,4]=>00110=>[2,2,1]
[4,-2,-3,5,-1]=>[-1,5,-3,-2,4]=>10110=>[1,1,2,1]
[4,-2,-3,-5,1]=>[1,-5,-3,-2,4]=>01110=>[1,3,1]
[4,-2,-3,-5,-1]=>[-1,-5,-3,-2,4]=>11110=>[4,1]
[-4,2,3,5,1]=>[1,5,3,2,-4]=>00001=>[4,1]
[-4,2,3,5,-1]=>[-1,5,3,2,-4]=>10001=>[1,3,1]
[-4,2,3,-5,1]=>[1,-5,3,2,-4]=>01001=>[1,1,2,1]
[-4,2,3,-5,-1]=>[-1,-5,3,2,-4]=>11001=>[2,2,1]
[-4,2,-3,5,1]=>[1,5,-3,2,-4]=>00101=>[2,1,1,1]
[-4,2,-3,5,-1]=>[-1,5,-3,2,-4]=>10101=>[1,1,1,1,1]
[-4,2,-3,-5,1]=>[1,-5,-3,2,-4]=>01101=>[1,2,1,1]
[-4,2,-3,-5,-1]=>[-1,-5,-3,2,-4]=>11101=>[3,1,1]
[-4,-2,3,5,1]=>[1,5,3,-2,-4]=>00011=>[3,2]
[-4,-2,3,5,-1]=>[-1,5,3,-2,-4]=>10011=>[1,2,2]
[-4,-2,3,-5,1]=>[1,-5,3,-2,-4]=>01011=>[1,1,1,2]
[-4,-2,3,-5,-1]=>[-1,-5,3,-2,-4]=>11011=>[2,1,2]
[-4,-2,-3,5,1]=>[1,5,-3,-2,-4]=>00111=>[2,3]
[-4,-2,-3,5,-1]=>[-1,5,-3,-2,-4]=>10111=>[1,1,3]
[-4,-2,-3,-5,1]=>[1,-5,-3,-2,-4]=>01111=>[1,4]
[-4,-2,-3,-5,-1]=>[-1,-5,-3,-2,-4]=>11111=>[5]
[4,2,5,1,3]=>[3,1,5,2,4]=>00000=>[5]
[4,2,5,1,-3]=>[-3,1,5,2,4]=>10000=>[1,4]
[4,2,5,-1,3]=>[3,-1,5,2,4]=>01000=>[1,1,3]
[4,2,5,-1,-3]=>[-3,-1,5,2,4]=>11000=>[2,3]
[4,2,-5,1,3]=>[3,1,-5,2,4]=>00100=>[2,1,2]
[4,2,-5,1,-3]=>[-3,1,-5,2,4]=>10100=>[1,1,1,2]
[4,2,-5,-1,3]=>[3,-1,-5,2,4]=>01100=>[1,2,2]
[4,2,-5,-1,-3]=>[-3,-1,-5,2,4]=>11100=>[3,2]
[4,-2,5,1,3]=>[3,1,5,-2,4]=>00010=>[3,1,1]
[4,-2,5,1,-3]=>[-3,1,5,-2,4]=>10010=>[1,2,1,1]
[4,-2,5,-1,3]=>[3,-1,5,-2,4]=>01010=>[1,1,1,1,1]
[4,-2,5,-1,-3]=>[-3,-1,5,-2,4]=>11010=>[2,1,1,1]
[4,-2,-5,1,3]=>[3,1,-5,-2,4]=>00110=>[2,2,1]
[4,-2,-5,1,-3]=>[-3,1,-5,-2,4]=>10110=>[1,1,2,1]
[4,-2,-5,-1,3]=>[3,-1,-5,-2,4]=>01110=>[1,3,1]
[4,-2,-5,-1,-3]=>[-3,-1,-5,-2,4]=>11110=>[4,1]
[-4,2,5,1,3]=>[3,1,5,2,-4]=>00001=>[4,1]
[-4,2,5,1,-3]=>[-3,1,5,2,-4]=>10001=>[1,3,1]
[-4,2,5,-1,3]=>[3,-1,5,2,-4]=>01001=>[1,1,2,1]
[-4,2,5,-1,-3]=>[-3,-1,5,2,-4]=>11001=>[2,2,1]
[-4,2,-5,1,3]=>[3,1,-5,2,-4]=>00101=>[2,1,1,1]
[-4,2,-5,1,-3]=>[-3,1,-5,2,-4]=>10101=>[1,1,1,1,1]
[-4,2,-5,-1,3]=>[3,-1,-5,2,-4]=>01101=>[1,2,1,1]
[-4,2,-5,-1,-3]=>[-3,-1,-5,2,-4]=>11101=>[3,1,1]
[-4,-2,5,1,3]=>[3,1,5,-2,-4]=>00011=>[3,2]
[-4,-2,5,1,-3]=>[-3,1,5,-2,-4]=>10011=>[1,2,2]
[-4,-2,5,-1,3]=>[3,-1,5,-2,-4]=>01011=>[1,1,1,2]
[-4,-2,5,-1,-3]=>[-3,-1,5,-2,-4]=>11011=>[2,1,2]
[-4,-2,-5,1,3]=>[3,1,-5,-2,-4]=>00111=>[2,3]
[-4,-2,-5,1,-3]=>[-3,1,-5,-2,-4]=>10111=>[1,1,3]
[-4,-2,-5,-1,3]=>[3,-1,-5,-2,-4]=>01111=>[1,4]
[-4,-2,-5,-1,-3]=>[-3,-1,-5,-2,-4]=>11111=>[5]
[4,2,5,3,1]=>[1,3,5,2,4]=>00000=>[5]
[4,2,5,3,-1]=>[-1,3,5,2,4]=>10000=>[1,4]
[4,2,5,-3,1]=>[1,-3,5,2,4]=>01000=>[1,1,3]
[4,2,5,-3,-1]=>[-1,-3,5,2,4]=>11000=>[2,3]
[4,2,-5,3,1]=>[1,3,-5,2,4]=>00100=>[2,1,2]
[4,2,-5,3,-1]=>[-1,3,-5,2,4]=>10100=>[1,1,1,2]
[4,2,-5,-3,1]=>[1,-3,-5,2,4]=>01100=>[1,2,2]
[4,2,-5,-3,-1]=>[-1,-3,-5,2,4]=>11100=>[3,2]
[4,-2,5,3,1]=>[1,3,5,-2,4]=>00010=>[3,1,1]
[4,-2,5,3,-1]=>[-1,3,5,-2,4]=>10010=>[1,2,1,1]
[4,-2,5,-3,1]=>[1,-3,5,-2,4]=>01010=>[1,1,1,1,1]
[4,-2,5,-3,-1]=>[-1,-3,5,-2,4]=>11010=>[2,1,1,1]
[4,-2,-5,3,1]=>[1,3,-5,-2,4]=>00110=>[2,2,1]
[4,-2,-5,3,-1]=>[-1,3,-5,-2,4]=>10110=>[1,1,2,1]
[4,-2,-5,-3,1]=>[1,-3,-5,-2,4]=>01110=>[1,3,1]
[4,-2,-5,-3,-1]=>[-1,-3,-5,-2,4]=>11110=>[4,1]
[-4,2,5,3,1]=>[1,3,5,2,-4]=>00001=>[4,1]
[-4,2,5,3,-1]=>[-1,3,5,2,-4]=>10001=>[1,3,1]
[-4,2,5,-3,1]=>[1,-3,5,2,-4]=>01001=>[1,1,2,1]
[-4,2,5,-3,-1]=>[-1,-3,5,2,-4]=>11001=>[2,2,1]
[-4,2,-5,3,1]=>[1,3,-5,2,-4]=>00101=>[2,1,1,1]
[-4,2,-5,3,-1]=>[-1,3,-5,2,-4]=>10101=>[1,1,1,1,1]
[-4,2,-5,-3,1]=>[1,-3,-5,2,-4]=>01101=>[1,2,1,1]
[-4,2,-5,-3,-1]=>[-1,-3,-5,2,-4]=>11101=>[3,1,1]
[-4,-2,5,3,1]=>[1,3,5,-2,-4]=>00011=>[3,2]
[-4,-2,5,3,-1]=>[-1,3,5,-2,-4]=>10011=>[1,2,2]
[-4,-2,5,-3,1]=>[1,-3,5,-2,-4]=>01011=>[1,1,1,2]
[-4,-2,5,-3,-1]=>[-1,-3,5,-2,-4]=>11011=>[2,1,2]
[-4,-2,-5,3,1]=>[1,3,-5,-2,-4]=>00111=>[2,3]
[-4,-2,-5,3,-1]=>[-1,3,-5,-2,-4]=>10111=>[1,1,3]
[-4,-2,-5,-3,1]=>[1,-3,-5,-2,-4]=>01111=>[1,4]
[-4,-2,-5,-3,-1]=>[-1,-3,-5,-2,-4]=>11111=>[5]
[4,3,1,2,5]=>[5,2,1,3,4]=>00000=>[5]
[4,3,1,2,-5]=>[-5,2,1,3,4]=>10000=>[1,4]
[4,3,1,-2,5]=>[5,-2,1,3,4]=>01000=>[1,1,3]
[4,3,1,-2,-5]=>[-5,-2,1,3,4]=>11000=>[2,3]
[4,3,-1,2,5]=>[5,2,-1,3,4]=>00100=>[2,1,2]
[4,3,-1,2,-5]=>[-5,2,-1,3,4]=>10100=>[1,1,1,2]
[4,3,-1,-2,5]=>[5,-2,-1,3,4]=>01100=>[1,2,2]
[4,3,-1,-2,-5]=>[-5,-2,-1,3,4]=>11100=>[3,2]
[4,-3,1,2,5]=>[5,2,1,-3,4]=>00010=>[3,1,1]
[4,-3,1,2,-5]=>[-5,2,1,-3,4]=>10010=>[1,2,1,1]
[4,-3,1,-2,5]=>[5,-2,1,-3,4]=>01010=>[1,1,1,1,1]
[4,-3,1,-2,-5]=>[-5,-2,1,-3,4]=>11010=>[2,1,1,1]
[4,-3,-1,2,5]=>[5,2,-1,-3,4]=>00110=>[2,2,1]
[4,-3,-1,2,-5]=>[-5,2,-1,-3,4]=>10110=>[1,1,2,1]
[4,-3,-1,-2,5]=>[5,-2,-1,-3,4]=>01110=>[1,3,1]
[4,-3,-1,-2,-5]=>[-5,-2,-1,-3,4]=>11110=>[4,1]
[-4,3,1,2,5]=>[5,2,1,3,-4]=>00001=>[4,1]
[-4,3,1,2,-5]=>[-5,2,1,3,-4]=>10001=>[1,3,1]
[-4,3,1,-2,5]=>[5,-2,1,3,-4]=>01001=>[1,1,2,1]
[-4,3,1,-2,-5]=>[-5,-2,1,3,-4]=>11001=>[2,2,1]
[-4,3,-1,2,5]=>[5,2,-1,3,-4]=>00101=>[2,1,1,1]
[-4,3,-1,2,-5]=>[-5,2,-1,3,-4]=>10101=>[1,1,1,1,1]
[-4,3,-1,-2,5]=>[5,-2,-1,3,-4]=>01101=>[1,2,1,1]
[-4,3,-1,-2,-5]=>[-5,-2,-1,3,-4]=>11101=>[3,1,1]
[-4,-3,1,2,5]=>[5,2,1,-3,-4]=>00011=>[3,2]
[-4,-3,1,2,-5]=>[-5,2,1,-3,-4]=>10011=>[1,2,2]
[-4,-3,1,-2,5]=>[5,-2,1,-3,-4]=>01011=>[1,1,1,2]
[-4,-3,1,-2,-5]=>[-5,-2,1,-3,-4]=>11011=>[2,1,2]
[-4,-3,-1,2,5]=>[5,2,-1,-3,-4]=>00111=>[2,3]
[-4,-3,-1,2,-5]=>[-5,2,-1,-3,-4]=>10111=>[1,1,3]
[-4,-3,-1,-2,5]=>[5,-2,-1,-3,-4]=>01111=>[1,4]
[-4,-3,-1,-2,-5]=>[-5,-2,-1,-3,-4]=>11111=>[5]
[4,3,1,5,2]=>[2,5,1,3,4]=>00000=>[5]
[4,3,1,5,-2]=>[-2,5,1,3,4]=>10000=>[1,4]
[4,3,1,-5,2]=>[2,-5,1,3,4]=>01000=>[1,1,3]
[4,3,1,-5,-2]=>[-2,-5,1,3,4]=>11000=>[2,3]
[4,3,-1,5,2]=>[2,5,-1,3,4]=>00100=>[2,1,2]
[4,3,-1,5,-2]=>[-2,5,-1,3,4]=>10100=>[1,1,1,2]
[4,3,-1,-5,2]=>[2,-5,-1,3,4]=>01100=>[1,2,2]
[4,3,-1,-5,-2]=>[-2,-5,-1,3,4]=>11100=>[3,2]
[4,-3,1,5,2]=>[2,5,1,-3,4]=>00010=>[3,1,1]
[4,-3,1,5,-2]=>[-2,5,1,-3,4]=>10010=>[1,2,1,1]
[4,-3,1,-5,2]=>[2,-5,1,-3,4]=>01010=>[1,1,1,1,1]
[4,-3,1,-5,-2]=>[-2,-5,1,-3,4]=>11010=>[2,1,1,1]
[4,-3,-1,5,2]=>[2,5,-1,-3,4]=>00110=>[2,2,1]
[4,-3,-1,5,-2]=>[-2,5,-1,-3,4]=>10110=>[1,1,2,1]
[4,-3,-1,-5,2]=>[2,-5,-1,-3,4]=>01110=>[1,3,1]
[4,-3,-1,-5,-2]=>[-2,-5,-1,-3,4]=>11110=>[4,1]
[-4,3,1,5,2]=>[2,5,1,3,-4]=>00001=>[4,1]
[-4,3,1,5,-2]=>[-2,5,1,3,-4]=>10001=>[1,3,1]
[-4,3,1,-5,2]=>[2,-5,1,3,-4]=>01001=>[1,1,2,1]
[-4,3,1,-5,-2]=>[-2,-5,1,3,-4]=>11001=>[2,2,1]
[-4,3,-1,5,2]=>[2,5,-1,3,-4]=>00101=>[2,1,1,1]
[-4,3,-1,5,-2]=>[-2,5,-1,3,-4]=>10101=>[1,1,1,1,1]
[-4,3,-1,-5,2]=>[2,-5,-1,3,-4]=>01101=>[1,2,1,1]
[-4,3,-1,-5,-2]=>[-2,-5,-1,3,-4]=>11101=>[3,1,1]
[-4,-3,1,5,2]=>[2,5,1,-3,-4]=>00011=>[3,2]
[-4,-3,1,5,-2]=>[-2,5,1,-3,-4]=>10011=>[1,2,2]
[-4,-3,1,-5,2]=>[2,-5,1,-3,-4]=>01011=>[1,1,1,2]
[-4,-3,1,-5,-2]=>[-2,-5,1,-3,-4]=>11011=>[2,1,2]
[-4,-3,-1,5,2]=>[2,5,-1,-3,-4]=>00111=>[2,3]
[-4,-3,-1,5,-2]=>[-2,5,-1,-3,-4]=>10111=>[1,1,3]
[-4,-3,-1,-5,2]=>[2,-5,-1,-3,-4]=>01111=>[1,4]
[-4,-3,-1,-5,-2]=>[-2,-5,-1,-3,-4]=>11111=>[5]
[4,3,2,1,5]=>[5,1,2,3,4]=>00000=>[5]
[4,3,2,1,-5]=>[-5,1,2,3,4]=>10000=>[1,4]
[4,3,2,-1,5]=>[5,-1,2,3,4]=>01000=>[1,1,3]
[4,3,2,-1,-5]=>[-5,-1,2,3,4]=>11000=>[2,3]
[4,3,-2,1,5]=>[5,1,-2,3,4]=>00100=>[2,1,2]
[4,3,-2,1,-5]=>[-5,1,-2,3,4]=>10100=>[1,1,1,2]
[4,3,-2,-1,5]=>[5,-1,-2,3,4]=>01100=>[1,2,2]
[4,3,-2,-1,-5]=>[-5,-1,-2,3,4]=>11100=>[3,2]
[4,-3,2,1,5]=>[5,1,2,-3,4]=>00010=>[3,1,1]
[4,-3,2,1,-5]=>[-5,1,2,-3,4]=>10010=>[1,2,1,1]
[4,-3,2,-1,5]=>[5,-1,2,-3,4]=>01010=>[1,1,1,1,1]
[4,-3,2,-1,-5]=>[-5,-1,2,-3,4]=>11010=>[2,1,1,1]
[4,-3,-2,1,5]=>[5,1,-2,-3,4]=>00110=>[2,2,1]
[4,-3,-2,1,-5]=>[-5,1,-2,-3,4]=>10110=>[1,1,2,1]
[4,-3,-2,-1,5]=>[5,-1,-2,-3,4]=>01110=>[1,3,1]
[4,-3,-2,-1,-5]=>[-5,-1,-2,-3,4]=>11110=>[4,1]
[-4,3,2,1,5]=>[5,1,2,3,-4]=>00001=>[4,1]
[-4,3,2,1,-5]=>[-5,1,2,3,-4]=>10001=>[1,3,1]
[-4,3,2,-1,5]=>[5,-1,2,3,-4]=>01001=>[1,1,2,1]
[-4,3,2,-1,-5]=>[-5,-1,2,3,-4]=>11001=>[2,2,1]
[-4,3,-2,1,5]=>[5,1,-2,3,-4]=>00101=>[2,1,1,1]
[-4,3,-2,1,-5]=>[-5,1,-2,3,-4]=>10101=>[1,1,1,1,1]
[-4,3,-2,-1,5]=>[5,-1,-2,3,-4]=>01101=>[1,2,1,1]
[-4,3,-2,-1,-5]=>[-5,-1,-2,3,-4]=>11101=>[3,1,1]
[-4,-3,2,1,5]=>[5,1,2,-3,-4]=>00011=>[3,2]
[-4,-3,2,1,-5]=>[-5,1,2,-3,-4]=>10011=>[1,2,2]
[-4,-3,2,-1,5]=>[5,-1,2,-3,-4]=>01011=>[1,1,1,2]
[-4,-3,2,-1,-5]=>[-5,-1,2,-3,-4]=>11011=>[2,1,2]
[-4,-3,-2,1,5]=>[5,1,-2,-3,-4]=>00111=>[2,3]
[-4,-3,-2,1,-5]=>[-5,1,-2,-3,-4]=>10111=>[1,1,3]
[-4,-3,-2,-1,5]=>[5,-1,-2,-3,-4]=>01111=>[1,4]
[-4,-3,-2,-1,-5]=>[-5,-1,-2,-3,-4]=>11111=>[5]
[4,3,2,5,1]=>[1,5,2,3,4]=>00000=>[5]
[4,3,2,5,-1]=>[-1,5,2,3,4]=>10000=>[1,4]
[4,3,2,-5,1]=>[1,-5,2,3,4]=>01000=>[1,1,3]
[4,3,2,-5,-1]=>[-1,-5,2,3,4]=>11000=>[2,3]
[4,3,-2,5,1]=>[1,5,-2,3,4]=>00100=>[2,1,2]
[4,3,-2,5,-1]=>[-1,5,-2,3,4]=>10100=>[1,1,1,2]
[4,3,-2,-5,1]=>[1,-5,-2,3,4]=>01100=>[1,2,2]
[4,3,-2,-5,-1]=>[-1,-5,-2,3,4]=>11100=>[3,2]
[4,-3,2,5,1]=>[1,5,2,-3,4]=>00010=>[3,1,1]
[4,-3,2,5,-1]=>[-1,5,2,-3,4]=>10010=>[1,2,1,1]
[4,-3,2,-5,1]=>[1,-5,2,-3,4]=>01010=>[1,1,1,1,1]
[4,-3,2,-5,-1]=>[-1,-5,2,-3,4]=>11010=>[2,1,1,1]
[4,-3,-2,5,1]=>[1,5,-2,-3,4]=>00110=>[2,2,1]
[4,-3,-2,5,-1]=>[-1,5,-2,-3,4]=>10110=>[1,1,2,1]
[4,-3,-2,-5,1]=>[1,-5,-2,-3,4]=>01110=>[1,3,1]
[4,-3,-2,-5,-1]=>[-1,-5,-2,-3,4]=>11110=>[4,1]
[-4,3,2,5,1]=>[1,5,2,3,-4]=>00001=>[4,1]
[-4,3,2,5,-1]=>[-1,5,2,3,-4]=>10001=>[1,3,1]
[-4,3,2,-5,1]=>[1,-5,2,3,-4]=>01001=>[1,1,2,1]
[-4,3,2,-5,-1]=>[-1,-5,2,3,-4]=>11001=>[2,2,1]
[-4,3,-2,5,1]=>[1,5,-2,3,-4]=>00101=>[2,1,1,1]
[-4,3,-2,5,-1]=>[-1,5,-2,3,-4]=>10101=>[1,1,1,1,1]
[-4,3,-2,-5,1]=>[1,-5,-2,3,-4]=>01101=>[1,2,1,1]
[-4,3,-2,-5,-1]=>[-1,-5,-2,3,-4]=>11101=>[3,1,1]
[-4,-3,2,5,1]=>[1,5,2,-3,-4]=>00011=>[3,2]
[-4,-3,2,5,-1]=>[-1,5,2,-3,-4]=>10011=>[1,2,2]
[-4,-3,2,-5,1]=>[1,-5,2,-3,-4]=>01011=>[1,1,1,2]
[-4,-3,2,-5,-1]=>[-1,-5,2,-3,-4]=>11011=>[2,1,2]
[-4,-3,-2,5,1]=>[1,5,-2,-3,-4]=>00111=>[2,3]
[-4,-3,-2,5,-1]=>[-1,5,-2,-3,-4]=>10111=>[1,1,3]
[-4,-3,-2,-5,1]=>[1,-5,-2,-3,-4]=>01111=>[1,4]
[-4,-3,-2,-5,-1]=>[-1,-5,-2,-3,-4]=>11111=>[5]
[4,3,5,1,2]=>[2,1,5,3,4]=>00000=>[5]
[4,3,5,1,-2]=>[-2,1,5,3,4]=>10000=>[1,4]
[4,3,5,-1,2]=>[2,-1,5,3,4]=>01000=>[1,1,3]
[4,3,5,-1,-2]=>[-2,-1,5,3,4]=>11000=>[2,3]
[4,3,-5,1,2]=>[2,1,-5,3,4]=>00100=>[2,1,2]
[4,3,-5,1,-2]=>[-2,1,-5,3,4]=>10100=>[1,1,1,2]
[4,3,-5,-1,2]=>[2,-1,-5,3,4]=>01100=>[1,2,2]
[4,3,-5,-1,-2]=>[-2,-1,-5,3,4]=>11100=>[3,2]
[4,-3,5,1,2]=>[2,1,5,-3,4]=>00010=>[3,1,1]
[4,-3,5,1,-2]=>[-2,1,5,-3,4]=>10010=>[1,2,1,1]
[4,-3,5,-1,2]=>[2,-1,5,-3,4]=>01010=>[1,1,1,1,1]
[4,-3,5,-1,-2]=>[-2,-1,5,-3,4]=>11010=>[2,1,1,1]
[4,-3,-5,1,2]=>[2,1,-5,-3,4]=>00110=>[2,2,1]
[4,-3,-5,1,-2]=>[-2,1,-5,-3,4]=>10110=>[1,1,2,1]
[4,-3,-5,-1,2]=>[2,-1,-5,-3,4]=>01110=>[1,3,1]
[4,-3,-5,-1,-2]=>[-2,-1,-5,-3,4]=>11110=>[4,1]
[-4,3,5,1,2]=>[2,1,5,3,-4]=>00001=>[4,1]
[-4,3,5,1,-2]=>[-2,1,5,3,-4]=>10001=>[1,3,1]
[-4,3,5,-1,2]=>[2,-1,5,3,-4]=>01001=>[1,1,2,1]
[-4,3,5,-1,-2]=>[-2,-1,5,3,-4]=>11001=>[2,2,1]
[-4,3,-5,1,2]=>[2,1,-5,3,-4]=>00101=>[2,1,1,1]
[-4,3,-5,1,-2]=>[-2,1,-5,3,-4]=>10101=>[1,1,1,1,1]
[-4,3,-5,-1,2]=>[2,-1,-5,3,-4]=>01101=>[1,2,1,1]
[-4,3,-5,-1,-2]=>[-2,-1,-5,3,-4]=>11101=>[3,1,1]
[-4,-3,5,1,2]=>[2,1,5,-3,-4]=>00011=>[3,2]
[-4,-3,5,1,-2]=>[-2,1,5,-3,-4]=>10011=>[1,2,2]
[-4,-3,5,-1,2]=>[2,-1,5,-3,-4]=>01011=>[1,1,1,2]
[-4,-3,5,-1,-2]=>[-2,-1,5,-3,-4]=>11011=>[2,1,2]
[-4,-3,-5,1,2]=>[2,1,-5,-3,-4]=>00111=>[2,3]
[-4,-3,-5,1,-2]=>[-2,1,-5,-3,-4]=>10111=>[1,1,3]
[-4,-3,-5,-1,2]=>[2,-1,-5,-3,-4]=>01111=>[1,4]
[-4,-3,-5,-1,-2]=>[-2,-1,-5,-3,-4]=>11111=>[5]
[4,3,5,2,1]=>[1,2,5,3,4]=>00000=>[5]
[4,3,5,2,-1]=>[-1,2,5,3,4]=>10000=>[1,4]
[4,3,5,-2,1]=>[1,-2,5,3,4]=>01000=>[1,1,3]
[4,3,5,-2,-1]=>[-1,-2,5,3,4]=>11000=>[2,3]
[4,3,-5,2,1]=>[1,2,-5,3,4]=>00100=>[2,1,2]
[4,3,-5,2,-1]=>[-1,2,-5,3,4]=>10100=>[1,1,1,2]
[4,3,-5,-2,1]=>[1,-2,-5,3,4]=>01100=>[1,2,2]
[4,3,-5,-2,-1]=>[-1,-2,-5,3,4]=>11100=>[3,2]
[4,-3,5,2,1]=>[1,2,5,-3,4]=>00010=>[3,1,1]
[4,-3,5,2,-1]=>[-1,2,5,-3,4]=>10010=>[1,2,1,1]
[4,-3,5,-2,1]=>[1,-2,5,-3,4]=>01010=>[1,1,1,1,1]
[4,-3,5,-2,-1]=>[-1,-2,5,-3,4]=>11010=>[2,1,1,1]
[4,-3,-5,2,1]=>[1,2,-5,-3,4]=>00110=>[2,2,1]
[4,-3,-5,2,-1]=>[-1,2,-5,-3,4]=>10110=>[1,1,2,1]
[4,-3,-5,-2,1]=>[1,-2,-5,-3,4]=>01110=>[1,3,1]
[4,-3,-5,-2,-1]=>[-1,-2,-5,-3,4]=>11110=>[4,1]
[-4,3,5,2,1]=>[1,2,5,3,-4]=>00001=>[4,1]
[-4,3,5,2,-1]=>[-1,2,5,3,-4]=>10001=>[1,3,1]
[-4,3,5,-2,1]=>[1,-2,5,3,-4]=>01001=>[1,1,2,1]
[-4,3,5,-2,-1]=>[-1,-2,5,3,-4]=>11001=>[2,2,1]
[-4,3,-5,2,1]=>[1,2,-5,3,-4]=>00101=>[2,1,1,1]
[-4,3,-5,2,-1]=>[-1,2,-5,3,-4]=>10101=>[1,1,1,1,1]
[-4,3,-5,-2,1]=>[1,-2,-5,3,-4]=>01101=>[1,2,1,1]
[-4,3,-5,-2,-1]=>[-1,-2,-5,3,-4]=>11101=>[3,1,1]
[-4,-3,5,2,1]=>[1,2,5,-3,-4]=>00011=>[3,2]
[-4,-3,5,2,-1]=>[-1,2,5,-3,-4]=>10011=>[1,2,2]
[-4,-3,5,-2,1]=>[1,-2,5,-3,-4]=>01011=>[1,1,1,2]
[-4,-3,5,-2,-1]=>[-1,-2,5,-3,-4]=>11011=>[2,1,2]
[-4,-3,-5,2,1]=>[1,2,-5,-3,-4]=>00111=>[2,3]
[-4,-3,-5,2,-1]=>[-1,2,-5,-3,-4]=>10111=>[1,1,3]
[-4,-3,-5,-2,1]=>[1,-2,-5,-3,-4]=>01111=>[1,4]
[-4,-3,-5,-2,-1]=>[-1,-2,-5,-3,-4]=>11111=>[5]
[4,5,1,2,3]=>[3,2,1,5,4]=>00000=>[5]
[4,5,1,2,-3]=>[-3,2,1,5,4]=>10000=>[1,4]
[4,5,1,-2,3]=>[3,-2,1,5,4]=>01000=>[1,1,3]
[4,5,1,-2,-3]=>[-3,-2,1,5,4]=>11000=>[2,3]
[4,5,-1,2,3]=>[3,2,-1,5,4]=>00100=>[2,1,2]
[4,5,-1,2,-3]=>[-3,2,-1,5,4]=>10100=>[1,1,1,2]
[4,5,-1,-2,3]=>[3,-2,-1,5,4]=>01100=>[1,2,2]
[4,5,-1,-2,-3]=>[-3,-2,-1,5,4]=>11100=>[3,2]
[4,-5,1,2,3]=>[3,2,1,-5,4]=>00010=>[3,1,1]
[4,-5,1,2,-3]=>[-3,2,1,-5,4]=>10010=>[1,2,1,1]
[4,-5,1,-2,3]=>[3,-2,1,-5,4]=>01010=>[1,1,1,1,1]
[4,-5,1,-2,-3]=>[-3,-2,1,-5,4]=>11010=>[2,1,1,1]
[4,-5,-1,2,3]=>[3,2,-1,-5,4]=>00110=>[2,2,1]
[4,-5,-1,2,-3]=>[-3,2,-1,-5,4]=>10110=>[1,1,2,1]
[4,-5,-1,-2,3]=>[3,-2,-1,-5,4]=>01110=>[1,3,1]
[4,-5,-1,-2,-3]=>[-3,-2,-1,-5,4]=>11110=>[4,1]
[-4,5,1,2,3]=>[3,2,1,5,-4]=>00001=>[4,1]
[-4,5,1,2,-3]=>[-3,2,1,5,-4]=>10001=>[1,3,1]
[-4,5,1,-2,3]=>[3,-2,1,5,-4]=>01001=>[1,1,2,1]
[-4,5,1,-2,-3]=>[-3,-2,1,5,-4]=>11001=>[2,2,1]
[-4,5,-1,2,3]=>[3,2,-1,5,-4]=>00101=>[2,1,1,1]
[-4,5,-1,2,-3]=>[-3,2,-1,5,-4]=>10101=>[1,1,1,1,1]
[-4,5,-1,-2,3]=>[3,-2,-1,5,-4]=>01101=>[1,2,1,1]
[-4,5,-1,-2,-3]=>[-3,-2,-1,5,-4]=>11101=>[3,1,1]
[-4,-5,1,2,3]=>[3,2,1,-5,-4]=>00011=>[3,2]
[-4,-5,1,2,-3]=>[-3,2,1,-5,-4]=>10011=>[1,2,2]
[-4,-5,1,-2,3]=>[3,-2,1,-5,-4]=>01011=>[1,1,1,2]
[-4,-5,1,-2,-3]=>[-3,-2,1,-5,-4]=>11011=>[2,1,2]
[-4,-5,-1,2,3]=>[3,2,-1,-5,-4]=>00111=>[2,3]
[-4,-5,-1,2,-3]=>[-3,2,-1,-5,-4]=>10111=>[1,1,3]
[-4,-5,-1,-2,3]=>[3,-2,-1,-5,-4]=>01111=>[1,4]
[-4,-5,-1,-2,-3]=>[-3,-2,-1,-5,-4]=>11111=>[5]
[4,5,1,3,2]=>[2,3,1,5,4]=>00000=>[5]
[4,5,1,3,-2]=>[-2,3,1,5,4]=>10000=>[1,4]
[4,5,1,-3,2]=>[2,-3,1,5,4]=>01000=>[1,1,3]
[4,5,1,-3,-2]=>[-2,-3,1,5,4]=>11000=>[2,3]
[4,5,-1,3,2]=>[2,3,-1,5,4]=>00100=>[2,1,2]
[4,5,-1,3,-2]=>[-2,3,-1,5,4]=>10100=>[1,1,1,2]
[4,5,-1,-3,2]=>[2,-3,-1,5,4]=>01100=>[1,2,2]
[4,5,-1,-3,-2]=>[-2,-3,-1,5,4]=>11100=>[3,2]
[4,-5,1,3,2]=>[2,3,1,-5,4]=>00010=>[3,1,1]
[4,-5,1,3,-2]=>[-2,3,1,-5,4]=>10010=>[1,2,1,1]
[4,-5,1,-3,2]=>[2,-3,1,-5,4]=>01010=>[1,1,1,1,1]
[4,-5,1,-3,-2]=>[-2,-3,1,-5,4]=>11010=>[2,1,1,1]
[4,-5,-1,3,2]=>[2,3,-1,-5,4]=>00110=>[2,2,1]
[4,-5,-1,3,-2]=>[-2,3,-1,-5,4]=>10110=>[1,1,2,1]
[4,-5,-1,-3,2]=>[2,-3,-1,-5,4]=>01110=>[1,3,1]
[4,-5,-1,-3,-2]=>[-2,-3,-1,-5,4]=>11110=>[4,1]
[-4,5,1,3,2]=>[2,3,1,5,-4]=>00001=>[4,1]
[-4,5,1,3,-2]=>[-2,3,1,5,-4]=>10001=>[1,3,1]
[-4,5,1,-3,2]=>[2,-3,1,5,-4]=>01001=>[1,1,2,1]
[-4,5,1,-3,-2]=>[-2,-3,1,5,-4]=>11001=>[2,2,1]
[-4,5,-1,3,2]=>[2,3,-1,5,-4]=>00101=>[2,1,1,1]
[-4,5,-1,3,-2]=>[-2,3,-1,5,-4]=>10101=>[1,1,1,1,1]
[-4,5,-1,-3,2]=>[2,-3,-1,5,-4]=>01101=>[1,2,1,1]
[-4,5,-1,-3,-2]=>[-2,-3,-1,5,-4]=>11101=>[3,1,1]
[-4,-5,1,3,2]=>[2,3,1,-5,-4]=>00011=>[3,2]
[-4,-5,1,3,-2]=>[-2,3,1,-5,-4]=>10011=>[1,2,2]
[-4,-5,1,-3,2]=>[2,-3,1,-5,-4]=>01011=>[1,1,1,2]
[-4,-5,1,-3,-2]=>[-2,-3,1,-5,-4]=>11011=>[2,1,2]
[-4,-5,-1,3,2]=>[2,3,-1,-5,-4]=>00111=>[2,3]
[-4,-5,-1,3,-2]=>[-2,3,-1,-5,-4]=>10111=>[1,1,3]
[-4,-5,-1,-3,2]=>[2,-3,-1,-5,-4]=>01111=>[1,4]
[-4,-5,-1,-3,-2]=>[-2,-3,-1,-5,-4]=>11111=>[5]
[4,5,2,1,3]=>[3,1,2,5,4]=>00000=>[5]
[4,5,2,1,-3]=>[-3,1,2,5,4]=>10000=>[1,4]
[4,5,2,-1,3]=>[3,-1,2,5,4]=>01000=>[1,1,3]
[4,5,2,-1,-3]=>[-3,-1,2,5,4]=>11000=>[2,3]
[4,5,-2,1,3]=>[3,1,-2,5,4]=>00100=>[2,1,2]
[4,5,-2,1,-3]=>[-3,1,-2,5,4]=>10100=>[1,1,1,2]
[4,5,-2,-1,3]=>[3,-1,-2,5,4]=>01100=>[1,2,2]
[4,5,-2,-1,-3]=>[-3,-1,-2,5,4]=>11100=>[3,2]
[4,-5,2,1,3]=>[3,1,2,-5,4]=>00010=>[3,1,1]
[4,-5,2,1,-3]=>[-3,1,2,-5,4]=>10010=>[1,2,1,1]
[4,-5,2,-1,3]=>[3,-1,2,-5,4]=>01010=>[1,1,1,1,1]
[4,-5,2,-1,-3]=>[-3,-1,2,-5,4]=>11010=>[2,1,1,1]
[4,-5,-2,1,3]=>[3,1,-2,-5,4]=>00110=>[2,2,1]
[4,-5,-2,1,-3]=>[-3,1,-2,-5,4]=>10110=>[1,1,2,1]
[4,-5,-2,-1,3]=>[3,-1,-2,-5,4]=>01110=>[1,3,1]
[4,-5,-2,-1,-3]=>[-3,-1,-2,-5,4]=>11110=>[4,1]
[-4,5,2,1,3]=>[3,1,2,5,-4]=>00001=>[4,1]
[-4,5,2,1,-3]=>[-3,1,2,5,-4]=>10001=>[1,3,1]
[-4,5,2,-1,3]=>[3,-1,2,5,-4]=>01001=>[1,1,2,1]
[-4,5,2,-1,-3]=>[-3,-1,2,5,-4]=>11001=>[2,2,1]
[-4,5,-2,1,3]=>[3,1,-2,5,-4]=>00101=>[2,1,1,1]
[-4,5,-2,1,-3]=>[-3,1,-2,5,-4]=>10101=>[1,1,1,1,1]
[-4,5,-2,-1,3]=>[3,-1,-2,5,-4]=>01101=>[1,2,1,1]
[-4,5,-2,-1,-3]=>[-3,-1,-2,5,-4]=>11101=>[3,1,1]
[-4,-5,2,1,3]=>[3,1,2,-5,-4]=>00011=>[3,2]
[-4,-5,2,1,-3]=>[-3,1,2,-5,-4]=>10011=>[1,2,2]
[-4,-5,2,-1,3]=>[3,-1,2,-5,-4]=>01011=>[1,1,1,2]
[-4,-5,2,-1,-3]=>[-3,-1,2,-5,-4]=>11011=>[2,1,2]
[-4,-5,-2,1,3]=>[3,1,-2,-5,-4]=>00111=>[2,3]
[-4,-5,-2,1,-3]=>[-3,1,-2,-5,-4]=>10111=>[1,1,3]
[-4,-5,-2,-1,3]=>[3,-1,-2,-5,-4]=>01111=>[1,4]
[-4,-5,-2,-1,-3]=>[-3,-1,-2,-5,-4]=>11111=>[5]
[4,5,2,3,1]=>[1,3,2,5,4]=>00000=>[5]
[4,5,2,3,-1]=>[-1,3,2,5,4]=>10000=>[1,4]
[4,5,2,-3,1]=>[1,-3,2,5,4]=>01000=>[1,1,3]
[4,5,2,-3,-1]=>[-1,-3,2,5,4]=>11000=>[2,3]
[4,5,-2,3,1]=>[1,3,-2,5,4]=>00100=>[2,1,2]
[4,5,-2,3,-1]=>[-1,3,-2,5,4]=>10100=>[1,1,1,2]
[4,5,-2,-3,1]=>[1,-3,-2,5,4]=>01100=>[1,2,2]
[4,5,-2,-3,-1]=>[-1,-3,-2,5,4]=>11100=>[3,2]
[4,-5,2,3,1]=>[1,3,2,-5,4]=>00010=>[3,1,1]
[4,-5,2,3,-1]=>[-1,3,2,-5,4]=>10010=>[1,2,1,1]
[4,-5,2,-3,1]=>[1,-3,2,-5,4]=>01010=>[1,1,1,1,1]
[4,-5,2,-3,-1]=>[-1,-3,2,-5,4]=>11010=>[2,1,1,1]
[4,-5,-2,3,1]=>[1,3,-2,-5,4]=>00110=>[2,2,1]
[4,-5,-2,3,-1]=>[-1,3,-2,-5,4]=>10110=>[1,1,2,1]
[4,-5,-2,-3,1]=>[1,-3,-2,-5,4]=>01110=>[1,3,1]
[4,-5,-2,-3,-1]=>[-1,-3,-2,-5,4]=>11110=>[4,1]
[-4,5,2,3,1]=>[1,3,2,5,-4]=>00001=>[4,1]
[-4,5,2,3,-1]=>[-1,3,2,5,-4]=>10001=>[1,3,1]
[-4,5,2,-3,1]=>[1,-3,2,5,-4]=>01001=>[1,1,2,1]
[-4,5,2,-3,-1]=>[-1,-3,2,5,-4]=>11001=>[2,2,1]
[-4,5,-2,3,1]=>[1,3,-2,5,-4]=>00101=>[2,1,1,1]
[-4,5,-2,3,-1]=>[-1,3,-2,5,-4]=>10101=>[1,1,1,1,1]
[-4,5,-2,-3,1]=>[1,-3,-2,5,-4]=>01101=>[1,2,1,1]
[-4,5,-2,-3,-1]=>[-1,-3,-2,5,-4]=>11101=>[3,1,1]
[-4,-5,2,3,1]=>[1,3,2,-5,-4]=>00011=>[3,2]
[-4,-5,2,3,-1]=>[-1,3,2,-5,-4]=>10011=>[1,2,2]
[-4,-5,2,-3,1]=>[1,-3,2,-5,-4]=>01011=>[1,1,1,2]
[-4,-5,2,-3,-1]=>[-1,-3,2,-5,-4]=>11011=>[2,1,2]
[-4,-5,-2,3,1]=>[1,3,-2,-5,-4]=>00111=>[2,3]
[-4,-5,-2,3,-1]=>[-1,3,-2,-5,-4]=>10111=>[1,1,3]
[-4,-5,-2,-3,1]=>[1,-3,-2,-5,-4]=>01111=>[1,4]
[-4,-5,-2,-3,-1]=>[-1,-3,-2,-5,-4]=>11111=>[5]
[4,5,3,1,2]=>[2,1,3,5,4]=>00000=>[5]
[4,5,3,1,-2]=>[-2,1,3,5,4]=>10000=>[1,4]
[4,5,3,-1,2]=>[2,-1,3,5,4]=>01000=>[1,1,3]
[4,5,3,-1,-2]=>[-2,-1,3,5,4]=>11000=>[2,3]
[4,5,-3,1,2]=>[2,1,-3,5,4]=>00100=>[2,1,2]
[4,5,-3,1,-2]=>[-2,1,-3,5,4]=>10100=>[1,1,1,2]
[4,5,-3,-1,2]=>[2,-1,-3,5,4]=>01100=>[1,2,2]
[4,5,-3,-1,-2]=>[-2,-1,-3,5,4]=>11100=>[3,2]
[4,-5,3,1,2]=>[2,1,3,-5,4]=>00010=>[3,1,1]
[4,-5,3,1,-2]=>[-2,1,3,-5,4]=>10010=>[1,2,1,1]
[4,-5,3,-1,2]=>[2,-1,3,-5,4]=>01010=>[1,1,1,1,1]
[4,-5,3,-1,-2]=>[-2,-1,3,-5,4]=>11010=>[2,1,1,1]
[4,-5,-3,1,2]=>[2,1,-3,-5,4]=>00110=>[2,2,1]
[4,-5,-3,1,-2]=>[-2,1,-3,-5,4]=>10110=>[1,1,2,1]
[4,-5,-3,-1,2]=>[2,-1,-3,-5,4]=>01110=>[1,3,1]
[4,-5,-3,-1,-2]=>[-2,-1,-3,-5,4]=>11110=>[4,1]
[-4,5,3,1,2]=>[2,1,3,5,-4]=>00001=>[4,1]
[-4,5,3,1,-2]=>[-2,1,3,5,-4]=>10001=>[1,3,1]
[-4,5,3,-1,2]=>[2,-1,3,5,-4]=>01001=>[1,1,2,1]
[-4,5,3,-1,-2]=>[-2,-1,3,5,-4]=>11001=>[2,2,1]
[-4,5,-3,1,2]=>[2,1,-3,5,-4]=>00101=>[2,1,1,1]
[-4,5,-3,1,-2]=>[-2,1,-3,5,-4]=>10101=>[1,1,1,1,1]
[-4,5,-3,-1,2]=>[2,-1,-3,5,-4]=>01101=>[1,2,1,1]
[-4,5,-3,-1,-2]=>[-2,-1,-3,5,-4]=>11101=>[3,1,1]
[-4,-5,3,1,2]=>[2,1,3,-5,-4]=>00011=>[3,2]
[-4,-5,3,1,-2]=>[-2,1,3,-5,-4]=>10011=>[1,2,2]
[-4,-5,3,-1,2]=>[2,-1,3,-5,-4]=>01011=>[1,1,1,2]
[-4,-5,3,-1,-2]=>[-2,-1,3,-5,-4]=>11011=>[2,1,2]
[-4,-5,-3,1,2]=>[2,1,-3,-5,-4]=>00111=>[2,3]
[-4,-5,-3,1,-2]=>[-2,1,-3,-5,-4]=>10111=>[1,1,3]
[-4,-5,-3,-1,2]=>[2,-1,-3,-5,-4]=>01111=>[1,4]
[-4,-5,-3,-1,-2]=>[-2,-1,-3,-5,-4]=>11111=>[5]
[4,5,3,2,1]=>[1,2,3,5,4]=>00000=>[5]
[4,5,3,2,-1]=>[-1,2,3,5,4]=>10000=>[1,4]
[4,5,3,-2,1]=>[1,-2,3,5,4]=>01000=>[1,1,3]
[4,5,3,-2,-1]=>[-1,-2,3,5,4]=>11000=>[2,3]
[4,5,-3,2,1]=>[1,2,-3,5,4]=>00100=>[2,1,2]
[4,5,-3,2,-1]=>[-1,2,-3,5,4]=>10100=>[1,1,1,2]
[4,5,-3,-2,1]=>[1,-2,-3,5,4]=>01100=>[1,2,2]
[4,5,-3,-2,-1]=>[-1,-2,-3,5,4]=>11100=>[3,2]
[4,-5,3,2,1]=>[1,2,3,-5,4]=>00010=>[3,1,1]
[4,-5,3,2,-1]=>[-1,2,3,-5,4]=>10010=>[1,2,1,1]
[4,-5,3,-2,1]=>[1,-2,3,-5,4]=>01010=>[1,1,1,1,1]
[4,-5,3,-2,-1]=>[-1,-2,3,-5,4]=>11010=>[2,1,1,1]
[4,-5,-3,2,1]=>[1,2,-3,-5,4]=>00110=>[2,2,1]
[4,-5,-3,2,-1]=>[-1,2,-3,-5,4]=>10110=>[1,1,2,1]
[4,-5,-3,-2,1]=>[1,-2,-3,-5,4]=>01110=>[1,3,1]
[4,-5,-3,-2,-1]=>[-1,-2,-3,-5,4]=>11110=>[4,1]
[-4,5,3,2,1]=>[1,2,3,5,-4]=>00001=>[4,1]
[-4,5,3,2,-1]=>[-1,2,3,5,-4]=>10001=>[1,3,1]
[-4,5,3,-2,1]=>[1,-2,3,5,-4]=>01001=>[1,1,2,1]
[-4,5,3,-2,-1]=>[-1,-2,3,5,-4]=>11001=>[2,2,1]
[-4,5,-3,2,1]=>[1,2,-3,5,-4]=>00101=>[2,1,1,1]
[-4,5,-3,2,-1]=>[-1,2,-3,5,-4]=>10101=>[1,1,1,1,1]
[-4,5,-3,-2,1]=>[1,-2,-3,5,-4]=>01101=>[1,2,1,1]
[-4,5,-3,-2,-1]=>[-1,-2,-3,5,-4]=>11101=>[3,1,1]
[-4,-5,3,2,1]=>[1,2,3,-5,-4]=>00011=>[3,2]
[-4,-5,3,2,-1]=>[-1,2,3,-5,-4]=>10011=>[1,2,2]
[-4,-5,3,-2,1]=>[1,-2,3,-5,-4]=>01011=>[1,1,1,2]
[-4,-5,3,-2,-1]=>[-1,-2,3,-5,-4]=>11011=>[2,1,2]
[-4,-5,-3,2,1]=>[1,2,-3,-5,-4]=>00111=>[2,3]
[-4,-5,-3,2,-1]=>[-1,2,-3,-5,-4]=>10111=>[1,1,3]
[-4,-5,-3,-2,1]=>[1,-2,-3,-5,-4]=>01111=>[1,4]
[-4,-5,-3,-2,-1]=>[-1,-2,-3,-5,-4]=>11111=>[5]
[5,1,2,3,4]=>[4,3,2,1,5]=>00000=>[5]
[5,1,2,3,-4]=>[-4,3,2,1,5]=>10000=>[1,4]
[5,1,2,-3,4]=>[4,-3,2,1,5]=>01000=>[1,1,3]
[5,1,2,-3,-4]=>[-4,-3,2,1,5]=>11000=>[2,3]
[5,1,-2,3,4]=>[4,3,-2,1,5]=>00100=>[2,1,2]
[5,1,-2,3,-4]=>[-4,3,-2,1,5]=>10100=>[1,1,1,2]
[5,1,-2,-3,4]=>[4,-3,-2,1,5]=>01100=>[1,2,2]
[5,1,-2,-3,-4]=>[-4,-3,-2,1,5]=>11100=>[3,2]
[5,-1,2,3,4]=>[4,3,2,-1,5]=>00010=>[3,1,1]
[5,-1,2,3,-4]=>[-4,3,2,-1,5]=>10010=>[1,2,1,1]
[5,-1,2,-3,4]=>[4,-3,2,-1,5]=>01010=>[1,1,1,1,1]
[5,-1,2,-3,-4]=>[-4,-3,2,-1,5]=>11010=>[2,1,1,1]
[5,-1,-2,3,4]=>[4,3,-2,-1,5]=>00110=>[2,2,1]
[5,-1,-2,3,-4]=>[-4,3,-2,-1,5]=>10110=>[1,1,2,1]
[5,-1,-2,-3,4]=>[4,-3,-2,-1,5]=>01110=>[1,3,1]
[5,-1,-2,-3,-4]=>[-4,-3,-2,-1,5]=>11110=>[4,1]
[-5,1,2,3,4]=>[4,3,2,1,-5]=>00001=>[4,1]
[-5,1,2,3,-4]=>[-4,3,2,1,-5]=>10001=>[1,3,1]
[-5,1,2,-3,4]=>[4,-3,2,1,-5]=>01001=>[1,1,2,1]
[-5,1,2,-3,-4]=>[-4,-3,2,1,-5]=>11001=>[2,2,1]
[-5,1,-2,3,4]=>[4,3,-2,1,-5]=>00101=>[2,1,1,1]
[-5,1,-2,3,-4]=>[-4,3,-2,1,-5]=>10101=>[1,1,1,1,1]
[-5,1,-2,-3,4]=>[4,-3,-2,1,-5]=>01101=>[1,2,1,1]
[-5,1,-2,-3,-4]=>[-4,-3,-2,1,-5]=>11101=>[3,1,1]
[-5,-1,2,3,4]=>[4,3,2,-1,-5]=>00011=>[3,2]
[-5,-1,2,3,-4]=>[-4,3,2,-1,-5]=>10011=>[1,2,2]
[-5,-1,2,-3,4]=>[4,-3,2,-1,-5]=>01011=>[1,1,1,2]
[-5,-1,2,-3,-4]=>[-4,-3,2,-1,-5]=>11011=>[2,1,2]
[-5,-1,-2,3,4]=>[4,3,-2,-1,-5]=>00111=>[2,3]
[-5,-1,-2,3,-4]=>[-4,3,-2,-1,-5]=>10111=>[1,1,3]
[-5,-1,-2,-3,4]=>[4,-3,-2,-1,-5]=>01111=>[1,4]
[-5,-1,-2,-3,-4]=>[-4,-3,-2,-1,-5]=>11111=>[5]
[5,1,2,4,3]=>[3,4,2,1,5]=>00000=>[5]
[5,1,2,4,-3]=>[-3,4,2,1,5]=>10000=>[1,4]
[5,1,2,-4,3]=>[3,-4,2,1,5]=>01000=>[1,1,3]
[5,1,2,-4,-3]=>[-3,-4,2,1,5]=>11000=>[2,3]
[5,1,-2,4,3]=>[3,4,-2,1,5]=>00100=>[2,1,2]
[5,1,-2,4,-3]=>[-3,4,-2,1,5]=>10100=>[1,1,1,2]
[5,1,-2,-4,3]=>[3,-4,-2,1,5]=>01100=>[1,2,2]
[5,1,-2,-4,-3]=>[-3,-4,-2,1,5]=>11100=>[3,2]
[5,-1,2,4,3]=>[3,4,2,-1,5]=>00010=>[3,1,1]
[5,-1,2,4,-3]=>[-3,4,2,-1,5]=>10010=>[1,2,1,1]
[5,-1,2,-4,3]=>[3,-4,2,-1,5]=>01010=>[1,1,1,1,1]
[5,-1,2,-4,-3]=>[-3,-4,2,-1,5]=>11010=>[2,1,1,1]
[5,-1,-2,4,3]=>[3,4,-2,-1,5]=>00110=>[2,2,1]
[5,-1,-2,4,-3]=>[-3,4,-2,-1,5]=>10110=>[1,1,2,1]
[5,-1,-2,-4,3]=>[3,-4,-2,-1,5]=>01110=>[1,3,1]
[5,-1,-2,-4,-3]=>[-3,-4,-2,-1,5]=>11110=>[4,1]
[-5,1,2,4,3]=>[3,4,2,1,-5]=>00001=>[4,1]
[-5,1,2,4,-3]=>[-3,4,2,1,-5]=>10001=>[1,3,1]
[-5,1,2,-4,3]=>[3,-4,2,1,-5]=>01001=>[1,1,2,1]
[-5,1,2,-4,-3]=>[-3,-4,2,1,-5]=>11001=>[2,2,1]
[-5,1,-2,4,3]=>[3,4,-2,1,-5]=>00101=>[2,1,1,1]
[-5,1,-2,4,-3]=>[-3,4,-2,1,-5]=>10101=>[1,1,1,1,1]
[-5,1,-2,-4,3]=>[3,-4,-2,1,-5]=>01101=>[1,2,1,1]
[-5,1,-2,-4,-3]=>[-3,-4,-2,1,-5]=>11101=>[3,1,1]
[-5,-1,2,4,3]=>[3,4,2,-1,-5]=>00011=>[3,2]
[-5,-1,2,4,-3]=>[-3,4,2,-1,-5]=>10011=>[1,2,2]
[-5,-1,2,-4,3]=>[3,-4,2,-1,-5]=>01011=>[1,1,1,2]
[-5,-1,2,-4,-3]=>[-3,-4,2,-1,-5]=>11011=>[2,1,2]
[-5,-1,-2,4,3]=>[3,4,-2,-1,-5]=>00111=>[2,3]
[-5,-1,-2,4,-3]=>[-3,4,-2,-1,-5]=>10111=>[1,1,3]
[-5,-1,-2,-4,3]=>[3,-4,-2,-1,-5]=>01111=>[1,4]
[-5,-1,-2,-4,-3]=>[-3,-4,-2,-1,-5]=>11111=>[5]
[5,1,3,2,4]=>[4,2,3,1,5]=>00000=>[5]
[5,1,3,2,-4]=>[-4,2,3,1,5]=>10000=>[1,4]
[5,1,3,-2,4]=>[4,-2,3,1,5]=>01000=>[1,1,3]
[5,1,3,-2,-4]=>[-4,-2,3,1,5]=>11000=>[2,3]
[5,1,-3,2,4]=>[4,2,-3,1,5]=>00100=>[2,1,2]
[5,1,-3,2,-4]=>[-4,2,-3,1,5]=>10100=>[1,1,1,2]
[5,1,-3,-2,4]=>[4,-2,-3,1,5]=>01100=>[1,2,2]
[5,1,-3,-2,-4]=>[-4,-2,-3,1,5]=>11100=>[3,2]
[5,-1,3,2,4]=>[4,2,3,-1,5]=>00010=>[3,1,1]
[5,-1,3,2,-4]=>[-4,2,3,-1,5]=>10010=>[1,2,1,1]
[5,-1,3,-2,4]=>[4,-2,3,-1,5]=>01010=>[1,1,1,1,1]
[5,-1,3,-2,-4]=>[-4,-2,3,-1,5]=>11010=>[2,1,1,1]
[5,-1,-3,2,4]=>[4,2,-3,-1,5]=>00110=>[2,2,1]
[5,-1,-3,2,-4]=>[-4,2,-3,-1,5]=>10110=>[1,1,2,1]
[5,-1,-3,-2,4]=>[4,-2,-3,-1,5]=>01110=>[1,3,1]
[5,-1,-3,-2,-4]=>[-4,-2,-3,-1,5]=>11110=>[4,1]
[-5,1,3,2,4]=>[4,2,3,1,-5]=>00001=>[4,1]
[-5,1,3,2,-4]=>[-4,2,3,1,-5]=>10001=>[1,3,1]
[-5,1,3,-2,4]=>[4,-2,3,1,-5]=>01001=>[1,1,2,1]
[-5,1,3,-2,-4]=>[-4,-2,3,1,-5]=>11001=>[2,2,1]
[-5,1,-3,2,4]=>[4,2,-3,1,-5]=>00101=>[2,1,1,1]
[-5,1,-3,2,-4]=>[-4,2,-3,1,-5]=>10101=>[1,1,1,1,1]
[-5,1,-3,-2,4]=>[4,-2,-3,1,-5]=>01101=>[1,2,1,1]
[-5,1,-3,-2,-4]=>[-4,-2,-3,1,-5]=>11101=>[3,1,1]
[-5,-1,3,2,4]=>[4,2,3,-1,-5]=>00011=>[3,2]
[-5,-1,3,2,-4]=>[-4,2,3,-1,-5]=>10011=>[1,2,2]
[-5,-1,3,-2,4]=>[4,-2,3,-1,-5]=>01011=>[1,1,1,2]
[-5,-1,3,-2,-4]=>[-4,-2,3,-1,-5]=>11011=>[2,1,2]
[-5,-1,-3,2,4]=>[4,2,-3,-1,-5]=>00111=>[2,3]
[-5,-1,-3,2,-4]=>[-4,2,-3,-1,-5]=>10111=>[1,1,3]
[-5,-1,-3,-2,4]=>[4,-2,-3,-1,-5]=>01111=>[1,4]
[-5,-1,-3,-2,-4]=>[-4,-2,-3,-1,-5]=>11111=>[5]
[5,1,3,4,2]=>[2,4,3,1,5]=>00000=>[5]
[5,1,3,4,-2]=>[-2,4,3,1,5]=>10000=>[1,4]
[5,1,3,-4,2]=>[2,-4,3,1,5]=>01000=>[1,1,3]
[5,1,3,-4,-2]=>[-2,-4,3,1,5]=>11000=>[2,3]
[5,1,-3,4,2]=>[2,4,-3,1,5]=>00100=>[2,1,2]
[5,1,-3,4,-2]=>[-2,4,-3,1,5]=>10100=>[1,1,1,2]
[5,1,-3,-4,2]=>[2,-4,-3,1,5]=>01100=>[1,2,2]
[5,1,-3,-4,-2]=>[-2,-4,-3,1,5]=>11100=>[3,2]
[5,-1,3,4,2]=>[2,4,3,-1,5]=>00010=>[3,1,1]
[5,-1,3,4,-2]=>[-2,4,3,-1,5]=>10010=>[1,2,1,1]
[5,-1,3,-4,2]=>[2,-4,3,-1,5]=>01010=>[1,1,1,1,1]
[5,-1,3,-4,-2]=>[-2,-4,3,-1,5]=>11010=>[2,1,1,1]
[5,-1,-3,4,2]=>[2,4,-3,-1,5]=>00110=>[2,2,1]
[5,-1,-3,4,-2]=>[-2,4,-3,-1,5]=>10110=>[1,1,2,1]
[5,-1,-3,-4,2]=>[2,-4,-3,-1,5]=>01110=>[1,3,1]
[5,-1,-3,-4,-2]=>[-2,-4,-3,-1,5]=>11110=>[4,1]
[-5,1,3,4,2]=>[2,4,3,1,-5]=>00001=>[4,1]
[-5,1,3,4,-2]=>[-2,4,3,1,-5]=>10001=>[1,3,1]
[-5,1,3,-4,2]=>[2,-4,3,1,-5]=>01001=>[1,1,2,1]
[-5,1,3,-4,-2]=>[-2,-4,3,1,-5]=>11001=>[2,2,1]
[-5,1,-3,4,2]=>[2,4,-3,1,-5]=>00101=>[2,1,1,1]
[-5,1,-3,4,-2]=>[-2,4,-3,1,-5]=>10101=>[1,1,1,1,1]
[-5,1,-3,-4,2]=>[2,-4,-3,1,-5]=>01101=>[1,2,1,1]
[-5,1,-3,-4,-2]=>[-2,-4,-3,1,-5]=>11101=>[3,1,1]
[-5,-1,3,4,2]=>[2,4,3,-1,-5]=>00011=>[3,2]
[-5,-1,3,4,-2]=>[-2,4,3,-1,-5]=>10011=>[1,2,2]
[-5,-1,3,-4,2]=>[2,-4,3,-1,-5]=>01011=>[1,1,1,2]
[-5,-1,3,-4,-2]=>[-2,-4,3,-1,-5]=>11011=>[2,1,2]
[-5,-1,-3,4,2]=>[2,4,-3,-1,-5]=>00111=>[2,3]
[-5,-1,-3,4,-2]=>[-2,4,-3,-1,-5]=>10111=>[1,1,3]
[-5,-1,-3,-4,2]=>[2,-4,-3,-1,-5]=>01111=>[1,4]
[-5,-1,-3,-4,-2]=>[-2,-4,-3,-1,-5]=>11111=>[5]
[5,1,4,2,3]=>[3,2,4,1,5]=>00000=>[5]
[5,1,4,2,-3]=>[-3,2,4,1,5]=>10000=>[1,4]
[5,1,4,-2,3]=>[3,-2,4,1,5]=>01000=>[1,1,3]
[5,1,4,-2,-3]=>[-3,-2,4,1,5]=>11000=>[2,3]
[5,1,-4,2,3]=>[3,2,-4,1,5]=>00100=>[2,1,2]
[5,1,-4,2,-3]=>[-3,2,-4,1,5]=>10100=>[1,1,1,2]
[5,1,-4,-2,3]=>[3,-2,-4,1,5]=>01100=>[1,2,2]
[5,1,-4,-2,-3]=>[-3,-2,-4,1,5]=>11100=>[3,2]
[5,-1,4,2,3]=>[3,2,4,-1,5]=>00010=>[3,1,1]
[5,-1,4,2,-3]=>[-3,2,4,-1,5]=>10010=>[1,2,1,1]
[5,-1,4,-2,3]=>[3,-2,4,-1,5]=>01010=>[1,1,1,1,1]
[5,-1,4,-2,-3]=>[-3,-2,4,-1,5]=>11010=>[2,1,1,1]
[5,-1,-4,2,3]=>[3,2,-4,-1,5]=>00110=>[2,2,1]
[5,-1,-4,2,-3]=>[-3,2,-4,-1,5]=>10110=>[1,1,2,1]
[5,-1,-4,-2,3]=>[3,-2,-4,-1,5]=>01110=>[1,3,1]
[5,-1,-4,-2,-3]=>[-3,-2,-4,-1,5]=>11110=>[4,1]
[-5,1,4,2,3]=>[3,2,4,1,-5]=>00001=>[4,1]
[-5,1,4,2,-3]=>[-3,2,4,1,-5]=>10001=>[1,3,1]
[-5,1,4,-2,3]=>[3,-2,4,1,-5]=>01001=>[1,1,2,1]
[-5,1,4,-2,-3]=>[-3,-2,4,1,-5]=>11001=>[2,2,1]
[-5,1,-4,2,3]=>[3,2,-4,1,-5]=>00101=>[2,1,1,1]
[-5,1,-4,2,-3]=>[-3,2,-4,1,-5]=>10101=>[1,1,1,1,1]
[-5,1,-4,-2,3]=>[3,-2,-4,1,-5]=>01101=>[1,2,1,1]
[-5,1,-4,-2,-3]=>[-3,-2,-4,1,-5]=>11101=>[3,1,1]
[-5,-1,4,2,3]=>[3,2,4,-1,-5]=>00011=>[3,2]
[-5,-1,4,2,-3]=>[-3,2,4,-1,-5]=>10011=>[1,2,2]
[-5,-1,4,-2,3]=>[3,-2,4,-1,-5]=>01011=>[1,1,1,2]
[-5,-1,4,-2,-3]=>[-3,-2,4,-1,-5]=>11011=>[2,1,2]
[-5,-1,-4,2,3]=>[3,2,-4,-1,-5]=>00111=>[2,3]
[-5,-1,-4,2,-3]=>[-3,2,-4,-1,-5]=>10111=>[1,1,3]
[-5,-1,-4,-2,3]=>[3,-2,-4,-1,-5]=>01111=>[1,4]
[-5,-1,-4,-2,-3]=>[-3,-2,-4,-1,-5]=>11111=>[5]
[5,1,4,3,2]=>[2,3,4,1,5]=>00000=>[5]
[5,1,4,3,-2]=>[-2,3,4,1,5]=>10000=>[1,4]
[5,1,4,-3,2]=>[2,-3,4,1,5]=>01000=>[1,1,3]
[5,1,4,-3,-2]=>[-2,-3,4,1,5]=>11000=>[2,3]
[5,1,-4,3,2]=>[2,3,-4,1,5]=>00100=>[2,1,2]
[5,1,-4,3,-2]=>[-2,3,-4,1,5]=>10100=>[1,1,1,2]
[5,1,-4,-3,2]=>[2,-3,-4,1,5]=>01100=>[1,2,2]
[5,1,-4,-3,-2]=>[-2,-3,-4,1,5]=>11100=>[3,2]
[5,-1,4,3,2]=>[2,3,4,-1,5]=>00010=>[3,1,1]
[5,-1,4,3,-2]=>[-2,3,4,-1,5]=>10010=>[1,2,1,1]
[5,-1,4,-3,2]=>[2,-3,4,-1,5]=>01010=>[1,1,1,1,1]
[5,-1,4,-3,-2]=>[-2,-3,4,-1,5]=>11010=>[2,1,1,1]
[5,-1,-4,3,2]=>[2,3,-4,-1,5]=>00110=>[2,2,1]
[5,-1,-4,3,-2]=>[-2,3,-4,-1,5]=>10110=>[1,1,2,1]
[5,-1,-4,-3,2]=>[2,-3,-4,-1,5]=>01110=>[1,3,1]
[5,-1,-4,-3,-2]=>[-2,-3,-4,-1,5]=>11110=>[4,1]
[-5,1,4,3,2]=>[2,3,4,1,-5]=>00001=>[4,1]
[-5,1,4,3,-2]=>[-2,3,4,1,-5]=>10001=>[1,3,1]
[-5,1,4,-3,2]=>[2,-3,4,1,-5]=>01001=>[1,1,2,1]
[-5,1,4,-3,-2]=>[-2,-3,4,1,-5]=>11001=>[2,2,1]
[-5,1,-4,3,2]=>[2,3,-4,1,-5]=>00101=>[2,1,1,1]
[-5,1,-4,3,-2]=>[-2,3,-4,1,-5]=>10101=>[1,1,1,1,1]
[-5,1,-4,-3,2]=>[2,-3,-4,1,-5]=>01101=>[1,2,1,1]
[-5,1,-4,-3,-2]=>[-2,-3,-4,1,-5]=>11101=>[3,1,1]
[-5,-1,4,3,2]=>[2,3,4,-1,-5]=>00011=>[3,2]
[-5,-1,4,3,-2]=>[-2,3,4,-1,-5]=>10011=>[1,2,2]
[-5,-1,4,-3,2]=>[2,-3,4,-1,-5]=>01011=>[1,1,1,2]
[-5,-1,4,-3,-2]=>[-2,-3,4,-1,-5]=>11011=>[2,1,2]
[-5,-1,-4,3,2]=>[2,3,-4,-1,-5]=>00111=>[2,3]
[-5,-1,-4,3,-2]=>[-2,3,-4,-1,-5]=>10111=>[1,1,3]
[-5,-1,-4,-3,2]=>[2,-3,-4,-1,-5]=>01111=>[1,4]
[-5,-1,-4,-3,-2]=>[-2,-3,-4,-1,-5]=>11111=>[5]
[5,2,1,3,4]=>[4,3,1,2,5]=>00000=>[5]
[5,2,1,3,-4]=>[-4,3,1,2,5]=>10000=>[1,4]
[5,2,1,-3,4]=>[4,-3,1,2,5]=>01000=>[1,1,3]
[5,2,1,-3,-4]=>[-4,-3,1,2,5]=>11000=>[2,3]
[5,2,-1,3,4]=>[4,3,-1,2,5]=>00100=>[2,1,2]
[5,2,-1,3,-4]=>[-4,3,-1,2,5]=>10100=>[1,1,1,2]
[5,2,-1,-3,4]=>[4,-3,-1,2,5]=>01100=>[1,2,2]
[5,2,-1,-3,-4]=>[-4,-3,-1,2,5]=>11100=>[3,2]
[5,-2,1,3,4]=>[4,3,1,-2,5]=>00010=>[3,1,1]
[5,-2,1,3,-4]=>[-4,3,1,-2,5]=>10010=>[1,2,1,1]
[5,-2,1,-3,4]=>[4,-3,1,-2,5]=>01010=>[1,1,1,1,1]
[5,-2,1,-3,-4]=>[-4,-3,1,-2,5]=>11010=>[2,1,1,1]
[5,-2,-1,3,4]=>[4,3,-1,-2,5]=>00110=>[2,2,1]
[5,-2,-1,3,-4]=>[-4,3,-1,-2,5]=>10110=>[1,1,2,1]
[5,-2,-1,-3,4]=>[4,-3,-1,-2,5]=>01110=>[1,3,1]
[5,-2,-1,-3,-4]=>[-4,-3,-1,-2,5]=>11110=>[4,1]
[-5,2,1,3,4]=>[4,3,1,2,-5]=>00001=>[4,1]
[-5,2,1,3,-4]=>[-4,3,1,2,-5]=>10001=>[1,3,1]
[-5,2,1,-3,4]=>[4,-3,1,2,-5]=>01001=>[1,1,2,1]
[-5,2,1,-3,-4]=>[-4,-3,1,2,-5]=>11001=>[2,2,1]
[-5,2,-1,3,4]=>[4,3,-1,2,-5]=>00101=>[2,1,1,1]
[-5,2,-1,3,-4]=>[-4,3,-1,2,-5]=>10101=>[1,1,1,1,1]
[-5,2,-1,-3,4]=>[4,-3,-1,2,-5]=>01101=>[1,2,1,1]
[-5,2,-1,-3,-4]=>[-4,-3,-1,2,-5]=>11101=>[3,1,1]
[-5,-2,1,3,4]=>[4,3,1,-2,-5]=>00011=>[3,2]
[-5,-2,1,3,-4]=>[-4,3,1,-2,-5]=>10011=>[1,2,2]
[-5,-2,1,-3,4]=>[4,-3,1,-2,-5]=>01011=>[1,1,1,2]
[-5,-2,1,-3,-4]=>[-4,-3,1,-2,-5]=>11011=>[2,1,2]
[-5,-2,-1,3,4]=>[4,3,-1,-2,-5]=>00111=>[2,3]
[-5,-2,-1,3,-4]=>[-4,3,-1,-2,-5]=>10111=>[1,1,3]
[-5,-2,-1,-3,4]=>[4,-3,-1,-2,-5]=>01111=>[1,4]
[-5,-2,-1,-3,-4]=>[-4,-3,-1,-2,-5]=>11111=>[5]
[5,2,1,4,3]=>[3,4,1,2,5]=>00000=>[5]
[5,2,1,4,-3]=>[-3,4,1,2,5]=>10000=>[1,4]
[5,2,1,-4,3]=>[3,-4,1,2,5]=>01000=>[1,1,3]
[5,2,1,-4,-3]=>[-3,-4,1,2,5]=>11000=>[2,3]
[5,2,-1,4,3]=>[3,4,-1,2,5]=>00100=>[2,1,2]
[5,2,-1,4,-3]=>[-3,4,-1,2,5]=>10100=>[1,1,1,2]
[5,2,-1,-4,3]=>[3,-4,-1,2,5]=>01100=>[1,2,2]
[5,2,-1,-4,-3]=>[-3,-4,-1,2,5]=>11100=>[3,2]
[5,-2,1,4,3]=>[3,4,1,-2,5]=>00010=>[3,1,1]
[5,-2,1,4,-3]=>[-3,4,1,-2,5]=>10010=>[1,2,1,1]
[5,-2,1,-4,3]=>[3,-4,1,-2,5]=>01010=>[1,1,1,1,1]
[5,-2,1,-4,-3]=>[-3,-4,1,-2,5]=>11010=>[2,1,1,1]
[5,-2,-1,4,3]=>[3,4,-1,-2,5]=>00110=>[2,2,1]
[5,-2,-1,4,-3]=>[-3,4,-1,-2,5]=>10110=>[1,1,2,1]
[5,-2,-1,-4,3]=>[3,-4,-1,-2,5]=>01110=>[1,3,1]
[5,-2,-1,-4,-3]=>[-3,-4,-1,-2,5]=>11110=>[4,1]
[-5,2,1,4,3]=>[3,4,1,2,-5]=>00001=>[4,1]
[-5,2,1,4,-3]=>[-3,4,1,2,-5]=>10001=>[1,3,1]
[-5,2,1,-4,3]=>[3,-4,1,2,-5]=>01001=>[1,1,2,1]
[-5,2,1,-4,-3]=>[-3,-4,1,2,-5]=>11001=>[2,2,1]
[-5,2,-1,4,3]=>[3,4,-1,2,-5]=>00101=>[2,1,1,1]
[-5,2,-1,4,-3]=>[-3,4,-1,2,-5]=>10101=>[1,1,1,1,1]
[-5,2,-1,-4,3]=>[3,-4,-1,2,-5]=>01101=>[1,2,1,1]
[-5,2,-1,-4,-3]=>[-3,-4,-1,2,-5]=>11101=>[3,1,1]
[-5,-2,1,4,3]=>[3,4,1,-2,-5]=>00011=>[3,2]
[-5,-2,1,4,-3]=>[-3,4,1,-2,-5]=>10011=>[1,2,2]
[-5,-2,1,-4,3]=>[3,-4,1,-2,-5]=>01011=>[1,1,1,2]
[-5,-2,1,-4,-3]=>[-3,-4,1,-2,-5]=>11011=>[2,1,2]
[-5,-2,-1,4,3]=>[3,4,-1,-2,-5]=>00111=>[2,3]
[-5,-2,-1,4,-3]=>[-3,4,-1,-2,-5]=>10111=>[1,1,3]
[-5,-2,-1,-4,3]=>[3,-4,-1,-2,-5]=>01111=>[1,4]
[-5,-2,-1,-4,-3]=>[-3,-4,-1,-2,-5]=>11111=>[5]
[5,2,3,1,4]=>[4,1,3,2,5]=>00000=>[5]
[5,2,3,1,-4]=>[-4,1,3,2,5]=>10000=>[1,4]
[5,2,3,-1,4]=>[4,-1,3,2,5]=>01000=>[1,1,3]
[5,2,3,-1,-4]=>[-4,-1,3,2,5]=>11000=>[2,3]
[5,2,-3,1,4]=>[4,1,-3,2,5]=>00100=>[2,1,2]
[5,2,-3,1,-4]=>[-4,1,-3,2,5]=>10100=>[1,1,1,2]
[5,2,-3,-1,4]=>[4,-1,-3,2,5]=>01100=>[1,2,2]
[5,2,-3,-1,-4]=>[-4,-1,-3,2,5]=>11100=>[3,2]
[5,-2,3,1,4]=>[4,1,3,-2,5]=>00010=>[3,1,1]
[5,-2,3,1,-4]=>[-4,1,3,-2,5]=>10010=>[1,2,1,1]
[5,-2,3,-1,4]=>[4,-1,3,-2,5]=>01010=>[1,1,1,1,1]
[5,-2,3,-1,-4]=>[-4,-1,3,-2,5]=>11010=>[2,1,1,1]
[5,-2,-3,1,4]=>[4,1,-3,-2,5]=>00110=>[2,2,1]
[5,-2,-3,1,-4]=>[-4,1,-3,-2,5]=>10110=>[1,1,2,1]
[5,-2,-3,-1,4]=>[4,-1,-3,-2,5]=>01110=>[1,3,1]
[5,-2,-3,-1,-4]=>[-4,-1,-3,-2,5]=>11110=>[4,1]
[-5,2,3,1,4]=>[4,1,3,2,-5]=>00001=>[4,1]
[-5,2,3,1,-4]=>[-4,1,3,2,-5]=>10001=>[1,3,1]
[-5,2,3,-1,4]=>[4,-1,3,2,-5]=>01001=>[1,1,2,1]
[-5,2,3,-1,-4]=>[-4,-1,3,2,-5]=>11001=>[2,2,1]
[-5,2,-3,1,4]=>[4,1,-3,2,-5]=>00101=>[2,1,1,1]
[-5,2,-3,1,-4]=>[-4,1,-3,2,-5]=>10101=>[1,1,1,1,1]
[-5,2,-3,-1,4]=>[4,-1,-3,2,-5]=>01101=>[1,2,1,1]
[-5,2,-3,-1,-4]=>[-4,-1,-3,2,-5]=>11101=>[3,1,1]
[-5,-2,3,1,4]=>[4,1,3,-2,-5]=>00011=>[3,2]
[-5,-2,3,1,-4]=>[-4,1,3,-2,-5]=>10011=>[1,2,2]
[-5,-2,3,-1,4]=>[4,-1,3,-2,-5]=>01011=>[1,1,1,2]
[-5,-2,3,-1,-4]=>[-4,-1,3,-2,-5]=>11011=>[2,1,2]
[-5,-2,-3,1,4]=>[4,1,-3,-2,-5]=>00111=>[2,3]
[-5,-2,-3,1,-4]=>[-4,1,-3,-2,-5]=>10111=>[1,1,3]
[-5,-2,-3,-1,4]=>[4,-1,-3,-2,-5]=>01111=>[1,4]
[-5,-2,-3,-1,-4]=>[-4,-1,-3,-2,-5]=>11111=>[5]
[5,2,3,4,1]=>[1,4,3,2,5]=>00000=>[5]
[5,2,3,4,-1]=>[-1,4,3,2,5]=>10000=>[1,4]
[5,2,3,-4,1]=>[1,-4,3,2,5]=>01000=>[1,1,3]
[5,2,3,-4,-1]=>[-1,-4,3,2,5]=>11000=>[2,3]
[5,2,-3,4,1]=>[1,4,-3,2,5]=>00100=>[2,1,2]
[5,2,-3,4,-1]=>[-1,4,-3,2,5]=>10100=>[1,1,1,2]
[5,2,-3,-4,1]=>[1,-4,-3,2,5]=>01100=>[1,2,2]
[5,2,-3,-4,-1]=>[-1,-4,-3,2,5]=>11100=>[3,2]
[5,-2,3,4,1]=>[1,4,3,-2,5]=>00010=>[3,1,1]
[5,-2,3,4,-1]=>[-1,4,3,-2,5]=>10010=>[1,2,1,1]
[5,-2,3,-4,1]=>[1,-4,3,-2,5]=>01010=>[1,1,1,1,1]
[5,-2,3,-4,-1]=>[-1,-4,3,-2,5]=>11010=>[2,1,1,1]
[5,-2,-3,4,1]=>[1,4,-3,-2,5]=>00110=>[2,2,1]
[5,-2,-3,4,-1]=>[-1,4,-3,-2,5]=>10110=>[1,1,2,1]
[5,-2,-3,-4,1]=>[1,-4,-3,-2,5]=>01110=>[1,3,1]
[5,-2,-3,-4,-1]=>[-1,-4,-3,-2,5]=>11110=>[4,1]
[-5,2,3,4,1]=>[1,4,3,2,-5]=>00001=>[4,1]
[-5,2,3,4,-1]=>[-1,4,3,2,-5]=>10001=>[1,3,1]
[-5,2,3,-4,1]=>[1,-4,3,2,-5]=>01001=>[1,1,2,1]
[-5,2,3,-4,-1]=>[-1,-4,3,2,-5]=>11001=>[2,2,1]
[-5,2,-3,4,1]=>[1,4,-3,2,-5]=>00101=>[2,1,1,1]
[-5,2,-3,4,-1]=>[-1,4,-3,2,-5]=>10101=>[1,1,1,1,1]
[-5,2,-3,-4,1]=>[1,-4,-3,2,-5]=>01101=>[1,2,1,1]
[-5,2,-3,-4,-1]=>[-1,-4,-3,2,-5]=>11101=>[3,1,1]
[-5,-2,3,4,1]=>[1,4,3,-2,-5]=>00011=>[3,2]
[-5,-2,3,4,-1]=>[-1,4,3,-2,-5]=>10011=>[1,2,2]
[-5,-2,3,-4,1]=>[1,-4,3,-2,-5]=>01011=>[1,1,1,2]
[-5,-2,3,-4,-1]=>[-1,-4,3,-2,-5]=>11011=>[2,1,2]
[-5,-2,-3,4,1]=>[1,4,-3,-2,-5]=>00111=>[2,3]
[-5,-2,-3,4,-1]=>[-1,4,-3,-2,-5]=>10111=>[1,1,3]
[-5,-2,-3,-4,1]=>[1,-4,-3,-2,-5]=>01111=>[1,4]
[-5,-2,-3,-4,-1]=>[-1,-4,-3,-2,-5]=>11111=>[5]
[5,2,4,1,3]=>[3,1,4,2,5]=>00000=>[5]
[5,2,4,1,-3]=>[-3,1,4,2,5]=>10000=>[1,4]
[5,2,4,-1,3]=>[3,-1,4,2,5]=>01000=>[1,1,3]
[5,2,4,-1,-3]=>[-3,-1,4,2,5]=>11000=>[2,3]
[5,2,-4,1,3]=>[3,1,-4,2,5]=>00100=>[2,1,2]
[5,2,-4,1,-3]=>[-3,1,-4,2,5]=>10100=>[1,1,1,2]
[5,2,-4,-1,3]=>[3,-1,-4,2,5]=>01100=>[1,2,2]
[5,2,-4,-1,-3]=>[-3,-1,-4,2,5]=>11100=>[3,2]
[5,-2,4,1,3]=>[3,1,4,-2,5]=>00010=>[3,1,1]
[5,-2,4,1,-3]=>[-3,1,4,-2,5]=>10010=>[1,2,1,1]
[5,-2,4,-1,3]=>[3,-1,4,-2,5]=>01010=>[1,1,1,1,1]
[5,-2,4,-1,-3]=>[-3,-1,4,-2,5]=>11010=>[2,1,1,1]
[5,-2,-4,1,3]=>[3,1,-4,-2,5]=>00110=>[2,2,1]
[5,-2,-4,1,-3]=>[-3,1,-4,-2,5]=>10110=>[1,1,2,1]
[5,-2,-4,-1,3]=>[3,-1,-4,-2,5]=>01110=>[1,3,1]
[5,-2,-4,-1,-3]=>[-3,-1,-4,-2,5]=>11110=>[4,1]
[-5,2,4,1,3]=>[3,1,4,2,-5]=>00001=>[4,1]
[-5,2,4,1,-3]=>[-3,1,4,2,-5]=>10001=>[1,3,1]
[-5,2,4,-1,3]=>[3,-1,4,2,-5]=>01001=>[1,1,2,1]
[-5,2,4,-1,-3]=>[-3,-1,4,2,-5]=>11001=>[2,2,1]
[-5,2,-4,1,3]=>[3,1,-4,2,-5]=>00101=>[2,1,1,1]
[-5,2,-4,1,-3]=>[-3,1,-4,2,-5]=>10101=>[1,1,1,1,1]
[-5,2,-4,-1,3]=>[3,-1,-4,2,-5]=>01101=>[1,2,1,1]
[-5,2,-4,-1,-3]=>[-3,-1,-4,2,-5]=>11101=>[3,1,1]
[-5,-2,4,1,3]=>[3,1,4,-2,-5]=>00011=>[3,2]
[-5,-2,4,1,-3]=>[-3,1,4,-2,-5]=>10011=>[1,2,2]
[-5,-2,4,-1,3]=>[3,-1,4,-2,-5]=>01011=>[1,1,1,2]
[-5,-2,4,-1,-3]=>[-3,-1,4,-2,-5]=>11011=>[2,1,2]
[-5,-2,-4,1,3]=>[3,1,-4,-2,-5]=>00111=>[2,3]
[-5,-2,-4,1,-3]=>[-3,1,-4,-2,-5]=>10111=>[1,1,3]
[-5,-2,-4,-1,3]=>[3,-1,-4,-2,-5]=>01111=>[1,4]
[-5,-2,-4,-1,-3]=>[-3,-1,-4,-2,-5]=>11111=>[5]
[5,2,4,3,1]=>[1,3,4,2,5]=>00000=>[5]
[5,2,4,3,-1]=>[-1,3,4,2,5]=>10000=>[1,4]
[5,2,4,-3,1]=>[1,-3,4,2,5]=>01000=>[1,1,3]
[5,2,4,-3,-1]=>[-1,-3,4,2,5]=>11000=>[2,3]
[5,2,-4,3,1]=>[1,3,-4,2,5]=>00100=>[2,1,2]
[5,2,-4,3,-1]=>[-1,3,-4,2,5]=>10100=>[1,1,1,2]
[5,2,-4,-3,1]=>[1,-3,-4,2,5]=>01100=>[1,2,2]
[5,2,-4,-3,-1]=>[-1,-3,-4,2,5]=>11100=>[3,2]
[5,-2,4,3,1]=>[1,3,4,-2,5]=>00010=>[3,1,1]
[5,-2,4,3,-1]=>[-1,3,4,-2,5]=>10010=>[1,2,1,1]
[5,-2,4,-3,1]=>[1,-3,4,-2,5]=>01010=>[1,1,1,1,1]
[5,-2,4,-3,-1]=>[-1,-3,4,-2,5]=>11010=>[2,1,1,1]
[5,-2,-4,3,1]=>[1,3,-4,-2,5]=>00110=>[2,2,1]
[5,-2,-4,3,-1]=>[-1,3,-4,-2,5]=>10110=>[1,1,2,1]
[5,-2,-4,-3,1]=>[1,-3,-4,-2,5]=>01110=>[1,3,1]
[5,-2,-4,-3,-1]=>[-1,-3,-4,-2,5]=>11110=>[4,1]
[-5,2,4,3,1]=>[1,3,4,2,-5]=>00001=>[4,1]
[-5,2,4,3,-1]=>[-1,3,4,2,-5]=>10001=>[1,3,1]
[-5,2,4,-3,1]=>[1,-3,4,2,-5]=>01001=>[1,1,2,1]
[-5,2,4,-3,-1]=>[-1,-3,4,2,-5]=>11001=>[2,2,1]
[-5,2,-4,3,1]=>[1,3,-4,2,-5]=>00101=>[2,1,1,1]
[-5,2,-4,3,-1]=>[-1,3,-4,2,-5]=>10101=>[1,1,1,1,1]
[-5,2,-4,-3,1]=>[1,-3,-4,2,-5]=>01101=>[1,2,1,1]
[-5,2,-4,-3,-1]=>[-1,-3,-4,2,-5]=>11101=>[3,1,1]
[-5,-2,4,3,1]=>[1,3,4,-2,-5]=>00011=>[3,2]
[-5,-2,4,3,-1]=>[-1,3,4,-2,-5]=>10011=>[1,2,2]
[-5,-2,4,-3,1]=>[1,-3,4,-2,-5]=>01011=>[1,1,1,2]
[-5,-2,4,-3,-1]=>[-1,-3,4,-2,-5]=>11011=>[2,1,2]
[-5,-2,-4,3,1]=>[1,3,-4,-2,-5]=>00111=>[2,3]
[-5,-2,-4,3,-1]=>[-1,3,-4,-2,-5]=>10111=>[1,1,3]
[-5,-2,-4,-3,1]=>[1,-3,-4,-2,-5]=>01111=>[1,4]
[-5,-2,-4,-3,-1]=>[-1,-3,-4,-2,-5]=>11111=>[5]
[5,3,1,2,4]=>[4,2,1,3,5]=>00000=>[5]
[5,3,1,2,-4]=>[-4,2,1,3,5]=>10000=>[1,4]
[5,3,1,-2,4]=>[4,-2,1,3,5]=>01000=>[1,1,3]
[5,3,1,-2,-4]=>[-4,-2,1,3,5]=>11000=>[2,3]
[5,3,-1,2,4]=>[4,2,-1,3,5]=>00100=>[2,1,2]
[5,3,-1,2,-4]=>[-4,2,-1,3,5]=>10100=>[1,1,1,2]
[5,3,-1,-2,4]=>[4,-2,-1,3,5]=>01100=>[1,2,2]
[5,3,-1,-2,-4]=>[-4,-2,-1,3,5]=>11100=>[3,2]
[5,-3,1,2,4]=>[4,2,1,-3,5]=>00010=>[3,1,1]
[5,-3,1,2,-4]=>[-4,2,1,-3,5]=>10010=>[1,2,1,1]
[5,-3,1,-2,4]=>[4,-2,1,-3,5]=>01010=>[1,1,1,1,1]
[5,-3,1,-2,-4]=>[-4,-2,1,-3,5]=>11010=>[2,1,1,1]
[5,-3,-1,2,4]=>[4,2,-1,-3,5]=>00110=>[2,2,1]
[5,-3,-1,2,-4]=>[-4,2,-1,-3,5]=>10110=>[1,1,2,1]
[5,-3,-1,-2,4]=>[4,-2,-1,-3,5]=>01110=>[1,3,1]
[5,-3,-1,-2,-4]=>[-4,-2,-1,-3,5]=>11110=>[4,1]
[-5,3,1,2,4]=>[4,2,1,3,-5]=>00001=>[4,1]
[-5,3,1,2,-4]=>[-4,2,1,3,-5]=>10001=>[1,3,1]
[-5,3,1,-2,4]=>[4,-2,1,3,-5]=>01001=>[1,1,2,1]
[-5,3,1,-2,-4]=>[-4,-2,1,3,-5]=>11001=>[2,2,1]
[-5,3,-1,2,4]=>[4,2,-1,3,-5]=>00101=>[2,1,1,1]
[-5,3,-1,2,-4]=>[-4,2,-1,3,-5]=>10101=>[1,1,1,1,1]
[-5,3,-1,-2,4]=>[4,-2,-1,3,-5]=>01101=>[1,2,1,1]
[-5,3,-1,-2,-4]=>[-4,-2,-1,3,-5]=>11101=>[3,1,1]
[-5,-3,1,2,4]=>[4,2,1,-3,-5]=>00011=>[3,2]
[-5,-3,1,2,-4]=>[-4,2,1,-3,-5]=>10011=>[1,2,2]
[-5,-3,1,-2,4]=>[4,-2,1,-3,-5]=>01011=>[1,1,1,2]
[-5,-3,1,-2,-4]=>[-4,-2,1,-3,-5]=>11011=>[2,1,2]
[-5,-3,-1,2,4]=>[4,2,-1,-3,-5]=>00111=>[2,3]
[-5,-3,-1,2,-4]=>[-4,2,-1,-3,-5]=>10111=>[1,1,3]
[-5,-3,-1,-2,4]=>[4,-2,-1,-3,-5]=>01111=>[1,4]
[-5,-3,-1,-2,-4]=>[-4,-2,-1,-3,-5]=>11111=>[5]
[5,3,1,4,2]=>[2,4,1,3,5]=>00000=>[5]
[5,3,1,4,-2]=>[-2,4,1,3,5]=>10000=>[1,4]
[5,3,1,-4,2]=>[2,-4,1,3,5]=>01000=>[1,1,3]
[5,3,1,-4,-2]=>[-2,-4,1,3,5]=>11000=>[2,3]
[5,3,-1,4,2]=>[2,4,-1,3,5]=>00100=>[2,1,2]
[5,3,-1,4,-2]=>[-2,4,-1,3,5]=>10100=>[1,1,1,2]
[5,3,-1,-4,2]=>[2,-4,-1,3,5]=>01100=>[1,2,2]
[5,3,-1,-4,-2]=>[-2,-4,-1,3,5]=>11100=>[3,2]
[5,-3,1,4,2]=>[2,4,1,-3,5]=>00010=>[3,1,1]
[5,-3,1,4,-2]=>[-2,4,1,-3,5]=>10010=>[1,2,1,1]
[5,-3,1,-4,2]=>[2,-4,1,-3,5]=>01010=>[1,1,1,1,1]
[5,-3,1,-4,-2]=>[-2,-4,1,-3,5]=>11010=>[2,1,1,1]
[5,-3,-1,4,2]=>[2,4,-1,-3,5]=>00110=>[2,2,1]
[5,-3,-1,4,-2]=>[-2,4,-1,-3,5]=>10110=>[1,1,2,1]
[5,-3,-1,-4,2]=>[2,-4,-1,-3,5]=>01110=>[1,3,1]
[5,-3,-1,-4,-2]=>[-2,-4,-1,-3,5]=>11110=>[4,1]
[-5,3,1,4,2]=>[2,4,1,3,-5]=>00001=>[4,1]
[-5,3,1,4,-2]=>[-2,4,1,3,-5]=>10001=>[1,3,1]
[-5,3,1,-4,2]=>[2,-4,1,3,-5]=>01001=>[1,1,2,1]
[-5,3,1,-4,-2]=>[-2,-4,1,3,-5]=>11001=>[2,2,1]
[-5,3,-1,4,2]=>[2,4,-1,3,-5]=>00101=>[2,1,1,1]
[-5,3,-1,4,-2]=>[-2,4,-1,3,-5]=>10101=>[1,1,1,1,1]
[-5,3,-1,-4,2]=>[2,-4,-1,3,-5]=>01101=>[1,2,1,1]
[-5,3,-1,-4,-2]=>[-2,-4,-1,3,-5]=>11101=>[3,1,1]
[-5,-3,1,4,2]=>[2,4,1,-3,-5]=>00011=>[3,2]
[-5,-3,1,4,-2]=>[-2,4,1,-3,-5]=>10011=>[1,2,2]
[-5,-3,1,-4,2]=>[2,-4,1,-3,-5]=>01011=>[1,1,1,2]
[-5,-3,1,-4,-2]=>[-2,-4,1,-3,-5]=>11011=>[2,1,2]
[-5,-3,-1,4,2]=>[2,4,-1,-3,-5]=>00111=>[2,3]
[-5,-3,-1,4,-2]=>[-2,4,-1,-3,-5]=>10111=>[1,1,3]
[-5,-3,-1,-4,2]=>[2,-4,-1,-3,-5]=>01111=>[1,4]
[-5,-3,-1,-4,-2]=>[-2,-4,-1,-3,-5]=>11111=>[5]
[5,3,2,1,4]=>[4,1,2,3,5]=>00000=>[5]
[5,3,2,1,-4]=>[-4,1,2,3,5]=>10000=>[1,4]
[5,3,2,-1,4]=>[4,-1,2,3,5]=>01000=>[1,1,3]
[5,3,2,-1,-4]=>[-4,-1,2,3,5]=>11000=>[2,3]
[5,3,-2,1,4]=>[4,1,-2,3,5]=>00100=>[2,1,2]
[5,3,-2,1,-4]=>[-4,1,-2,3,5]=>10100=>[1,1,1,2]
[5,3,-2,-1,4]=>[4,-1,-2,3,5]=>01100=>[1,2,2]
[5,3,-2,-1,-4]=>[-4,-1,-2,3,5]=>11100=>[3,2]
[5,-3,2,1,4]=>[4,1,2,-3,5]=>00010=>[3,1,1]
[5,-3,2,1,-4]=>[-4,1,2,-3,5]=>10010=>[1,2,1,1]
[5,-3,2,-1,4]=>[4,-1,2,-3,5]=>01010=>[1,1,1,1,1]
[5,-3,2,-1,-4]=>[-4,-1,2,-3,5]=>11010=>[2,1,1,1]
[5,-3,-2,1,4]=>[4,1,-2,-3,5]=>00110=>[2,2,1]
[5,-3,-2,1,-4]=>[-4,1,-2,-3,5]=>10110=>[1,1,2,1]
[5,-3,-2,-1,4]=>[4,-1,-2,-3,5]=>01110=>[1,3,1]
[5,-3,-2,-1,-4]=>[-4,-1,-2,-3,5]=>11110=>[4,1]
[-5,3,2,1,4]=>[4,1,2,3,-5]=>00001=>[4,1]
[-5,3,2,1,-4]=>[-4,1,2,3,-5]=>10001=>[1,3,1]
[-5,3,2,-1,4]=>[4,-1,2,3,-5]=>01001=>[1,1,2,1]
[-5,3,2,-1,-4]=>[-4,-1,2,3,-5]=>11001=>[2,2,1]
[-5,3,-2,1,4]=>[4,1,-2,3,-5]=>00101=>[2,1,1,1]
[-5,3,-2,1,-4]=>[-4,1,-2,3,-5]=>10101=>[1,1,1,1,1]
[-5,3,-2,-1,4]=>[4,-1,-2,3,-5]=>01101=>[1,2,1,1]
[-5,3,-2,-1,-4]=>[-4,-1,-2,3,-5]=>11101=>[3,1,1]
[-5,-3,2,1,4]=>[4,1,2,-3,-5]=>00011=>[3,2]
[-5,-3,2,1,-4]=>[-4,1,2,-3,-5]=>10011=>[1,2,2]
[-5,-3,2,-1,4]=>[4,-1,2,-3,-5]=>01011=>[1,1,1,2]
[-5,-3,2,-1,-4]=>[-4,-1,2,-3,-5]=>11011=>[2,1,2]
[-5,-3,-2,1,4]=>[4,1,-2,-3,-5]=>00111=>[2,3]
[-5,-3,-2,1,-4]=>[-4,1,-2,-3,-5]=>10111=>[1,1,3]
[-5,-3,-2,-1,4]=>[4,-1,-2,-3,-5]=>01111=>[1,4]
[-5,-3,-2,-1,-4]=>[-4,-1,-2,-3,-5]=>11111=>[5]
[5,3,2,4,1]=>[1,4,2,3,5]=>00000=>[5]
[5,3,2,4,-1]=>[-1,4,2,3,5]=>10000=>[1,4]
[5,3,2,-4,1]=>[1,-4,2,3,5]=>01000=>[1,1,3]
[5,3,2,-4,-1]=>[-1,-4,2,3,5]=>11000=>[2,3]
[5,3,-2,4,1]=>[1,4,-2,3,5]=>00100=>[2,1,2]
[5,3,-2,4,-1]=>[-1,4,-2,3,5]=>10100=>[1,1,1,2]
[5,3,-2,-4,1]=>[1,-4,-2,3,5]=>01100=>[1,2,2]
[5,3,-2,-4,-1]=>[-1,-4,-2,3,5]=>11100=>[3,2]
[5,-3,2,4,1]=>[1,4,2,-3,5]=>00010=>[3,1,1]
[5,-3,2,4,-1]=>[-1,4,2,-3,5]=>10010=>[1,2,1,1]
[5,-3,2,-4,1]=>[1,-4,2,-3,5]=>01010=>[1,1,1,1,1]
[5,-3,2,-4,-1]=>[-1,-4,2,-3,5]=>11010=>[2,1,1,1]
[5,-3,-2,4,1]=>[1,4,-2,-3,5]=>00110=>[2,2,1]
[5,-3,-2,4,-1]=>[-1,4,-2,-3,5]=>10110=>[1,1,2,1]
[5,-3,-2,-4,1]=>[1,-4,-2,-3,5]=>01110=>[1,3,1]
[5,-3,-2,-4,-1]=>[-1,-4,-2,-3,5]=>11110=>[4,1]
[-5,3,2,4,1]=>[1,4,2,3,-5]=>00001=>[4,1]
[-5,3,2,4,-1]=>[-1,4,2,3,-5]=>10001=>[1,3,1]
[-5,3,2,-4,1]=>[1,-4,2,3,-5]=>01001=>[1,1,2,1]
[-5,3,2,-4,-1]=>[-1,-4,2,3,-5]=>11001=>[2,2,1]
[-5,3,-2,4,1]=>[1,4,-2,3,-5]=>00101=>[2,1,1,1]
[-5,3,-2,4,-1]=>[-1,4,-2,3,-5]=>10101=>[1,1,1,1,1]
[-5,3,-2,-4,1]=>[1,-4,-2,3,-5]=>01101=>[1,2,1,1]
[-5,3,-2,-4,-1]=>[-1,-4,-2,3,-5]=>11101=>[3,1,1]
[-5,-3,2,4,1]=>[1,4,2,-3,-5]=>00011=>[3,2]
[-5,-3,2,4,-1]=>[-1,4,2,-3,-5]=>10011=>[1,2,2]
[-5,-3,2,-4,1]=>[1,-4,2,-3,-5]=>01011=>[1,1,1,2]
[-5,-3,2,-4,-1]=>[-1,-4,2,-3,-5]=>11011=>[2,1,2]
[-5,-3,-2,4,1]=>[1,4,-2,-3,-5]=>00111=>[2,3]
[-5,-3,-2,4,-1]=>[-1,4,-2,-3,-5]=>10111=>[1,1,3]
[-5,-3,-2,-4,1]=>[1,-4,-2,-3,-5]=>01111=>[1,4]
[-5,-3,-2,-4,-1]=>[-1,-4,-2,-3,-5]=>11111=>[5]
[5,3,4,1,2]=>[2,1,4,3,5]=>00000=>[5]
[5,3,4,1,-2]=>[-2,1,4,3,5]=>10000=>[1,4]
[5,3,4,-1,2]=>[2,-1,4,3,5]=>01000=>[1,1,3]
[5,3,4,-1,-2]=>[-2,-1,4,3,5]=>11000=>[2,3]
[5,3,-4,1,2]=>[2,1,-4,3,5]=>00100=>[2,1,2]
[5,3,-4,1,-2]=>[-2,1,-4,3,5]=>10100=>[1,1,1,2]
[5,3,-4,-1,2]=>[2,-1,-4,3,5]=>01100=>[1,2,2]
[5,3,-4,-1,-2]=>[-2,-1,-4,3,5]=>11100=>[3,2]
[5,-3,4,1,2]=>[2,1,4,-3,5]=>00010=>[3,1,1]
[5,-3,4,1,-2]=>[-2,1,4,-3,5]=>10010=>[1,2,1,1]
[5,-3,4,-1,2]=>[2,-1,4,-3,5]=>01010=>[1,1,1,1,1]
[5,-3,4,-1,-2]=>[-2,-1,4,-3,5]=>11010=>[2,1,1,1]
[5,-3,-4,1,2]=>[2,1,-4,-3,5]=>00110=>[2,2,1]
[5,-3,-4,1,-2]=>[-2,1,-4,-3,5]=>10110=>[1,1,2,1]
[5,-3,-4,-1,2]=>[2,-1,-4,-3,5]=>01110=>[1,3,1]
[5,-3,-4,-1,-2]=>[-2,-1,-4,-3,5]=>11110=>[4,1]
[-5,3,4,1,2]=>[2,1,4,3,-5]=>00001=>[4,1]
[-5,3,4,1,-2]=>[-2,1,4,3,-5]=>10001=>[1,3,1]
[-5,3,4,-1,2]=>[2,-1,4,3,-5]=>01001=>[1,1,2,1]
[-5,3,4,-1,-2]=>[-2,-1,4,3,-5]=>11001=>[2,2,1]
[-5,3,-4,1,2]=>[2,1,-4,3,-5]=>00101=>[2,1,1,1]
[-5,3,-4,1,-2]=>[-2,1,-4,3,-5]=>10101=>[1,1,1,1,1]
[-5,3,-4,-1,2]=>[2,-1,-4,3,-5]=>01101=>[1,2,1,1]
[-5,3,-4,-1,-2]=>[-2,-1,-4,3,-5]=>11101=>[3,1,1]
[-5,-3,4,1,2]=>[2,1,4,-3,-5]=>00011=>[3,2]
[-5,-3,4,1,-2]=>[-2,1,4,-3,-5]=>10011=>[1,2,2]
[-5,-3,4,-1,2]=>[2,-1,4,-3,-5]=>01011=>[1,1,1,2]
[-5,-3,4,-1,-2]=>[-2,-1,4,-3,-5]=>11011=>[2,1,2]
[-5,-3,-4,1,2]=>[2,1,-4,-3,-5]=>00111=>[2,3]
[-5,-3,-4,1,-2]=>[-2,1,-4,-3,-5]=>10111=>[1,1,3]
[-5,-3,-4,-1,2]=>[2,-1,-4,-3,-5]=>01111=>[1,4]
[-5,-3,-4,-1,-2]=>[-2,-1,-4,-3,-5]=>11111=>[5]
[5,3,4,2,1]=>[1,2,4,3,5]=>00000=>[5]
[5,3,4,2,-1]=>[-1,2,4,3,5]=>10000=>[1,4]
[5,3,4,-2,1]=>[1,-2,4,3,5]=>01000=>[1,1,3]
[5,3,4,-2,-1]=>[-1,-2,4,3,5]=>11000=>[2,3]
[5,3,-4,2,1]=>[1,2,-4,3,5]=>00100=>[2,1,2]
[5,3,-4,2,-1]=>[-1,2,-4,3,5]=>10100=>[1,1,1,2]
[5,3,-4,-2,1]=>[1,-2,-4,3,5]=>01100=>[1,2,2]
[5,3,-4,-2,-1]=>[-1,-2,-4,3,5]=>11100=>[3,2]
[5,-3,4,2,1]=>[1,2,4,-3,5]=>00010=>[3,1,1]
[5,-3,4,2,-1]=>[-1,2,4,-3,5]=>10010=>[1,2,1,1]
[5,-3,4,-2,1]=>[1,-2,4,-3,5]=>01010=>[1,1,1,1,1]
[5,-3,4,-2,-1]=>[-1,-2,4,-3,5]=>11010=>[2,1,1,1]
[5,-3,-4,2,1]=>[1,2,-4,-3,5]=>00110=>[2,2,1]
[5,-3,-4,2,-1]=>[-1,2,-4,-3,5]=>10110=>[1,1,2,1]
[5,-3,-4,-2,1]=>[1,-2,-4,-3,5]=>01110=>[1,3,1]
[5,-3,-4,-2,-1]=>[-1,-2,-4,-3,5]=>11110=>[4,1]
[-5,3,4,2,1]=>[1,2,4,3,-5]=>00001=>[4,1]
[-5,3,4,2,-1]=>[-1,2,4,3,-5]=>10001=>[1,3,1]
[-5,3,4,-2,1]=>[1,-2,4,3,-5]=>01001=>[1,1,2,1]
[-5,3,4,-2,-1]=>[-1,-2,4,3,-5]=>11001=>[2,2,1]
[-5,3,-4,2,1]=>[1,2,-4,3,-5]=>00101=>[2,1,1,1]
[-5,3,-4,2,-1]=>[-1,2,-4,3,-5]=>10101=>[1,1,1,1,1]
[-5,3,-4,-2,1]=>[1,-2,-4,3,-5]=>01101=>[1,2,1,1]
[-5,3,-4,-2,-1]=>[-1,-2,-4,3,-5]=>11101=>[3,1,1]
[-5,-3,4,2,1]=>[1,2,4,-3,-5]=>00011=>[3,2]
[-5,-3,4,2,-1]=>[-1,2,4,-3,-5]=>10011=>[1,2,2]
[-5,-3,4,-2,1]=>[1,-2,4,-3,-5]=>01011=>[1,1,1,2]
[-5,-3,4,-2,-1]=>[-1,-2,4,-3,-5]=>11011=>[2,1,2]
[-5,-3,-4,2,1]=>[1,2,-4,-3,-5]=>00111=>[2,3]
[-5,-3,-4,2,-1]=>[-1,2,-4,-3,-5]=>10111=>[1,1,3]
[-5,-3,-4,-2,1]=>[1,-2,-4,-3,-5]=>01111=>[1,4]
[-5,-3,-4,-2,-1]=>[-1,-2,-4,-3,-5]=>11111=>[5]
[5,4,1,2,3]=>[3,2,1,4,5]=>00000=>[5]
[5,4,1,2,-3]=>[-3,2,1,4,5]=>10000=>[1,4]
[5,4,1,-2,3]=>[3,-2,1,4,5]=>01000=>[1,1,3]
[5,4,1,-2,-3]=>[-3,-2,1,4,5]=>11000=>[2,3]
[5,4,-1,2,3]=>[3,2,-1,4,5]=>00100=>[2,1,2]
[5,4,-1,2,-3]=>[-3,2,-1,4,5]=>10100=>[1,1,1,2]
[5,4,-1,-2,3]=>[3,-2,-1,4,5]=>01100=>[1,2,2]
[5,4,-1,-2,-3]=>[-3,-2,-1,4,5]=>11100=>[3,2]
[5,-4,1,2,3]=>[3,2,1,-4,5]=>00010=>[3,1,1]
[5,-4,1,2,-3]=>[-3,2,1,-4,5]=>10010=>[1,2,1,1]
[5,-4,1,-2,3]=>[3,-2,1,-4,5]=>01010=>[1,1,1,1,1]
[5,-4,1,-2,-3]=>[-3,-2,1,-4,5]=>11010=>[2,1,1,1]
[5,-4,-1,2,3]=>[3,2,-1,-4,5]=>00110=>[2,2,1]
[5,-4,-1,2,-3]=>[-3,2,-1,-4,5]=>10110=>[1,1,2,1]
[5,-4,-1,-2,3]=>[3,-2,-1,-4,5]=>01110=>[1,3,1]
[5,-4,-1,-2,-3]=>[-3,-2,-1,-4,5]=>11110=>[4,1]
[-5,4,1,2,3]=>[3,2,1,4,-5]=>00001=>[4,1]
[-5,4,1,2,-3]=>[-3,2,1,4,-5]=>10001=>[1,3,1]
[-5,4,1,-2,3]=>[3,-2,1,4,-5]=>01001=>[1,1,2,1]
[-5,4,1,-2,-3]=>[-3,-2,1,4,-5]=>11001=>[2,2,1]
[-5,4,-1,2,3]=>[3,2,-1,4,-5]=>00101=>[2,1,1,1]
[-5,4,-1,2,-3]=>[-3,2,-1,4,-5]=>10101=>[1,1,1,1,1]
[-5,4,-1,-2,3]=>[3,-2,-1,4,-5]=>01101=>[1,2,1,1]
[-5,4,-1,-2,-3]=>[-3,-2,-1,4,-5]=>11101=>[3,1,1]
[-5,-4,1,2,3]=>[3,2,1,-4,-5]=>00011=>[3,2]
[-5,-4,1,2,-3]=>[-3,2,1,-4,-5]=>10011=>[1,2,2]
[-5,-4,1,-2,3]=>[3,-2,1,-4,-5]=>01011=>[1,1,1,2]
[-5,-4,1,-2,-3]=>[-3,-2,1,-4,-5]=>11011=>[2,1,2]
[-5,-4,-1,2,3]=>[3,2,-1,-4,-5]=>00111=>[2,3]
[-5,-4,-1,2,-3]=>[-3,2,-1,-4,-5]=>10111=>[1,1,3]
[-5,-4,-1,-2,3]=>[3,-2,-1,-4,-5]=>01111=>[1,4]
[-5,-4,-1,-2,-3]=>[-3,-2,-1,-4,-5]=>11111=>[5]
[5,4,1,3,2]=>[2,3,1,4,5]=>00000=>[5]
[5,4,1,3,-2]=>[-2,3,1,4,5]=>10000=>[1,4]
[5,4,1,-3,2]=>[2,-3,1,4,5]=>01000=>[1,1,3]
[5,4,1,-3,-2]=>[-2,-3,1,4,5]=>11000=>[2,3]
[5,4,-1,3,2]=>[2,3,-1,4,5]=>00100=>[2,1,2]
[5,4,-1,3,-2]=>[-2,3,-1,4,5]=>10100=>[1,1,1,2]
[5,4,-1,-3,2]=>[2,-3,-1,4,5]=>01100=>[1,2,2]
[5,4,-1,-3,-2]=>[-2,-3,-1,4,5]=>11100=>[3,2]
[5,-4,1,3,2]=>[2,3,1,-4,5]=>00010=>[3,1,1]
[5,-4,1,3,-2]=>[-2,3,1,-4,5]=>10010=>[1,2,1,1]
[5,-4,1,-3,2]=>[2,-3,1,-4,5]=>01010=>[1,1,1,1,1]
[5,-4,1,-3,-2]=>[-2,-3,1,-4,5]=>11010=>[2,1,1,1]
[5,-4,-1,3,2]=>[2,3,-1,-4,5]=>00110=>[2,2,1]
[5,-4,-1,3,-2]=>[-2,3,-1,-4,5]=>10110=>[1,1,2,1]
[5,-4,-1,-3,2]=>[2,-3,-1,-4,5]=>01110=>[1,3,1]
[5,-4,-1,-3,-2]=>[-2,-3,-1,-4,5]=>11110=>[4,1]
[-5,4,1,3,2]=>[2,3,1,4,-5]=>00001=>[4,1]
[-5,4,1,3,-2]=>[-2,3,1,4,-5]=>10001=>[1,3,1]
[-5,4,1,-3,2]=>[2,-3,1,4,-5]=>01001=>[1,1,2,1]
[-5,4,1,-3,-2]=>[-2,-3,1,4,-5]=>11001=>[2,2,1]
[-5,4,-1,3,2]=>[2,3,-1,4,-5]=>00101=>[2,1,1,1]
[-5,4,-1,3,-2]=>[-2,3,-1,4,-5]=>10101=>[1,1,1,1,1]
[-5,4,-1,-3,2]=>[2,-3,-1,4,-5]=>01101=>[1,2,1,1]
[-5,4,-1,-3,-2]=>[-2,-3,-1,4,-5]=>11101=>[3,1,1]
[-5,-4,1,3,2]=>[2,3,1,-4,-5]=>00011=>[3,2]
[-5,-4,1,3,-2]=>[-2,3,1,-4,-5]=>10011=>[1,2,2]
[-5,-4,1,-3,2]=>[2,-3,1,-4,-5]=>01011=>[1,1,1,2]
[-5,-4,1,-3,-2]=>[-2,-3,1,-4,-5]=>11011=>[2,1,2]
[-5,-4,-1,3,2]=>[2,3,-1,-4,-5]=>00111=>[2,3]
[-5,-4,-1,3,-2]=>[-2,3,-1,-4,-5]=>10111=>[1,1,3]
[-5,-4,-1,-3,2]=>[2,-3,-1,-4,-5]=>01111=>[1,4]
[-5,-4,-1,-3,-2]=>[-2,-3,-1,-4,-5]=>11111=>[5]
[5,4,2,1,3]=>[3,1,2,4,5]=>00000=>[5]
[5,4,2,1,-3]=>[-3,1,2,4,5]=>10000=>[1,4]
[5,4,2,-1,3]=>[3,-1,2,4,5]=>01000=>[1,1,3]
[5,4,2,-1,-3]=>[-3,-1,2,4,5]=>11000=>[2,3]
[5,4,-2,1,3]=>[3,1,-2,4,5]=>00100=>[2,1,2]
[5,4,-2,1,-3]=>[-3,1,-2,4,5]=>10100=>[1,1,1,2]
[5,4,-2,-1,3]=>[3,-1,-2,4,5]=>01100=>[1,2,2]
[5,4,-2,-1,-3]=>[-3,-1,-2,4,5]=>11100=>[3,2]
[5,-4,2,1,3]=>[3,1,2,-4,5]=>00010=>[3,1,1]
[5,-4,2,1,-3]=>[-3,1,2,-4,5]=>10010=>[1,2,1,1]
[5,-4,2,-1,3]=>[3,-1,2,-4,5]=>01010=>[1,1,1,1,1]
[5,-4,2,-1,-3]=>[-3,-1,2,-4,5]=>11010=>[2,1,1,1]
[5,-4,-2,1,3]=>[3,1,-2,-4,5]=>00110=>[2,2,1]
[5,-4,-2,1,-3]=>[-3,1,-2,-4,5]=>10110=>[1,1,2,1]
[5,-4,-2,-1,3]=>[3,-1,-2,-4,5]=>01110=>[1,3,1]
[5,-4,-2,-1,-3]=>[-3,-1,-2,-4,5]=>11110=>[4,1]
[-5,4,2,1,3]=>[3,1,2,4,-5]=>00001=>[4,1]
[-5,4,2,1,-3]=>[-3,1,2,4,-5]=>10001=>[1,3,1]
[-5,4,2,-1,3]=>[3,-1,2,4,-5]=>01001=>[1,1,2,1]
[-5,4,2,-1,-3]=>[-3,-1,2,4,-5]=>11001=>[2,2,1]
[-5,4,-2,1,3]=>[3,1,-2,4,-5]=>00101=>[2,1,1,1]
[-5,4,-2,1,-3]=>[-3,1,-2,4,-5]=>10101=>[1,1,1,1,1]
[-5,4,-2,-1,3]=>[3,-1,-2,4,-5]=>01101=>[1,2,1,1]
[-5,4,-2,-1,-3]=>[-3,-1,-2,4,-5]=>11101=>[3,1,1]
[-5,-4,2,1,3]=>[3,1,2,-4,-5]=>00011=>[3,2]
[-5,-4,2,1,-3]=>[-3,1,2,-4,-5]=>10011=>[1,2,2]
[-5,-4,2,-1,3]=>[3,-1,2,-4,-5]=>01011=>[1,1,1,2]
[-5,-4,2,-1,-3]=>[-3,-1,2,-4,-5]=>11011=>[2,1,2]
[-5,-4,-2,1,3]=>[3,1,-2,-4,-5]=>00111=>[2,3]
[-5,-4,-2,1,-3]=>[-3,1,-2,-4,-5]=>10111=>[1,1,3]
[-5,-4,-2,-1,3]=>[3,-1,-2,-4,-5]=>01111=>[1,4]
[-5,-4,-2,-1,-3]=>[-3,-1,-2,-4,-5]=>11111=>[5]
[5,4,2,3,1]=>[1,3,2,4,5]=>00000=>[5]
[5,4,2,3,-1]=>[-1,3,2,4,5]=>10000=>[1,4]
[5,4,2,-3,1]=>[1,-3,2,4,5]=>01000=>[1,1,3]
[5,4,2,-3,-1]=>[-1,-3,2,4,5]=>11000=>[2,3]
[5,4,-2,3,1]=>[1,3,-2,4,5]=>00100=>[2,1,2]
[5,4,-2,3,-1]=>[-1,3,-2,4,5]=>10100=>[1,1,1,2]
[5,4,-2,-3,1]=>[1,-3,-2,4,5]=>01100=>[1,2,2]
[5,4,-2,-3,-1]=>[-1,-3,-2,4,5]=>11100=>[3,2]
[5,-4,2,3,1]=>[1,3,2,-4,5]=>00010=>[3,1,1]
[5,-4,2,3,-1]=>[-1,3,2,-4,5]=>10010=>[1,2,1,1]
[5,-4,2,-3,1]=>[1,-3,2,-4,5]=>01010=>[1,1,1,1,1]
[5,-4,2,-3,-1]=>[-1,-3,2,-4,5]=>11010=>[2,1,1,1]
[5,-4,-2,3,1]=>[1,3,-2,-4,5]=>00110=>[2,2,1]
[5,-4,-2,3,-1]=>[-1,3,-2,-4,5]=>10110=>[1,1,2,1]
[5,-4,-2,-3,1]=>[1,-3,-2,-4,5]=>01110=>[1,3,1]
[5,-4,-2,-3,-1]=>[-1,-3,-2,-4,5]=>11110=>[4,1]
[-5,4,2,3,1]=>[1,3,2,4,-5]=>00001=>[4,1]
[-5,4,2,3,-1]=>[-1,3,2,4,-5]=>10001=>[1,3,1]
[-5,4,2,-3,1]=>[1,-3,2,4,-5]=>01001=>[1,1,2,1]
[-5,4,2,-3,-1]=>[-1,-3,2,4,-5]=>11001=>[2,2,1]
[-5,4,-2,3,1]=>[1,3,-2,4,-5]=>00101=>[2,1,1,1]
[-5,4,-2,3,-1]=>[-1,3,-2,4,-5]=>10101=>[1,1,1,1,1]
[-5,4,-2,-3,1]=>[1,-3,-2,4,-5]=>01101=>[1,2,1,1]
[-5,4,-2,-3,-1]=>[-1,-3,-2,4,-5]=>11101=>[3,1,1]
[-5,-4,2,3,1]=>[1,3,2,-4,-5]=>00011=>[3,2]
[-5,-4,2,3,-1]=>[-1,3,2,-4,-5]=>10011=>[1,2,2]
[-5,-4,2,-3,1]=>[1,-3,2,-4,-5]=>01011=>[1,1,1,2]
[-5,-4,2,-3,-1]=>[-1,-3,2,-4,-5]=>11011=>[2,1,2]
[-5,-4,-2,3,1]=>[1,3,-2,-4,-5]=>00111=>[2,3]
[-5,-4,-2,3,-1]=>[-1,3,-2,-4,-5]=>10111=>[1,1,3]
[-5,-4,-2,-3,1]=>[1,-3,-2,-4,-5]=>01111=>[1,4]
[-5,-4,-2,-3,-1]=>[-1,-3,-2,-4,-5]=>11111=>[5]
[5,4,3,1,2]=>[2,1,3,4,5]=>00000=>[5]
[5,4,3,1,-2]=>[-2,1,3,4,5]=>10000=>[1,4]
[5,4,3,-1,2]=>[2,-1,3,4,5]=>01000=>[1,1,3]
[5,4,3,-1,-2]=>[-2,-1,3,4,5]=>11000=>[2,3]
[5,4,-3,1,2]=>[2,1,-3,4,5]=>00100=>[2,1,2]
[5,4,-3,1,-2]=>[-2,1,-3,4,5]=>10100=>[1,1,1,2]
[5,4,-3,-1,2]=>[2,-1,-3,4,5]=>01100=>[1,2,2]
[5,4,-3,-1,-2]=>[-2,-1,-3,4,5]=>11100=>[3,2]
[5,-4,3,1,2]=>[2,1,3,-4,5]=>00010=>[3,1,1]
[5,-4,3,1,-2]=>[-2,1,3,-4,5]=>10010=>[1,2,1,1]
[5,-4,3,-1,2]=>[2,-1,3,-4,5]=>01010=>[1,1,1,1,1]
[5,-4,3,-1,-2]=>[-2,-1,3,-4,5]=>11010=>[2,1,1,1]
[5,-4,-3,1,2]=>[2,1,-3,-4,5]=>00110=>[2,2,1]
[5,-4,-3,1,-2]=>[-2,1,-3,-4,5]=>10110=>[1,1,2,1]
[5,-4,-3,-1,2]=>[2,-1,-3,-4,5]=>01110=>[1,3,1]
[5,-4,-3,-1,-2]=>[-2,-1,-3,-4,5]=>11110=>[4,1]
[-5,4,3,1,2]=>[2,1,3,4,-5]=>00001=>[4,1]
[-5,4,3,1,-2]=>[-2,1,3,4,-5]=>10001=>[1,3,1]
[-5,4,3,-1,2]=>[2,-1,3,4,-5]=>01001=>[1,1,2,1]
[-5,4,3,-1,-2]=>[-2,-1,3,4,-5]=>11001=>[2,2,1]
[-5,4,-3,1,2]=>[2,1,-3,4,-5]=>00101=>[2,1,1,1]
[-5,4,-3,1,-2]=>[-2,1,-3,4,-5]=>10101=>[1,1,1,1,1]
[-5,4,-3,-1,2]=>[2,-1,-3,4,-5]=>01101=>[1,2,1,1]
[-5,4,-3,-1,-2]=>[-2,-1,-3,4,-5]=>11101=>[3,1,1]
[-5,-4,3,1,2]=>[2,1,3,-4,-5]=>00011=>[3,2]
[-5,-4,3,1,-2]=>[-2,1,3,-4,-5]=>10011=>[1,2,2]
[-5,-4,3,-1,2]=>[2,-1,3,-4,-5]=>01011=>[1,1,1,2]
[-5,-4,3,-1,-2]=>[-2,-1,3,-4,-5]=>11011=>[2,1,2]
[-5,-4,-3,1,2]=>[2,1,-3,-4,-5]=>00111=>[2,3]
[-5,-4,-3,1,-2]=>[-2,1,-3,-4,-5]=>10111=>[1,1,3]
[-5,-4,-3,-1,2]=>[2,-1,-3,-4,-5]=>01111=>[1,4]
[-5,-4,-3,-1,-2]=>[-2,-1,-3,-4,-5]=>11111=>[5]
[5,4,3,2,1]=>[1,2,3,4,5]=>00000=>[5]
[5,4,3,2,-1]=>[-1,2,3,4,5]=>10000=>[1,4]
[5,4,3,-2,1]=>[1,-2,3,4,5]=>01000=>[1,1,3]
[5,4,3,-2,-1]=>[-1,-2,3,4,5]=>11000=>[2,3]
[5,4,-3,2,1]=>[1,2,-3,4,5]=>00100=>[2,1,2]
[5,4,-3,2,-1]=>[-1,2,-3,4,5]=>10100=>[1,1,1,2]
[5,4,-3,-2,1]=>[1,-2,-3,4,5]=>01100=>[1,2,2]
[5,4,-3,-2,-1]=>[-1,-2,-3,4,5]=>11100=>[3,2]
[5,-4,3,2,1]=>[1,2,3,-4,5]=>00010=>[3,1,1]
[5,-4,3,2,-1]=>[-1,2,3,-4,5]=>10010=>[1,2,1,1]
[5,-4,3,-2,1]=>[1,-2,3,-4,5]=>01010=>[1,1,1,1,1]
[5,-4,3,-2,-1]=>[-1,-2,3,-4,5]=>11010=>[2,1,1,1]
[5,-4,-3,2,1]=>[1,2,-3,-4,5]=>00110=>[2,2,1]
[5,-4,-3,2,-1]=>[-1,2,-3,-4,5]=>10110=>[1,1,2,1]
[5,-4,-3,-2,1]=>[1,-2,-3,-4,5]=>01110=>[1,3,1]
[5,-4,-3,-2,-1]=>[-1,-2,-3,-4,5]=>11110=>[4,1]
[-5,4,3,2,1]=>[1,2,3,4,-5]=>00001=>[4,1]
[-5,4,3,2,-1]=>[-1,2,3,4,-5]=>10001=>[1,3,1]
[-5,4,3,-2,1]=>[1,-2,3,4,-5]=>01001=>[1,1,2,1]
[-5,4,3,-2,-1]=>[-1,-2,3,4,-5]=>11001=>[2,2,1]
[-5,4,-3,2,1]=>[1,2,-3,4,-5]=>00101=>[2,1,1,1]
[-5,4,-3,2,-1]=>[-1,2,-3,4,-5]=>10101=>[1,1,1,1,1]
[-5,4,-3,-2,1]=>[1,-2,-3,4,-5]=>01101=>[1,2,1,1]
[-5,4,-3,-2,-1]=>[-1,-2,-3,4,-5]=>11101=>[3,1,1]
[-5,-4,3,2,1]=>[1,2,3,-4,-5]=>00011=>[3,2]
[-5,-4,3,2,-1]=>[-1,2,3,-4,-5]=>10011=>[1,2,2]
[-5,-4,3,-2,1]=>[1,-2,3,-4,-5]=>01011=>[1,1,1,2]
[-5,-4,3,-2,-1]=>[-1,-2,3,-4,-5]=>11011=>[2,1,2]
[-5,-4,-3,2,1]=>[1,2,-3,-4,-5]=>00111=>[2,3]
[-5,-4,-3,2,-1]=>[-1,2,-3,-4,-5]=>10111=>[1,1,3]
[-5,-4,-3,-2,1]=>[1,-2,-3,-4,-5]=>01111=>[1,4]
[-5,-4,-3,-2,-1]=>[-1,-2,-3,-4,-5]=>11111=>[5]
[6,2,3,4,5,-1]=>[-1,5,4,3,2,6]=>100000=>[1,5]
[5,2,3,4,6,-1]=>[-1,6,4,3,2,5]=>100000=>[1,5]
[4,2,3,6,5,-1]=>[-1,5,6,3,2,4]=>100000=>[1,5]
[4,2,3,5,6,-1]=>[-1,6,5,3,2,4]=>100000=>[1,5]
[3,2,6,4,5,-1]=>[-1,5,4,6,2,3]=>100000=>[1,5]
[3,2,5,4,6,-1]=>[-1,6,4,5,2,3]=>100000=>[1,5]
[3,2,4,6,5,-1]=>[-1,5,6,4,2,3]=>100000=>[1,5]
[3,2,4,5,6,-1]=>[-1,6,5,4,2,3]=>100000=>[1,5]
[2,6,3,4,5,-1]=>[-1,5,4,3,6,2]=>100000=>[1,5]
[2,5,3,4,6,-1]=>[-1,6,4,3,5,2]=>100000=>[1,5]
[2,4,3,6,5,-1]=>[-1,5,6,3,4,2]=>100000=>[1,5]
[2,4,3,5,6,-1]=>[-1,6,5,3,4,2]=>100000=>[1,5]
[5,6,2,3,4,-1]=>[-1,4,3,2,6,5]=>100000=>[1,5]
[4,5,2,3,6,-1]=>[-1,6,3,2,5,4]=>100000=>[1,5]
[3,4,2,5,6,-1]=>[-1,6,5,2,4,3]=>100000=>[1,5]
[2,3,6,4,5,-1]=>[-1,5,4,6,3,2]=>100000=>[1,5]
[2,3,5,4,6,-1]=>[-1,6,4,5,3,2]=>100000=>[1,5]
[2,5,6,3,4,-1]=>[-1,4,3,6,5,2]=>100000=>[1,5]
[2,4,5,3,6,-1]=>[-1,6,3,5,4,2]=>100000=>[1,5]
[4,5,6,2,3,-1]=>[-1,3,2,6,5,4]=>100000=>[1,5]
[3,4,5,2,6,-1]=>[-1,6,2,5,4,3]=>100000=>[1,5]
[2,3,4,6,5,-1]=>[-1,5,6,4,3,2]=>100000=>[1,5]
[2,4,5,6,3,-1]=>[-1,3,6,5,4,2]=>100000=>[1,5]
[3,4,5,6,2,-1]=>[-1,2,6,5,4,3]=>100000=>[1,5]
[2,3,4,5,6,-1]=>[-1,6,5,4,3,2]=>100000=>[1,5]
[2,3,4,5,-1,6]=>[6,-1,5,4,3,2]=>010000=>[1,1,4]
[2,3,4,-1,5,6]=>[6,5,-1,4,3,2]=>001000=>[2,1,3]
[2,3,-1,4,5,6]=>[6,5,4,-1,3,2]=>000100=>[3,1,2]
[2,3,6,5,4,-1]=>[-1,4,5,6,3,2]=>100000=>[1,5]
[2,-1,3,4,5,6]=>[6,5,4,3,-1,2]=>000010=>[4,1,1]
[2,6,3,5,4,-1]=>[-1,4,5,3,6,2]=>100000=>[1,5]
[2,5,4,3,6,-1]=>[-1,6,3,4,5,2]=>100000=>[1,5]
[2,6,4,3,5,-1]=>[-1,5,3,4,6,2]=>100000=>[1,5]
[2,6,5,3,4,-1]=>[-1,4,3,5,6,2]=>100000=>[1,5]
[2,6,5,4,3,-1]=>[-1,3,4,5,6,2]=>100000=>[1,5]
[3,2,4,5,-1,6]=>[6,-1,5,4,2,3]=>010000=>[1,1,4]
[3,2,6,5,4,-1]=>[-1,4,5,6,2,3]=>100000=>[1,5]
[6,2,3,5,4,-1]=>[-1,4,5,3,2,6]=>100000=>[1,5]
[5,2,4,3,6,-1]=>[-1,6,3,4,2,5]=>100000=>[1,5]
[6,2,4,3,5,-1]=>[-1,5,3,4,2,6]=>100000=>[1,5]
[6,2,5,3,4,-1]=>[-1,4,3,5,2,6]=>100000=>[1,5]
[6,2,5,4,3,-1]=>[-1,3,4,5,2,6]=>100000=>[1,5]
[4,3,2,5,6,-1]=>[-1,6,5,2,3,4]=>100000=>[1,5]
[4,3,2,6,5,-1]=>[-1,5,6,2,3,4]=>100000=>[1,5]
[5,3,2,4,6,-1]=>[-1,6,4,2,3,5]=>100000=>[1,5]
[6,3,2,4,5,-1]=>[-1,5,4,2,3,6]=>100000=>[1,5]
[6,3,2,5,4,-1]=>[-1,4,5,2,3,6]=>100000=>[1,5]
[5,4,2,3,6,-1]=>[-1,6,3,2,4,5]=>100000=>[1,5]
[6,4,2,3,5,-1]=>[-1,5,3,2,4,6]=>100000=>[1,5]
[6,5,2,3,4,-1]=>[-1,4,3,2,5,6]=>100000=>[1,5]
[6,5,2,4,3,-1]=>[-1,3,4,2,5,6]=>100000=>[1,5]
[5,4,3,2,6,-1]=>[-1,6,2,3,4,5]=>100000=>[1,5]
[6,4,3,2,5,-1]=>[-1,5,2,3,4,6]=>100000=>[1,5]
[6,5,3,2,4,-1]=>[-1,4,2,3,5,6]=>100000=>[1,5]
[6,5,4,2,3,-1]=>[-1,3,2,4,5,6]=>100000=>[1,5]
[6,5,4,3,2,-1]=>[-1,2,3,4,5,6]=>100000=>[1,5]
[3,4,5,6,-1,2]=>[2,-1,6,5,4,3]=>010000=>[1,1,4]
[4,5,6,-1,2,3]=>[3,2,-1,6,5,4]=>001000=>[2,1,3]
[2,-6,-5,-4,-3,1]=>[1,-3,-4,-5,-6,2]=>011110=>[1,4,1]
[5,4,3,2,1,-6]=>[-6,1,2,3,4,5]=>100000=>[1,5]
[5,4,3,1,2,-6]=>[-6,2,1,3,4,5]=>100000=>[1,5]
[5,4,1,3,2,-6]=>[-6,2,3,1,4,5]=>100000=>[1,5]
[5,4,2,1,3,-6]=>[-6,3,1,2,4,5]=>100000=>[1,5]
[5,2,1,4,3,-6]=>[-6,3,4,1,2,5]=>100000=>[1,5]
[5,3,2,1,4,-6]=>[-6,4,1,2,3,5]=>100000=>[1,5]
[4,2,1,3,5,-6]=>[-6,5,3,1,2,4]=>100000=>[1,5]
[2,1,4,3,5,-6]=>[-6,5,3,4,1,2]=>100000=>[1,5]
[3,2,1,6,5,-4]=>[-4,5,6,1,2,3]=>100000=>[1,5]
[4,3,2,1,6,-5]=>[-5,6,1,2,3,4]=>100000=>[1,5]
[4,3,1,2,6,-5]=>[-5,6,2,1,3,4]=>100000=>[1,5]
[1,-3,-4,-5,-6,2]=>[2,-6,-5,-4,-3,1]=>011110=>[1,4,1]
[3,2,5,4,1,-6]=>[-6,1,4,5,2,3]=>100000=>[1,5]
[6,4,3,1,2,-5]=>[-5,2,1,3,4,6]=>100000=>[1,5]
[5,3,2,4,1,-6]=>[-6,1,4,2,3,5]=>100000=>[1,5]
[4,3,5,2,1,-6]=>[-6,1,2,5,3,4]=>100000=>[1,5]
[4,3,2,5,1,-6]=>[-6,1,5,2,3,4]=>100000=>[1,5]
[3,2,4,1,5,-6]=>[-6,5,1,4,2,3]=>100000=>[1,5]
[6,4,3,2,1,-5]=>[-5,1,2,3,4,6]=>100000=>[1,5]
[6,4,2,1,3,-5]=>[-5,3,1,2,4,6]=>100000=>[1,5]
[5,3,6,2,1,-4]=>[-4,1,2,6,3,5]=>100000=>[1,5]
[5,3,2,1,6,-4]=>[-4,6,1,2,3,5]=>100000=>[1,5]
[6,5,3,4,2,-1]=>[-1,2,4,3,5,6]=>100000=>[1,5]
[6,4,5,3,2,-1]=>[-1,2,3,5,4,6]=>100000=>[1,5]
[6,4,5,2,3,-1]=>[-1,3,2,5,4,6]=>100000=>[1,5]
[6,4,3,5,2,-1]=>[-1,2,5,3,4,6]=>100000=>[1,5]
[6,3,4,5,2,-1]=>[-1,2,5,4,3,6]=>100000=>[1,5]
[6,3,4,2,5,-1]=>[-1,5,2,4,3,6]=>100000=>[1,5]
[5,6,4,3,2,-1]=>[-1,2,3,4,6,5]=>100000=>[1,5]
[5,6,4,2,3,-1]=>[-1,3,2,4,6,5]=>100000=>[1,5]
[5,6,3,4,2,-1]=>[-1,2,4,3,6,5]=>100000=>[1,5]
[5,6,3,2,4,-1]=>[-1,4,2,3,6,5]=>100000=>[1,5]
[5,4,6,3,2,-1]=>[-1,2,3,6,4,5]=>100000=>[1,5]
[5,4,6,2,3,-1]=>[-1,3,2,6,4,5]=>100000=>[1,5]
[5,4,3,6,2,-1]=>[-1,2,6,3,4,5]=>100000=>[1,5]
[5,3,4,6,2,-1]=>[-1,2,6,4,3,5]=>100000=>[1,5]
[5,3,4,2,6,-1]=>[-1,6,2,4,3,5]=>100000=>[1,5]
[4,5,6,3,2,-1]=>[-1,2,3,6,5,4]=>100000=>[1,5]
[4,5,3,6,2,-1]=>[-1,2,6,3,5,4]=>100000=>[1,5]
[4,5,3,2,6,-1]=>[-1,6,2,3,5,4]=>100000=>[1,5]
[4,3,5,6,-1,2]=>[2,-1,6,5,3,4]=>010000=>[1,1,4]
[4,3,5,6,2,-1]=>[-1,2,6,5,3,4]=>100000=>[1,5]
[4,3,5,2,6,-1]=>[-1,6,2,5,3,4]=>100000=>[1,5]
[2,6,4,5,3,-1]=>[-1,3,5,4,6,2]=>100000=>[1,5]
[6,2,4,5,3,-1]=>[-1,3,5,4,2,6]=>100000=>[1,5]
[6,3,5,4,2,-1]=>[-1,2,4,5,3,6]=>100000=>[1,5]
[2,1,5,3,6,-4]=>[-4,6,3,5,1,2]=>100000=>[1,5]
[5,2,1,6,3,-4]=>[-4,3,6,1,2,5]=>100000=>[1,5]
[5,2,6,1,3,-4]=>[-4,3,1,6,2,5]=>100000=>[1,5]
[6,3,1,4,2,-5]=>[-5,2,4,1,3,6]=>100000=>[1,5]
[5,1,-4,6,2,-3]=>[-3,2,6,-4,1,5]=>100100=>[1,2,1,2]
[6,1,-5,-4,-3,-2]=>[-2,-3,-4,-5,1,6]=>111100=>[4,2]
[6,3,1,-2,-5,-4]=>[-4,-5,-2,1,3,6]=>111000=>[3,3]
[1,-6,3,2,5,4]=>[4,5,2,3,-6,1]=>000010=>[4,1,1]
[1,-6,4,3,5,2]=>[2,5,3,4,-6,1]=>000010=>[4,1,1]
[1,-6,5,4,3,2]=>[2,3,4,5,-6,1]=>000010=>[4,1,1]
[2,1,-6,5,4,3]=>[3,4,5,-6,1,2]=>000100=>[3,1,2]
[2,1,3,-6,5,4]=>[4,5,-6,3,1,2]=>001000=>[2,1,3]
[3,2,1,-6,5,4]=>[4,5,-6,1,2,3]=>001000=>[2,1,3]
[4,3,2,1,-6,5]=>[5,-6,1,2,3,4]=>010000=>[1,1,4]
[4,6,5,3,2,-1]=>[-1,2,3,5,6,4]=>100000=>[1,5]
[3,6,5,4,2,-1]=>[-1,2,4,5,6,3]=>100000=>[1,5]
[3,5,6,4,2,-1]=>[-1,2,4,6,5,3]=>100000=>[1,5]
[3,5,4,6,2,-1]=>[-1,2,6,4,5,3]=>100000=>[1,5]
[2,5,6,4,3,-1]=>[-1,3,4,6,5,2]=>100000=>[1,5]
[2,5,4,6,3,-1]=>[-1,3,6,4,5,2]=>100000=>[1,5]
[3,1,-4,-5,-6,2]=>[2,-6,-5,-4,1,3]=>011100=>[1,3,2]
[6,5,4,3,1,-2]=>[-2,1,3,4,5,6]=>100000=>[1,5]
[4,2,1,6,3,-5]=>[-5,3,6,1,2,4]=>100000=>[1,5]
[6,5,4,2,1,-3]=>[-3,1,2,4,5,6]=>100000=>[1,5]
[6,3,2,1,5,-4]=>[-4,5,1,2,3,6]=>100000=>[1,5]
[6,5,3,2,1,-4]=>[-4,1,2,3,5,6]=>100000=>[1,5]
[5,4,3,-6,2,1]=>[1,2,-6,3,4,5]=>001000=>[2,1,3]
[3,1,6,5,4,-2]=>[-2,4,5,6,1,3]=>100000=>[1,5]
[5,4,3,1,6,-2]=>[-2,6,1,3,4,5]=>100000=>[1,5]
[4,3,6,5,1,-2]=>[-2,1,5,6,3,4]=>100000=>[1,5]
[5,4,6,3,1,-2]=>[-2,1,3,6,4,5]=>100000=>[1,5]
[3,2,6,5,1,-4]=>[-4,1,5,6,2,3]=>100000=>[1,5]
[6,5,2,1,3,-4]=>[-4,3,1,2,5,6]=>100000=>[1,5]
[6,2,1,5,3,-4]=>[-4,3,5,1,2,6]=>100000=>[1,5]
[4,2,1,5,3,-6]=>[-6,3,5,1,2,4]=>100000=>[1,5]
[6,3,2,5,1,-4]=>[-4,1,5,2,3,6]=>100000=>[1,5]
[2,1,6,5,3,-4]=>[-4,3,5,6,1,2]=>100000=>[1,5]
[5,1,6,-4,-3,-2]=>[-2,-3,-4,6,1,5]=>111000=>[3,3]
[5,3,6,-4,1,-2]=>[-2,1,-4,6,3,5]=>101000=>[1,1,1,3]
[6,4,3,5,1,-2]=>[-2,1,5,3,4,6]=>100000=>[1,5]
[4,3,1,-6,-5,2]=>[2,-5,-6,1,3,4]=>011000=>[1,2,3]
[3,1,-4,2,-6,5]=>[5,-6,2,-4,1,3]=>010100=>[1,1,1,1,2]
[1,-5,4,2,-6,3]=>[3,-6,2,4,-5,1]=>010010=>[1,1,2,1,1]
[5,1,-6,4,2,3]=>[3,2,4,-6,1,5]=>000100=>[3,1,2]
[1,-5,2,-4,-6,3]=>[3,-6,-4,2,-5,1]=>011010=>[1,2,1,1,1]
[1,-6,5,2,-4,3]=>[3,-4,2,5,-6,1]=>010010=>[1,1,2,1,1]
[2,1,5,4,-6,3]=>[3,-6,4,5,1,2]=>010000=>[1,1,4]
[6,1,-5,2,-4,3]=>[3,-4,2,-5,1,6]=>010100=>[1,1,1,1,2]
[3,2,-6,1,5,4]=>[4,5,1,-6,2,3]=>000100=>[3,1,2]
[6,3,1,-2,-5,4]=>[4,-5,-2,1,3,6]=>011000=>[1,2,3]
[6,4,1,-3,-5,2]=>[2,-5,-3,1,4,6]=>011000=>[1,2,3]
[5,3,1,-6,2,4]=>[4,2,-6,1,3,5]=>001000=>[2,1,3]
[2,3,4,5,6,7,8,-1]=>[-1,8,7,6,5,4,3,2]=>10000000=>[1,7]
[2,-6,5,4,1,3]=>[3,1,4,5,-6,2]=>000010=>[4,1,1]
[4,1,5,-3,2,6]=>[6,2,-3,5,1,4]=>001000=>[2,1,3]
[5,3,1,-4,2,6]=>[6,2,-4,1,3,5]=>001000=>[2,1,3]
[3,6,4,5,2,-1]=>[-1,2,5,4,6,3]=>100000=>[1,5]
[4,6,5,2,3,-1]=>[-1,3,2,5,6,4]=>100000=>[1,5]
[5,6,2,4,3,-1]=>[-1,3,4,2,6,5]=>100000=>[1,5]
[6,4,1,-3,-5,-2]=>[-2,-5,-3,1,4,6]=>111000=>[3,3]
[5,4,2,1,3,7,-6]=>[-6,7,3,1,2,4,5]=>1000000=>[1,6]
[4,3,2,1,6,7,-5]=>[-5,7,6,1,2,3,4]=>1000000=>[1,6]
[7,6,5,4,3,2,-1]=>[-1,2,3,4,5,6,7]=>1000000=>[1,6]
[3,1,-6,2,5,4]=>[4,5,2,-6,1,3]=>000100=>[3,1,2]
[4,1,3,-6,2,5]=>[5,2,-6,3,1,4]=>001000=>[2,1,3]
Map
reverse
Description
The reversal of a signed permutation.
Map
signs
Description
The binary word recording the signs of a signed permutation.
This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.
This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
searching the database
Sorry, this map was not found in the database.