Identifier
Mp00267:
Signed permutations
—signs⟶
Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
[1]=>0=>[1]=>[1]
[-1]=>1=>[1]=>[1]
[1,2]=>00=>[2]=>[2]
[1,-2]=>01=>[1,1]=>[1,1]
[-1,2]=>10=>[1,1]=>[1,1]
[-1,-2]=>11=>[2]=>[2]
[2,1]=>00=>[2]=>[2]
[2,-1]=>01=>[1,1]=>[1,1]
[-2,1]=>10=>[1,1]=>[1,1]
[-2,-1]=>11=>[2]=>[2]
[1,2,3]=>000=>[3]=>[3]
[1,2,-3]=>001=>[2,1]=>[1,2]
[1,-2,3]=>010=>[1,1,1]=>[1,1,1]
[1,-2,-3]=>011=>[1,2]=>[2,1]
[-1,2,3]=>100=>[1,2]=>[2,1]
[-1,2,-3]=>101=>[1,1,1]=>[1,1,1]
[-1,-2,3]=>110=>[2,1]=>[1,2]
[-1,-2,-3]=>111=>[3]=>[3]
[1,3,2]=>000=>[3]=>[3]
[1,3,-2]=>001=>[2,1]=>[1,2]
[1,-3,2]=>010=>[1,1,1]=>[1,1,1]
[1,-3,-2]=>011=>[1,2]=>[2,1]
[-1,3,2]=>100=>[1,2]=>[2,1]
[-1,3,-2]=>101=>[1,1,1]=>[1,1,1]
[-1,-3,2]=>110=>[2,1]=>[1,2]
[-1,-3,-2]=>111=>[3]=>[3]
[2,1,3]=>000=>[3]=>[3]
[2,1,-3]=>001=>[2,1]=>[1,2]
[2,-1,3]=>010=>[1,1,1]=>[1,1,1]
[2,-1,-3]=>011=>[1,2]=>[2,1]
[-2,1,3]=>100=>[1,2]=>[2,1]
[-2,1,-3]=>101=>[1,1,1]=>[1,1,1]
[-2,-1,3]=>110=>[2,1]=>[1,2]
[-2,-1,-3]=>111=>[3]=>[3]
[2,3,1]=>000=>[3]=>[3]
[2,3,-1]=>001=>[2,1]=>[1,2]
[2,-3,1]=>010=>[1,1,1]=>[1,1,1]
[2,-3,-1]=>011=>[1,2]=>[2,1]
[-2,3,1]=>100=>[1,2]=>[2,1]
[-2,3,-1]=>101=>[1,1,1]=>[1,1,1]
[-2,-3,1]=>110=>[2,1]=>[1,2]
[-2,-3,-1]=>111=>[3]=>[3]
[3,1,2]=>000=>[3]=>[3]
[3,1,-2]=>001=>[2,1]=>[1,2]
[3,-1,2]=>010=>[1,1,1]=>[1,1,1]
[3,-1,-2]=>011=>[1,2]=>[2,1]
[-3,1,2]=>100=>[1,2]=>[2,1]
[-3,1,-2]=>101=>[1,1,1]=>[1,1,1]
[-3,-1,2]=>110=>[2,1]=>[1,2]
[-3,-1,-2]=>111=>[3]=>[3]
[3,2,1]=>000=>[3]=>[3]
[3,2,-1]=>001=>[2,1]=>[1,2]
[3,-2,1]=>010=>[1,1,1]=>[1,1,1]
[3,-2,-1]=>011=>[1,2]=>[2,1]
[-3,2,1]=>100=>[1,2]=>[2,1]
[-3,2,-1]=>101=>[1,1,1]=>[1,1,1]
[-3,-2,1]=>110=>[2,1]=>[1,2]
[-3,-2,-1]=>111=>[3]=>[3]
[1,2,3,4]=>0000=>[4]=>[4]
[1,2,3,-4]=>0001=>[3,1]=>[1,3]
[1,2,-3,4]=>0010=>[2,1,1]=>[1,1,2]
[1,2,-3,-4]=>0011=>[2,2]=>[2,2]
[1,-2,3,4]=>0100=>[1,1,2]=>[2,1,1]
[1,-2,3,-4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,-2,-3,4]=>0110=>[1,2,1]=>[1,2,1]
[1,-2,-3,-4]=>0111=>[1,3]=>[3,1]
[-1,2,3,4]=>1000=>[1,3]=>[3,1]
[-1,2,3,-4]=>1001=>[1,2,1]=>[1,2,1]
[-1,2,-3,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-1,2,-3,-4]=>1011=>[1,1,2]=>[2,1,1]
[-1,-2,3,4]=>1100=>[2,2]=>[2,2]
[-1,-2,3,-4]=>1101=>[2,1,1]=>[1,1,2]
[-1,-2,-3,4]=>1110=>[3,1]=>[1,3]
[-1,-2,-3,-4]=>1111=>[4]=>[4]
[1,2,4,3]=>0000=>[4]=>[4]
[1,2,4,-3]=>0001=>[3,1]=>[1,3]
[1,2,-4,3]=>0010=>[2,1,1]=>[1,1,2]
[1,2,-4,-3]=>0011=>[2,2]=>[2,2]
[1,-2,4,3]=>0100=>[1,1,2]=>[2,1,1]
[1,-2,4,-3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,-2,-4,3]=>0110=>[1,2,1]=>[1,2,1]
[1,-2,-4,-3]=>0111=>[1,3]=>[3,1]
[-1,2,4,3]=>1000=>[1,3]=>[3,1]
[-1,2,4,-3]=>1001=>[1,2,1]=>[1,2,1]
[-1,2,-4,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-1,2,-4,-3]=>1011=>[1,1,2]=>[2,1,1]
[-1,-2,4,3]=>1100=>[2,2]=>[2,2]
[-1,-2,4,-3]=>1101=>[2,1,1]=>[1,1,2]
[-1,-2,-4,3]=>1110=>[3,1]=>[1,3]
[-1,-2,-4,-3]=>1111=>[4]=>[4]
[1,3,2,4]=>0000=>[4]=>[4]
[1,3,2,-4]=>0001=>[3,1]=>[1,3]
[1,3,-2,4]=>0010=>[2,1,1]=>[1,1,2]
[1,3,-2,-4]=>0011=>[2,2]=>[2,2]
[1,-3,2,4]=>0100=>[1,1,2]=>[2,1,1]
[1,-3,2,-4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,-3,-2,4]=>0110=>[1,2,1]=>[1,2,1]
[1,-3,-2,-4]=>0111=>[1,3]=>[3,1]
[-1,3,2,4]=>1000=>[1,3]=>[3,1]
[-1,3,2,-4]=>1001=>[1,2,1]=>[1,2,1]
[-1,3,-2,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-1,3,-2,-4]=>1011=>[1,1,2]=>[2,1,1]
[-1,-3,2,4]=>1100=>[2,2]=>[2,2]
[-1,-3,2,-4]=>1101=>[2,1,1]=>[1,1,2]
[-1,-3,-2,4]=>1110=>[3,1]=>[1,3]
[-1,-3,-2,-4]=>1111=>[4]=>[4]
[1,3,4,2]=>0000=>[4]=>[4]
[1,3,4,-2]=>0001=>[3,1]=>[1,3]
[1,3,-4,2]=>0010=>[2,1,1]=>[1,1,2]
[1,3,-4,-2]=>0011=>[2,2]=>[2,2]
[1,-3,4,2]=>0100=>[1,1,2]=>[2,1,1]
[1,-3,4,-2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,-3,-4,2]=>0110=>[1,2,1]=>[1,2,1]
[1,-3,-4,-2]=>0111=>[1,3]=>[3,1]
[-1,3,4,2]=>1000=>[1,3]=>[3,1]
[-1,3,4,-2]=>1001=>[1,2,1]=>[1,2,1]
[-1,3,-4,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-1,3,-4,-2]=>1011=>[1,1,2]=>[2,1,1]
[-1,-3,4,2]=>1100=>[2,2]=>[2,2]
[-1,-3,4,-2]=>1101=>[2,1,1]=>[1,1,2]
[-1,-3,-4,2]=>1110=>[3,1]=>[1,3]
[-1,-3,-4,-2]=>1111=>[4]=>[4]
[1,4,2,3]=>0000=>[4]=>[4]
[1,4,2,-3]=>0001=>[3,1]=>[1,3]
[1,4,-2,3]=>0010=>[2,1,1]=>[1,1,2]
[1,4,-2,-3]=>0011=>[2,2]=>[2,2]
[1,-4,2,3]=>0100=>[1,1,2]=>[2,1,1]
[1,-4,2,-3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,-4,-2,3]=>0110=>[1,2,1]=>[1,2,1]
[1,-4,-2,-3]=>0111=>[1,3]=>[3,1]
[-1,4,2,3]=>1000=>[1,3]=>[3,1]
[-1,4,2,-3]=>1001=>[1,2,1]=>[1,2,1]
[-1,4,-2,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-1,4,-2,-3]=>1011=>[1,1,2]=>[2,1,1]
[-1,-4,2,3]=>1100=>[2,2]=>[2,2]
[-1,-4,2,-3]=>1101=>[2,1,1]=>[1,1,2]
[-1,-4,-2,3]=>1110=>[3,1]=>[1,3]
[-1,-4,-2,-3]=>1111=>[4]=>[4]
[1,4,3,2]=>0000=>[4]=>[4]
[1,4,3,-2]=>0001=>[3,1]=>[1,3]
[1,4,-3,2]=>0010=>[2,1,1]=>[1,1,2]
[1,4,-3,-2]=>0011=>[2,2]=>[2,2]
[1,-4,3,2]=>0100=>[1,1,2]=>[2,1,1]
[1,-4,3,-2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,-4,-3,2]=>0110=>[1,2,1]=>[1,2,1]
[1,-4,-3,-2]=>0111=>[1,3]=>[3,1]
[-1,4,3,2]=>1000=>[1,3]=>[3,1]
[-1,4,3,-2]=>1001=>[1,2,1]=>[1,2,1]
[-1,4,-3,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-1,4,-3,-2]=>1011=>[1,1,2]=>[2,1,1]
[-1,-4,3,2]=>1100=>[2,2]=>[2,2]
[-1,-4,3,-2]=>1101=>[2,1,1]=>[1,1,2]
[-1,-4,-3,2]=>1110=>[3,1]=>[1,3]
[-1,-4,-3,-2]=>1111=>[4]=>[4]
[2,1,3,4]=>0000=>[4]=>[4]
[2,1,3,-4]=>0001=>[3,1]=>[1,3]
[2,1,-3,4]=>0010=>[2,1,1]=>[1,1,2]
[2,1,-3,-4]=>0011=>[2,2]=>[2,2]
[2,-1,3,4]=>0100=>[1,1,2]=>[2,1,1]
[2,-1,3,-4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,-1,-3,4]=>0110=>[1,2,1]=>[1,2,1]
[2,-1,-3,-4]=>0111=>[1,3]=>[3,1]
[-2,1,3,4]=>1000=>[1,3]=>[3,1]
[-2,1,3,-4]=>1001=>[1,2,1]=>[1,2,1]
[-2,1,-3,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-2,1,-3,-4]=>1011=>[1,1,2]=>[2,1,1]
[-2,-1,3,4]=>1100=>[2,2]=>[2,2]
[-2,-1,3,-4]=>1101=>[2,1,1]=>[1,1,2]
[-2,-1,-3,4]=>1110=>[3,1]=>[1,3]
[-2,-1,-3,-4]=>1111=>[4]=>[4]
[2,1,4,3]=>0000=>[4]=>[4]
[2,1,4,-3]=>0001=>[3,1]=>[1,3]
[2,1,-4,3]=>0010=>[2,1,1]=>[1,1,2]
[2,1,-4,-3]=>0011=>[2,2]=>[2,2]
[2,-1,4,3]=>0100=>[1,1,2]=>[2,1,1]
[2,-1,4,-3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,-1,-4,3]=>0110=>[1,2,1]=>[1,2,1]
[2,-1,-4,-3]=>0111=>[1,3]=>[3,1]
[-2,1,4,3]=>1000=>[1,3]=>[3,1]
[-2,1,4,-3]=>1001=>[1,2,1]=>[1,2,1]
[-2,1,-4,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-2,1,-4,-3]=>1011=>[1,1,2]=>[2,1,1]
[-2,-1,4,3]=>1100=>[2,2]=>[2,2]
[-2,-1,4,-3]=>1101=>[2,1,1]=>[1,1,2]
[-2,-1,-4,3]=>1110=>[3,1]=>[1,3]
[-2,-1,-4,-3]=>1111=>[4]=>[4]
[2,3,1,4]=>0000=>[4]=>[4]
[2,3,1,-4]=>0001=>[3,1]=>[1,3]
[2,3,-1,4]=>0010=>[2,1,1]=>[1,1,2]
[2,3,-1,-4]=>0011=>[2,2]=>[2,2]
[2,-3,1,4]=>0100=>[1,1,2]=>[2,1,1]
[2,-3,1,-4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,-3,-1,4]=>0110=>[1,2,1]=>[1,2,1]
[2,-3,-1,-4]=>0111=>[1,3]=>[3,1]
[-2,3,1,4]=>1000=>[1,3]=>[3,1]
[-2,3,1,-4]=>1001=>[1,2,1]=>[1,2,1]
[-2,3,-1,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-2,3,-1,-4]=>1011=>[1,1,2]=>[2,1,1]
[-2,-3,1,4]=>1100=>[2,2]=>[2,2]
[-2,-3,1,-4]=>1101=>[2,1,1]=>[1,1,2]
[-2,-3,-1,4]=>1110=>[3,1]=>[1,3]
[-2,-3,-1,-4]=>1111=>[4]=>[4]
[2,3,4,1]=>0000=>[4]=>[4]
[2,3,4,-1]=>0001=>[3,1]=>[1,3]
[2,3,-4,1]=>0010=>[2,1,1]=>[1,1,2]
[2,3,-4,-1]=>0011=>[2,2]=>[2,2]
[2,-3,4,1]=>0100=>[1,1,2]=>[2,1,1]
[2,-3,4,-1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,-3,-4,1]=>0110=>[1,2,1]=>[1,2,1]
[2,-3,-4,-1]=>0111=>[1,3]=>[3,1]
[-2,3,4,1]=>1000=>[1,3]=>[3,1]
[-2,3,4,-1]=>1001=>[1,2,1]=>[1,2,1]
[-2,3,-4,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-2,3,-4,-1]=>1011=>[1,1,2]=>[2,1,1]
[-2,-3,4,1]=>1100=>[2,2]=>[2,2]
[-2,-3,4,-1]=>1101=>[2,1,1]=>[1,1,2]
[-2,-3,-4,1]=>1110=>[3,1]=>[1,3]
[-2,-3,-4,-1]=>1111=>[4]=>[4]
[2,4,1,3]=>0000=>[4]=>[4]
[2,4,1,-3]=>0001=>[3,1]=>[1,3]
[2,4,-1,3]=>0010=>[2,1,1]=>[1,1,2]
[2,4,-1,-3]=>0011=>[2,2]=>[2,2]
[2,-4,1,3]=>0100=>[1,1,2]=>[2,1,1]
[2,-4,1,-3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,-4,-1,3]=>0110=>[1,2,1]=>[1,2,1]
[2,-4,-1,-3]=>0111=>[1,3]=>[3,1]
[-2,4,1,3]=>1000=>[1,3]=>[3,1]
[-2,4,1,-3]=>1001=>[1,2,1]=>[1,2,1]
[-2,4,-1,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-2,4,-1,-3]=>1011=>[1,1,2]=>[2,1,1]
[-2,-4,1,3]=>1100=>[2,2]=>[2,2]
[-2,-4,1,-3]=>1101=>[2,1,1]=>[1,1,2]
[-2,-4,-1,3]=>1110=>[3,1]=>[1,3]
[-2,-4,-1,-3]=>1111=>[4]=>[4]
[2,4,3,1]=>0000=>[4]=>[4]
[2,4,3,-1]=>0001=>[3,1]=>[1,3]
[2,4,-3,1]=>0010=>[2,1,1]=>[1,1,2]
[2,4,-3,-1]=>0011=>[2,2]=>[2,2]
[2,-4,3,1]=>0100=>[1,1,2]=>[2,1,1]
[2,-4,3,-1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,-4,-3,1]=>0110=>[1,2,1]=>[1,2,1]
[2,-4,-3,-1]=>0111=>[1,3]=>[3,1]
[-2,4,3,1]=>1000=>[1,3]=>[3,1]
[-2,4,3,-1]=>1001=>[1,2,1]=>[1,2,1]
[-2,4,-3,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-2,4,-3,-1]=>1011=>[1,1,2]=>[2,1,1]
[-2,-4,3,1]=>1100=>[2,2]=>[2,2]
[-2,-4,3,-1]=>1101=>[2,1,1]=>[1,1,2]
[-2,-4,-3,1]=>1110=>[3,1]=>[1,3]
[-2,-4,-3,-1]=>1111=>[4]=>[4]
[3,1,2,4]=>0000=>[4]=>[4]
[3,1,2,-4]=>0001=>[3,1]=>[1,3]
[3,1,-2,4]=>0010=>[2,1,1]=>[1,1,2]
[3,1,-2,-4]=>0011=>[2,2]=>[2,2]
[3,-1,2,4]=>0100=>[1,1,2]=>[2,1,1]
[3,-1,2,-4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,-1,-2,4]=>0110=>[1,2,1]=>[1,2,1]
[3,-1,-2,-4]=>0111=>[1,3]=>[3,1]
[-3,1,2,4]=>1000=>[1,3]=>[3,1]
[-3,1,2,-4]=>1001=>[1,2,1]=>[1,2,1]
[-3,1,-2,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-3,1,-2,-4]=>1011=>[1,1,2]=>[2,1,1]
[-3,-1,2,4]=>1100=>[2,2]=>[2,2]
[-3,-1,2,-4]=>1101=>[2,1,1]=>[1,1,2]
[-3,-1,-2,4]=>1110=>[3,1]=>[1,3]
[-3,-1,-2,-4]=>1111=>[4]=>[4]
[3,1,4,2]=>0000=>[4]=>[4]
[3,1,4,-2]=>0001=>[3,1]=>[1,3]
[3,1,-4,2]=>0010=>[2,1,1]=>[1,1,2]
[3,1,-4,-2]=>0011=>[2,2]=>[2,2]
[3,-1,4,2]=>0100=>[1,1,2]=>[2,1,1]
[3,-1,4,-2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,-1,-4,2]=>0110=>[1,2,1]=>[1,2,1]
[3,-1,-4,-2]=>0111=>[1,3]=>[3,1]
[-3,1,4,2]=>1000=>[1,3]=>[3,1]
[-3,1,4,-2]=>1001=>[1,2,1]=>[1,2,1]
[-3,1,-4,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-3,1,-4,-2]=>1011=>[1,1,2]=>[2,1,1]
[-3,-1,4,2]=>1100=>[2,2]=>[2,2]
[-3,-1,4,-2]=>1101=>[2,1,1]=>[1,1,2]
[-3,-1,-4,2]=>1110=>[3,1]=>[1,3]
[-3,-1,-4,-2]=>1111=>[4]=>[4]
[3,2,1,4]=>0000=>[4]=>[4]
[3,2,1,-4]=>0001=>[3,1]=>[1,3]
[3,2,-1,4]=>0010=>[2,1,1]=>[1,1,2]
[3,2,-1,-4]=>0011=>[2,2]=>[2,2]
[3,-2,1,4]=>0100=>[1,1,2]=>[2,1,1]
[3,-2,1,-4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,-2,-1,4]=>0110=>[1,2,1]=>[1,2,1]
[3,-2,-1,-4]=>0111=>[1,3]=>[3,1]
[-3,2,1,4]=>1000=>[1,3]=>[3,1]
[-3,2,1,-4]=>1001=>[1,2,1]=>[1,2,1]
[-3,2,-1,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-3,2,-1,-4]=>1011=>[1,1,2]=>[2,1,1]
[-3,-2,1,4]=>1100=>[2,2]=>[2,2]
[-3,-2,1,-4]=>1101=>[2,1,1]=>[1,1,2]
[-3,-2,-1,4]=>1110=>[3,1]=>[1,3]
[-3,-2,-1,-4]=>1111=>[4]=>[4]
[3,2,4,1]=>0000=>[4]=>[4]
[3,2,4,-1]=>0001=>[3,1]=>[1,3]
[3,2,-4,1]=>0010=>[2,1,1]=>[1,1,2]
[3,2,-4,-1]=>0011=>[2,2]=>[2,2]
[3,-2,4,1]=>0100=>[1,1,2]=>[2,1,1]
[3,-2,4,-1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,-2,-4,1]=>0110=>[1,2,1]=>[1,2,1]
[3,-2,-4,-1]=>0111=>[1,3]=>[3,1]
[-3,2,4,1]=>1000=>[1,3]=>[3,1]
[-3,2,4,-1]=>1001=>[1,2,1]=>[1,2,1]
[-3,2,-4,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-3,2,-4,-1]=>1011=>[1,1,2]=>[2,1,1]
[-3,-2,4,1]=>1100=>[2,2]=>[2,2]
[-3,-2,4,-1]=>1101=>[2,1,1]=>[1,1,2]
[-3,-2,-4,1]=>1110=>[3,1]=>[1,3]
[-3,-2,-4,-1]=>1111=>[4]=>[4]
[3,4,1,2]=>0000=>[4]=>[4]
[3,4,1,-2]=>0001=>[3,1]=>[1,3]
[3,4,-1,2]=>0010=>[2,1,1]=>[1,1,2]
[3,4,-1,-2]=>0011=>[2,2]=>[2,2]
[3,-4,1,2]=>0100=>[1,1,2]=>[2,1,1]
[3,-4,1,-2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,-4,-1,2]=>0110=>[1,2,1]=>[1,2,1]
[3,-4,-1,-2]=>0111=>[1,3]=>[3,1]
[-3,4,1,2]=>1000=>[1,3]=>[3,1]
[-3,4,1,-2]=>1001=>[1,2,1]=>[1,2,1]
[-3,4,-1,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-3,4,-1,-2]=>1011=>[1,1,2]=>[2,1,1]
[-3,-4,1,2]=>1100=>[2,2]=>[2,2]
[-3,-4,1,-2]=>1101=>[2,1,1]=>[1,1,2]
[-3,-4,-1,2]=>1110=>[3,1]=>[1,3]
[-3,-4,-1,-2]=>1111=>[4]=>[4]
[3,4,2,1]=>0000=>[4]=>[4]
[3,4,2,-1]=>0001=>[3,1]=>[1,3]
[3,4,-2,1]=>0010=>[2,1,1]=>[1,1,2]
[3,4,-2,-1]=>0011=>[2,2]=>[2,2]
[3,-4,2,1]=>0100=>[1,1,2]=>[2,1,1]
[3,-4,2,-1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,-4,-2,1]=>0110=>[1,2,1]=>[1,2,1]
[3,-4,-2,-1]=>0111=>[1,3]=>[3,1]
[-3,4,2,1]=>1000=>[1,3]=>[3,1]
[-3,4,2,-1]=>1001=>[1,2,1]=>[1,2,1]
[-3,4,-2,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-3,4,-2,-1]=>1011=>[1,1,2]=>[2,1,1]
[-3,-4,2,1]=>1100=>[2,2]=>[2,2]
[-3,-4,2,-1]=>1101=>[2,1,1]=>[1,1,2]
[-3,-4,-2,1]=>1110=>[3,1]=>[1,3]
[-3,-4,-2,-1]=>1111=>[4]=>[4]
[4,1,2,3]=>0000=>[4]=>[4]
[4,1,2,-3]=>0001=>[3,1]=>[1,3]
[4,1,-2,3]=>0010=>[2,1,1]=>[1,1,2]
[4,1,-2,-3]=>0011=>[2,2]=>[2,2]
[4,-1,2,3]=>0100=>[1,1,2]=>[2,1,1]
[4,-1,2,-3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,-1,-2,3]=>0110=>[1,2,1]=>[1,2,1]
[4,-1,-2,-3]=>0111=>[1,3]=>[3,1]
[-4,1,2,3]=>1000=>[1,3]=>[3,1]
[-4,1,2,-3]=>1001=>[1,2,1]=>[1,2,1]
[-4,1,-2,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-4,1,-2,-3]=>1011=>[1,1,2]=>[2,1,1]
[-4,-1,2,3]=>1100=>[2,2]=>[2,2]
[-4,-1,2,-3]=>1101=>[2,1,1]=>[1,1,2]
[-4,-1,-2,3]=>1110=>[3,1]=>[1,3]
[-4,-1,-2,-3]=>1111=>[4]=>[4]
[4,1,3,2]=>0000=>[4]=>[4]
[4,1,3,-2]=>0001=>[3,1]=>[1,3]
[4,1,-3,2]=>0010=>[2,1,1]=>[1,1,2]
[4,1,-3,-2]=>0011=>[2,2]=>[2,2]
[4,-1,3,2]=>0100=>[1,1,2]=>[2,1,1]
[4,-1,3,-2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,-1,-3,2]=>0110=>[1,2,1]=>[1,2,1]
[4,-1,-3,-2]=>0111=>[1,3]=>[3,1]
[-4,1,3,2]=>1000=>[1,3]=>[3,1]
[-4,1,3,-2]=>1001=>[1,2,1]=>[1,2,1]
[-4,1,-3,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-4,1,-3,-2]=>1011=>[1,1,2]=>[2,1,1]
[-4,-1,3,2]=>1100=>[2,2]=>[2,2]
[-4,-1,3,-2]=>1101=>[2,1,1]=>[1,1,2]
[-4,-1,-3,2]=>1110=>[3,1]=>[1,3]
[-4,-1,-3,-2]=>1111=>[4]=>[4]
[4,2,1,3]=>0000=>[4]=>[4]
[4,2,1,-3]=>0001=>[3,1]=>[1,3]
[4,2,-1,3]=>0010=>[2,1,1]=>[1,1,2]
[4,2,-1,-3]=>0011=>[2,2]=>[2,2]
[4,-2,1,3]=>0100=>[1,1,2]=>[2,1,1]
[4,-2,1,-3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,-2,-1,3]=>0110=>[1,2,1]=>[1,2,1]
[4,-2,-1,-3]=>0111=>[1,3]=>[3,1]
[-4,2,1,3]=>1000=>[1,3]=>[3,1]
[-4,2,1,-3]=>1001=>[1,2,1]=>[1,2,1]
[-4,2,-1,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-4,2,-1,-3]=>1011=>[1,1,2]=>[2,1,1]
[-4,-2,1,3]=>1100=>[2,2]=>[2,2]
[-4,-2,1,-3]=>1101=>[2,1,1]=>[1,1,2]
[-4,-2,-1,3]=>1110=>[3,1]=>[1,3]
[-4,-2,-1,-3]=>1111=>[4]=>[4]
[4,2,3,1]=>0000=>[4]=>[4]
[4,2,3,-1]=>0001=>[3,1]=>[1,3]
[4,2,-3,1]=>0010=>[2,1,1]=>[1,1,2]
[4,2,-3,-1]=>0011=>[2,2]=>[2,2]
[4,-2,3,1]=>0100=>[1,1,2]=>[2,1,1]
[4,-2,3,-1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,-2,-3,1]=>0110=>[1,2,1]=>[1,2,1]
[4,-2,-3,-1]=>0111=>[1,3]=>[3,1]
[-4,2,3,1]=>1000=>[1,3]=>[3,1]
[-4,2,3,-1]=>1001=>[1,2,1]=>[1,2,1]
[-4,2,-3,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-4,2,-3,-1]=>1011=>[1,1,2]=>[2,1,1]
[-4,-2,3,1]=>1100=>[2,2]=>[2,2]
[-4,-2,3,-1]=>1101=>[2,1,1]=>[1,1,2]
[-4,-2,-3,1]=>1110=>[3,1]=>[1,3]
[-4,-2,-3,-1]=>1111=>[4]=>[4]
[4,3,1,2]=>0000=>[4]=>[4]
[4,3,1,-2]=>0001=>[3,1]=>[1,3]
[4,3,-1,2]=>0010=>[2,1,1]=>[1,1,2]
[4,3,-1,-2]=>0011=>[2,2]=>[2,2]
[4,-3,1,2]=>0100=>[1,1,2]=>[2,1,1]
[4,-3,1,-2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,-3,-1,2]=>0110=>[1,2,1]=>[1,2,1]
[4,-3,-1,-2]=>0111=>[1,3]=>[3,1]
[-4,3,1,2]=>1000=>[1,3]=>[3,1]
[-4,3,1,-2]=>1001=>[1,2,1]=>[1,2,1]
[-4,3,-1,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-4,3,-1,-2]=>1011=>[1,1,2]=>[2,1,1]
[-4,-3,1,2]=>1100=>[2,2]=>[2,2]
[-4,-3,1,-2]=>1101=>[2,1,1]=>[1,1,2]
[-4,-3,-1,2]=>1110=>[3,1]=>[1,3]
[-4,-3,-1,-2]=>1111=>[4]=>[4]
[4,3,2,1]=>0000=>[4]=>[4]
[4,3,2,-1]=>0001=>[3,1]=>[1,3]
[4,3,-2,1]=>0010=>[2,1,1]=>[1,1,2]
[4,3,-2,-1]=>0011=>[2,2]=>[2,2]
[4,-3,2,1]=>0100=>[1,1,2]=>[2,1,1]
[4,-3,2,-1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,-3,-2,1]=>0110=>[1,2,1]=>[1,2,1]
[4,-3,-2,-1]=>0111=>[1,3]=>[3,1]
[-4,3,2,1]=>1000=>[1,3]=>[3,1]
[-4,3,2,-1]=>1001=>[1,2,1]=>[1,2,1]
[-4,3,-2,1]=>1010=>[1,1,1,1]=>[1,1,1,1]
[-4,3,-2,-1]=>1011=>[1,1,2]=>[2,1,1]
[-4,-3,2,1]=>1100=>[2,2]=>[2,2]
[-4,-3,2,-1]=>1101=>[2,1,1]=>[1,1,2]
[-4,-3,-2,1]=>1110=>[3,1]=>[1,3]
[-4,-3,-2,-1]=>1111=>[4]=>[4]
[1,2,3,4,5]=>00000=>[5]=>[5]
[1,2,3,4,-5]=>00001=>[4,1]=>[1,4]
[1,2,3,-4,5]=>00010=>[3,1,1]=>[1,1,3]
[1,2,3,-4,-5]=>00011=>[3,2]=>[2,3]
[1,2,-3,4,5]=>00100=>[2,1,2]=>[2,1,2]
[1,2,-3,4,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,-3,-4,5]=>00110=>[2,2,1]=>[1,2,2]
[1,2,-3,-4,-5]=>00111=>[2,3]=>[3,2]
[1,-2,3,4,5]=>01000=>[1,1,3]=>[3,1,1]
[1,-2,3,4,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-2,3,-4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-2,3,-4,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-2,-3,4,5]=>01100=>[1,2,2]=>[2,2,1]
[1,-2,-3,4,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-2,-3,-4,5]=>01110=>[1,3,1]=>[1,3,1]
[1,-2,-3,-4,-5]=>01111=>[1,4]=>[4,1]
[-1,2,3,4,5]=>10000=>[1,4]=>[4,1]
[-1,2,3,4,-5]=>10001=>[1,3,1]=>[1,3,1]
[-1,2,3,-4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,2,3,-4,-5]=>10011=>[1,2,2]=>[2,2,1]
[-1,2,-3,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,2,-3,4,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,2,-3,-4,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,2,-3,-4,-5]=>10111=>[1,1,3]=>[3,1,1]
[-1,-2,3,4,5]=>11000=>[2,3]=>[3,2]
[-1,-2,3,4,-5]=>11001=>[2,2,1]=>[1,2,2]
[-1,-2,3,-4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-2,3,-4,-5]=>11011=>[2,1,2]=>[2,1,2]
[-1,-2,-3,4,5]=>11100=>[3,2]=>[2,3]
[-1,-2,-3,4,-5]=>11101=>[3,1,1]=>[1,1,3]
[-1,-2,-3,-4,5]=>11110=>[4,1]=>[1,4]
[-1,-2,-3,-4,-5]=>11111=>[5]=>[5]
[1,2,3,5,4]=>00000=>[5]=>[5]
[1,2,3,5,-4]=>00001=>[4,1]=>[1,4]
[1,2,3,-5,4]=>00010=>[3,1,1]=>[1,1,3]
[1,2,3,-5,-4]=>00011=>[3,2]=>[2,3]
[1,2,-3,5,4]=>00100=>[2,1,2]=>[2,1,2]
[1,2,-3,5,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,-3,-5,4]=>00110=>[2,2,1]=>[1,2,2]
[1,2,-3,-5,-4]=>00111=>[2,3]=>[3,2]
[1,-2,3,5,4]=>01000=>[1,1,3]=>[3,1,1]
[1,-2,3,5,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-2,3,-5,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-2,3,-5,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-2,-3,5,4]=>01100=>[1,2,2]=>[2,2,1]
[1,-2,-3,5,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-2,-3,-5,4]=>01110=>[1,3,1]=>[1,3,1]
[1,-2,-3,-5,-4]=>01111=>[1,4]=>[4,1]
[-1,2,3,5,4]=>10000=>[1,4]=>[4,1]
[-1,2,3,5,-4]=>10001=>[1,3,1]=>[1,3,1]
[-1,2,3,-5,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,2,3,-5,-4]=>10011=>[1,2,2]=>[2,2,1]
[-1,2,-3,5,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,2,-3,5,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,2,-3,-5,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,2,-3,-5,-4]=>10111=>[1,1,3]=>[3,1,1]
[-1,-2,3,5,4]=>11000=>[2,3]=>[3,2]
[-1,-2,3,5,-4]=>11001=>[2,2,1]=>[1,2,2]
[-1,-2,3,-5,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-2,3,-5,-4]=>11011=>[2,1,2]=>[2,1,2]
[-1,-2,-3,5,4]=>11100=>[3,2]=>[2,3]
[-1,-2,-3,5,-4]=>11101=>[3,1,1]=>[1,1,3]
[-1,-2,-3,-5,4]=>11110=>[4,1]=>[1,4]
[-1,-2,-3,-5,-4]=>11111=>[5]=>[5]
[1,2,4,3,5]=>00000=>[5]=>[5]
[1,2,4,3,-5]=>00001=>[4,1]=>[1,4]
[1,2,4,-3,5]=>00010=>[3,1,1]=>[1,1,3]
[1,2,4,-3,-5]=>00011=>[3,2]=>[2,3]
[1,2,-4,3,5]=>00100=>[2,1,2]=>[2,1,2]
[1,2,-4,3,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,-4,-3,5]=>00110=>[2,2,1]=>[1,2,2]
[1,2,-4,-3,-5]=>00111=>[2,3]=>[3,2]
[1,-2,4,3,5]=>01000=>[1,1,3]=>[3,1,1]
[1,-2,4,3,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-2,4,-3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-2,4,-3,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-2,-4,3,5]=>01100=>[1,2,2]=>[2,2,1]
[1,-2,-4,3,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-2,-4,-3,5]=>01110=>[1,3,1]=>[1,3,1]
[1,-2,-4,-3,-5]=>01111=>[1,4]=>[4,1]
[-1,2,4,3,5]=>10000=>[1,4]=>[4,1]
[-1,2,4,3,-5]=>10001=>[1,3,1]=>[1,3,1]
[-1,2,4,-3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,2,4,-3,-5]=>10011=>[1,2,2]=>[2,2,1]
[-1,2,-4,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,2,-4,3,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,2,-4,-3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,2,-4,-3,-5]=>10111=>[1,1,3]=>[3,1,1]
[-1,-2,4,3,5]=>11000=>[2,3]=>[3,2]
[-1,-2,4,3,-5]=>11001=>[2,2,1]=>[1,2,2]
[-1,-2,4,-3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-2,4,-3,-5]=>11011=>[2,1,2]=>[2,1,2]
[-1,-2,-4,3,5]=>11100=>[3,2]=>[2,3]
[-1,-2,-4,3,-5]=>11101=>[3,1,1]=>[1,1,3]
[-1,-2,-4,-3,5]=>11110=>[4,1]=>[1,4]
[-1,-2,-4,-3,-5]=>11111=>[5]=>[5]
[1,2,4,5,3]=>00000=>[5]=>[5]
[1,2,4,5,-3]=>00001=>[4,1]=>[1,4]
[1,2,4,-5,3]=>00010=>[3,1,1]=>[1,1,3]
[1,2,4,-5,-3]=>00011=>[3,2]=>[2,3]
[1,2,-4,5,3]=>00100=>[2,1,2]=>[2,1,2]
[1,2,-4,5,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,-4,-5,3]=>00110=>[2,2,1]=>[1,2,2]
[1,2,-4,-5,-3]=>00111=>[2,3]=>[3,2]
[1,-2,4,5,3]=>01000=>[1,1,3]=>[3,1,1]
[1,-2,4,5,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-2,4,-5,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-2,4,-5,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-2,-4,5,3]=>01100=>[1,2,2]=>[2,2,1]
[1,-2,-4,5,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-2,-4,-5,3]=>01110=>[1,3,1]=>[1,3,1]
[1,-2,-4,-5,-3]=>01111=>[1,4]=>[4,1]
[-1,2,4,5,3]=>10000=>[1,4]=>[4,1]
[-1,2,4,5,-3]=>10001=>[1,3,1]=>[1,3,1]
[-1,2,4,-5,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,2,4,-5,-3]=>10011=>[1,2,2]=>[2,2,1]
[-1,2,-4,5,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,2,-4,5,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,2,-4,-5,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,2,-4,-5,-3]=>10111=>[1,1,3]=>[3,1,1]
[-1,-2,4,5,3]=>11000=>[2,3]=>[3,2]
[-1,-2,4,5,-3]=>11001=>[2,2,1]=>[1,2,2]
[-1,-2,4,-5,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-2,4,-5,-3]=>11011=>[2,1,2]=>[2,1,2]
[-1,-2,-4,5,3]=>11100=>[3,2]=>[2,3]
[-1,-2,-4,5,-3]=>11101=>[3,1,1]=>[1,1,3]
[-1,-2,-4,-5,3]=>11110=>[4,1]=>[1,4]
[-1,-2,-4,-5,-3]=>11111=>[5]=>[5]
[1,2,5,3,4]=>00000=>[5]=>[5]
[1,2,5,3,-4]=>00001=>[4,1]=>[1,4]
[1,2,5,-3,4]=>00010=>[3,1,1]=>[1,1,3]
[1,2,5,-3,-4]=>00011=>[3,2]=>[2,3]
[1,2,-5,3,4]=>00100=>[2,1,2]=>[2,1,2]
[1,2,-5,3,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,-5,-3,4]=>00110=>[2,2,1]=>[1,2,2]
[1,2,-5,-3,-4]=>00111=>[2,3]=>[3,2]
[1,-2,5,3,4]=>01000=>[1,1,3]=>[3,1,1]
[1,-2,5,3,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-2,5,-3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-2,5,-3,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-2,-5,3,4]=>01100=>[1,2,2]=>[2,2,1]
[1,-2,-5,3,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-2,-5,-3,4]=>01110=>[1,3,1]=>[1,3,1]
[1,-2,-5,-3,-4]=>01111=>[1,4]=>[4,1]
[-1,2,5,3,4]=>10000=>[1,4]=>[4,1]
[-1,2,5,3,-4]=>10001=>[1,3,1]=>[1,3,1]
[-1,2,5,-3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,2,5,-3,-4]=>10011=>[1,2,2]=>[2,2,1]
[-1,2,-5,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,2,-5,3,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,2,-5,-3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,2,-5,-3,-4]=>10111=>[1,1,3]=>[3,1,1]
[-1,-2,5,3,4]=>11000=>[2,3]=>[3,2]
[-1,-2,5,3,-4]=>11001=>[2,2,1]=>[1,2,2]
[-1,-2,5,-3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-2,5,-3,-4]=>11011=>[2,1,2]=>[2,1,2]
[-1,-2,-5,3,4]=>11100=>[3,2]=>[2,3]
[-1,-2,-5,3,-4]=>11101=>[3,1,1]=>[1,1,3]
[-1,-2,-5,-3,4]=>11110=>[4,1]=>[1,4]
[-1,-2,-5,-3,-4]=>11111=>[5]=>[5]
[1,2,5,4,3]=>00000=>[5]=>[5]
[1,2,5,4,-3]=>00001=>[4,1]=>[1,4]
[1,2,5,-4,3]=>00010=>[3,1,1]=>[1,1,3]
[1,2,5,-4,-3]=>00011=>[3,2]=>[2,3]
[1,2,-5,4,3]=>00100=>[2,1,2]=>[2,1,2]
[1,2,-5,4,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,-5,-4,3]=>00110=>[2,2,1]=>[1,2,2]
[1,2,-5,-4,-3]=>00111=>[2,3]=>[3,2]
[1,-2,5,4,3]=>01000=>[1,1,3]=>[3,1,1]
[1,-2,5,4,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-2,5,-4,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-2,5,-4,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-2,-5,4,3]=>01100=>[1,2,2]=>[2,2,1]
[1,-2,-5,4,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-2,-5,-4,3]=>01110=>[1,3,1]=>[1,3,1]
[1,-2,-5,-4,-3]=>01111=>[1,4]=>[4,1]
[-1,2,5,4,3]=>10000=>[1,4]=>[4,1]
[-1,2,5,4,-3]=>10001=>[1,3,1]=>[1,3,1]
[-1,2,5,-4,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,2,5,-4,-3]=>10011=>[1,2,2]=>[2,2,1]
[-1,2,-5,4,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,2,-5,4,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,2,-5,-4,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,2,-5,-4,-3]=>10111=>[1,1,3]=>[3,1,1]
[-1,-2,5,4,3]=>11000=>[2,3]=>[3,2]
[-1,-2,5,4,-3]=>11001=>[2,2,1]=>[1,2,2]
[-1,-2,5,-4,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-2,5,-4,-3]=>11011=>[2,1,2]=>[2,1,2]
[-1,-2,-5,4,3]=>11100=>[3,2]=>[2,3]
[-1,-2,-5,4,-3]=>11101=>[3,1,1]=>[1,1,3]
[-1,-2,-5,-4,3]=>11110=>[4,1]=>[1,4]
[-1,-2,-5,-4,-3]=>11111=>[5]=>[5]
[1,3,2,4,5]=>00000=>[5]=>[5]
[1,3,2,4,-5]=>00001=>[4,1]=>[1,4]
[1,3,2,-4,5]=>00010=>[3,1,1]=>[1,1,3]
[1,3,2,-4,-5]=>00011=>[3,2]=>[2,3]
[1,3,-2,4,5]=>00100=>[2,1,2]=>[2,1,2]
[1,3,-2,4,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,-2,-4,5]=>00110=>[2,2,1]=>[1,2,2]
[1,3,-2,-4,-5]=>00111=>[2,3]=>[3,2]
[1,-3,2,4,5]=>01000=>[1,1,3]=>[3,1,1]
[1,-3,2,4,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-3,2,-4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-3,2,-4,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-3,-2,4,5]=>01100=>[1,2,2]=>[2,2,1]
[1,-3,-2,4,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-3,-2,-4,5]=>01110=>[1,3,1]=>[1,3,1]
[1,-3,-2,-4,-5]=>01111=>[1,4]=>[4,1]
[-1,3,2,4,5]=>10000=>[1,4]=>[4,1]
[-1,3,2,4,-5]=>10001=>[1,3,1]=>[1,3,1]
[-1,3,2,-4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,3,2,-4,-5]=>10011=>[1,2,2]=>[2,2,1]
[-1,3,-2,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,3,-2,4,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,3,-2,-4,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,3,-2,-4,-5]=>10111=>[1,1,3]=>[3,1,1]
[-1,-3,2,4,5]=>11000=>[2,3]=>[3,2]
[-1,-3,2,4,-5]=>11001=>[2,2,1]=>[1,2,2]
[-1,-3,2,-4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-3,2,-4,-5]=>11011=>[2,1,2]=>[2,1,2]
[-1,-3,-2,4,5]=>11100=>[3,2]=>[2,3]
[-1,-3,-2,4,-5]=>11101=>[3,1,1]=>[1,1,3]
[-1,-3,-2,-4,5]=>11110=>[4,1]=>[1,4]
[-1,-3,-2,-4,-5]=>11111=>[5]=>[5]
[1,3,2,5,4]=>00000=>[5]=>[5]
[1,3,2,5,-4]=>00001=>[4,1]=>[1,4]
[1,3,2,-5,4]=>00010=>[3,1,1]=>[1,1,3]
[1,3,2,-5,-4]=>00011=>[3,2]=>[2,3]
[1,3,-2,5,4]=>00100=>[2,1,2]=>[2,1,2]
[1,3,-2,5,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,-2,-5,4]=>00110=>[2,2,1]=>[1,2,2]
[1,3,-2,-5,-4]=>00111=>[2,3]=>[3,2]
[1,-3,2,5,4]=>01000=>[1,1,3]=>[3,1,1]
[1,-3,2,5,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-3,2,-5,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-3,2,-5,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-3,-2,5,4]=>01100=>[1,2,2]=>[2,2,1]
[1,-3,-2,5,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-3,-2,-5,4]=>01110=>[1,3,1]=>[1,3,1]
[1,-3,-2,-5,-4]=>01111=>[1,4]=>[4,1]
[-1,3,2,5,4]=>10000=>[1,4]=>[4,1]
[-1,3,2,5,-4]=>10001=>[1,3,1]=>[1,3,1]
[-1,3,2,-5,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,3,2,-5,-4]=>10011=>[1,2,2]=>[2,2,1]
[-1,3,-2,5,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,3,-2,5,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,3,-2,-5,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,3,-2,-5,-4]=>10111=>[1,1,3]=>[3,1,1]
[-1,-3,2,5,4]=>11000=>[2,3]=>[3,2]
[-1,-3,2,5,-4]=>11001=>[2,2,1]=>[1,2,2]
[-1,-3,2,-5,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-3,2,-5,-4]=>11011=>[2,1,2]=>[2,1,2]
[-1,-3,-2,5,4]=>11100=>[3,2]=>[2,3]
[-1,-3,-2,5,-4]=>11101=>[3,1,1]=>[1,1,3]
[-1,-3,-2,-5,4]=>11110=>[4,1]=>[1,4]
[-1,-3,-2,-5,-4]=>11111=>[5]=>[5]
[1,3,4,2,5]=>00000=>[5]=>[5]
[1,3,4,2,-5]=>00001=>[4,1]=>[1,4]
[1,3,4,-2,5]=>00010=>[3,1,1]=>[1,1,3]
[1,3,4,-2,-5]=>00011=>[3,2]=>[2,3]
[1,3,-4,2,5]=>00100=>[2,1,2]=>[2,1,2]
[1,3,-4,2,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,-4,-2,5]=>00110=>[2,2,1]=>[1,2,2]
[1,3,-4,-2,-5]=>00111=>[2,3]=>[3,2]
[1,-3,4,2,5]=>01000=>[1,1,3]=>[3,1,1]
[1,-3,4,2,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-3,4,-2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-3,4,-2,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-3,-4,2,5]=>01100=>[1,2,2]=>[2,2,1]
[1,-3,-4,2,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-3,-4,-2,5]=>01110=>[1,3,1]=>[1,3,1]
[1,-3,-4,-2,-5]=>01111=>[1,4]=>[4,1]
[-1,3,4,2,5]=>10000=>[1,4]=>[4,1]
[-1,3,4,2,-5]=>10001=>[1,3,1]=>[1,3,1]
[-1,3,4,-2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,3,4,-2,-5]=>10011=>[1,2,2]=>[2,2,1]
[-1,3,-4,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,3,-4,2,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,3,-4,-2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,3,-4,-2,-5]=>10111=>[1,1,3]=>[3,1,1]
[-1,-3,4,2,5]=>11000=>[2,3]=>[3,2]
[-1,-3,4,2,-5]=>11001=>[2,2,1]=>[1,2,2]
[-1,-3,4,-2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-3,4,-2,-5]=>11011=>[2,1,2]=>[2,1,2]
[-1,-3,-4,2,5]=>11100=>[3,2]=>[2,3]
[-1,-3,-4,2,-5]=>11101=>[3,1,1]=>[1,1,3]
[-1,-3,-4,-2,5]=>11110=>[4,1]=>[1,4]
[-1,-3,-4,-2,-5]=>11111=>[5]=>[5]
[1,3,4,5,2]=>00000=>[5]=>[5]
[1,3,4,5,-2]=>00001=>[4,1]=>[1,4]
[1,3,4,-5,2]=>00010=>[3,1,1]=>[1,1,3]
[1,3,4,-5,-2]=>00011=>[3,2]=>[2,3]
[1,3,-4,5,2]=>00100=>[2,1,2]=>[2,1,2]
[1,3,-4,5,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,-4,-5,2]=>00110=>[2,2,1]=>[1,2,2]
[1,3,-4,-5,-2]=>00111=>[2,3]=>[3,2]
[1,-3,4,5,2]=>01000=>[1,1,3]=>[3,1,1]
[1,-3,4,5,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-3,4,-5,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-3,4,-5,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-3,-4,5,2]=>01100=>[1,2,2]=>[2,2,1]
[1,-3,-4,5,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-3,-4,-5,2]=>01110=>[1,3,1]=>[1,3,1]
[1,-3,-4,-5,-2]=>01111=>[1,4]=>[4,1]
[-1,3,4,5,2]=>10000=>[1,4]=>[4,1]
[-1,3,4,5,-2]=>10001=>[1,3,1]=>[1,3,1]
[-1,3,4,-5,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,3,4,-5,-2]=>10011=>[1,2,2]=>[2,2,1]
[-1,3,-4,5,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,3,-4,5,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,3,-4,-5,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,3,-4,-5,-2]=>10111=>[1,1,3]=>[3,1,1]
[-1,-3,4,5,2]=>11000=>[2,3]=>[3,2]
[-1,-3,4,5,-2]=>11001=>[2,2,1]=>[1,2,2]
[-1,-3,4,-5,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-3,4,-5,-2]=>11011=>[2,1,2]=>[2,1,2]
[-1,-3,-4,5,2]=>11100=>[3,2]=>[2,3]
[-1,-3,-4,5,-2]=>11101=>[3,1,1]=>[1,1,3]
[-1,-3,-4,-5,2]=>11110=>[4,1]=>[1,4]
[-1,-3,-4,-5,-2]=>11111=>[5]=>[5]
[1,3,5,2,4]=>00000=>[5]=>[5]
[1,3,5,2,-4]=>00001=>[4,1]=>[1,4]
[1,3,5,-2,4]=>00010=>[3,1,1]=>[1,1,3]
[1,3,5,-2,-4]=>00011=>[3,2]=>[2,3]
[1,3,-5,2,4]=>00100=>[2,1,2]=>[2,1,2]
[1,3,-5,2,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,-5,-2,4]=>00110=>[2,2,1]=>[1,2,2]
[1,3,-5,-2,-4]=>00111=>[2,3]=>[3,2]
[1,-3,5,2,4]=>01000=>[1,1,3]=>[3,1,1]
[1,-3,5,2,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-3,5,-2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-3,5,-2,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-3,-5,2,4]=>01100=>[1,2,2]=>[2,2,1]
[1,-3,-5,2,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-3,-5,-2,4]=>01110=>[1,3,1]=>[1,3,1]
[1,-3,-5,-2,-4]=>01111=>[1,4]=>[4,1]
[-1,3,5,2,4]=>10000=>[1,4]=>[4,1]
[-1,3,5,2,-4]=>10001=>[1,3,1]=>[1,3,1]
[-1,3,5,-2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,3,5,-2,-4]=>10011=>[1,2,2]=>[2,2,1]
[-1,3,-5,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,3,-5,2,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,3,-5,-2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,3,-5,-2,-4]=>10111=>[1,1,3]=>[3,1,1]
[-1,-3,5,2,4]=>11000=>[2,3]=>[3,2]
[-1,-3,5,2,-4]=>11001=>[2,2,1]=>[1,2,2]
[-1,-3,5,-2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-3,5,-2,-4]=>11011=>[2,1,2]=>[2,1,2]
[-1,-3,-5,2,4]=>11100=>[3,2]=>[2,3]
[-1,-3,-5,2,-4]=>11101=>[3,1,1]=>[1,1,3]
[-1,-3,-5,-2,4]=>11110=>[4,1]=>[1,4]
[-1,-3,-5,-2,-4]=>11111=>[5]=>[5]
[1,3,5,4,2]=>00000=>[5]=>[5]
[1,3,5,4,-2]=>00001=>[4,1]=>[1,4]
[1,3,5,-4,2]=>00010=>[3,1,1]=>[1,1,3]
[1,3,5,-4,-2]=>00011=>[3,2]=>[2,3]
[1,3,-5,4,2]=>00100=>[2,1,2]=>[2,1,2]
[1,3,-5,4,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,-5,-4,2]=>00110=>[2,2,1]=>[1,2,2]
[1,3,-5,-4,-2]=>00111=>[2,3]=>[3,2]
[1,-3,5,4,2]=>01000=>[1,1,3]=>[3,1,1]
[1,-3,5,4,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-3,5,-4,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-3,5,-4,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-3,-5,4,2]=>01100=>[1,2,2]=>[2,2,1]
[1,-3,-5,4,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-3,-5,-4,2]=>01110=>[1,3,1]=>[1,3,1]
[1,-3,-5,-4,-2]=>01111=>[1,4]=>[4,1]
[-1,3,5,4,2]=>10000=>[1,4]=>[4,1]
[-1,3,5,4,-2]=>10001=>[1,3,1]=>[1,3,1]
[-1,3,5,-4,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,3,5,-4,-2]=>10011=>[1,2,2]=>[2,2,1]
[-1,3,-5,4,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,3,-5,4,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,3,-5,-4,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,3,-5,-4,-2]=>10111=>[1,1,3]=>[3,1,1]
[-1,-3,5,4,2]=>11000=>[2,3]=>[3,2]
[-1,-3,5,4,-2]=>11001=>[2,2,1]=>[1,2,2]
[-1,-3,5,-4,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-3,5,-4,-2]=>11011=>[2,1,2]=>[2,1,2]
[-1,-3,-5,4,2]=>11100=>[3,2]=>[2,3]
[-1,-3,-5,4,-2]=>11101=>[3,1,1]=>[1,1,3]
[-1,-3,-5,-4,2]=>11110=>[4,1]=>[1,4]
[-1,-3,-5,-4,-2]=>11111=>[5]=>[5]
[1,4,2,3,5]=>00000=>[5]=>[5]
[1,4,2,3,-5]=>00001=>[4,1]=>[1,4]
[1,4,2,-3,5]=>00010=>[3,1,1]=>[1,1,3]
[1,4,2,-3,-5]=>00011=>[3,2]=>[2,3]
[1,4,-2,3,5]=>00100=>[2,1,2]=>[2,1,2]
[1,4,-2,3,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,-2,-3,5]=>00110=>[2,2,1]=>[1,2,2]
[1,4,-2,-3,-5]=>00111=>[2,3]=>[3,2]
[1,-4,2,3,5]=>01000=>[1,1,3]=>[3,1,1]
[1,-4,2,3,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-4,2,-3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-4,2,-3,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-4,-2,3,5]=>01100=>[1,2,2]=>[2,2,1]
[1,-4,-2,3,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-4,-2,-3,5]=>01110=>[1,3,1]=>[1,3,1]
[1,-4,-2,-3,-5]=>01111=>[1,4]=>[4,1]
[-1,4,2,3,5]=>10000=>[1,4]=>[4,1]
[-1,4,2,3,-5]=>10001=>[1,3,1]=>[1,3,1]
[-1,4,2,-3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,4,2,-3,-5]=>10011=>[1,2,2]=>[2,2,1]
[-1,4,-2,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,4,-2,3,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,4,-2,-3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,4,-2,-3,-5]=>10111=>[1,1,3]=>[3,1,1]
[-1,-4,2,3,5]=>11000=>[2,3]=>[3,2]
[-1,-4,2,3,-5]=>11001=>[2,2,1]=>[1,2,2]
[-1,-4,2,-3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-4,2,-3,-5]=>11011=>[2,1,2]=>[2,1,2]
[-1,-4,-2,3,5]=>11100=>[3,2]=>[2,3]
[-1,-4,-2,3,-5]=>11101=>[3,1,1]=>[1,1,3]
[-1,-4,-2,-3,5]=>11110=>[4,1]=>[1,4]
[-1,-4,-2,-3,-5]=>11111=>[5]=>[5]
[1,4,2,5,3]=>00000=>[5]=>[5]
[1,4,2,5,-3]=>00001=>[4,1]=>[1,4]
[1,4,2,-5,3]=>00010=>[3,1,1]=>[1,1,3]
[1,4,2,-5,-3]=>00011=>[3,2]=>[2,3]
[1,4,-2,5,3]=>00100=>[2,1,2]=>[2,1,2]
[1,4,-2,5,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,-2,-5,3]=>00110=>[2,2,1]=>[1,2,2]
[1,4,-2,-5,-3]=>00111=>[2,3]=>[3,2]
[1,-4,2,5,3]=>01000=>[1,1,3]=>[3,1,1]
[1,-4,2,5,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-4,2,-5,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-4,2,-5,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-4,-2,5,3]=>01100=>[1,2,2]=>[2,2,1]
[1,-4,-2,5,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-4,-2,-5,3]=>01110=>[1,3,1]=>[1,3,1]
[1,-4,-2,-5,-3]=>01111=>[1,4]=>[4,1]
[-1,4,2,5,3]=>10000=>[1,4]=>[4,1]
[-1,4,2,5,-3]=>10001=>[1,3,1]=>[1,3,1]
[-1,4,2,-5,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,4,2,-5,-3]=>10011=>[1,2,2]=>[2,2,1]
[-1,4,-2,5,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,4,-2,5,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,4,-2,-5,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,4,-2,-5,-3]=>10111=>[1,1,3]=>[3,1,1]
[-1,-4,2,5,3]=>11000=>[2,3]=>[3,2]
[-1,-4,2,5,-3]=>11001=>[2,2,1]=>[1,2,2]
[-1,-4,2,-5,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-4,2,-5,-3]=>11011=>[2,1,2]=>[2,1,2]
[-1,-4,-2,5,3]=>11100=>[3,2]=>[2,3]
[-1,-4,-2,5,-3]=>11101=>[3,1,1]=>[1,1,3]
[-1,-4,-2,-5,3]=>11110=>[4,1]=>[1,4]
[-1,-4,-2,-5,-3]=>11111=>[5]=>[5]
[1,4,3,2,5]=>00000=>[5]=>[5]
[1,4,3,2,-5]=>00001=>[4,1]=>[1,4]
[1,4,3,-2,5]=>00010=>[3,1,1]=>[1,1,3]
[1,4,3,-2,-5]=>00011=>[3,2]=>[2,3]
[1,4,-3,2,5]=>00100=>[2,1,2]=>[2,1,2]
[1,4,-3,2,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,-3,-2,5]=>00110=>[2,2,1]=>[1,2,2]
[1,4,-3,-2,-5]=>00111=>[2,3]=>[3,2]
[1,-4,3,2,5]=>01000=>[1,1,3]=>[3,1,1]
[1,-4,3,2,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-4,3,-2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-4,3,-2,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-4,-3,2,5]=>01100=>[1,2,2]=>[2,2,1]
[1,-4,-3,2,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-4,-3,-2,5]=>01110=>[1,3,1]=>[1,3,1]
[1,-4,-3,-2,-5]=>01111=>[1,4]=>[4,1]
[-1,4,3,2,5]=>10000=>[1,4]=>[4,1]
[-1,4,3,2,-5]=>10001=>[1,3,1]=>[1,3,1]
[-1,4,3,-2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,4,3,-2,-5]=>10011=>[1,2,2]=>[2,2,1]
[-1,4,-3,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,4,-3,2,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,4,-3,-2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,4,-3,-2,-5]=>10111=>[1,1,3]=>[3,1,1]
[-1,-4,3,2,5]=>11000=>[2,3]=>[3,2]
[-1,-4,3,2,-5]=>11001=>[2,2,1]=>[1,2,2]
[-1,-4,3,-2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-4,3,-2,-5]=>11011=>[2,1,2]=>[2,1,2]
[-1,-4,-3,2,5]=>11100=>[3,2]=>[2,3]
[-1,-4,-3,2,-5]=>11101=>[3,1,1]=>[1,1,3]
[-1,-4,-3,-2,5]=>11110=>[4,1]=>[1,4]
[-1,-4,-3,-2,-5]=>11111=>[5]=>[5]
[1,4,3,5,2]=>00000=>[5]=>[5]
[1,4,3,5,-2]=>00001=>[4,1]=>[1,4]
[1,4,3,-5,2]=>00010=>[3,1,1]=>[1,1,3]
[1,4,3,-5,-2]=>00011=>[3,2]=>[2,3]
[1,4,-3,5,2]=>00100=>[2,1,2]=>[2,1,2]
[1,4,-3,5,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,-3,-5,2]=>00110=>[2,2,1]=>[1,2,2]
[1,4,-3,-5,-2]=>00111=>[2,3]=>[3,2]
[1,-4,3,5,2]=>01000=>[1,1,3]=>[3,1,1]
[1,-4,3,5,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-4,3,-5,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-4,3,-5,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-4,-3,5,2]=>01100=>[1,2,2]=>[2,2,1]
[1,-4,-3,5,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-4,-3,-5,2]=>01110=>[1,3,1]=>[1,3,1]
[1,-4,-3,-5,-2]=>01111=>[1,4]=>[4,1]
[-1,4,3,5,2]=>10000=>[1,4]=>[4,1]
[-1,4,3,5,-2]=>10001=>[1,3,1]=>[1,3,1]
[-1,4,3,-5,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,4,3,-5,-2]=>10011=>[1,2,2]=>[2,2,1]
[-1,4,-3,5,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,4,-3,5,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,4,-3,-5,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,4,-3,-5,-2]=>10111=>[1,1,3]=>[3,1,1]
[-1,-4,3,5,2]=>11000=>[2,3]=>[3,2]
[-1,-4,3,5,-2]=>11001=>[2,2,1]=>[1,2,2]
[-1,-4,3,-5,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-4,3,-5,-2]=>11011=>[2,1,2]=>[2,1,2]
[-1,-4,-3,5,2]=>11100=>[3,2]=>[2,3]
[-1,-4,-3,5,-2]=>11101=>[3,1,1]=>[1,1,3]
[-1,-4,-3,-5,2]=>11110=>[4,1]=>[1,4]
[-1,-4,-3,-5,-2]=>11111=>[5]=>[5]
[1,4,5,2,3]=>00000=>[5]=>[5]
[1,4,5,2,-3]=>00001=>[4,1]=>[1,4]
[1,4,5,-2,3]=>00010=>[3,1,1]=>[1,1,3]
[1,4,5,-2,-3]=>00011=>[3,2]=>[2,3]
[1,4,-5,2,3]=>00100=>[2,1,2]=>[2,1,2]
[1,4,-5,2,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,-5,-2,3]=>00110=>[2,2,1]=>[1,2,2]
[1,4,-5,-2,-3]=>00111=>[2,3]=>[3,2]
[1,-4,5,2,3]=>01000=>[1,1,3]=>[3,1,1]
[1,-4,5,2,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-4,5,-2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-4,5,-2,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-4,-5,2,3]=>01100=>[1,2,2]=>[2,2,1]
[1,-4,-5,2,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-4,-5,-2,3]=>01110=>[1,3,1]=>[1,3,1]
[1,-4,-5,-2,-3]=>01111=>[1,4]=>[4,1]
[-1,4,5,2,3]=>10000=>[1,4]=>[4,1]
[-1,4,5,2,-3]=>10001=>[1,3,1]=>[1,3,1]
[-1,4,5,-2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,4,5,-2,-3]=>10011=>[1,2,2]=>[2,2,1]
[-1,4,-5,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,4,-5,2,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,4,-5,-2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,4,-5,-2,-3]=>10111=>[1,1,3]=>[3,1,1]
[-1,-4,5,2,3]=>11000=>[2,3]=>[3,2]
[-1,-4,5,2,-3]=>11001=>[2,2,1]=>[1,2,2]
[-1,-4,5,-2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-4,5,-2,-3]=>11011=>[2,1,2]=>[2,1,2]
[-1,-4,-5,2,3]=>11100=>[3,2]=>[2,3]
[-1,-4,-5,2,-3]=>11101=>[3,1,1]=>[1,1,3]
[-1,-4,-5,-2,3]=>11110=>[4,1]=>[1,4]
[-1,-4,-5,-2,-3]=>11111=>[5]=>[5]
[1,4,5,3,2]=>00000=>[5]=>[5]
[1,4,5,3,-2]=>00001=>[4,1]=>[1,4]
[1,4,5,-3,2]=>00010=>[3,1,1]=>[1,1,3]
[1,4,5,-3,-2]=>00011=>[3,2]=>[2,3]
[1,4,-5,3,2]=>00100=>[2,1,2]=>[2,1,2]
[1,4,-5,3,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,-5,-3,2]=>00110=>[2,2,1]=>[1,2,2]
[1,4,-5,-3,-2]=>00111=>[2,3]=>[3,2]
[1,-4,5,3,2]=>01000=>[1,1,3]=>[3,1,1]
[1,-4,5,3,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-4,5,-3,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-4,5,-3,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-4,-5,3,2]=>01100=>[1,2,2]=>[2,2,1]
[1,-4,-5,3,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-4,-5,-3,2]=>01110=>[1,3,1]=>[1,3,1]
[1,-4,-5,-3,-2]=>01111=>[1,4]=>[4,1]
[-1,4,5,3,2]=>10000=>[1,4]=>[4,1]
[-1,4,5,3,-2]=>10001=>[1,3,1]=>[1,3,1]
[-1,4,5,-3,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,4,5,-3,-2]=>10011=>[1,2,2]=>[2,2,1]
[-1,4,-5,3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,4,-5,3,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,4,-5,-3,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,4,-5,-3,-2]=>10111=>[1,1,3]=>[3,1,1]
[-1,-4,5,3,2]=>11000=>[2,3]=>[3,2]
[-1,-4,5,3,-2]=>11001=>[2,2,1]=>[1,2,2]
[-1,-4,5,-3,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-4,5,-3,-2]=>11011=>[2,1,2]=>[2,1,2]
[-1,-4,-5,3,2]=>11100=>[3,2]=>[2,3]
[-1,-4,-5,3,-2]=>11101=>[3,1,1]=>[1,1,3]
[-1,-4,-5,-3,2]=>11110=>[4,1]=>[1,4]
[-1,-4,-5,-3,-2]=>11111=>[5]=>[5]
[1,5,2,3,4]=>00000=>[5]=>[5]
[1,5,2,3,-4]=>00001=>[4,1]=>[1,4]
[1,5,2,-3,4]=>00010=>[3,1,1]=>[1,1,3]
[1,5,2,-3,-4]=>00011=>[3,2]=>[2,3]
[1,5,-2,3,4]=>00100=>[2,1,2]=>[2,1,2]
[1,5,-2,3,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,-2,-3,4]=>00110=>[2,2,1]=>[1,2,2]
[1,5,-2,-3,-4]=>00111=>[2,3]=>[3,2]
[1,-5,2,3,4]=>01000=>[1,1,3]=>[3,1,1]
[1,-5,2,3,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-5,2,-3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-5,2,-3,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-5,-2,3,4]=>01100=>[1,2,2]=>[2,2,1]
[1,-5,-2,3,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-5,-2,-3,4]=>01110=>[1,3,1]=>[1,3,1]
[1,-5,-2,-3,-4]=>01111=>[1,4]=>[4,1]
[-1,5,2,3,4]=>10000=>[1,4]=>[4,1]
[-1,5,2,3,-4]=>10001=>[1,3,1]=>[1,3,1]
[-1,5,2,-3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,5,2,-3,-4]=>10011=>[1,2,2]=>[2,2,1]
[-1,5,-2,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,5,-2,3,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,5,-2,-3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,5,-2,-3,-4]=>10111=>[1,1,3]=>[3,1,1]
[-1,-5,2,3,4]=>11000=>[2,3]=>[3,2]
[-1,-5,2,3,-4]=>11001=>[2,2,1]=>[1,2,2]
[-1,-5,2,-3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-5,2,-3,-4]=>11011=>[2,1,2]=>[2,1,2]
[-1,-5,-2,3,4]=>11100=>[3,2]=>[2,3]
[-1,-5,-2,3,-4]=>11101=>[3,1,1]=>[1,1,3]
[-1,-5,-2,-3,4]=>11110=>[4,1]=>[1,4]
[-1,-5,-2,-3,-4]=>11111=>[5]=>[5]
[1,5,2,4,3]=>00000=>[5]=>[5]
[1,5,2,4,-3]=>00001=>[4,1]=>[1,4]
[1,5,2,-4,3]=>00010=>[3,1,1]=>[1,1,3]
[1,5,2,-4,-3]=>00011=>[3,2]=>[2,3]
[1,5,-2,4,3]=>00100=>[2,1,2]=>[2,1,2]
[1,5,-2,4,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,-2,-4,3]=>00110=>[2,2,1]=>[1,2,2]
[1,5,-2,-4,-3]=>00111=>[2,3]=>[3,2]
[1,-5,2,4,3]=>01000=>[1,1,3]=>[3,1,1]
[1,-5,2,4,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-5,2,-4,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-5,2,-4,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-5,-2,4,3]=>01100=>[1,2,2]=>[2,2,1]
[1,-5,-2,4,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-5,-2,-4,3]=>01110=>[1,3,1]=>[1,3,1]
[1,-5,-2,-4,-3]=>01111=>[1,4]=>[4,1]
[-1,5,2,4,3]=>10000=>[1,4]=>[4,1]
[-1,5,2,4,-3]=>10001=>[1,3,1]=>[1,3,1]
[-1,5,2,-4,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,5,2,-4,-3]=>10011=>[1,2,2]=>[2,2,1]
[-1,5,-2,4,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,5,-2,4,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,5,-2,-4,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,5,-2,-4,-3]=>10111=>[1,1,3]=>[3,1,1]
[-1,-5,2,4,3]=>11000=>[2,3]=>[3,2]
[-1,-5,2,4,-3]=>11001=>[2,2,1]=>[1,2,2]
[-1,-5,2,-4,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-5,2,-4,-3]=>11011=>[2,1,2]=>[2,1,2]
[-1,-5,-2,4,3]=>11100=>[3,2]=>[2,3]
[-1,-5,-2,4,-3]=>11101=>[3,1,1]=>[1,1,3]
[-1,-5,-2,-4,3]=>11110=>[4,1]=>[1,4]
[-1,-5,-2,-4,-3]=>11111=>[5]=>[5]
[1,5,3,2,4]=>00000=>[5]=>[5]
[1,5,3,2,-4]=>00001=>[4,1]=>[1,4]
[1,5,3,-2,4]=>00010=>[3,1,1]=>[1,1,3]
[1,5,3,-2,-4]=>00011=>[3,2]=>[2,3]
[1,5,-3,2,4]=>00100=>[2,1,2]=>[2,1,2]
[1,5,-3,2,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,-3,-2,4]=>00110=>[2,2,1]=>[1,2,2]
[1,5,-3,-2,-4]=>00111=>[2,3]=>[3,2]
[1,-5,3,2,4]=>01000=>[1,1,3]=>[3,1,1]
[1,-5,3,2,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-5,3,-2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-5,3,-2,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-5,-3,2,4]=>01100=>[1,2,2]=>[2,2,1]
[1,-5,-3,2,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-5,-3,-2,4]=>01110=>[1,3,1]=>[1,3,1]
[1,-5,-3,-2,-4]=>01111=>[1,4]=>[4,1]
[-1,5,3,2,4]=>10000=>[1,4]=>[4,1]
[-1,5,3,2,-4]=>10001=>[1,3,1]=>[1,3,1]
[-1,5,3,-2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,5,3,-2,-4]=>10011=>[1,2,2]=>[2,2,1]
[-1,5,-3,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,5,-3,2,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,5,-3,-2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,5,-3,-2,-4]=>10111=>[1,1,3]=>[3,1,1]
[-1,-5,3,2,4]=>11000=>[2,3]=>[3,2]
[-1,-5,3,2,-4]=>11001=>[2,2,1]=>[1,2,2]
[-1,-5,3,-2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-5,3,-2,-4]=>11011=>[2,1,2]=>[2,1,2]
[-1,-5,-3,2,4]=>11100=>[3,2]=>[2,3]
[-1,-5,-3,2,-4]=>11101=>[3,1,1]=>[1,1,3]
[-1,-5,-3,-2,4]=>11110=>[4,1]=>[1,4]
[-1,-5,-3,-2,-4]=>11111=>[5]=>[5]
[1,5,3,4,2]=>00000=>[5]=>[5]
[1,5,3,4,-2]=>00001=>[4,1]=>[1,4]
[1,5,3,-4,2]=>00010=>[3,1,1]=>[1,1,3]
[1,5,3,-4,-2]=>00011=>[3,2]=>[2,3]
[1,5,-3,4,2]=>00100=>[2,1,2]=>[2,1,2]
[1,5,-3,4,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,-3,-4,2]=>00110=>[2,2,1]=>[1,2,2]
[1,5,-3,-4,-2]=>00111=>[2,3]=>[3,2]
[1,-5,3,4,2]=>01000=>[1,1,3]=>[3,1,1]
[1,-5,3,4,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-5,3,-4,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-5,3,-4,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-5,-3,4,2]=>01100=>[1,2,2]=>[2,2,1]
[1,-5,-3,4,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-5,-3,-4,2]=>01110=>[1,3,1]=>[1,3,1]
[1,-5,-3,-4,-2]=>01111=>[1,4]=>[4,1]
[-1,5,3,4,2]=>10000=>[1,4]=>[4,1]
[-1,5,3,4,-2]=>10001=>[1,3,1]=>[1,3,1]
[-1,5,3,-4,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,5,3,-4,-2]=>10011=>[1,2,2]=>[2,2,1]
[-1,5,-3,4,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,5,-3,4,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,5,-3,-4,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,5,-3,-4,-2]=>10111=>[1,1,3]=>[3,1,1]
[-1,-5,3,4,2]=>11000=>[2,3]=>[3,2]
[-1,-5,3,4,-2]=>11001=>[2,2,1]=>[1,2,2]
[-1,-5,3,-4,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-5,3,-4,-2]=>11011=>[2,1,2]=>[2,1,2]
[-1,-5,-3,4,2]=>11100=>[3,2]=>[2,3]
[-1,-5,-3,4,-2]=>11101=>[3,1,1]=>[1,1,3]
[-1,-5,-3,-4,2]=>11110=>[4,1]=>[1,4]
[-1,-5,-3,-4,-2]=>11111=>[5]=>[5]
[1,5,4,2,3]=>00000=>[5]=>[5]
[1,5,4,2,-3]=>00001=>[4,1]=>[1,4]
[1,5,4,-2,3]=>00010=>[3,1,1]=>[1,1,3]
[1,5,4,-2,-3]=>00011=>[3,2]=>[2,3]
[1,5,-4,2,3]=>00100=>[2,1,2]=>[2,1,2]
[1,5,-4,2,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,-4,-2,3]=>00110=>[2,2,1]=>[1,2,2]
[1,5,-4,-2,-3]=>00111=>[2,3]=>[3,2]
[1,-5,4,2,3]=>01000=>[1,1,3]=>[3,1,1]
[1,-5,4,2,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-5,4,-2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-5,4,-2,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-5,-4,2,3]=>01100=>[1,2,2]=>[2,2,1]
[1,-5,-4,2,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-5,-4,-2,3]=>01110=>[1,3,1]=>[1,3,1]
[1,-5,-4,-2,-3]=>01111=>[1,4]=>[4,1]
[-1,5,4,2,3]=>10000=>[1,4]=>[4,1]
[-1,5,4,2,-3]=>10001=>[1,3,1]=>[1,3,1]
[-1,5,4,-2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,5,4,-2,-3]=>10011=>[1,2,2]=>[2,2,1]
[-1,5,-4,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,5,-4,2,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,5,-4,-2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,5,-4,-2,-3]=>10111=>[1,1,3]=>[3,1,1]
[-1,-5,4,2,3]=>11000=>[2,3]=>[3,2]
[-1,-5,4,2,-3]=>11001=>[2,2,1]=>[1,2,2]
[-1,-5,4,-2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-5,4,-2,-3]=>11011=>[2,1,2]=>[2,1,2]
[-1,-5,-4,2,3]=>11100=>[3,2]=>[2,3]
[-1,-5,-4,2,-3]=>11101=>[3,1,1]=>[1,1,3]
[-1,-5,-4,-2,3]=>11110=>[4,1]=>[1,4]
[-1,-5,-4,-2,-3]=>11111=>[5]=>[5]
[1,5,4,3,2]=>00000=>[5]=>[5]
[1,5,4,3,-2]=>00001=>[4,1]=>[1,4]
[1,5,4,-3,2]=>00010=>[3,1,1]=>[1,1,3]
[1,5,4,-3,-2]=>00011=>[3,2]=>[2,3]
[1,5,-4,3,2]=>00100=>[2,1,2]=>[2,1,2]
[1,5,-4,3,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,-4,-3,2]=>00110=>[2,2,1]=>[1,2,2]
[1,5,-4,-3,-2]=>00111=>[2,3]=>[3,2]
[1,-5,4,3,2]=>01000=>[1,1,3]=>[3,1,1]
[1,-5,4,3,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,-5,4,-3,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,-5,4,-3,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,-5,-4,3,2]=>01100=>[1,2,2]=>[2,2,1]
[1,-5,-4,3,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,-5,-4,-3,2]=>01110=>[1,3,1]=>[1,3,1]
[1,-5,-4,-3,-2]=>01111=>[1,4]=>[4,1]
[-1,5,4,3,2]=>10000=>[1,4]=>[4,1]
[-1,5,4,3,-2]=>10001=>[1,3,1]=>[1,3,1]
[-1,5,4,-3,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-1,5,4,-3,-2]=>10011=>[1,2,2]=>[2,2,1]
[-1,5,-4,3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-1,5,-4,3,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-1,5,-4,-3,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-1,5,-4,-3,-2]=>10111=>[1,1,3]=>[3,1,1]
[-1,-5,4,3,2]=>11000=>[2,3]=>[3,2]
[-1,-5,4,3,-2]=>11001=>[2,2,1]=>[1,2,2]
[-1,-5,4,-3,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-1,-5,4,-3,-2]=>11011=>[2,1,2]=>[2,1,2]
[-1,-5,-4,3,2]=>11100=>[3,2]=>[2,3]
[-1,-5,-4,3,-2]=>11101=>[3,1,1]=>[1,1,3]
[-1,-5,-4,-3,2]=>11110=>[4,1]=>[1,4]
[-1,-5,-4,-3,-2]=>11111=>[5]=>[5]
[2,1,3,4,5]=>00000=>[5]=>[5]
[2,1,3,4,-5]=>00001=>[4,1]=>[1,4]
[2,1,3,-4,5]=>00010=>[3,1,1]=>[1,1,3]
[2,1,3,-4,-5]=>00011=>[3,2]=>[2,3]
[2,1,-3,4,5]=>00100=>[2,1,2]=>[2,1,2]
[2,1,-3,4,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,1,-3,-4,5]=>00110=>[2,2,1]=>[1,2,2]
[2,1,-3,-4,-5]=>00111=>[2,3]=>[3,2]
[2,-1,3,4,5]=>01000=>[1,1,3]=>[3,1,1]
[2,-1,3,4,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-1,3,-4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-1,3,-4,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-1,-3,4,5]=>01100=>[1,2,2]=>[2,2,1]
[2,-1,-3,4,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-1,-3,-4,5]=>01110=>[1,3,1]=>[1,3,1]
[2,-1,-3,-4,-5]=>01111=>[1,4]=>[4,1]
[-2,1,3,4,5]=>10000=>[1,4]=>[4,1]
[-2,1,3,4,-5]=>10001=>[1,3,1]=>[1,3,1]
[-2,1,3,-4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,1,3,-4,-5]=>10011=>[1,2,2]=>[2,2,1]
[-2,1,-3,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,1,-3,4,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,1,-3,-4,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,1,-3,-4,-5]=>10111=>[1,1,3]=>[3,1,1]
[-2,-1,3,4,5]=>11000=>[2,3]=>[3,2]
[-2,-1,3,4,-5]=>11001=>[2,2,1]=>[1,2,2]
[-2,-1,3,-4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-1,3,-4,-5]=>11011=>[2,1,2]=>[2,1,2]
[-2,-1,-3,4,5]=>11100=>[3,2]=>[2,3]
[-2,-1,-3,4,-5]=>11101=>[3,1,1]=>[1,1,3]
[-2,-1,-3,-4,5]=>11110=>[4,1]=>[1,4]
[-2,-1,-3,-4,-5]=>11111=>[5]=>[5]
[2,1,3,5,4]=>00000=>[5]=>[5]
[2,1,3,5,-4]=>00001=>[4,1]=>[1,4]
[2,1,3,-5,4]=>00010=>[3,1,1]=>[1,1,3]
[2,1,3,-5,-4]=>00011=>[3,2]=>[2,3]
[2,1,-3,5,4]=>00100=>[2,1,2]=>[2,1,2]
[2,1,-3,5,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,1,-3,-5,4]=>00110=>[2,2,1]=>[1,2,2]
[2,1,-3,-5,-4]=>00111=>[2,3]=>[3,2]
[2,-1,3,5,4]=>01000=>[1,1,3]=>[3,1,1]
[2,-1,3,5,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-1,3,-5,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-1,3,-5,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-1,-3,5,4]=>01100=>[1,2,2]=>[2,2,1]
[2,-1,-3,5,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-1,-3,-5,4]=>01110=>[1,3,1]=>[1,3,1]
[2,-1,-3,-5,-4]=>01111=>[1,4]=>[4,1]
[-2,1,3,5,4]=>10000=>[1,4]=>[4,1]
[-2,1,3,5,-4]=>10001=>[1,3,1]=>[1,3,1]
[-2,1,3,-5,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,1,3,-5,-4]=>10011=>[1,2,2]=>[2,2,1]
[-2,1,-3,5,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,1,-3,5,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,1,-3,-5,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,1,-3,-5,-4]=>10111=>[1,1,3]=>[3,1,1]
[-2,-1,3,5,4]=>11000=>[2,3]=>[3,2]
[-2,-1,3,5,-4]=>11001=>[2,2,1]=>[1,2,2]
[-2,-1,3,-5,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-1,3,-5,-4]=>11011=>[2,1,2]=>[2,1,2]
[-2,-1,-3,5,4]=>11100=>[3,2]=>[2,3]
[-2,-1,-3,5,-4]=>11101=>[3,1,1]=>[1,1,3]
[-2,-1,-3,-5,4]=>11110=>[4,1]=>[1,4]
[-2,-1,-3,-5,-4]=>11111=>[5]=>[5]
[2,1,4,3,5]=>00000=>[5]=>[5]
[2,1,4,3,-5]=>00001=>[4,1]=>[1,4]
[2,1,4,-3,5]=>00010=>[3,1,1]=>[1,1,3]
[2,1,4,-3,-5]=>00011=>[3,2]=>[2,3]
[2,1,-4,3,5]=>00100=>[2,1,2]=>[2,1,2]
[2,1,-4,3,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,1,-4,-3,5]=>00110=>[2,2,1]=>[1,2,2]
[2,1,-4,-3,-5]=>00111=>[2,3]=>[3,2]
[2,-1,4,3,5]=>01000=>[1,1,3]=>[3,1,1]
[2,-1,4,3,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-1,4,-3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-1,4,-3,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-1,-4,3,5]=>01100=>[1,2,2]=>[2,2,1]
[2,-1,-4,3,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-1,-4,-3,5]=>01110=>[1,3,1]=>[1,3,1]
[2,-1,-4,-3,-5]=>01111=>[1,4]=>[4,1]
[-2,1,4,3,5]=>10000=>[1,4]=>[4,1]
[-2,1,4,3,-5]=>10001=>[1,3,1]=>[1,3,1]
[-2,1,4,-3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,1,4,-3,-5]=>10011=>[1,2,2]=>[2,2,1]
[-2,1,-4,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,1,-4,3,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,1,-4,-3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,1,-4,-3,-5]=>10111=>[1,1,3]=>[3,1,1]
[-2,-1,4,3,5]=>11000=>[2,3]=>[3,2]
[-2,-1,4,3,-5]=>11001=>[2,2,1]=>[1,2,2]
[-2,-1,4,-3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-1,4,-3,-5]=>11011=>[2,1,2]=>[2,1,2]
[-2,-1,-4,3,5]=>11100=>[3,2]=>[2,3]
[-2,-1,-4,3,-5]=>11101=>[3,1,1]=>[1,1,3]
[-2,-1,-4,-3,5]=>11110=>[4,1]=>[1,4]
[-2,-1,-4,-3,-5]=>11111=>[5]=>[5]
[2,1,4,5,3]=>00000=>[5]=>[5]
[2,1,4,5,-3]=>00001=>[4,1]=>[1,4]
[2,1,4,-5,3]=>00010=>[3,1,1]=>[1,1,3]
[2,1,4,-5,-3]=>00011=>[3,2]=>[2,3]
[2,1,-4,5,3]=>00100=>[2,1,2]=>[2,1,2]
[2,1,-4,5,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,1,-4,-5,3]=>00110=>[2,2,1]=>[1,2,2]
[2,1,-4,-5,-3]=>00111=>[2,3]=>[3,2]
[2,-1,4,5,3]=>01000=>[1,1,3]=>[3,1,1]
[2,-1,4,5,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-1,4,-5,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-1,4,-5,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-1,-4,5,3]=>01100=>[1,2,2]=>[2,2,1]
[2,-1,-4,5,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-1,-4,-5,3]=>01110=>[1,3,1]=>[1,3,1]
[2,-1,-4,-5,-3]=>01111=>[1,4]=>[4,1]
[-2,1,4,5,3]=>10000=>[1,4]=>[4,1]
[-2,1,4,5,-3]=>10001=>[1,3,1]=>[1,3,1]
[-2,1,4,-5,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,1,4,-5,-3]=>10011=>[1,2,2]=>[2,2,1]
[-2,1,-4,5,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,1,-4,5,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,1,-4,-5,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,1,-4,-5,-3]=>10111=>[1,1,3]=>[3,1,1]
[-2,-1,4,5,3]=>11000=>[2,3]=>[3,2]
[-2,-1,4,5,-3]=>11001=>[2,2,1]=>[1,2,2]
[-2,-1,4,-5,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-1,4,-5,-3]=>11011=>[2,1,2]=>[2,1,2]
[-2,-1,-4,5,3]=>11100=>[3,2]=>[2,3]
[-2,-1,-4,5,-3]=>11101=>[3,1,1]=>[1,1,3]
[-2,-1,-4,-5,3]=>11110=>[4,1]=>[1,4]
[-2,-1,-4,-5,-3]=>11111=>[5]=>[5]
[2,1,5,3,4]=>00000=>[5]=>[5]
[2,1,5,3,-4]=>00001=>[4,1]=>[1,4]
[2,1,5,-3,4]=>00010=>[3,1,1]=>[1,1,3]
[2,1,5,-3,-4]=>00011=>[3,2]=>[2,3]
[2,1,-5,3,4]=>00100=>[2,1,2]=>[2,1,2]
[2,1,-5,3,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,1,-5,-3,4]=>00110=>[2,2,1]=>[1,2,2]
[2,1,-5,-3,-4]=>00111=>[2,3]=>[3,2]
[2,-1,5,3,4]=>01000=>[1,1,3]=>[3,1,1]
[2,-1,5,3,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-1,5,-3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-1,5,-3,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-1,-5,3,4]=>01100=>[1,2,2]=>[2,2,1]
[2,-1,-5,3,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-1,-5,-3,4]=>01110=>[1,3,1]=>[1,3,1]
[2,-1,-5,-3,-4]=>01111=>[1,4]=>[4,1]
[-2,1,5,3,4]=>10000=>[1,4]=>[4,1]
[-2,1,5,3,-4]=>10001=>[1,3,1]=>[1,3,1]
[-2,1,5,-3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,1,5,-3,-4]=>10011=>[1,2,2]=>[2,2,1]
[-2,1,-5,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,1,-5,3,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,1,-5,-3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,1,-5,-3,-4]=>10111=>[1,1,3]=>[3,1,1]
[-2,-1,5,3,4]=>11000=>[2,3]=>[3,2]
[-2,-1,5,3,-4]=>11001=>[2,2,1]=>[1,2,2]
[-2,-1,5,-3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-1,5,-3,-4]=>11011=>[2,1,2]=>[2,1,2]
[-2,-1,-5,3,4]=>11100=>[3,2]=>[2,3]
[-2,-1,-5,3,-4]=>11101=>[3,1,1]=>[1,1,3]
[-2,-1,-5,-3,4]=>11110=>[4,1]=>[1,4]
[-2,-1,-5,-3,-4]=>11111=>[5]=>[5]
[2,1,5,4,3]=>00000=>[5]=>[5]
[2,1,5,4,-3]=>00001=>[4,1]=>[1,4]
[2,1,5,-4,3]=>00010=>[3,1,1]=>[1,1,3]
[2,1,5,-4,-3]=>00011=>[3,2]=>[2,3]
[2,1,-5,4,3]=>00100=>[2,1,2]=>[2,1,2]
[2,1,-5,4,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,1,-5,-4,3]=>00110=>[2,2,1]=>[1,2,2]
[2,1,-5,-4,-3]=>00111=>[2,3]=>[3,2]
[2,-1,5,4,3]=>01000=>[1,1,3]=>[3,1,1]
[2,-1,5,4,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-1,5,-4,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-1,5,-4,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-1,-5,4,3]=>01100=>[1,2,2]=>[2,2,1]
[2,-1,-5,4,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-1,-5,-4,3]=>01110=>[1,3,1]=>[1,3,1]
[2,-1,-5,-4,-3]=>01111=>[1,4]=>[4,1]
[-2,1,5,4,3]=>10000=>[1,4]=>[4,1]
[-2,1,5,4,-3]=>10001=>[1,3,1]=>[1,3,1]
[-2,1,5,-4,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,1,5,-4,-3]=>10011=>[1,2,2]=>[2,2,1]
[-2,1,-5,4,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,1,-5,4,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,1,-5,-4,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,1,-5,-4,-3]=>10111=>[1,1,3]=>[3,1,1]
[-2,-1,5,4,3]=>11000=>[2,3]=>[3,2]
[-2,-1,5,4,-3]=>11001=>[2,2,1]=>[1,2,2]
[-2,-1,5,-4,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-1,5,-4,-3]=>11011=>[2,1,2]=>[2,1,2]
[-2,-1,-5,4,3]=>11100=>[3,2]=>[2,3]
[-2,-1,-5,4,-3]=>11101=>[3,1,1]=>[1,1,3]
[-2,-1,-5,-4,3]=>11110=>[4,1]=>[1,4]
[-2,-1,-5,-4,-3]=>11111=>[5]=>[5]
[2,3,1,4,5]=>00000=>[5]=>[5]
[2,3,1,4,-5]=>00001=>[4,1]=>[1,4]
[2,3,1,-4,5]=>00010=>[3,1,1]=>[1,1,3]
[2,3,1,-4,-5]=>00011=>[3,2]=>[2,3]
[2,3,-1,4,5]=>00100=>[2,1,2]=>[2,1,2]
[2,3,-1,4,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,-1,-4,5]=>00110=>[2,2,1]=>[1,2,2]
[2,3,-1,-4,-5]=>00111=>[2,3]=>[3,2]
[2,-3,1,4,5]=>01000=>[1,1,3]=>[3,1,1]
[2,-3,1,4,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-3,1,-4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-3,1,-4,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-3,-1,4,5]=>01100=>[1,2,2]=>[2,2,1]
[2,-3,-1,4,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-3,-1,-4,5]=>01110=>[1,3,1]=>[1,3,1]
[2,-3,-1,-4,-5]=>01111=>[1,4]=>[4,1]
[-2,3,1,4,5]=>10000=>[1,4]=>[4,1]
[-2,3,1,4,-5]=>10001=>[1,3,1]=>[1,3,1]
[-2,3,1,-4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,3,1,-4,-5]=>10011=>[1,2,2]=>[2,2,1]
[-2,3,-1,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,3,-1,4,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,3,-1,-4,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,3,-1,-4,-5]=>10111=>[1,1,3]=>[3,1,1]
[-2,-3,1,4,5]=>11000=>[2,3]=>[3,2]
[-2,-3,1,4,-5]=>11001=>[2,2,1]=>[1,2,2]
[-2,-3,1,-4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-3,1,-4,-5]=>11011=>[2,1,2]=>[2,1,2]
[-2,-3,-1,4,5]=>11100=>[3,2]=>[2,3]
[-2,-3,-1,4,-5]=>11101=>[3,1,1]=>[1,1,3]
[-2,-3,-1,-4,5]=>11110=>[4,1]=>[1,4]
[-2,-3,-1,-4,-5]=>11111=>[5]=>[5]
[2,3,1,5,4]=>00000=>[5]=>[5]
[2,3,1,5,-4]=>00001=>[4,1]=>[1,4]
[2,3,1,-5,4]=>00010=>[3,1,1]=>[1,1,3]
[2,3,1,-5,-4]=>00011=>[3,2]=>[2,3]
[2,3,-1,5,4]=>00100=>[2,1,2]=>[2,1,2]
[2,3,-1,5,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,-1,-5,4]=>00110=>[2,2,1]=>[1,2,2]
[2,3,-1,-5,-4]=>00111=>[2,3]=>[3,2]
[2,-3,1,5,4]=>01000=>[1,1,3]=>[3,1,1]
[2,-3,1,5,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-3,1,-5,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-3,1,-5,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-3,-1,5,4]=>01100=>[1,2,2]=>[2,2,1]
[2,-3,-1,5,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-3,-1,-5,4]=>01110=>[1,3,1]=>[1,3,1]
[2,-3,-1,-5,-4]=>01111=>[1,4]=>[4,1]
[-2,3,1,5,4]=>10000=>[1,4]=>[4,1]
[-2,3,1,5,-4]=>10001=>[1,3,1]=>[1,3,1]
[-2,3,1,-5,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,3,1,-5,-4]=>10011=>[1,2,2]=>[2,2,1]
[-2,3,-1,5,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,3,-1,5,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,3,-1,-5,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,3,-1,-5,-4]=>10111=>[1,1,3]=>[3,1,1]
[-2,-3,1,5,4]=>11000=>[2,3]=>[3,2]
[-2,-3,1,5,-4]=>11001=>[2,2,1]=>[1,2,2]
[-2,-3,1,-5,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-3,1,-5,-4]=>11011=>[2,1,2]=>[2,1,2]
[-2,-3,-1,5,4]=>11100=>[3,2]=>[2,3]
[-2,-3,-1,5,-4]=>11101=>[3,1,1]=>[1,1,3]
[-2,-3,-1,-5,4]=>11110=>[4,1]=>[1,4]
[-2,-3,-1,-5,-4]=>11111=>[5]=>[5]
[2,3,4,1,5]=>00000=>[5]=>[5]
[2,3,4,1,-5]=>00001=>[4,1]=>[1,4]
[2,3,4,-1,5]=>00010=>[3,1,1]=>[1,1,3]
[2,3,4,-1,-5]=>00011=>[3,2]=>[2,3]
[2,3,-4,1,5]=>00100=>[2,1,2]=>[2,1,2]
[2,3,-4,1,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,-4,-1,5]=>00110=>[2,2,1]=>[1,2,2]
[2,3,-4,-1,-5]=>00111=>[2,3]=>[3,2]
[2,-3,4,1,5]=>01000=>[1,1,3]=>[3,1,1]
[2,-3,4,1,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-3,4,-1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-3,4,-1,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-3,-4,1,5]=>01100=>[1,2,2]=>[2,2,1]
[2,-3,-4,1,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-3,-4,-1,5]=>01110=>[1,3,1]=>[1,3,1]
[2,-3,-4,-1,-5]=>01111=>[1,4]=>[4,1]
[-2,3,4,1,5]=>10000=>[1,4]=>[4,1]
[-2,3,4,1,-5]=>10001=>[1,3,1]=>[1,3,1]
[-2,3,4,-1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,3,4,-1,-5]=>10011=>[1,2,2]=>[2,2,1]
[-2,3,-4,1,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,3,-4,1,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,3,-4,-1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,3,-4,-1,-5]=>10111=>[1,1,3]=>[3,1,1]
[-2,-3,4,1,5]=>11000=>[2,3]=>[3,2]
[-2,-3,4,1,-5]=>11001=>[2,2,1]=>[1,2,2]
[-2,-3,4,-1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-3,4,-1,-5]=>11011=>[2,1,2]=>[2,1,2]
[-2,-3,-4,1,5]=>11100=>[3,2]=>[2,3]
[-2,-3,-4,1,-5]=>11101=>[3,1,1]=>[1,1,3]
[-2,-3,-4,-1,5]=>11110=>[4,1]=>[1,4]
[-2,-3,-4,-1,-5]=>11111=>[5]=>[5]
[2,3,4,5,1]=>00000=>[5]=>[5]
[2,3,4,5,-1]=>00001=>[4,1]=>[1,4]
[2,3,4,-5,1]=>00010=>[3,1,1]=>[1,1,3]
[2,3,4,-5,-1]=>00011=>[3,2]=>[2,3]
[2,3,-4,5,1]=>00100=>[2,1,2]=>[2,1,2]
[2,3,-4,5,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,-4,-5,1]=>00110=>[2,2,1]=>[1,2,2]
[2,3,-4,-5,-1]=>00111=>[2,3]=>[3,2]
[2,-3,4,5,1]=>01000=>[1,1,3]=>[3,1,1]
[2,-3,4,5,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-3,4,-5,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-3,4,-5,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-3,-4,5,1]=>01100=>[1,2,2]=>[2,2,1]
[2,-3,-4,5,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-3,-4,-5,1]=>01110=>[1,3,1]=>[1,3,1]
[2,-3,-4,-5,-1]=>01111=>[1,4]=>[4,1]
[-2,3,4,5,1]=>10000=>[1,4]=>[4,1]
[-2,3,4,5,-1]=>10001=>[1,3,1]=>[1,3,1]
[-2,3,4,-5,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,3,4,-5,-1]=>10011=>[1,2,2]=>[2,2,1]
[-2,3,-4,5,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,3,-4,5,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,3,-4,-5,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,3,-4,-5,-1]=>10111=>[1,1,3]=>[3,1,1]
[-2,-3,4,5,1]=>11000=>[2,3]=>[3,2]
[-2,-3,4,5,-1]=>11001=>[2,2,1]=>[1,2,2]
[-2,-3,4,-5,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-3,4,-5,-1]=>11011=>[2,1,2]=>[2,1,2]
[-2,-3,-4,5,1]=>11100=>[3,2]=>[2,3]
[-2,-3,-4,5,-1]=>11101=>[3,1,1]=>[1,1,3]
[-2,-3,-4,-5,1]=>11110=>[4,1]=>[1,4]
[-2,-3,-4,-5,-1]=>11111=>[5]=>[5]
[2,3,5,1,4]=>00000=>[5]=>[5]
[2,3,5,1,-4]=>00001=>[4,1]=>[1,4]
[2,3,5,-1,4]=>00010=>[3,1,1]=>[1,1,3]
[2,3,5,-1,-4]=>00011=>[3,2]=>[2,3]
[2,3,-5,1,4]=>00100=>[2,1,2]=>[2,1,2]
[2,3,-5,1,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,-5,-1,4]=>00110=>[2,2,1]=>[1,2,2]
[2,3,-5,-1,-4]=>00111=>[2,3]=>[3,2]
[2,-3,5,1,4]=>01000=>[1,1,3]=>[3,1,1]
[2,-3,5,1,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-3,5,-1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-3,5,-1,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-3,-5,1,4]=>01100=>[1,2,2]=>[2,2,1]
[2,-3,-5,1,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-3,-5,-1,4]=>01110=>[1,3,1]=>[1,3,1]
[2,-3,-5,-1,-4]=>01111=>[1,4]=>[4,1]
[-2,3,5,1,4]=>10000=>[1,4]=>[4,1]
[-2,3,5,1,-4]=>10001=>[1,3,1]=>[1,3,1]
[-2,3,5,-1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,3,5,-1,-4]=>10011=>[1,2,2]=>[2,2,1]
[-2,3,-5,1,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,3,-5,1,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,3,-5,-1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,3,-5,-1,-4]=>10111=>[1,1,3]=>[3,1,1]
[-2,-3,5,1,4]=>11000=>[2,3]=>[3,2]
[-2,-3,5,1,-4]=>11001=>[2,2,1]=>[1,2,2]
[-2,-3,5,-1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-3,5,-1,-4]=>11011=>[2,1,2]=>[2,1,2]
[-2,-3,-5,1,4]=>11100=>[3,2]=>[2,3]
[-2,-3,-5,1,-4]=>11101=>[3,1,1]=>[1,1,3]
[-2,-3,-5,-1,4]=>11110=>[4,1]=>[1,4]
[-2,-3,-5,-1,-4]=>11111=>[5]=>[5]
[2,3,5,4,1]=>00000=>[5]=>[5]
[2,3,5,4,-1]=>00001=>[4,1]=>[1,4]
[2,3,5,-4,1]=>00010=>[3,1,1]=>[1,1,3]
[2,3,5,-4,-1]=>00011=>[3,2]=>[2,3]
[2,3,-5,4,1]=>00100=>[2,1,2]=>[2,1,2]
[2,3,-5,4,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,-5,-4,1]=>00110=>[2,2,1]=>[1,2,2]
[2,3,-5,-4,-1]=>00111=>[2,3]=>[3,2]
[2,-3,5,4,1]=>01000=>[1,1,3]=>[3,1,1]
[2,-3,5,4,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-3,5,-4,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-3,5,-4,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-3,-5,4,1]=>01100=>[1,2,2]=>[2,2,1]
[2,-3,-5,4,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-3,-5,-4,1]=>01110=>[1,3,1]=>[1,3,1]
[2,-3,-5,-4,-1]=>01111=>[1,4]=>[4,1]
[-2,3,5,4,1]=>10000=>[1,4]=>[4,1]
[-2,3,5,4,-1]=>10001=>[1,3,1]=>[1,3,1]
[-2,3,5,-4,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,3,5,-4,-1]=>10011=>[1,2,2]=>[2,2,1]
[-2,3,-5,4,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,3,-5,4,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,3,-5,-4,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,3,-5,-4,-1]=>10111=>[1,1,3]=>[3,1,1]
[-2,-3,5,4,1]=>11000=>[2,3]=>[3,2]
[-2,-3,5,4,-1]=>11001=>[2,2,1]=>[1,2,2]
[-2,-3,5,-4,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-3,5,-4,-1]=>11011=>[2,1,2]=>[2,1,2]
[-2,-3,-5,4,1]=>11100=>[3,2]=>[2,3]
[-2,-3,-5,4,-1]=>11101=>[3,1,1]=>[1,1,3]
[-2,-3,-5,-4,1]=>11110=>[4,1]=>[1,4]
[-2,-3,-5,-4,-1]=>11111=>[5]=>[5]
[2,4,1,3,5]=>00000=>[5]=>[5]
[2,4,1,3,-5]=>00001=>[4,1]=>[1,4]
[2,4,1,-3,5]=>00010=>[3,1,1]=>[1,1,3]
[2,4,1,-3,-5]=>00011=>[3,2]=>[2,3]
[2,4,-1,3,5]=>00100=>[2,1,2]=>[2,1,2]
[2,4,-1,3,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,-1,-3,5]=>00110=>[2,2,1]=>[1,2,2]
[2,4,-1,-3,-5]=>00111=>[2,3]=>[3,2]
[2,-4,1,3,5]=>01000=>[1,1,3]=>[3,1,1]
[2,-4,1,3,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-4,1,-3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-4,1,-3,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-4,-1,3,5]=>01100=>[1,2,2]=>[2,2,1]
[2,-4,-1,3,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-4,-1,-3,5]=>01110=>[1,3,1]=>[1,3,1]
[2,-4,-1,-3,-5]=>01111=>[1,4]=>[4,1]
[-2,4,1,3,5]=>10000=>[1,4]=>[4,1]
[-2,4,1,3,-5]=>10001=>[1,3,1]=>[1,3,1]
[-2,4,1,-3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,4,1,-3,-5]=>10011=>[1,2,2]=>[2,2,1]
[-2,4,-1,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,4,-1,3,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,4,-1,-3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,4,-1,-3,-5]=>10111=>[1,1,3]=>[3,1,1]
[-2,-4,1,3,5]=>11000=>[2,3]=>[3,2]
[-2,-4,1,3,-5]=>11001=>[2,2,1]=>[1,2,2]
[-2,-4,1,-3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-4,1,-3,-5]=>11011=>[2,1,2]=>[2,1,2]
[-2,-4,-1,3,5]=>11100=>[3,2]=>[2,3]
[-2,-4,-1,3,-5]=>11101=>[3,1,1]=>[1,1,3]
[-2,-4,-1,-3,5]=>11110=>[4,1]=>[1,4]
[-2,-4,-1,-3,-5]=>11111=>[5]=>[5]
[2,4,1,5,3]=>00000=>[5]=>[5]
[2,4,1,5,-3]=>00001=>[4,1]=>[1,4]
[2,4,1,-5,3]=>00010=>[3,1,1]=>[1,1,3]
[2,4,1,-5,-3]=>00011=>[3,2]=>[2,3]
[2,4,-1,5,3]=>00100=>[2,1,2]=>[2,1,2]
[2,4,-1,5,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,-1,-5,3]=>00110=>[2,2,1]=>[1,2,2]
[2,4,-1,-5,-3]=>00111=>[2,3]=>[3,2]
[2,-4,1,5,3]=>01000=>[1,1,3]=>[3,1,1]
[2,-4,1,5,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-4,1,-5,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-4,1,-5,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-4,-1,5,3]=>01100=>[1,2,2]=>[2,2,1]
[2,-4,-1,5,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-4,-1,-5,3]=>01110=>[1,3,1]=>[1,3,1]
[2,-4,-1,-5,-3]=>01111=>[1,4]=>[4,1]
[-2,4,1,5,3]=>10000=>[1,4]=>[4,1]
[-2,4,1,5,-3]=>10001=>[1,3,1]=>[1,3,1]
[-2,4,1,-5,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,4,1,-5,-3]=>10011=>[1,2,2]=>[2,2,1]
[-2,4,-1,5,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,4,-1,5,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,4,-1,-5,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,4,-1,-5,-3]=>10111=>[1,1,3]=>[3,1,1]
[-2,-4,1,5,3]=>11000=>[2,3]=>[3,2]
[-2,-4,1,5,-3]=>11001=>[2,2,1]=>[1,2,2]
[-2,-4,1,-5,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-4,1,-5,-3]=>11011=>[2,1,2]=>[2,1,2]
[-2,-4,-1,5,3]=>11100=>[3,2]=>[2,3]
[-2,-4,-1,5,-3]=>11101=>[3,1,1]=>[1,1,3]
[-2,-4,-1,-5,3]=>11110=>[4,1]=>[1,4]
[-2,-4,-1,-5,-3]=>11111=>[5]=>[5]
[2,4,3,1,5]=>00000=>[5]=>[5]
[2,4,3,1,-5]=>00001=>[4,1]=>[1,4]
[2,4,3,-1,5]=>00010=>[3,1,1]=>[1,1,3]
[2,4,3,-1,-5]=>00011=>[3,2]=>[2,3]
[2,4,-3,1,5]=>00100=>[2,1,2]=>[2,1,2]
[2,4,-3,1,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,-3,-1,5]=>00110=>[2,2,1]=>[1,2,2]
[2,4,-3,-1,-5]=>00111=>[2,3]=>[3,2]
[2,-4,3,1,5]=>01000=>[1,1,3]=>[3,1,1]
[2,-4,3,1,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-4,3,-1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-4,3,-1,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-4,-3,1,5]=>01100=>[1,2,2]=>[2,2,1]
[2,-4,-3,1,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-4,-3,-1,5]=>01110=>[1,3,1]=>[1,3,1]
[2,-4,-3,-1,-5]=>01111=>[1,4]=>[4,1]
[-2,4,3,1,5]=>10000=>[1,4]=>[4,1]
[-2,4,3,1,-5]=>10001=>[1,3,1]=>[1,3,1]
[-2,4,3,-1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,4,3,-1,-5]=>10011=>[1,2,2]=>[2,2,1]
[-2,4,-3,1,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,4,-3,1,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,4,-3,-1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,4,-3,-1,-5]=>10111=>[1,1,3]=>[3,1,1]
[-2,-4,3,1,5]=>11000=>[2,3]=>[3,2]
[-2,-4,3,1,-5]=>11001=>[2,2,1]=>[1,2,2]
[-2,-4,3,-1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-4,3,-1,-5]=>11011=>[2,1,2]=>[2,1,2]
[-2,-4,-3,1,5]=>11100=>[3,2]=>[2,3]
[-2,-4,-3,1,-5]=>11101=>[3,1,1]=>[1,1,3]
[-2,-4,-3,-1,5]=>11110=>[4,1]=>[1,4]
[-2,-4,-3,-1,-5]=>11111=>[5]=>[5]
[2,4,3,5,1]=>00000=>[5]=>[5]
[2,4,3,5,-1]=>00001=>[4,1]=>[1,4]
[2,4,3,-5,1]=>00010=>[3,1,1]=>[1,1,3]
[2,4,3,-5,-1]=>00011=>[3,2]=>[2,3]
[2,4,-3,5,1]=>00100=>[2,1,2]=>[2,1,2]
[2,4,-3,5,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,-3,-5,1]=>00110=>[2,2,1]=>[1,2,2]
[2,4,-3,-5,-1]=>00111=>[2,3]=>[3,2]
[2,-4,3,5,1]=>01000=>[1,1,3]=>[3,1,1]
[2,-4,3,5,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-4,3,-5,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-4,3,-5,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-4,-3,5,1]=>01100=>[1,2,2]=>[2,2,1]
[2,-4,-3,5,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-4,-3,-5,1]=>01110=>[1,3,1]=>[1,3,1]
[2,-4,-3,-5,-1]=>01111=>[1,4]=>[4,1]
[-2,4,3,5,1]=>10000=>[1,4]=>[4,1]
[-2,4,3,5,-1]=>10001=>[1,3,1]=>[1,3,1]
[-2,4,3,-5,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,4,3,-5,-1]=>10011=>[1,2,2]=>[2,2,1]
[-2,4,-3,5,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,4,-3,5,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,4,-3,-5,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,4,-3,-5,-1]=>10111=>[1,1,3]=>[3,1,1]
[-2,-4,3,5,1]=>11000=>[2,3]=>[3,2]
[-2,-4,3,5,-1]=>11001=>[2,2,1]=>[1,2,2]
[-2,-4,3,-5,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-4,3,-5,-1]=>11011=>[2,1,2]=>[2,1,2]
[-2,-4,-3,5,1]=>11100=>[3,2]=>[2,3]
[-2,-4,-3,5,-1]=>11101=>[3,1,1]=>[1,1,3]
[-2,-4,-3,-5,1]=>11110=>[4,1]=>[1,4]
[-2,-4,-3,-5,-1]=>11111=>[5]=>[5]
[2,4,5,1,3]=>00000=>[5]=>[5]
[2,4,5,1,-3]=>00001=>[4,1]=>[1,4]
[2,4,5,-1,3]=>00010=>[3,1,1]=>[1,1,3]
[2,4,5,-1,-3]=>00011=>[3,2]=>[2,3]
[2,4,-5,1,3]=>00100=>[2,1,2]=>[2,1,2]
[2,4,-5,1,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,-5,-1,3]=>00110=>[2,2,1]=>[1,2,2]
[2,4,-5,-1,-3]=>00111=>[2,3]=>[3,2]
[2,-4,5,1,3]=>01000=>[1,1,3]=>[3,1,1]
[2,-4,5,1,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-4,5,-1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-4,5,-1,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-4,-5,1,3]=>01100=>[1,2,2]=>[2,2,1]
[2,-4,-5,1,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-4,-5,-1,3]=>01110=>[1,3,1]=>[1,3,1]
[2,-4,-5,-1,-3]=>01111=>[1,4]=>[4,1]
[-2,4,5,1,3]=>10000=>[1,4]=>[4,1]
[-2,4,5,1,-3]=>10001=>[1,3,1]=>[1,3,1]
[-2,4,5,-1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,4,5,-1,-3]=>10011=>[1,2,2]=>[2,2,1]
[-2,4,-5,1,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,4,-5,1,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,4,-5,-1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,4,-5,-1,-3]=>10111=>[1,1,3]=>[3,1,1]
[-2,-4,5,1,3]=>11000=>[2,3]=>[3,2]
[-2,-4,5,1,-3]=>11001=>[2,2,1]=>[1,2,2]
[-2,-4,5,-1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-4,5,-1,-3]=>11011=>[2,1,2]=>[2,1,2]
[-2,-4,-5,1,3]=>11100=>[3,2]=>[2,3]
[-2,-4,-5,1,-3]=>11101=>[3,1,1]=>[1,1,3]
[-2,-4,-5,-1,3]=>11110=>[4,1]=>[1,4]
[-2,-4,-5,-1,-3]=>11111=>[5]=>[5]
[2,4,5,3,1]=>00000=>[5]=>[5]
[2,4,5,3,-1]=>00001=>[4,1]=>[1,4]
[2,4,5,-3,1]=>00010=>[3,1,1]=>[1,1,3]
[2,4,5,-3,-1]=>00011=>[3,2]=>[2,3]
[2,4,-5,3,1]=>00100=>[2,1,2]=>[2,1,2]
[2,4,-5,3,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,-5,-3,1]=>00110=>[2,2,1]=>[1,2,2]
[2,4,-5,-3,-1]=>00111=>[2,3]=>[3,2]
[2,-4,5,3,1]=>01000=>[1,1,3]=>[3,1,1]
[2,-4,5,3,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-4,5,-3,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-4,5,-3,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-4,-5,3,1]=>01100=>[1,2,2]=>[2,2,1]
[2,-4,-5,3,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-4,-5,-3,1]=>01110=>[1,3,1]=>[1,3,1]
[2,-4,-5,-3,-1]=>01111=>[1,4]=>[4,1]
[-2,4,5,3,1]=>10000=>[1,4]=>[4,1]
[-2,4,5,3,-1]=>10001=>[1,3,1]=>[1,3,1]
[-2,4,5,-3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,4,5,-3,-1]=>10011=>[1,2,2]=>[2,2,1]
[-2,4,-5,3,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,4,-5,3,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,4,-5,-3,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,4,-5,-3,-1]=>10111=>[1,1,3]=>[3,1,1]
[-2,-4,5,3,1]=>11000=>[2,3]=>[3,2]
[-2,-4,5,3,-1]=>11001=>[2,2,1]=>[1,2,2]
[-2,-4,5,-3,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-4,5,-3,-1]=>11011=>[2,1,2]=>[2,1,2]
[-2,-4,-5,3,1]=>11100=>[3,2]=>[2,3]
[-2,-4,-5,3,-1]=>11101=>[3,1,1]=>[1,1,3]
[-2,-4,-5,-3,1]=>11110=>[4,1]=>[1,4]
[-2,-4,-5,-3,-1]=>11111=>[5]=>[5]
[2,5,1,3,4]=>00000=>[5]=>[5]
[2,5,1,3,-4]=>00001=>[4,1]=>[1,4]
[2,5,1,-3,4]=>00010=>[3,1,1]=>[1,1,3]
[2,5,1,-3,-4]=>00011=>[3,2]=>[2,3]
[2,5,-1,3,4]=>00100=>[2,1,2]=>[2,1,2]
[2,5,-1,3,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,-1,-3,4]=>00110=>[2,2,1]=>[1,2,2]
[2,5,-1,-3,-4]=>00111=>[2,3]=>[3,2]
[2,-5,1,3,4]=>01000=>[1,1,3]=>[3,1,1]
[2,-5,1,3,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-5,1,-3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-5,1,-3,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-5,-1,3,4]=>01100=>[1,2,2]=>[2,2,1]
[2,-5,-1,3,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-5,-1,-3,4]=>01110=>[1,3,1]=>[1,3,1]
[2,-5,-1,-3,-4]=>01111=>[1,4]=>[4,1]
[-2,5,1,3,4]=>10000=>[1,4]=>[4,1]
[-2,5,1,3,-4]=>10001=>[1,3,1]=>[1,3,1]
[-2,5,1,-3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,5,1,-3,-4]=>10011=>[1,2,2]=>[2,2,1]
[-2,5,-1,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,5,-1,3,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,5,-1,-3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,5,-1,-3,-4]=>10111=>[1,1,3]=>[3,1,1]
[-2,-5,1,3,4]=>11000=>[2,3]=>[3,2]
[-2,-5,1,3,-4]=>11001=>[2,2,1]=>[1,2,2]
[-2,-5,1,-3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-5,1,-3,-4]=>11011=>[2,1,2]=>[2,1,2]
[-2,-5,-1,3,4]=>11100=>[3,2]=>[2,3]
[-2,-5,-1,3,-4]=>11101=>[3,1,1]=>[1,1,3]
[-2,-5,-1,-3,4]=>11110=>[4,1]=>[1,4]
[-2,-5,-1,-3,-4]=>11111=>[5]=>[5]
[2,5,1,4,3]=>00000=>[5]=>[5]
[2,5,1,4,-3]=>00001=>[4,1]=>[1,4]
[2,5,1,-4,3]=>00010=>[3,1,1]=>[1,1,3]
[2,5,1,-4,-3]=>00011=>[3,2]=>[2,3]
[2,5,-1,4,3]=>00100=>[2,1,2]=>[2,1,2]
[2,5,-1,4,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,-1,-4,3]=>00110=>[2,2,1]=>[1,2,2]
[2,5,-1,-4,-3]=>00111=>[2,3]=>[3,2]
[2,-5,1,4,3]=>01000=>[1,1,3]=>[3,1,1]
[2,-5,1,4,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-5,1,-4,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-5,1,-4,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-5,-1,4,3]=>01100=>[1,2,2]=>[2,2,1]
[2,-5,-1,4,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-5,-1,-4,3]=>01110=>[1,3,1]=>[1,3,1]
[2,-5,-1,-4,-3]=>01111=>[1,4]=>[4,1]
[-2,5,1,4,3]=>10000=>[1,4]=>[4,1]
[-2,5,1,4,-3]=>10001=>[1,3,1]=>[1,3,1]
[-2,5,1,-4,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,5,1,-4,-3]=>10011=>[1,2,2]=>[2,2,1]
[-2,5,-1,4,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,5,-1,4,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,5,-1,-4,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,5,-1,-4,-3]=>10111=>[1,1,3]=>[3,1,1]
[-2,-5,1,4,3]=>11000=>[2,3]=>[3,2]
[-2,-5,1,4,-3]=>11001=>[2,2,1]=>[1,2,2]
[-2,-5,1,-4,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-5,1,-4,-3]=>11011=>[2,1,2]=>[2,1,2]
[-2,-5,-1,4,3]=>11100=>[3,2]=>[2,3]
[-2,-5,-1,4,-3]=>11101=>[3,1,1]=>[1,1,3]
[-2,-5,-1,-4,3]=>11110=>[4,1]=>[1,4]
[-2,-5,-1,-4,-3]=>11111=>[5]=>[5]
[2,5,3,1,4]=>00000=>[5]=>[5]
[2,5,3,1,-4]=>00001=>[4,1]=>[1,4]
[2,5,3,-1,4]=>00010=>[3,1,1]=>[1,1,3]
[2,5,3,-1,-4]=>00011=>[3,2]=>[2,3]
[2,5,-3,1,4]=>00100=>[2,1,2]=>[2,1,2]
[2,5,-3,1,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,-3,-1,4]=>00110=>[2,2,1]=>[1,2,2]
[2,5,-3,-1,-4]=>00111=>[2,3]=>[3,2]
[2,-5,3,1,4]=>01000=>[1,1,3]=>[3,1,1]
[2,-5,3,1,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-5,3,-1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-5,3,-1,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-5,-3,1,4]=>01100=>[1,2,2]=>[2,2,1]
[2,-5,-3,1,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-5,-3,-1,4]=>01110=>[1,3,1]=>[1,3,1]
[2,-5,-3,-1,-4]=>01111=>[1,4]=>[4,1]
[-2,5,3,1,4]=>10000=>[1,4]=>[4,1]
[-2,5,3,1,-4]=>10001=>[1,3,1]=>[1,3,1]
[-2,5,3,-1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,5,3,-1,-4]=>10011=>[1,2,2]=>[2,2,1]
[-2,5,-3,1,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,5,-3,1,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,5,-3,-1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,5,-3,-1,-4]=>10111=>[1,1,3]=>[3,1,1]
[-2,-5,3,1,4]=>11000=>[2,3]=>[3,2]
[-2,-5,3,1,-4]=>11001=>[2,2,1]=>[1,2,2]
[-2,-5,3,-1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-5,3,-1,-4]=>11011=>[2,1,2]=>[2,1,2]
[-2,-5,-3,1,4]=>11100=>[3,2]=>[2,3]
[-2,-5,-3,1,-4]=>11101=>[3,1,1]=>[1,1,3]
[-2,-5,-3,-1,4]=>11110=>[4,1]=>[1,4]
[-2,-5,-3,-1,-4]=>11111=>[5]=>[5]
[2,5,3,4,1]=>00000=>[5]=>[5]
[2,5,3,4,-1]=>00001=>[4,1]=>[1,4]
[2,5,3,-4,1]=>00010=>[3,1,1]=>[1,1,3]
[2,5,3,-4,-1]=>00011=>[3,2]=>[2,3]
[2,5,-3,4,1]=>00100=>[2,1,2]=>[2,1,2]
[2,5,-3,4,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,-3,-4,1]=>00110=>[2,2,1]=>[1,2,2]
[2,5,-3,-4,-1]=>00111=>[2,3]=>[3,2]
[2,-5,3,4,1]=>01000=>[1,1,3]=>[3,1,1]
[2,-5,3,4,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-5,3,-4,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-5,3,-4,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-5,-3,4,1]=>01100=>[1,2,2]=>[2,2,1]
[2,-5,-3,4,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-5,-3,-4,1]=>01110=>[1,3,1]=>[1,3,1]
[2,-5,-3,-4,-1]=>01111=>[1,4]=>[4,1]
[-2,5,3,4,1]=>10000=>[1,4]=>[4,1]
[-2,5,3,4,-1]=>10001=>[1,3,1]=>[1,3,1]
[-2,5,3,-4,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,5,3,-4,-1]=>10011=>[1,2,2]=>[2,2,1]
[-2,5,-3,4,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,5,-3,4,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,5,-3,-4,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,5,-3,-4,-1]=>10111=>[1,1,3]=>[3,1,1]
[-2,-5,3,4,1]=>11000=>[2,3]=>[3,2]
[-2,-5,3,4,-1]=>11001=>[2,2,1]=>[1,2,2]
[-2,-5,3,-4,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-5,3,-4,-1]=>11011=>[2,1,2]=>[2,1,2]
[-2,-5,-3,4,1]=>11100=>[3,2]=>[2,3]
[-2,-5,-3,4,-1]=>11101=>[3,1,1]=>[1,1,3]
[-2,-5,-3,-4,1]=>11110=>[4,1]=>[1,4]
[-2,-5,-3,-4,-1]=>11111=>[5]=>[5]
[2,5,4,1,3]=>00000=>[5]=>[5]
[2,5,4,1,-3]=>00001=>[4,1]=>[1,4]
[2,5,4,-1,3]=>00010=>[3,1,1]=>[1,1,3]
[2,5,4,-1,-3]=>00011=>[3,2]=>[2,3]
[2,5,-4,1,3]=>00100=>[2,1,2]=>[2,1,2]
[2,5,-4,1,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,-4,-1,3]=>00110=>[2,2,1]=>[1,2,2]
[2,5,-4,-1,-3]=>00111=>[2,3]=>[3,2]
[2,-5,4,1,3]=>01000=>[1,1,3]=>[3,1,1]
[2,-5,4,1,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-5,4,-1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-5,4,-1,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-5,-4,1,3]=>01100=>[1,2,2]=>[2,2,1]
[2,-5,-4,1,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-5,-4,-1,3]=>01110=>[1,3,1]=>[1,3,1]
[2,-5,-4,-1,-3]=>01111=>[1,4]=>[4,1]
[-2,5,4,1,3]=>10000=>[1,4]=>[4,1]
[-2,5,4,1,-3]=>10001=>[1,3,1]=>[1,3,1]
[-2,5,4,-1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,5,4,-1,-3]=>10011=>[1,2,2]=>[2,2,1]
[-2,5,-4,1,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,5,-4,1,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,5,-4,-1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,5,-4,-1,-3]=>10111=>[1,1,3]=>[3,1,1]
[-2,-5,4,1,3]=>11000=>[2,3]=>[3,2]
[-2,-5,4,1,-3]=>11001=>[2,2,1]=>[1,2,2]
[-2,-5,4,-1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-5,4,-1,-3]=>11011=>[2,1,2]=>[2,1,2]
[-2,-5,-4,1,3]=>11100=>[3,2]=>[2,3]
[-2,-5,-4,1,-3]=>11101=>[3,1,1]=>[1,1,3]
[-2,-5,-4,-1,3]=>11110=>[4,1]=>[1,4]
[-2,-5,-4,-1,-3]=>11111=>[5]=>[5]
[2,5,4,3,1]=>00000=>[5]=>[5]
[2,5,4,3,-1]=>00001=>[4,1]=>[1,4]
[2,5,4,-3,1]=>00010=>[3,1,1]=>[1,1,3]
[2,5,4,-3,-1]=>00011=>[3,2]=>[2,3]
[2,5,-4,3,1]=>00100=>[2,1,2]=>[2,1,2]
[2,5,-4,3,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,-4,-3,1]=>00110=>[2,2,1]=>[1,2,2]
[2,5,-4,-3,-1]=>00111=>[2,3]=>[3,2]
[2,-5,4,3,1]=>01000=>[1,1,3]=>[3,1,1]
[2,-5,4,3,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,-5,4,-3,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,-5,4,-3,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,-5,-4,3,1]=>01100=>[1,2,2]=>[2,2,1]
[2,-5,-4,3,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,-5,-4,-3,1]=>01110=>[1,3,1]=>[1,3,1]
[2,-5,-4,-3,-1]=>01111=>[1,4]=>[4,1]
[-2,5,4,3,1]=>10000=>[1,4]=>[4,1]
[-2,5,4,3,-1]=>10001=>[1,3,1]=>[1,3,1]
[-2,5,4,-3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-2,5,4,-3,-1]=>10011=>[1,2,2]=>[2,2,1]
[-2,5,-4,3,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-2,5,-4,3,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-2,5,-4,-3,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-2,5,-4,-3,-1]=>10111=>[1,1,3]=>[3,1,1]
[-2,-5,4,3,1]=>11000=>[2,3]=>[3,2]
[-2,-5,4,3,-1]=>11001=>[2,2,1]=>[1,2,2]
[-2,-5,4,-3,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-2,-5,4,-3,-1]=>11011=>[2,1,2]=>[2,1,2]
[-2,-5,-4,3,1]=>11100=>[3,2]=>[2,3]
[-2,-5,-4,3,-1]=>11101=>[3,1,1]=>[1,1,3]
[-2,-5,-4,-3,1]=>11110=>[4,1]=>[1,4]
[-2,-5,-4,-3,-1]=>11111=>[5]=>[5]
[3,1,2,4,5]=>00000=>[5]=>[5]
[3,1,2,4,-5]=>00001=>[4,1]=>[1,4]
[3,1,2,-4,5]=>00010=>[3,1,1]=>[1,1,3]
[3,1,2,-4,-5]=>00011=>[3,2]=>[2,3]
[3,1,-2,4,5]=>00100=>[2,1,2]=>[2,1,2]
[3,1,-2,4,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,1,-2,-4,5]=>00110=>[2,2,1]=>[1,2,2]
[3,1,-2,-4,-5]=>00111=>[2,3]=>[3,2]
[3,-1,2,4,5]=>01000=>[1,1,3]=>[3,1,1]
[3,-1,2,4,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-1,2,-4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-1,2,-4,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-1,-2,4,5]=>01100=>[1,2,2]=>[2,2,1]
[3,-1,-2,4,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-1,-2,-4,5]=>01110=>[1,3,1]=>[1,3,1]
[3,-1,-2,-4,-5]=>01111=>[1,4]=>[4,1]
[-3,1,2,4,5]=>10000=>[1,4]=>[4,1]
[-3,1,2,4,-5]=>10001=>[1,3,1]=>[1,3,1]
[-3,1,2,-4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,1,2,-4,-5]=>10011=>[1,2,2]=>[2,2,1]
[-3,1,-2,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,1,-2,4,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,1,-2,-4,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,1,-2,-4,-5]=>10111=>[1,1,3]=>[3,1,1]
[-3,-1,2,4,5]=>11000=>[2,3]=>[3,2]
[-3,-1,2,4,-5]=>11001=>[2,2,1]=>[1,2,2]
[-3,-1,2,-4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-1,2,-4,-5]=>11011=>[2,1,2]=>[2,1,2]
[-3,-1,-2,4,5]=>11100=>[3,2]=>[2,3]
[-3,-1,-2,4,-5]=>11101=>[3,1,1]=>[1,1,3]
[-3,-1,-2,-4,5]=>11110=>[4,1]=>[1,4]
[-3,-1,-2,-4,-5]=>11111=>[5]=>[5]
[3,1,2,5,4]=>00000=>[5]=>[5]
[3,1,2,5,-4]=>00001=>[4,1]=>[1,4]
[3,1,2,-5,4]=>00010=>[3,1,1]=>[1,1,3]
[3,1,2,-5,-4]=>00011=>[3,2]=>[2,3]
[3,1,-2,5,4]=>00100=>[2,1,2]=>[2,1,2]
[3,1,-2,5,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,1,-2,-5,4]=>00110=>[2,2,1]=>[1,2,2]
[3,1,-2,-5,-4]=>00111=>[2,3]=>[3,2]
[3,-1,2,5,4]=>01000=>[1,1,3]=>[3,1,1]
[3,-1,2,5,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-1,2,-5,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-1,2,-5,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-1,-2,5,4]=>01100=>[1,2,2]=>[2,2,1]
[3,-1,-2,5,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-1,-2,-5,4]=>01110=>[1,3,1]=>[1,3,1]
[3,-1,-2,-5,-4]=>01111=>[1,4]=>[4,1]
[-3,1,2,5,4]=>10000=>[1,4]=>[4,1]
[-3,1,2,5,-4]=>10001=>[1,3,1]=>[1,3,1]
[-3,1,2,-5,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,1,2,-5,-4]=>10011=>[1,2,2]=>[2,2,1]
[-3,1,-2,5,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,1,-2,5,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,1,-2,-5,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,1,-2,-5,-4]=>10111=>[1,1,3]=>[3,1,1]
[-3,-1,2,5,4]=>11000=>[2,3]=>[3,2]
[-3,-1,2,5,-4]=>11001=>[2,2,1]=>[1,2,2]
[-3,-1,2,-5,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-1,2,-5,-4]=>11011=>[2,1,2]=>[2,1,2]
[-3,-1,-2,5,4]=>11100=>[3,2]=>[2,3]
[-3,-1,-2,5,-4]=>11101=>[3,1,1]=>[1,1,3]
[-3,-1,-2,-5,4]=>11110=>[4,1]=>[1,4]
[-3,-1,-2,-5,-4]=>11111=>[5]=>[5]
[3,1,4,2,5]=>00000=>[5]=>[5]
[3,1,4,2,-5]=>00001=>[4,1]=>[1,4]
[3,1,4,-2,5]=>00010=>[3,1,1]=>[1,1,3]
[3,1,4,-2,-5]=>00011=>[3,2]=>[2,3]
[3,1,-4,2,5]=>00100=>[2,1,2]=>[2,1,2]
[3,1,-4,2,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,1,-4,-2,5]=>00110=>[2,2,1]=>[1,2,2]
[3,1,-4,-2,-5]=>00111=>[2,3]=>[3,2]
[3,-1,4,2,5]=>01000=>[1,1,3]=>[3,1,1]
[3,-1,4,2,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-1,4,-2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-1,4,-2,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-1,-4,2,5]=>01100=>[1,2,2]=>[2,2,1]
[3,-1,-4,2,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-1,-4,-2,5]=>01110=>[1,3,1]=>[1,3,1]
[3,-1,-4,-2,-5]=>01111=>[1,4]=>[4,1]
[-3,1,4,2,5]=>10000=>[1,4]=>[4,1]
[-3,1,4,2,-5]=>10001=>[1,3,1]=>[1,3,1]
[-3,1,4,-2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,1,4,-2,-5]=>10011=>[1,2,2]=>[2,2,1]
[-3,1,-4,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,1,-4,2,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,1,-4,-2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,1,-4,-2,-5]=>10111=>[1,1,3]=>[3,1,1]
[-3,-1,4,2,5]=>11000=>[2,3]=>[3,2]
[-3,-1,4,2,-5]=>11001=>[2,2,1]=>[1,2,2]
[-3,-1,4,-2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-1,4,-2,-5]=>11011=>[2,1,2]=>[2,1,2]
[-3,-1,-4,2,5]=>11100=>[3,2]=>[2,3]
[-3,-1,-4,2,-5]=>11101=>[3,1,1]=>[1,1,3]
[-3,-1,-4,-2,5]=>11110=>[4,1]=>[1,4]
[-3,-1,-4,-2,-5]=>11111=>[5]=>[5]
[3,1,4,5,2]=>00000=>[5]=>[5]
[3,1,4,5,-2]=>00001=>[4,1]=>[1,4]
[3,1,4,-5,2]=>00010=>[3,1,1]=>[1,1,3]
[3,1,4,-5,-2]=>00011=>[3,2]=>[2,3]
[3,1,-4,5,2]=>00100=>[2,1,2]=>[2,1,2]
[3,1,-4,5,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,1,-4,-5,2]=>00110=>[2,2,1]=>[1,2,2]
[3,1,-4,-5,-2]=>00111=>[2,3]=>[3,2]
[3,-1,4,5,2]=>01000=>[1,1,3]=>[3,1,1]
[3,-1,4,5,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-1,4,-5,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-1,4,-5,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-1,-4,5,2]=>01100=>[1,2,2]=>[2,2,1]
[3,-1,-4,5,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-1,-4,-5,2]=>01110=>[1,3,1]=>[1,3,1]
[3,-1,-4,-5,-2]=>01111=>[1,4]=>[4,1]
[-3,1,4,5,2]=>10000=>[1,4]=>[4,1]
[-3,1,4,5,-2]=>10001=>[1,3,1]=>[1,3,1]
[-3,1,4,-5,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,1,4,-5,-2]=>10011=>[1,2,2]=>[2,2,1]
[-3,1,-4,5,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,1,-4,5,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,1,-4,-5,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,1,-4,-5,-2]=>10111=>[1,1,3]=>[3,1,1]
[-3,-1,4,5,2]=>11000=>[2,3]=>[3,2]
[-3,-1,4,5,-2]=>11001=>[2,2,1]=>[1,2,2]
[-3,-1,4,-5,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-1,4,-5,-2]=>11011=>[2,1,2]=>[2,1,2]
[-3,-1,-4,5,2]=>11100=>[3,2]=>[2,3]
[-3,-1,-4,5,-2]=>11101=>[3,1,1]=>[1,1,3]
[-3,-1,-4,-5,2]=>11110=>[4,1]=>[1,4]
[-3,-1,-4,-5,-2]=>11111=>[5]=>[5]
[3,1,5,2,4]=>00000=>[5]=>[5]
[3,1,5,2,-4]=>00001=>[4,1]=>[1,4]
[3,1,5,-2,4]=>00010=>[3,1,1]=>[1,1,3]
[3,1,5,-2,-4]=>00011=>[3,2]=>[2,3]
[3,1,-5,2,4]=>00100=>[2,1,2]=>[2,1,2]
[3,1,-5,2,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,1,-5,-2,4]=>00110=>[2,2,1]=>[1,2,2]
[3,1,-5,-2,-4]=>00111=>[2,3]=>[3,2]
[3,-1,5,2,4]=>01000=>[1,1,3]=>[3,1,1]
[3,-1,5,2,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-1,5,-2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-1,5,-2,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-1,-5,2,4]=>01100=>[1,2,2]=>[2,2,1]
[3,-1,-5,2,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-1,-5,-2,4]=>01110=>[1,3,1]=>[1,3,1]
[3,-1,-5,-2,-4]=>01111=>[1,4]=>[4,1]
[-3,1,5,2,4]=>10000=>[1,4]=>[4,1]
[-3,1,5,2,-4]=>10001=>[1,3,1]=>[1,3,1]
[-3,1,5,-2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,1,5,-2,-4]=>10011=>[1,2,2]=>[2,2,1]
[-3,1,-5,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,1,-5,2,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,1,-5,-2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,1,-5,-2,-4]=>10111=>[1,1,3]=>[3,1,1]
[-3,-1,5,2,4]=>11000=>[2,3]=>[3,2]
[-3,-1,5,2,-4]=>11001=>[2,2,1]=>[1,2,2]
[-3,-1,5,-2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-1,5,-2,-4]=>11011=>[2,1,2]=>[2,1,2]
[-3,-1,-5,2,4]=>11100=>[3,2]=>[2,3]
[-3,-1,-5,2,-4]=>11101=>[3,1,1]=>[1,1,3]
[-3,-1,-5,-2,4]=>11110=>[4,1]=>[1,4]
[-3,-1,-5,-2,-4]=>11111=>[5]=>[5]
[3,1,5,4,2]=>00000=>[5]=>[5]
[3,1,5,4,-2]=>00001=>[4,1]=>[1,4]
[3,1,5,-4,2]=>00010=>[3,1,1]=>[1,1,3]
[3,1,5,-4,-2]=>00011=>[3,2]=>[2,3]
[3,1,-5,4,2]=>00100=>[2,1,2]=>[2,1,2]
[3,1,-5,4,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,1,-5,-4,2]=>00110=>[2,2,1]=>[1,2,2]
[3,1,-5,-4,-2]=>00111=>[2,3]=>[3,2]
[3,-1,5,4,2]=>01000=>[1,1,3]=>[3,1,1]
[3,-1,5,4,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-1,5,-4,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-1,5,-4,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-1,-5,4,2]=>01100=>[1,2,2]=>[2,2,1]
[3,-1,-5,4,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-1,-5,-4,2]=>01110=>[1,3,1]=>[1,3,1]
[3,-1,-5,-4,-2]=>01111=>[1,4]=>[4,1]
[-3,1,5,4,2]=>10000=>[1,4]=>[4,1]
[-3,1,5,4,-2]=>10001=>[1,3,1]=>[1,3,1]
[-3,1,5,-4,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,1,5,-4,-2]=>10011=>[1,2,2]=>[2,2,1]
[-3,1,-5,4,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,1,-5,4,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,1,-5,-4,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,1,-5,-4,-2]=>10111=>[1,1,3]=>[3,1,1]
[-3,-1,5,4,2]=>11000=>[2,3]=>[3,2]
[-3,-1,5,4,-2]=>11001=>[2,2,1]=>[1,2,2]
[-3,-1,5,-4,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-1,5,-4,-2]=>11011=>[2,1,2]=>[2,1,2]
[-3,-1,-5,4,2]=>11100=>[3,2]=>[2,3]
[-3,-1,-5,4,-2]=>11101=>[3,1,1]=>[1,1,3]
[-3,-1,-5,-4,2]=>11110=>[4,1]=>[1,4]
[-3,-1,-5,-4,-2]=>11111=>[5]=>[5]
[3,2,1,4,5]=>00000=>[5]=>[5]
[3,2,1,4,-5]=>00001=>[4,1]=>[1,4]
[3,2,1,-4,5]=>00010=>[3,1,1]=>[1,1,3]
[3,2,1,-4,-5]=>00011=>[3,2]=>[2,3]
[3,2,-1,4,5]=>00100=>[2,1,2]=>[2,1,2]
[3,2,-1,4,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,2,-1,-4,5]=>00110=>[2,2,1]=>[1,2,2]
[3,2,-1,-4,-5]=>00111=>[2,3]=>[3,2]
[3,-2,1,4,5]=>01000=>[1,1,3]=>[3,1,1]
[3,-2,1,4,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-2,1,-4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-2,1,-4,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-2,-1,4,5]=>01100=>[1,2,2]=>[2,2,1]
[3,-2,-1,4,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-2,-1,-4,5]=>01110=>[1,3,1]=>[1,3,1]
[3,-2,-1,-4,-5]=>01111=>[1,4]=>[4,1]
[-3,2,1,4,5]=>10000=>[1,4]=>[4,1]
[-3,2,1,4,-5]=>10001=>[1,3,1]=>[1,3,1]
[-3,2,1,-4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,2,1,-4,-5]=>10011=>[1,2,2]=>[2,2,1]
[-3,2,-1,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,2,-1,4,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,2,-1,-4,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,2,-1,-4,-5]=>10111=>[1,1,3]=>[3,1,1]
[-3,-2,1,4,5]=>11000=>[2,3]=>[3,2]
[-3,-2,1,4,-5]=>11001=>[2,2,1]=>[1,2,2]
[-3,-2,1,-4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-2,1,-4,-5]=>11011=>[2,1,2]=>[2,1,2]
[-3,-2,-1,4,5]=>11100=>[3,2]=>[2,3]
[-3,-2,-1,4,-5]=>11101=>[3,1,1]=>[1,1,3]
[-3,-2,-1,-4,5]=>11110=>[4,1]=>[1,4]
[-3,-2,-1,-4,-5]=>11111=>[5]=>[5]
[3,2,1,5,4]=>00000=>[5]=>[5]
[3,2,1,5,-4]=>00001=>[4,1]=>[1,4]
[3,2,1,-5,4]=>00010=>[3,1,1]=>[1,1,3]
[3,2,1,-5,-4]=>00011=>[3,2]=>[2,3]
[3,2,-1,5,4]=>00100=>[2,1,2]=>[2,1,2]
[3,2,-1,5,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,2,-1,-5,4]=>00110=>[2,2,1]=>[1,2,2]
[3,2,-1,-5,-4]=>00111=>[2,3]=>[3,2]
[3,-2,1,5,4]=>01000=>[1,1,3]=>[3,1,1]
[3,-2,1,5,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-2,1,-5,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-2,1,-5,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-2,-1,5,4]=>01100=>[1,2,2]=>[2,2,1]
[3,-2,-1,5,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-2,-1,-5,4]=>01110=>[1,3,1]=>[1,3,1]
[3,-2,-1,-5,-4]=>01111=>[1,4]=>[4,1]
[-3,2,1,5,4]=>10000=>[1,4]=>[4,1]
[-3,2,1,5,-4]=>10001=>[1,3,1]=>[1,3,1]
[-3,2,1,-5,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,2,1,-5,-4]=>10011=>[1,2,2]=>[2,2,1]
[-3,2,-1,5,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,2,-1,5,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,2,-1,-5,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,2,-1,-5,-4]=>10111=>[1,1,3]=>[3,1,1]
[-3,-2,1,5,4]=>11000=>[2,3]=>[3,2]
[-3,-2,1,5,-4]=>11001=>[2,2,1]=>[1,2,2]
[-3,-2,1,-5,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-2,1,-5,-4]=>11011=>[2,1,2]=>[2,1,2]
[-3,-2,-1,5,4]=>11100=>[3,2]=>[2,3]
[-3,-2,-1,5,-4]=>11101=>[3,1,1]=>[1,1,3]
[-3,-2,-1,-5,4]=>11110=>[4,1]=>[1,4]
[-3,-2,-1,-5,-4]=>11111=>[5]=>[5]
[3,2,4,1,5]=>00000=>[5]=>[5]
[3,2,4,1,-5]=>00001=>[4,1]=>[1,4]
[3,2,4,-1,5]=>00010=>[3,1,1]=>[1,1,3]
[3,2,4,-1,-5]=>00011=>[3,2]=>[2,3]
[3,2,-4,1,5]=>00100=>[2,1,2]=>[2,1,2]
[3,2,-4,1,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,2,-4,-1,5]=>00110=>[2,2,1]=>[1,2,2]
[3,2,-4,-1,-5]=>00111=>[2,3]=>[3,2]
[3,-2,4,1,5]=>01000=>[1,1,3]=>[3,1,1]
[3,-2,4,1,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-2,4,-1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-2,4,-1,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-2,-4,1,5]=>01100=>[1,2,2]=>[2,2,1]
[3,-2,-4,1,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-2,-4,-1,5]=>01110=>[1,3,1]=>[1,3,1]
[3,-2,-4,-1,-5]=>01111=>[1,4]=>[4,1]
[-3,2,4,1,5]=>10000=>[1,4]=>[4,1]
[-3,2,4,1,-5]=>10001=>[1,3,1]=>[1,3,1]
[-3,2,4,-1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,2,4,-1,-5]=>10011=>[1,2,2]=>[2,2,1]
[-3,2,-4,1,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,2,-4,1,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,2,-4,-1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,2,-4,-1,-5]=>10111=>[1,1,3]=>[3,1,1]
[-3,-2,4,1,5]=>11000=>[2,3]=>[3,2]
[-3,-2,4,1,-5]=>11001=>[2,2,1]=>[1,2,2]
[-3,-2,4,-1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-2,4,-1,-5]=>11011=>[2,1,2]=>[2,1,2]
[-3,-2,-4,1,5]=>11100=>[3,2]=>[2,3]
[-3,-2,-4,1,-5]=>11101=>[3,1,1]=>[1,1,3]
[-3,-2,-4,-1,5]=>11110=>[4,1]=>[1,4]
[-3,-2,-4,-1,-5]=>11111=>[5]=>[5]
[3,2,4,5,1]=>00000=>[5]=>[5]
[3,2,4,5,-1]=>00001=>[4,1]=>[1,4]
[3,2,4,-5,1]=>00010=>[3,1,1]=>[1,1,3]
[3,2,4,-5,-1]=>00011=>[3,2]=>[2,3]
[3,2,-4,5,1]=>00100=>[2,1,2]=>[2,1,2]
[3,2,-4,5,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,2,-4,-5,1]=>00110=>[2,2,1]=>[1,2,2]
[3,2,-4,-5,-1]=>00111=>[2,3]=>[3,2]
[3,-2,4,5,1]=>01000=>[1,1,3]=>[3,1,1]
[3,-2,4,5,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-2,4,-5,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-2,4,-5,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-2,-4,5,1]=>01100=>[1,2,2]=>[2,2,1]
[3,-2,-4,5,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-2,-4,-5,1]=>01110=>[1,3,1]=>[1,3,1]
[3,-2,-4,-5,-1]=>01111=>[1,4]=>[4,1]
[-3,2,4,5,1]=>10000=>[1,4]=>[4,1]
[-3,2,4,5,-1]=>10001=>[1,3,1]=>[1,3,1]
[-3,2,4,-5,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,2,4,-5,-1]=>10011=>[1,2,2]=>[2,2,1]
[-3,2,-4,5,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,2,-4,5,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,2,-4,-5,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,2,-4,-5,-1]=>10111=>[1,1,3]=>[3,1,1]
[-3,-2,4,5,1]=>11000=>[2,3]=>[3,2]
[-3,-2,4,5,-1]=>11001=>[2,2,1]=>[1,2,2]
[-3,-2,4,-5,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-2,4,-5,-1]=>11011=>[2,1,2]=>[2,1,2]
[-3,-2,-4,5,1]=>11100=>[3,2]=>[2,3]
[-3,-2,-4,5,-1]=>11101=>[3,1,1]=>[1,1,3]
[-3,-2,-4,-5,1]=>11110=>[4,1]=>[1,4]
[-3,-2,-4,-5,-1]=>11111=>[5]=>[5]
[3,2,5,1,4]=>00000=>[5]=>[5]
[3,2,5,1,-4]=>00001=>[4,1]=>[1,4]
[3,2,5,-1,4]=>00010=>[3,1,1]=>[1,1,3]
[3,2,5,-1,-4]=>00011=>[3,2]=>[2,3]
[3,2,-5,1,4]=>00100=>[2,1,2]=>[2,1,2]
[3,2,-5,1,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,2,-5,-1,4]=>00110=>[2,2,1]=>[1,2,2]
[3,2,-5,-1,-4]=>00111=>[2,3]=>[3,2]
[3,-2,5,1,4]=>01000=>[1,1,3]=>[3,1,1]
[3,-2,5,1,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-2,5,-1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-2,5,-1,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-2,-5,1,4]=>01100=>[1,2,2]=>[2,2,1]
[3,-2,-5,1,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-2,-5,-1,4]=>01110=>[1,3,1]=>[1,3,1]
[3,-2,-5,-1,-4]=>01111=>[1,4]=>[4,1]
[-3,2,5,1,4]=>10000=>[1,4]=>[4,1]
[-3,2,5,1,-4]=>10001=>[1,3,1]=>[1,3,1]
[-3,2,5,-1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,2,5,-1,-4]=>10011=>[1,2,2]=>[2,2,1]
[-3,2,-5,1,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,2,-5,1,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,2,-5,-1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,2,-5,-1,-4]=>10111=>[1,1,3]=>[3,1,1]
[-3,-2,5,1,4]=>11000=>[2,3]=>[3,2]
[-3,-2,5,1,-4]=>11001=>[2,2,1]=>[1,2,2]
[-3,-2,5,-1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-2,5,-1,-4]=>11011=>[2,1,2]=>[2,1,2]
[-3,-2,-5,1,4]=>11100=>[3,2]=>[2,3]
[-3,-2,-5,1,-4]=>11101=>[3,1,1]=>[1,1,3]
[-3,-2,-5,-1,4]=>11110=>[4,1]=>[1,4]
[-3,-2,-5,-1,-4]=>11111=>[5]=>[5]
[3,2,5,4,1]=>00000=>[5]=>[5]
[3,2,5,4,-1]=>00001=>[4,1]=>[1,4]
[3,2,5,-4,1]=>00010=>[3,1,1]=>[1,1,3]
[3,2,5,-4,-1]=>00011=>[3,2]=>[2,3]
[3,2,-5,4,1]=>00100=>[2,1,2]=>[2,1,2]
[3,2,-5,4,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,2,-5,-4,1]=>00110=>[2,2,1]=>[1,2,2]
[3,2,-5,-4,-1]=>00111=>[2,3]=>[3,2]
[3,-2,5,4,1]=>01000=>[1,1,3]=>[3,1,1]
[3,-2,5,4,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-2,5,-4,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-2,5,-4,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-2,-5,4,1]=>01100=>[1,2,2]=>[2,2,1]
[3,-2,-5,4,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-2,-5,-4,1]=>01110=>[1,3,1]=>[1,3,1]
[3,-2,-5,-4,-1]=>01111=>[1,4]=>[4,1]
[-3,2,5,4,1]=>10000=>[1,4]=>[4,1]
[-3,2,5,4,-1]=>10001=>[1,3,1]=>[1,3,1]
[-3,2,5,-4,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,2,5,-4,-1]=>10011=>[1,2,2]=>[2,2,1]
[-3,2,-5,4,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,2,-5,4,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,2,-5,-4,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,2,-5,-4,-1]=>10111=>[1,1,3]=>[3,1,1]
[-3,-2,5,4,1]=>11000=>[2,3]=>[3,2]
[-3,-2,5,4,-1]=>11001=>[2,2,1]=>[1,2,2]
[-3,-2,5,-4,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-2,5,-4,-1]=>11011=>[2,1,2]=>[2,1,2]
[-3,-2,-5,4,1]=>11100=>[3,2]=>[2,3]
[-3,-2,-5,4,-1]=>11101=>[3,1,1]=>[1,1,3]
[-3,-2,-5,-4,1]=>11110=>[4,1]=>[1,4]
[-3,-2,-5,-4,-1]=>11111=>[5]=>[5]
[3,4,1,2,5]=>00000=>[5]=>[5]
[3,4,1,2,-5]=>00001=>[4,1]=>[1,4]
[3,4,1,-2,5]=>00010=>[3,1,1]=>[1,1,3]
[3,4,1,-2,-5]=>00011=>[3,2]=>[2,3]
[3,4,-1,2,5]=>00100=>[2,1,2]=>[2,1,2]
[3,4,-1,2,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,-1,-2,5]=>00110=>[2,2,1]=>[1,2,2]
[3,4,-1,-2,-5]=>00111=>[2,3]=>[3,2]
[3,-4,1,2,5]=>01000=>[1,1,3]=>[3,1,1]
[3,-4,1,2,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-4,1,-2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-4,1,-2,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-4,-1,2,5]=>01100=>[1,2,2]=>[2,2,1]
[3,-4,-1,2,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-4,-1,-2,5]=>01110=>[1,3,1]=>[1,3,1]
[3,-4,-1,-2,-5]=>01111=>[1,4]=>[4,1]
[-3,4,1,2,5]=>10000=>[1,4]=>[4,1]
[-3,4,1,2,-5]=>10001=>[1,3,1]=>[1,3,1]
[-3,4,1,-2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,4,1,-2,-5]=>10011=>[1,2,2]=>[2,2,1]
[-3,4,-1,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,4,-1,2,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,4,-1,-2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,4,-1,-2,-5]=>10111=>[1,1,3]=>[3,1,1]
[-3,-4,1,2,5]=>11000=>[2,3]=>[3,2]
[-3,-4,1,2,-5]=>11001=>[2,2,1]=>[1,2,2]
[-3,-4,1,-2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-4,1,-2,-5]=>11011=>[2,1,2]=>[2,1,2]
[-3,-4,-1,2,5]=>11100=>[3,2]=>[2,3]
[-3,-4,-1,2,-5]=>11101=>[3,1,1]=>[1,1,3]
[-3,-4,-1,-2,5]=>11110=>[4,1]=>[1,4]
[-3,-4,-1,-2,-5]=>11111=>[5]=>[5]
[3,4,1,5,2]=>00000=>[5]=>[5]
[3,4,1,5,-2]=>00001=>[4,1]=>[1,4]
[3,4,1,-5,2]=>00010=>[3,1,1]=>[1,1,3]
[3,4,1,-5,-2]=>00011=>[3,2]=>[2,3]
[3,4,-1,5,2]=>00100=>[2,1,2]=>[2,1,2]
[3,4,-1,5,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,-1,-5,2]=>00110=>[2,2,1]=>[1,2,2]
[3,4,-1,-5,-2]=>00111=>[2,3]=>[3,2]
[3,-4,1,5,2]=>01000=>[1,1,3]=>[3,1,1]
[3,-4,1,5,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-4,1,-5,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-4,1,-5,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-4,-1,5,2]=>01100=>[1,2,2]=>[2,2,1]
[3,-4,-1,5,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-4,-1,-5,2]=>01110=>[1,3,1]=>[1,3,1]
[3,-4,-1,-5,-2]=>01111=>[1,4]=>[4,1]
[-3,4,1,5,2]=>10000=>[1,4]=>[4,1]
[-3,4,1,5,-2]=>10001=>[1,3,1]=>[1,3,1]
[-3,4,1,-5,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,4,1,-5,-2]=>10011=>[1,2,2]=>[2,2,1]
[-3,4,-1,5,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,4,-1,5,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,4,-1,-5,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,4,-1,-5,-2]=>10111=>[1,1,3]=>[3,1,1]
[-3,-4,1,5,2]=>11000=>[2,3]=>[3,2]
[-3,-4,1,5,-2]=>11001=>[2,2,1]=>[1,2,2]
[-3,-4,1,-5,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-4,1,-5,-2]=>11011=>[2,1,2]=>[2,1,2]
[-3,-4,-1,5,2]=>11100=>[3,2]=>[2,3]
[-3,-4,-1,5,-2]=>11101=>[3,1,1]=>[1,1,3]
[-3,-4,-1,-5,2]=>11110=>[4,1]=>[1,4]
[-3,-4,-1,-5,-2]=>11111=>[5]=>[5]
[3,4,2,1,5]=>00000=>[5]=>[5]
[3,4,2,1,-5]=>00001=>[4,1]=>[1,4]
[3,4,2,-1,5]=>00010=>[3,1,1]=>[1,1,3]
[3,4,2,-1,-5]=>00011=>[3,2]=>[2,3]
[3,4,-2,1,5]=>00100=>[2,1,2]=>[2,1,2]
[3,4,-2,1,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,-2,-1,5]=>00110=>[2,2,1]=>[1,2,2]
[3,4,-2,-1,-5]=>00111=>[2,3]=>[3,2]
[3,-4,2,1,5]=>01000=>[1,1,3]=>[3,1,1]
[3,-4,2,1,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-4,2,-1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-4,2,-1,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-4,-2,1,5]=>01100=>[1,2,2]=>[2,2,1]
[3,-4,-2,1,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-4,-2,-1,5]=>01110=>[1,3,1]=>[1,3,1]
[3,-4,-2,-1,-5]=>01111=>[1,4]=>[4,1]
[-3,4,2,1,5]=>10000=>[1,4]=>[4,1]
[-3,4,2,1,-5]=>10001=>[1,3,1]=>[1,3,1]
[-3,4,2,-1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,4,2,-1,-5]=>10011=>[1,2,2]=>[2,2,1]
[-3,4,-2,1,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,4,-2,1,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,4,-2,-1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,4,-2,-1,-5]=>10111=>[1,1,3]=>[3,1,1]
[-3,-4,2,1,5]=>11000=>[2,3]=>[3,2]
[-3,-4,2,1,-5]=>11001=>[2,2,1]=>[1,2,2]
[-3,-4,2,-1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-4,2,-1,-5]=>11011=>[2,1,2]=>[2,1,2]
[-3,-4,-2,1,5]=>11100=>[3,2]=>[2,3]
[-3,-4,-2,1,-5]=>11101=>[3,1,1]=>[1,1,3]
[-3,-4,-2,-1,5]=>11110=>[4,1]=>[1,4]
[-3,-4,-2,-1,-5]=>11111=>[5]=>[5]
[3,4,2,5,1]=>00000=>[5]=>[5]
[3,4,2,5,-1]=>00001=>[4,1]=>[1,4]
[3,4,2,-5,1]=>00010=>[3,1,1]=>[1,1,3]
[3,4,2,-5,-1]=>00011=>[3,2]=>[2,3]
[3,4,-2,5,1]=>00100=>[2,1,2]=>[2,1,2]
[3,4,-2,5,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,-2,-5,1]=>00110=>[2,2,1]=>[1,2,2]
[3,4,-2,-5,-1]=>00111=>[2,3]=>[3,2]
[3,-4,2,5,1]=>01000=>[1,1,3]=>[3,1,1]
[3,-4,2,5,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-4,2,-5,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-4,2,-5,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-4,-2,5,1]=>01100=>[1,2,2]=>[2,2,1]
[3,-4,-2,5,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-4,-2,-5,1]=>01110=>[1,3,1]=>[1,3,1]
[3,-4,-2,-5,-1]=>01111=>[1,4]=>[4,1]
[-3,4,2,5,1]=>10000=>[1,4]=>[4,1]
[-3,4,2,5,-1]=>10001=>[1,3,1]=>[1,3,1]
[-3,4,2,-5,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,4,2,-5,-1]=>10011=>[1,2,2]=>[2,2,1]
[-3,4,-2,5,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,4,-2,5,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,4,-2,-5,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,4,-2,-5,-1]=>10111=>[1,1,3]=>[3,1,1]
[-3,-4,2,5,1]=>11000=>[2,3]=>[3,2]
[-3,-4,2,5,-1]=>11001=>[2,2,1]=>[1,2,2]
[-3,-4,2,-5,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-4,2,-5,-1]=>11011=>[2,1,2]=>[2,1,2]
[-3,-4,-2,5,1]=>11100=>[3,2]=>[2,3]
[-3,-4,-2,5,-1]=>11101=>[3,1,1]=>[1,1,3]
[-3,-4,-2,-5,1]=>11110=>[4,1]=>[1,4]
[-3,-4,-2,-5,-1]=>11111=>[5]=>[5]
[3,4,5,1,2]=>00000=>[5]=>[5]
[3,4,5,1,-2]=>00001=>[4,1]=>[1,4]
[3,4,5,-1,2]=>00010=>[3,1,1]=>[1,1,3]
[3,4,5,-1,-2]=>00011=>[3,2]=>[2,3]
[3,4,-5,1,2]=>00100=>[2,1,2]=>[2,1,2]
[3,4,-5,1,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,-5,-1,2]=>00110=>[2,2,1]=>[1,2,2]
[3,4,-5,-1,-2]=>00111=>[2,3]=>[3,2]
[3,-4,5,1,2]=>01000=>[1,1,3]=>[3,1,1]
[3,-4,5,1,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-4,5,-1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-4,5,-1,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-4,-5,1,2]=>01100=>[1,2,2]=>[2,2,1]
[3,-4,-5,1,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-4,-5,-1,2]=>01110=>[1,3,1]=>[1,3,1]
[3,-4,-5,-1,-2]=>01111=>[1,4]=>[4,1]
[-3,4,5,1,2]=>10000=>[1,4]=>[4,1]
[-3,4,5,1,-2]=>10001=>[1,3,1]=>[1,3,1]
[-3,4,5,-1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,4,5,-1,-2]=>10011=>[1,2,2]=>[2,2,1]
[-3,4,-5,1,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,4,-5,1,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,4,-5,-1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,4,-5,-1,-2]=>10111=>[1,1,3]=>[3,1,1]
[-3,-4,5,1,2]=>11000=>[2,3]=>[3,2]
[-3,-4,5,1,-2]=>11001=>[2,2,1]=>[1,2,2]
[-3,-4,5,-1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-4,5,-1,-2]=>11011=>[2,1,2]=>[2,1,2]
[-3,-4,-5,1,2]=>11100=>[3,2]=>[2,3]
[-3,-4,-5,1,-2]=>11101=>[3,1,1]=>[1,1,3]
[-3,-4,-5,-1,2]=>11110=>[4,1]=>[1,4]
[-3,-4,-5,-1,-2]=>11111=>[5]=>[5]
[3,4,5,2,1]=>00000=>[5]=>[5]
[3,4,5,2,-1]=>00001=>[4,1]=>[1,4]
[3,4,5,-2,1]=>00010=>[3,1,1]=>[1,1,3]
[3,4,5,-2,-1]=>00011=>[3,2]=>[2,3]
[3,4,-5,2,1]=>00100=>[2,1,2]=>[2,1,2]
[3,4,-5,2,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,-5,-2,1]=>00110=>[2,2,1]=>[1,2,2]
[3,4,-5,-2,-1]=>00111=>[2,3]=>[3,2]
[3,-4,5,2,1]=>01000=>[1,1,3]=>[3,1,1]
[3,-4,5,2,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-4,5,-2,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-4,5,-2,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-4,-5,2,1]=>01100=>[1,2,2]=>[2,2,1]
[3,-4,-5,2,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-4,-5,-2,1]=>01110=>[1,3,1]=>[1,3,1]
[3,-4,-5,-2,-1]=>01111=>[1,4]=>[4,1]
[-3,4,5,2,1]=>10000=>[1,4]=>[4,1]
[-3,4,5,2,-1]=>10001=>[1,3,1]=>[1,3,1]
[-3,4,5,-2,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,4,5,-2,-1]=>10011=>[1,2,2]=>[2,2,1]
[-3,4,-5,2,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,4,-5,2,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,4,-5,-2,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,4,-5,-2,-1]=>10111=>[1,1,3]=>[3,1,1]
[-3,-4,5,2,1]=>11000=>[2,3]=>[3,2]
[-3,-4,5,2,-1]=>11001=>[2,2,1]=>[1,2,2]
[-3,-4,5,-2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-4,5,-2,-1]=>11011=>[2,1,2]=>[2,1,2]
[-3,-4,-5,2,1]=>11100=>[3,2]=>[2,3]
[-3,-4,-5,2,-1]=>11101=>[3,1,1]=>[1,1,3]
[-3,-4,-5,-2,1]=>11110=>[4,1]=>[1,4]
[-3,-4,-5,-2,-1]=>11111=>[5]=>[5]
[3,5,1,2,4]=>00000=>[5]=>[5]
[3,5,1,2,-4]=>00001=>[4,1]=>[1,4]
[3,5,1,-2,4]=>00010=>[3,1,1]=>[1,1,3]
[3,5,1,-2,-4]=>00011=>[3,2]=>[2,3]
[3,5,-1,2,4]=>00100=>[2,1,2]=>[2,1,2]
[3,5,-1,2,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,-1,-2,4]=>00110=>[2,2,1]=>[1,2,2]
[3,5,-1,-2,-4]=>00111=>[2,3]=>[3,2]
[3,-5,1,2,4]=>01000=>[1,1,3]=>[3,1,1]
[3,-5,1,2,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-5,1,-2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-5,1,-2,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-5,-1,2,4]=>01100=>[1,2,2]=>[2,2,1]
[3,-5,-1,2,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-5,-1,-2,4]=>01110=>[1,3,1]=>[1,3,1]
[3,-5,-1,-2,-4]=>01111=>[1,4]=>[4,1]
[-3,5,1,2,4]=>10000=>[1,4]=>[4,1]
[-3,5,1,2,-4]=>10001=>[1,3,1]=>[1,3,1]
[-3,5,1,-2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,5,1,-2,-4]=>10011=>[1,2,2]=>[2,2,1]
[-3,5,-1,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,5,-1,2,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,5,-1,-2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,5,-1,-2,-4]=>10111=>[1,1,3]=>[3,1,1]
[-3,-5,1,2,4]=>11000=>[2,3]=>[3,2]
[-3,-5,1,2,-4]=>11001=>[2,2,1]=>[1,2,2]
[-3,-5,1,-2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-5,1,-2,-4]=>11011=>[2,1,2]=>[2,1,2]
[-3,-5,-1,2,4]=>11100=>[3,2]=>[2,3]
[-3,-5,-1,2,-4]=>11101=>[3,1,1]=>[1,1,3]
[-3,-5,-1,-2,4]=>11110=>[4,1]=>[1,4]
[-3,-5,-1,-2,-4]=>11111=>[5]=>[5]
[3,5,1,4,2]=>00000=>[5]=>[5]
[3,5,1,4,-2]=>00001=>[4,1]=>[1,4]
[3,5,1,-4,2]=>00010=>[3,1,1]=>[1,1,3]
[3,5,1,-4,-2]=>00011=>[3,2]=>[2,3]
[3,5,-1,4,2]=>00100=>[2,1,2]=>[2,1,2]
[3,5,-1,4,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,-1,-4,2]=>00110=>[2,2,1]=>[1,2,2]
[3,5,-1,-4,-2]=>00111=>[2,3]=>[3,2]
[3,-5,1,4,2]=>01000=>[1,1,3]=>[3,1,1]
[3,-5,1,4,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-5,1,-4,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-5,1,-4,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-5,-1,4,2]=>01100=>[1,2,2]=>[2,2,1]
[3,-5,-1,4,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-5,-1,-4,2]=>01110=>[1,3,1]=>[1,3,1]
[3,-5,-1,-4,-2]=>01111=>[1,4]=>[4,1]
[-3,5,1,4,2]=>10000=>[1,4]=>[4,1]
[-3,5,1,4,-2]=>10001=>[1,3,1]=>[1,3,1]
[-3,5,1,-4,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,5,1,-4,-2]=>10011=>[1,2,2]=>[2,2,1]
[-3,5,-1,4,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,5,-1,4,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,5,-1,-4,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,5,-1,-4,-2]=>10111=>[1,1,3]=>[3,1,1]
[-3,-5,1,4,2]=>11000=>[2,3]=>[3,2]
[-3,-5,1,4,-2]=>11001=>[2,2,1]=>[1,2,2]
[-3,-5,1,-4,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-5,1,-4,-2]=>11011=>[2,1,2]=>[2,1,2]
[-3,-5,-1,4,2]=>11100=>[3,2]=>[2,3]
[-3,-5,-1,4,-2]=>11101=>[3,1,1]=>[1,1,3]
[-3,-5,-1,-4,2]=>11110=>[4,1]=>[1,4]
[-3,-5,-1,-4,-2]=>11111=>[5]=>[5]
[3,5,2,1,4]=>00000=>[5]=>[5]
[3,5,2,1,-4]=>00001=>[4,1]=>[1,4]
[3,5,2,-1,4]=>00010=>[3,1,1]=>[1,1,3]
[3,5,2,-1,-4]=>00011=>[3,2]=>[2,3]
[3,5,-2,1,4]=>00100=>[2,1,2]=>[2,1,2]
[3,5,-2,1,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,-2,-1,4]=>00110=>[2,2,1]=>[1,2,2]
[3,5,-2,-1,-4]=>00111=>[2,3]=>[3,2]
[3,-5,2,1,4]=>01000=>[1,1,3]=>[3,1,1]
[3,-5,2,1,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-5,2,-1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-5,2,-1,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-5,-2,1,4]=>01100=>[1,2,2]=>[2,2,1]
[3,-5,-2,1,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-5,-2,-1,4]=>01110=>[1,3,1]=>[1,3,1]
[3,-5,-2,-1,-4]=>01111=>[1,4]=>[4,1]
[-3,5,2,1,4]=>10000=>[1,4]=>[4,1]
[-3,5,2,1,-4]=>10001=>[1,3,1]=>[1,3,1]
[-3,5,2,-1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,5,2,-1,-4]=>10011=>[1,2,2]=>[2,2,1]
[-3,5,-2,1,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,5,-2,1,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,5,-2,-1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,5,-2,-1,-4]=>10111=>[1,1,3]=>[3,1,1]
[-3,-5,2,1,4]=>11000=>[2,3]=>[3,2]
[-3,-5,2,1,-4]=>11001=>[2,2,1]=>[1,2,2]
[-3,-5,2,-1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-5,2,-1,-4]=>11011=>[2,1,2]=>[2,1,2]
[-3,-5,-2,1,4]=>11100=>[3,2]=>[2,3]
[-3,-5,-2,1,-4]=>11101=>[3,1,1]=>[1,1,3]
[-3,-5,-2,-1,4]=>11110=>[4,1]=>[1,4]
[-3,-5,-2,-1,-4]=>11111=>[5]=>[5]
[3,5,2,4,1]=>00000=>[5]=>[5]
[3,5,2,4,-1]=>00001=>[4,1]=>[1,4]
[3,5,2,-4,1]=>00010=>[3,1,1]=>[1,1,3]
[3,5,2,-4,-1]=>00011=>[3,2]=>[2,3]
[3,5,-2,4,1]=>00100=>[2,1,2]=>[2,1,2]
[3,5,-2,4,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,-2,-4,1]=>00110=>[2,2,1]=>[1,2,2]
[3,5,-2,-4,-1]=>00111=>[2,3]=>[3,2]
[3,-5,2,4,1]=>01000=>[1,1,3]=>[3,1,1]
[3,-5,2,4,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-5,2,-4,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-5,2,-4,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-5,-2,4,1]=>01100=>[1,2,2]=>[2,2,1]
[3,-5,-2,4,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-5,-2,-4,1]=>01110=>[1,3,1]=>[1,3,1]
[3,-5,-2,-4,-1]=>01111=>[1,4]=>[4,1]
[-3,5,2,4,1]=>10000=>[1,4]=>[4,1]
[-3,5,2,4,-1]=>10001=>[1,3,1]=>[1,3,1]
[-3,5,2,-4,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,5,2,-4,-1]=>10011=>[1,2,2]=>[2,2,1]
[-3,5,-2,4,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,5,-2,4,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,5,-2,-4,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,5,-2,-4,-1]=>10111=>[1,1,3]=>[3,1,1]
[-3,-5,2,4,1]=>11000=>[2,3]=>[3,2]
[-3,-5,2,4,-1]=>11001=>[2,2,1]=>[1,2,2]
[-3,-5,2,-4,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-5,2,-4,-1]=>11011=>[2,1,2]=>[2,1,2]
[-3,-5,-2,4,1]=>11100=>[3,2]=>[2,3]
[-3,-5,-2,4,-1]=>11101=>[3,1,1]=>[1,1,3]
[-3,-5,-2,-4,1]=>11110=>[4,1]=>[1,4]
[-3,-5,-2,-4,-1]=>11111=>[5]=>[5]
[3,5,4,1,2]=>00000=>[5]=>[5]
[3,5,4,1,-2]=>00001=>[4,1]=>[1,4]
[3,5,4,-1,2]=>00010=>[3,1,1]=>[1,1,3]
[3,5,4,-1,-2]=>00011=>[3,2]=>[2,3]
[3,5,-4,1,2]=>00100=>[2,1,2]=>[2,1,2]
[3,5,-4,1,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,-4,-1,2]=>00110=>[2,2,1]=>[1,2,2]
[3,5,-4,-1,-2]=>00111=>[2,3]=>[3,2]
[3,-5,4,1,2]=>01000=>[1,1,3]=>[3,1,1]
[3,-5,4,1,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-5,4,-1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-5,4,-1,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-5,-4,1,2]=>01100=>[1,2,2]=>[2,2,1]
[3,-5,-4,1,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-5,-4,-1,2]=>01110=>[1,3,1]=>[1,3,1]
[3,-5,-4,-1,-2]=>01111=>[1,4]=>[4,1]
[-3,5,4,1,2]=>10000=>[1,4]=>[4,1]
[-3,5,4,1,-2]=>10001=>[1,3,1]=>[1,3,1]
[-3,5,4,-1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,5,4,-1,-2]=>10011=>[1,2,2]=>[2,2,1]
[-3,5,-4,1,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,5,-4,1,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,5,-4,-1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,5,-4,-1,-2]=>10111=>[1,1,3]=>[3,1,1]
[-3,-5,4,1,2]=>11000=>[2,3]=>[3,2]
[-3,-5,4,1,-2]=>11001=>[2,2,1]=>[1,2,2]
[-3,-5,4,-1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-5,4,-1,-2]=>11011=>[2,1,2]=>[2,1,2]
[-3,-5,-4,1,2]=>11100=>[3,2]=>[2,3]
[-3,-5,-4,1,-2]=>11101=>[3,1,1]=>[1,1,3]
[-3,-5,-4,-1,2]=>11110=>[4,1]=>[1,4]
[-3,-5,-4,-1,-2]=>11111=>[5]=>[5]
[3,5,4,2,1]=>00000=>[5]=>[5]
[3,5,4,2,-1]=>00001=>[4,1]=>[1,4]
[3,5,4,-2,1]=>00010=>[3,1,1]=>[1,1,3]
[3,5,4,-2,-1]=>00011=>[3,2]=>[2,3]
[3,5,-4,2,1]=>00100=>[2,1,2]=>[2,1,2]
[3,5,-4,2,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,-4,-2,1]=>00110=>[2,2,1]=>[1,2,2]
[3,5,-4,-2,-1]=>00111=>[2,3]=>[3,2]
[3,-5,4,2,1]=>01000=>[1,1,3]=>[3,1,1]
[3,-5,4,2,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,-5,4,-2,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,-5,4,-2,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,-5,-4,2,1]=>01100=>[1,2,2]=>[2,2,1]
[3,-5,-4,2,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,-5,-4,-2,1]=>01110=>[1,3,1]=>[1,3,1]
[3,-5,-4,-2,-1]=>01111=>[1,4]=>[4,1]
[-3,5,4,2,1]=>10000=>[1,4]=>[4,1]
[-3,5,4,2,-1]=>10001=>[1,3,1]=>[1,3,1]
[-3,5,4,-2,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-3,5,4,-2,-1]=>10011=>[1,2,2]=>[2,2,1]
[-3,5,-4,2,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-3,5,-4,2,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-3,5,-4,-2,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-3,5,-4,-2,-1]=>10111=>[1,1,3]=>[3,1,1]
[-3,-5,4,2,1]=>11000=>[2,3]=>[3,2]
[-3,-5,4,2,-1]=>11001=>[2,2,1]=>[1,2,2]
[-3,-5,4,-2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-3,-5,4,-2,-1]=>11011=>[2,1,2]=>[2,1,2]
[-3,-5,-4,2,1]=>11100=>[3,2]=>[2,3]
[-3,-5,-4,2,-1]=>11101=>[3,1,1]=>[1,1,3]
[-3,-5,-4,-2,1]=>11110=>[4,1]=>[1,4]
[-3,-5,-4,-2,-1]=>11111=>[5]=>[5]
[4,1,2,3,5]=>00000=>[5]=>[5]
[4,1,2,3,-5]=>00001=>[4,1]=>[1,4]
[4,1,2,-3,5]=>00010=>[3,1,1]=>[1,1,3]
[4,1,2,-3,-5]=>00011=>[3,2]=>[2,3]
[4,1,-2,3,5]=>00100=>[2,1,2]=>[2,1,2]
[4,1,-2,3,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,1,-2,-3,5]=>00110=>[2,2,1]=>[1,2,2]
[4,1,-2,-3,-5]=>00111=>[2,3]=>[3,2]
[4,-1,2,3,5]=>01000=>[1,1,3]=>[3,1,1]
[4,-1,2,3,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-1,2,-3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-1,2,-3,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-1,-2,3,5]=>01100=>[1,2,2]=>[2,2,1]
[4,-1,-2,3,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-1,-2,-3,5]=>01110=>[1,3,1]=>[1,3,1]
[4,-1,-2,-3,-5]=>01111=>[1,4]=>[4,1]
[-4,1,2,3,5]=>10000=>[1,4]=>[4,1]
[-4,1,2,3,-5]=>10001=>[1,3,1]=>[1,3,1]
[-4,1,2,-3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,1,2,-3,-5]=>10011=>[1,2,2]=>[2,2,1]
[-4,1,-2,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,1,-2,3,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,1,-2,-3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,1,-2,-3,-5]=>10111=>[1,1,3]=>[3,1,1]
[-4,-1,2,3,5]=>11000=>[2,3]=>[3,2]
[-4,-1,2,3,-5]=>11001=>[2,2,1]=>[1,2,2]
[-4,-1,2,-3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-1,2,-3,-5]=>11011=>[2,1,2]=>[2,1,2]
[-4,-1,-2,3,5]=>11100=>[3,2]=>[2,3]
[-4,-1,-2,3,-5]=>11101=>[3,1,1]=>[1,1,3]
[-4,-1,-2,-3,5]=>11110=>[4,1]=>[1,4]
[-4,-1,-2,-3,-5]=>11111=>[5]=>[5]
[4,1,2,5,3]=>00000=>[5]=>[5]
[4,1,2,5,-3]=>00001=>[4,1]=>[1,4]
[4,1,2,-5,3]=>00010=>[3,1,1]=>[1,1,3]
[4,1,2,-5,-3]=>00011=>[3,2]=>[2,3]
[4,1,-2,5,3]=>00100=>[2,1,2]=>[2,1,2]
[4,1,-2,5,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,1,-2,-5,3]=>00110=>[2,2,1]=>[1,2,2]
[4,1,-2,-5,-3]=>00111=>[2,3]=>[3,2]
[4,-1,2,5,3]=>01000=>[1,1,3]=>[3,1,1]
[4,-1,2,5,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-1,2,-5,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-1,2,-5,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-1,-2,5,3]=>01100=>[1,2,2]=>[2,2,1]
[4,-1,-2,5,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-1,-2,-5,3]=>01110=>[1,3,1]=>[1,3,1]
[4,-1,-2,-5,-3]=>01111=>[1,4]=>[4,1]
[-4,1,2,5,3]=>10000=>[1,4]=>[4,1]
[-4,1,2,5,-3]=>10001=>[1,3,1]=>[1,3,1]
[-4,1,2,-5,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,1,2,-5,-3]=>10011=>[1,2,2]=>[2,2,1]
[-4,1,-2,5,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,1,-2,5,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,1,-2,-5,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,1,-2,-5,-3]=>10111=>[1,1,3]=>[3,1,1]
[-4,-1,2,5,3]=>11000=>[2,3]=>[3,2]
[-4,-1,2,5,-3]=>11001=>[2,2,1]=>[1,2,2]
[-4,-1,2,-5,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-1,2,-5,-3]=>11011=>[2,1,2]=>[2,1,2]
[-4,-1,-2,5,3]=>11100=>[3,2]=>[2,3]
[-4,-1,-2,5,-3]=>11101=>[3,1,1]=>[1,1,3]
[-4,-1,-2,-5,3]=>11110=>[4,1]=>[1,4]
[-4,-1,-2,-5,-3]=>11111=>[5]=>[5]
[4,1,3,2,5]=>00000=>[5]=>[5]
[4,1,3,2,-5]=>00001=>[4,1]=>[1,4]
[4,1,3,-2,5]=>00010=>[3,1,1]=>[1,1,3]
[4,1,3,-2,-5]=>00011=>[3,2]=>[2,3]
[4,1,-3,2,5]=>00100=>[2,1,2]=>[2,1,2]
[4,1,-3,2,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,1,-3,-2,5]=>00110=>[2,2,1]=>[1,2,2]
[4,1,-3,-2,-5]=>00111=>[2,3]=>[3,2]
[4,-1,3,2,5]=>01000=>[1,1,3]=>[3,1,1]
[4,-1,3,2,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-1,3,-2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-1,3,-2,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-1,-3,2,5]=>01100=>[1,2,2]=>[2,2,1]
[4,-1,-3,2,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-1,-3,-2,5]=>01110=>[1,3,1]=>[1,3,1]
[4,-1,-3,-2,-5]=>01111=>[1,4]=>[4,1]
[-4,1,3,2,5]=>10000=>[1,4]=>[4,1]
[-4,1,3,2,-5]=>10001=>[1,3,1]=>[1,3,1]
[-4,1,3,-2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,1,3,-2,-5]=>10011=>[1,2,2]=>[2,2,1]
[-4,1,-3,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,1,-3,2,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,1,-3,-2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,1,-3,-2,-5]=>10111=>[1,1,3]=>[3,1,1]
[-4,-1,3,2,5]=>11000=>[2,3]=>[3,2]
[-4,-1,3,2,-5]=>11001=>[2,2,1]=>[1,2,2]
[-4,-1,3,-2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-1,3,-2,-5]=>11011=>[2,1,2]=>[2,1,2]
[-4,-1,-3,2,5]=>11100=>[3,2]=>[2,3]
[-4,-1,-3,2,-5]=>11101=>[3,1,1]=>[1,1,3]
[-4,-1,-3,-2,5]=>11110=>[4,1]=>[1,4]
[-4,-1,-3,-2,-5]=>11111=>[5]=>[5]
[4,1,3,5,2]=>00000=>[5]=>[5]
[4,1,3,5,-2]=>00001=>[4,1]=>[1,4]
[4,1,3,-5,2]=>00010=>[3,1,1]=>[1,1,3]
[4,1,3,-5,-2]=>00011=>[3,2]=>[2,3]
[4,1,-3,5,2]=>00100=>[2,1,2]=>[2,1,2]
[4,1,-3,5,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,1,-3,-5,2]=>00110=>[2,2,1]=>[1,2,2]
[4,1,-3,-5,-2]=>00111=>[2,3]=>[3,2]
[4,-1,3,5,2]=>01000=>[1,1,3]=>[3,1,1]
[4,-1,3,5,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-1,3,-5,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-1,3,-5,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-1,-3,5,2]=>01100=>[1,2,2]=>[2,2,1]
[4,-1,-3,5,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-1,-3,-5,2]=>01110=>[1,3,1]=>[1,3,1]
[4,-1,-3,-5,-2]=>01111=>[1,4]=>[4,1]
[-4,1,3,5,2]=>10000=>[1,4]=>[4,1]
[-4,1,3,5,-2]=>10001=>[1,3,1]=>[1,3,1]
[-4,1,3,-5,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,1,3,-5,-2]=>10011=>[1,2,2]=>[2,2,1]
[-4,1,-3,5,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,1,-3,5,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,1,-3,-5,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,1,-3,-5,-2]=>10111=>[1,1,3]=>[3,1,1]
[-4,-1,3,5,2]=>11000=>[2,3]=>[3,2]
[-4,-1,3,5,-2]=>11001=>[2,2,1]=>[1,2,2]
[-4,-1,3,-5,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-1,3,-5,-2]=>11011=>[2,1,2]=>[2,1,2]
[-4,-1,-3,5,2]=>11100=>[3,2]=>[2,3]
[-4,-1,-3,5,-2]=>11101=>[3,1,1]=>[1,1,3]
[-4,-1,-3,-5,2]=>11110=>[4,1]=>[1,4]
[-4,-1,-3,-5,-2]=>11111=>[5]=>[5]
[4,1,5,2,3]=>00000=>[5]=>[5]
[4,1,5,2,-3]=>00001=>[4,1]=>[1,4]
[4,1,5,-2,3]=>00010=>[3,1,1]=>[1,1,3]
[4,1,5,-2,-3]=>00011=>[3,2]=>[2,3]
[4,1,-5,2,3]=>00100=>[2,1,2]=>[2,1,2]
[4,1,-5,2,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,1,-5,-2,3]=>00110=>[2,2,1]=>[1,2,2]
[4,1,-5,-2,-3]=>00111=>[2,3]=>[3,2]
[4,-1,5,2,3]=>01000=>[1,1,3]=>[3,1,1]
[4,-1,5,2,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-1,5,-2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-1,5,-2,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-1,-5,2,3]=>01100=>[1,2,2]=>[2,2,1]
[4,-1,-5,2,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-1,-5,-2,3]=>01110=>[1,3,1]=>[1,3,1]
[4,-1,-5,-2,-3]=>01111=>[1,4]=>[4,1]
[-4,1,5,2,3]=>10000=>[1,4]=>[4,1]
[-4,1,5,2,-3]=>10001=>[1,3,1]=>[1,3,1]
[-4,1,5,-2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,1,5,-2,-3]=>10011=>[1,2,2]=>[2,2,1]
[-4,1,-5,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,1,-5,2,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,1,-5,-2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,1,-5,-2,-3]=>10111=>[1,1,3]=>[3,1,1]
[-4,-1,5,2,3]=>11000=>[2,3]=>[3,2]
[-4,-1,5,2,-3]=>11001=>[2,2,1]=>[1,2,2]
[-4,-1,5,-2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-1,5,-2,-3]=>11011=>[2,1,2]=>[2,1,2]
[-4,-1,-5,2,3]=>11100=>[3,2]=>[2,3]
[-4,-1,-5,2,-3]=>11101=>[3,1,1]=>[1,1,3]
[-4,-1,-5,-2,3]=>11110=>[4,1]=>[1,4]
[-4,-1,-5,-2,-3]=>11111=>[5]=>[5]
[4,1,5,3,2]=>00000=>[5]=>[5]
[4,1,5,3,-2]=>00001=>[4,1]=>[1,4]
[4,1,5,-3,2]=>00010=>[3,1,1]=>[1,1,3]
[4,1,5,-3,-2]=>00011=>[3,2]=>[2,3]
[4,1,-5,3,2]=>00100=>[2,1,2]=>[2,1,2]
[4,1,-5,3,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,1,-5,-3,2]=>00110=>[2,2,1]=>[1,2,2]
[4,1,-5,-3,-2]=>00111=>[2,3]=>[3,2]
[4,-1,5,3,2]=>01000=>[1,1,3]=>[3,1,1]
[4,-1,5,3,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-1,5,-3,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-1,5,-3,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-1,-5,3,2]=>01100=>[1,2,2]=>[2,2,1]
[4,-1,-5,3,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-1,-5,-3,2]=>01110=>[1,3,1]=>[1,3,1]
[4,-1,-5,-3,-2]=>01111=>[1,4]=>[4,1]
[-4,1,5,3,2]=>10000=>[1,4]=>[4,1]
[-4,1,5,3,-2]=>10001=>[1,3,1]=>[1,3,1]
[-4,1,5,-3,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,1,5,-3,-2]=>10011=>[1,2,2]=>[2,2,1]
[-4,1,-5,3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,1,-5,3,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,1,-5,-3,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,1,-5,-3,-2]=>10111=>[1,1,3]=>[3,1,1]
[-4,-1,5,3,2]=>11000=>[2,3]=>[3,2]
[-4,-1,5,3,-2]=>11001=>[2,2,1]=>[1,2,2]
[-4,-1,5,-3,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-1,5,-3,-2]=>11011=>[2,1,2]=>[2,1,2]
[-4,-1,-5,3,2]=>11100=>[3,2]=>[2,3]
[-4,-1,-5,3,-2]=>11101=>[3,1,1]=>[1,1,3]
[-4,-1,-5,-3,2]=>11110=>[4,1]=>[1,4]
[-4,-1,-5,-3,-2]=>11111=>[5]=>[5]
[4,2,1,3,5]=>00000=>[5]=>[5]
[4,2,1,3,-5]=>00001=>[4,1]=>[1,4]
[4,2,1,-3,5]=>00010=>[3,1,1]=>[1,1,3]
[4,2,1,-3,-5]=>00011=>[3,2]=>[2,3]
[4,2,-1,3,5]=>00100=>[2,1,2]=>[2,1,2]
[4,2,-1,3,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,2,-1,-3,5]=>00110=>[2,2,1]=>[1,2,2]
[4,2,-1,-3,-5]=>00111=>[2,3]=>[3,2]
[4,-2,1,3,5]=>01000=>[1,1,3]=>[3,1,1]
[4,-2,1,3,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-2,1,-3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-2,1,-3,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-2,-1,3,5]=>01100=>[1,2,2]=>[2,2,1]
[4,-2,-1,3,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-2,-1,-3,5]=>01110=>[1,3,1]=>[1,3,1]
[4,-2,-1,-3,-5]=>01111=>[1,4]=>[4,1]
[-4,2,1,3,5]=>10000=>[1,4]=>[4,1]
[-4,2,1,3,-5]=>10001=>[1,3,1]=>[1,3,1]
[-4,2,1,-3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,2,1,-3,-5]=>10011=>[1,2,2]=>[2,2,1]
[-4,2,-1,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,2,-1,3,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,2,-1,-3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,2,-1,-3,-5]=>10111=>[1,1,3]=>[3,1,1]
[-4,-2,1,3,5]=>11000=>[2,3]=>[3,2]
[-4,-2,1,3,-5]=>11001=>[2,2,1]=>[1,2,2]
[-4,-2,1,-3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-2,1,-3,-5]=>11011=>[2,1,2]=>[2,1,2]
[-4,-2,-1,3,5]=>11100=>[3,2]=>[2,3]
[-4,-2,-1,3,-5]=>11101=>[3,1,1]=>[1,1,3]
[-4,-2,-1,-3,5]=>11110=>[4,1]=>[1,4]
[-4,-2,-1,-3,-5]=>11111=>[5]=>[5]
[4,2,1,5,3]=>00000=>[5]=>[5]
[4,2,1,5,-3]=>00001=>[4,1]=>[1,4]
[4,2,1,-5,3]=>00010=>[3,1,1]=>[1,1,3]
[4,2,1,-5,-3]=>00011=>[3,2]=>[2,3]
[4,2,-1,5,3]=>00100=>[2,1,2]=>[2,1,2]
[4,2,-1,5,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,2,-1,-5,3]=>00110=>[2,2,1]=>[1,2,2]
[4,2,-1,-5,-3]=>00111=>[2,3]=>[3,2]
[4,-2,1,5,3]=>01000=>[1,1,3]=>[3,1,1]
[4,-2,1,5,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-2,1,-5,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-2,1,-5,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-2,-1,5,3]=>01100=>[1,2,2]=>[2,2,1]
[4,-2,-1,5,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-2,-1,-5,3]=>01110=>[1,3,1]=>[1,3,1]
[4,-2,-1,-5,-3]=>01111=>[1,4]=>[4,1]
[-4,2,1,5,3]=>10000=>[1,4]=>[4,1]
[-4,2,1,5,-3]=>10001=>[1,3,1]=>[1,3,1]
[-4,2,1,-5,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,2,1,-5,-3]=>10011=>[1,2,2]=>[2,2,1]
[-4,2,-1,5,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,2,-1,5,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,2,-1,-5,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,2,-1,-5,-3]=>10111=>[1,1,3]=>[3,1,1]
[-4,-2,1,5,3]=>11000=>[2,3]=>[3,2]
[-4,-2,1,5,-3]=>11001=>[2,2,1]=>[1,2,2]
[-4,-2,1,-5,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-2,1,-5,-3]=>11011=>[2,1,2]=>[2,1,2]
[-4,-2,-1,5,3]=>11100=>[3,2]=>[2,3]
[-4,-2,-1,5,-3]=>11101=>[3,1,1]=>[1,1,3]
[-4,-2,-1,-5,3]=>11110=>[4,1]=>[1,4]
[-4,-2,-1,-5,-3]=>11111=>[5]=>[5]
[4,2,3,1,5]=>00000=>[5]=>[5]
[4,2,3,1,-5]=>00001=>[4,1]=>[1,4]
[4,2,3,-1,5]=>00010=>[3,1,1]=>[1,1,3]
[4,2,3,-1,-5]=>00011=>[3,2]=>[2,3]
[4,2,-3,1,5]=>00100=>[2,1,2]=>[2,1,2]
[4,2,-3,1,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,2,-3,-1,5]=>00110=>[2,2,1]=>[1,2,2]
[4,2,-3,-1,-5]=>00111=>[2,3]=>[3,2]
[4,-2,3,1,5]=>01000=>[1,1,3]=>[3,1,1]
[4,-2,3,1,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-2,3,-1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-2,3,-1,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-2,-3,1,5]=>01100=>[1,2,2]=>[2,2,1]
[4,-2,-3,1,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-2,-3,-1,5]=>01110=>[1,3,1]=>[1,3,1]
[4,-2,-3,-1,-5]=>01111=>[1,4]=>[4,1]
[-4,2,3,1,5]=>10000=>[1,4]=>[4,1]
[-4,2,3,1,-5]=>10001=>[1,3,1]=>[1,3,1]
[-4,2,3,-1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,2,3,-1,-5]=>10011=>[1,2,2]=>[2,2,1]
[-4,2,-3,1,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,2,-3,1,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,2,-3,-1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,2,-3,-1,-5]=>10111=>[1,1,3]=>[3,1,1]
[-4,-2,3,1,5]=>11000=>[2,3]=>[3,2]
[-4,-2,3,1,-5]=>11001=>[2,2,1]=>[1,2,2]
[-4,-2,3,-1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-2,3,-1,-5]=>11011=>[2,1,2]=>[2,1,2]
[-4,-2,-3,1,5]=>11100=>[3,2]=>[2,3]
[-4,-2,-3,1,-5]=>11101=>[3,1,1]=>[1,1,3]
[-4,-2,-3,-1,5]=>11110=>[4,1]=>[1,4]
[-4,-2,-3,-1,-5]=>11111=>[5]=>[5]
[4,2,3,5,1]=>00000=>[5]=>[5]
[4,2,3,5,-1]=>00001=>[4,1]=>[1,4]
[4,2,3,-5,1]=>00010=>[3,1,1]=>[1,1,3]
[4,2,3,-5,-1]=>00011=>[3,2]=>[2,3]
[4,2,-3,5,1]=>00100=>[2,1,2]=>[2,1,2]
[4,2,-3,5,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,2,-3,-5,1]=>00110=>[2,2,1]=>[1,2,2]
[4,2,-3,-5,-1]=>00111=>[2,3]=>[3,2]
[4,-2,3,5,1]=>01000=>[1,1,3]=>[3,1,1]
[4,-2,3,5,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-2,3,-5,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-2,3,-5,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-2,-3,5,1]=>01100=>[1,2,2]=>[2,2,1]
[4,-2,-3,5,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-2,-3,-5,1]=>01110=>[1,3,1]=>[1,3,1]
[4,-2,-3,-5,-1]=>01111=>[1,4]=>[4,1]
[-4,2,3,5,1]=>10000=>[1,4]=>[4,1]
[-4,2,3,5,-1]=>10001=>[1,3,1]=>[1,3,1]
[-4,2,3,-5,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,2,3,-5,-1]=>10011=>[1,2,2]=>[2,2,1]
[-4,2,-3,5,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,2,-3,5,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,2,-3,-5,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,2,-3,-5,-1]=>10111=>[1,1,3]=>[3,1,1]
[-4,-2,3,5,1]=>11000=>[2,3]=>[3,2]
[-4,-2,3,5,-1]=>11001=>[2,2,1]=>[1,2,2]
[-4,-2,3,-5,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-2,3,-5,-1]=>11011=>[2,1,2]=>[2,1,2]
[-4,-2,-3,5,1]=>11100=>[3,2]=>[2,3]
[-4,-2,-3,5,-1]=>11101=>[3,1,1]=>[1,1,3]
[-4,-2,-3,-5,1]=>11110=>[4,1]=>[1,4]
[-4,-2,-3,-5,-1]=>11111=>[5]=>[5]
[4,2,5,1,3]=>00000=>[5]=>[5]
[4,2,5,1,-3]=>00001=>[4,1]=>[1,4]
[4,2,5,-1,3]=>00010=>[3,1,1]=>[1,1,3]
[4,2,5,-1,-3]=>00011=>[3,2]=>[2,3]
[4,2,-5,1,3]=>00100=>[2,1,2]=>[2,1,2]
[4,2,-5,1,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,2,-5,-1,3]=>00110=>[2,2,1]=>[1,2,2]
[4,2,-5,-1,-3]=>00111=>[2,3]=>[3,2]
[4,-2,5,1,3]=>01000=>[1,1,3]=>[3,1,1]
[4,-2,5,1,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-2,5,-1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-2,5,-1,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-2,-5,1,3]=>01100=>[1,2,2]=>[2,2,1]
[4,-2,-5,1,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-2,-5,-1,3]=>01110=>[1,3,1]=>[1,3,1]
[4,-2,-5,-1,-3]=>01111=>[1,4]=>[4,1]
[-4,2,5,1,3]=>10000=>[1,4]=>[4,1]
[-4,2,5,1,-3]=>10001=>[1,3,1]=>[1,3,1]
[-4,2,5,-1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,2,5,-1,-3]=>10011=>[1,2,2]=>[2,2,1]
[-4,2,-5,1,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,2,-5,1,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,2,-5,-1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,2,-5,-1,-3]=>10111=>[1,1,3]=>[3,1,1]
[-4,-2,5,1,3]=>11000=>[2,3]=>[3,2]
[-4,-2,5,1,-3]=>11001=>[2,2,1]=>[1,2,2]
[-4,-2,5,-1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-2,5,-1,-3]=>11011=>[2,1,2]=>[2,1,2]
[-4,-2,-5,1,3]=>11100=>[3,2]=>[2,3]
[-4,-2,-5,1,-3]=>11101=>[3,1,1]=>[1,1,3]
[-4,-2,-5,-1,3]=>11110=>[4,1]=>[1,4]
[-4,-2,-5,-1,-3]=>11111=>[5]=>[5]
[4,2,5,3,1]=>00000=>[5]=>[5]
[4,2,5,3,-1]=>00001=>[4,1]=>[1,4]
[4,2,5,-3,1]=>00010=>[3,1,1]=>[1,1,3]
[4,2,5,-3,-1]=>00011=>[3,2]=>[2,3]
[4,2,-5,3,1]=>00100=>[2,1,2]=>[2,1,2]
[4,2,-5,3,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,2,-5,-3,1]=>00110=>[2,2,1]=>[1,2,2]
[4,2,-5,-3,-1]=>00111=>[2,3]=>[3,2]
[4,-2,5,3,1]=>01000=>[1,1,3]=>[3,1,1]
[4,-2,5,3,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-2,5,-3,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-2,5,-3,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-2,-5,3,1]=>01100=>[1,2,2]=>[2,2,1]
[4,-2,-5,3,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-2,-5,-3,1]=>01110=>[1,3,1]=>[1,3,1]
[4,-2,-5,-3,-1]=>01111=>[1,4]=>[4,1]
[-4,2,5,3,1]=>10000=>[1,4]=>[4,1]
[-4,2,5,3,-1]=>10001=>[1,3,1]=>[1,3,1]
[-4,2,5,-3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,2,5,-3,-1]=>10011=>[1,2,2]=>[2,2,1]
[-4,2,-5,3,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,2,-5,3,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,2,-5,-3,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,2,-5,-3,-1]=>10111=>[1,1,3]=>[3,1,1]
[-4,-2,5,3,1]=>11000=>[2,3]=>[3,2]
[-4,-2,5,3,-1]=>11001=>[2,2,1]=>[1,2,2]
[-4,-2,5,-3,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-2,5,-3,-1]=>11011=>[2,1,2]=>[2,1,2]
[-4,-2,-5,3,1]=>11100=>[3,2]=>[2,3]
[-4,-2,-5,3,-1]=>11101=>[3,1,1]=>[1,1,3]
[-4,-2,-5,-3,1]=>11110=>[4,1]=>[1,4]
[-4,-2,-5,-3,-1]=>11111=>[5]=>[5]
[4,3,1,2,5]=>00000=>[5]=>[5]
[4,3,1,2,-5]=>00001=>[4,1]=>[1,4]
[4,3,1,-2,5]=>00010=>[3,1,1]=>[1,1,3]
[4,3,1,-2,-5]=>00011=>[3,2]=>[2,3]
[4,3,-1,2,5]=>00100=>[2,1,2]=>[2,1,2]
[4,3,-1,2,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,3,-1,-2,5]=>00110=>[2,2,1]=>[1,2,2]
[4,3,-1,-2,-5]=>00111=>[2,3]=>[3,2]
[4,-3,1,2,5]=>01000=>[1,1,3]=>[3,1,1]
[4,-3,1,2,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-3,1,-2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-3,1,-2,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-3,-1,2,5]=>01100=>[1,2,2]=>[2,2,1]
[4,-3,-1,2,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-3,-1,-2,5]=>01110=>[1,3,1]=>[1,3,1]
[4,-3,-1,-2,-5]=>01111=>[1,4]=>[4,1]
[-4,3,1,2,5]=>10000=>[1,4]=>[4,1]
[-4,3,1,2,-5]=>10001=>[1,3,1]=>[1,3,1]
[-4,3,1,-2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,3,1,-2,-5]=>10011=>[1,2,2]=>[2,2,1]
[-4,3,-1,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,3,-1,2,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,3,-1,-2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,3,-1,-2,-5]=>10111=>[1,1,3]=>[3,1,1]
[-4,-3,1,2,5]=>11000=>[2,3]=>[3,2]
[-4,-3,1,2,-5]=>11001=>[2,2,1]=>[1,2,2]
[-4,-3,1,-2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-3,1,-2,-5]=>11011=>[2,1,2]=>[2,1,2]
[-4,-3,-1,2,5]=>11100=>[3,2]=>[2,3]
[-4,-3,-1,2,-5]=>11101=>[3,1,1]=>[1,1,3]
[-4,-3,-1,-2,5]=>11110=>[4,1]=>[1,4]
[-4,-3,-1,-2,-5]=>11111=>[5]=>[5]
[4,3,1,5,2]=>00000=>[5]=>[5]
[4,3,1,5,-2]=>00001=>[4,1]=>[1,4]
[4,3,1,-5,2]=>00010=>[3,1,1]=>[1,1,3]
[4,3,1,-5,-2]=>00011=>[3,2]=>[2,3]
[4,3,-1,5,2]=>00100=>[2,1,2]=>[2,1,2]
[4,3,-1,5,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,3,-1,-5,2]=>00110=>[2,2,1]=>[1,2,2]
[4,3,-1,-5,-2]=>00111=>[2,3]=>[3,2]
[4,-3,1,5,2]=>01000=>[1,1,3]=>[3,1,1]
[4,-3,1,5,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-3,1,-5,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-3,1,-5,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-3,-1,5,2]=>01100=>[1,2,2]=>[2,2,1]
[4,-3,-1,5,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-3,-1,-5,2]=>01110=>[1,3,1]=>[1,3,1]
[4,-3,-1,-5,-2]=>01111=>[1,4]=>[4,1]
[-4,3,1,5,2]=>10000=>[1,4]=>[4,1]
[-4,3,1,5,-2]=>10001=>[1,3,1]=>[1,3,1]
[-4,3,1,-5,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,3,1,-5,-2]=>10011=>[1,2,2]=>[2,2,1]
[-4,3,-1,5,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,3,-1,5,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,3,-1,-5,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,3,-1,-5,-2]=>10111=>[1,1,3]=>[3,1,1]
[-4,-3,1,5,2]=>11000=>[2,3]=>[3,2]
[-4,-3,1,5,-2]=>11001=>[2,2,1]=>[1,2,2]
[-4,-3,1,-5,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-3,1,-5,-2]=>11011=>[2,1,2]=>[2,1,2]
[-4,-3,-1,5,2]=>11100=>[3,2]=>[2,3]
[-4,-3,-1,5,-2]=>11101=>[3,1,1]=>[1,1,3]
[-4,-3,-1,-5,2]=>11110=>[4,1]=>[1,4]
[-4,-3,-1,-5,-2]=>11111=>[5]=>[5]
[4,3,2,1,5]=>00000=>[5]=>[5]
[4,3,2,1,-5]=>00001=>[4,1]=>[1,4]
[4,3,2,-1,5]=>00010=>[3,1,1]=>[1,1,3]
[4,3,2,-1,-5]=>00011=>[3,2]=>[2,3]
[4,3,-2,1,5]=>00100=>[2,1,2]=>[2,1,2]
[4,3,-2,1,-5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,3,-2,-1,5]=>00110=>[2,2,1]=>[1,2,2]
[4,3,-2,-1,-5]=>00111=>[2,3]=>[3,2]
[4,-3,2,1,5]=>01000=>[1,1,3]=>[3,1,1]
[4,-3,2,1,-5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-3,2,-1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-3,2,-1,-5]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-3,-2,1,5]=>01100=>[1,2,2]=>[2,2,1]
[4,-3,-2,1,-5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-3,-2,-1,5]=>01110=>[1,3,1]=>[1,3,1]
[4,-3,-2,-1,-5]=>01111=>[1,4]=>[4,1]
[-4,3,2,1,5]=>10000=>[1,4]=>[4,1]
[-4,3,2,1,-5]=>10001=>[1,3,1]=>[1,3,1]
[-4,3,2,-1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,3,2,-1,-5]=>10011=>[1,2,2]=>[2,2,1]
[-4,3,-2,1,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,3,-2,1,-5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,3,-2,-1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,3,-2,-1,-5]=>10111=>[1,1,3]=>[3,1,1]
[-4,-3,2,1,5]=>11000=>[2,3]=>[3,2]
[-4,-3,2,1,-5]=>11001=>[2,2,1]=>[1,2,2]
[-4,-3,2,-1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-3,2,-1,-5]=>11011=>[2,1,2]=>[2,1,2]
[-4,-3,-2,1,5]=>11100=>[3,2]=>[2,3]
[-4,-3,-2,1,-5]=>11101=>[3,1,1]=>[1,1,3]
[-4,-3,-2,-1,5]=>11110=>[4,1]=>[1,4]
[-4,-3,-2,-1,-5]=>11111=>[5]=>[5]
[4,3,2,5,1]=>00000=>[5]=>[5]
[4,3,2,5,-1]=>00001=>[4,1]=>[1,4]
[4,3,2,-5,1]=>00010=>[3,1,1]=>[1,1,3]
[4,3,2,-5,-1]=>00011=>[3,2]=>[2,3]
[4,3,-2,5,1]=>00100=>[2,1,2]=>[2,1,2]
[4,3,-2,5,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,3,-2,-5,1]=>00110=>[2,2,1]=>[1,2,2]
[4,3,-2,-5,-1]=>00111=>[2,3]=>[3,2]
[4,-3,2,5,1]=>01000=>[1,1,3]=>[3,1,1]
[4,-3,2,5,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-3,2,-5,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-3,2,-5,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-3,-2,5,1]=>01100=>[1,2,2]=>[2,2,1]
[4,-3,-2,5,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-3,-2,-5,1]=>01110=>[1,3,1]=>[1,3,1]
[4,-3,-2,-5,-1]=>01111=>[1,4]=>[4,1]
[-4,3,2,5,1]=>10000=>[1,4]=>[4,1]
[-4,3,2,5,-1]=>10001=>[1,3,1]=>[1,3,1]
[-4,3,2,-5,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,3,2,-5,-1]=>10011=>[1,2,2]=>[2,2,1]
[-4,3,-2,5,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,3,-2,5,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,3,-2,-5,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,3,-2,-5,-1]=>10111=>[1,1,3]=>[3,1,1]
[-4,-3,2,5,1]=>11000=>[2,3]=>[3,2]
[-4,-3,2,5,-1]=>11001=>[2,2,1]=>[1,2,2]
[-4,-3,2,-5,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-3,2,-5,-1]=>11011=>[2,1,2]=>[2,1,2]
[-4,-3,-2,5,1]=>11100=>[3,2]=>[2,3]
[-4,-3,-2,5,-1]=>11101=>[3,1,1]=>[1,1,3]
[-4,-3,-2,-5,1]=>11110=>[4,1]=>[1,4]
[-4,-3,-2,-5,-1]=>11111=>[5]=>[5]
[4,3,5,1,2]=>00000=>[5]=>[5]
[4,3,5,1,-2]=>00001=>[4,1]=>[1,4]
[4,3,5,-1,2]=>00010=>[3,1,1]=>[1,1,3]
[4,3,5,-1,-2]=>00011=>[3,2]=>[2,3]
[4,3,-5,1,2]=>00100=>[2,1,2]=>[2,1,2]
[4,3,-5,1,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,3,-5,-1,2]=>00110=>[2,2,1]=>[1,2,2]
[4,3,-5,-1,-2]=>00111=>[2,3]=>[3,2]
[4,-3,5,1,2]=>01000=>[1,1,3]=>[3,1,1]
[4,-3,5,1,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-3,5,-1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-3,5,-1,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-3,-5,1,2]=>01100=>[1,2,2]=>[2,2,1]
[4,-3,-5,1,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-3,-5,-1,2]=>01110=>[1,3,1]=>[1,3,1]
[4,-3,-5,-1,-2]=>01111=>[1,4]=>[4,1]
[-4,3,5,1,2]=>10000=>[1,4]=>[4,1]
[-4,3,5,1,-2]=>10001=>[1,3,1]=>[1,3,1]
[-4,3,5,-1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,3,5,-1,-2]=>10011=>[1,2,2]=>[2,2,1]
[-4,3,-5,1,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,3,-5,1,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,3,-5,-1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,3,-5,-1,-2]=>10111=>[1,1,3]=>[3,1,1]
[-4,-3,5,1,2]=>11000=>[2,3]=>[3,2]
[-4,-3,5,1,-2]=>11001=>[2,2,1]=>[1,2,2]
[-4,-3,5,-1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-3,5,-1,-2]=>11011=>[2,1,2]=>[2,1,2]
[-4,-3,-5,1,2]=>11100=>[3,2]=>[2,3]
[-4,-3,-5,1,-2]=>11101=>[3,1,1]=>[1,1,3]
[-4,-3,-5,-1,2]=>11110=>[4,1]=>[1,4]
[-4,-3,-5,-1,-2]=>11111=>[5]=>[5]
[4,3,5,2,1]=>00000=>[5]=>[5]
[4,3,5,2,-1]=>00001=>[4,1]=>[1,4]
[4,3,5,-2,1]=>00010=>[3,1,1]=>[1,1,3]
[4,3,5,-2,-1]=>00011=>[3,2]=>[2,3]
[4,3,-5,2,1]=>00100=>[2,1,2]=>[2,1,2]
[4,3,-5,2,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,3,-5,-2,1]=>00110=>[2,2,1]=>[1,2,2]
[4,3,-5,-2,-1]=>00111=>[2,3]=>[3,2]
[4,-3,5,2,1]=>01000=>[1,1,3]=>[3,1,1]
[4,-3,5,2,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-3,5,-2,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-3,5,-2,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-3,-5,2,1]=>01100=>[1,2,2]=>[2,2,1]
[4,-3,-5,2,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-3,-5,-2,1]=>01110=>[1,3,1]=>[1,3,1]
[4,-3,-5,-2,-1]=>01111=>[1,4]=>[4,1]
[-4,3,5,2,1]=>10000=>[1,4]=>[4,1]
[-4,3,5,2,-1]=>10001=>[1,3,1]=>[1,3,1]
[-4,3,5,-2,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,3,5,-2,-1]=>10011=>[1,2,2]=>[2,2,1]
[-4,3,-5,2,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,3,-5,2,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,3,-5,-2,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,3,-5,-2,-1]=>10111=>[1,1,3]=>[3,1,1]
[-4,-3,5,2,1]=>11000=>[2,3]=>[3,2]
[-4,-3,5,2,-1]=>11001=>[2,2,1]=>[1,2,2]
[-4,-3,5,-2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-3,5,-2,-1]=>11011=>[2,1,2]=>[2,1,2]
[-4,-3,-5,2,1]=>11100=>[3,2]=>[2,3]
[-4,-3,-5,2,-1]=>11101=>[3,1,1]=>[1,1,3]
[-4,-3,-5,-2,1]=>11110=>[4,1]=>[1,4]
[-4,-3,-5,-2,-1]=>11111=>[5]=>[5]
[4,5,1,2,3]=>00000=>[5]=>[5]
[4,5,1,2,-3]=>00001=>[4,1]=>[1,4]
[4,5,1,-2,3]=>00010=>[3,1,1]=>[1,1,3]
[4,5,1,-2,-3]=>00011=>[3,2]=>[2,3]
[4,5,-1,2,3]=>00100=>[2,1,2]=>[2,1,2]
[4,5,-1,2,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,-1,-2,3]=>00110=>[2,2,1]=>[1,2,2]
[4,5,-1,-2,-3]=>00111=>[2,3]=>[3,2]
[4,-5,1,2,3]=>01000=>[1,1,3]=>[3,1,1]
[4,-5,1,2,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-5,1,-2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-5,1,-2,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-5,-1,2,3]=>01100=>[1,2,2]=>[2,2,1]
[4,-5,-1,2,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-5,-1,-2,3]=>01110=>[1,3,1]=>[1,3,1]
[4,-5,-1,-2,-3]=>01111=>[1,4]=>[4,1]
[-4,5,1,2,3]=>10000=>[1,4]=>[4,1]
[-4,5,1,2,-3]=>10001=>[1,3,1]=>[1,3,1]
[-4,5,1,-2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,5,1,-2,-3]=>10011=>[1,2,2]=>[2,2,1]
[-4,5,-1,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,5,-1,2,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,5,-1,-2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,5,-1,-2,-3]=>10111=>[1,1,3]=>[3,1,1]
[-4,-5,1,2,3]=>11000=>[2,3]=>[3,2]
[-4,-5,1,2,-3]=>11001=>[2,2,1]=>[1,2,2]
[-4,-5,1,-2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-5,1,-2,-3]=>11011=>[2,1,2]=>[2,1,2]
[-4,-5,-1,2,3]=>11100=>[3,2]=>[2,3]
[-4,-5,-1,2,-3]=>11101=>[3,1,1]=>[1,1,3]
[-4,-5,-1,-2,3]=>11110=>[4,1]=>[1,4]
[-4,-5,-1,-2,-3]=>11111=>[5]=>[5]
[4,5,1,3,2]=>00000=>[5]=>[5]
[4,5,1,3,-2]=>00001=>[4,1]=>[1,4]
[4,5,1,-3,2]=>00010=>[3,1,1]=>[1,1,3]
[4,5,1,-3,-2]=>00011=>[3,2]=>[2,3]
[4,5,-1,3,2]=>00100=>[2,1,2]=>[2,1,2]
[4,5,-1,3,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,-1,-3,2]=>00110=>[2,2,1]=>[1,2,2]
[4,5,-1,-3,-2]=>00111=>[2,3]=>[3,2]
[4,-5,1,3,2]=>01000=>[1,1,3]=>[3,1,1]
[4,-5,1,3,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-5,1,-3,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-5,1,-3,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-5,-1,3,2]=>01100=>[1,2,2]=>[2,2,1]
[4,-5,-1,3,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-5,-1,-3,2]=>01110=>[1,3,1]=>[1,3,1]
[4,-5,-1,-3,-2]=>01111=>[1,4]=>[4,1]
[-4,5,1,3,2]=>10000=>[1,4]=>[4,1]
[-4,5,1,3,-2]=>10001=>[1,3,1]=>[1,3,1]
[-4,5,1,-3,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,5,1,-3,-2]=>10011=>[1,2,2]=>[2,2,1]
[-4,5,-1,3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,5,-1,3,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,5,-1,-3,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,5,-1,-3,-2]=>10111=>[1,1,3]=>[3,1,1]
[-4,-5,1,3,2]=>11000=>[2,3]=>[3,2]
[-4,-5,1,3,-2]=>11001=>[2,2,1]=>[1,2,2]
[-4,-5,1,-3,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-5,1,-3,-2]=>11011=>[2,1,2]=>[2,1,2]
[-4,-5,-1,3,2]=>11100=>[3,2]=>[2,3]
[-4,-5,-1,3,-2]=>11101=>[3,1,1]=>[1,1,3]
[-4,-5,-1,-3,2]=>11110=>[4,1]=>[1,4]
[-4,-5,-1,-3,-2]=>11111=>[5]=>[5]
[4,5,2,1,3]=>00000=>[5]=>[5]
[4,5,2,1,-3]=>00001=>[4,1]=>[1,4]
[4,5,2,-1,3]=>00010=>[3,1,1]=>[1,1,3]
[4,5,2,-1,-3]=>00011=>[3,2]=>[2,3]
[4,5,-2,1,3]=>00100=>[2,1,2]=>[2,1,2]
[4,5,-2,1,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,-2,-1,3]=>00110=>[2,2,1]=>[1,2,2]
[4,5,-2,-1,-3]=>00111=>[2,3]=>[3,2]
[4,-5,2,1,3]=>01000=>[1,1,3]=>[3,1,1]
[4,-5,2,1,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-5,2,-1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-5,2,-1,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-5,-2,1,3]=>01100=>[1,2,2]=>[2,2,1]
[4,-5,-2,1,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-5,-2,-1,3]=>01110=>[1,3,1]=>[1,3,1]
[4,-5,-2,-1,-3]=>01111=>[1,4]=>[4,1]
[-4,5,2,1,3]=>10000=>[1,4]=>[4,1]
[-4,5,2,1,-3]=>10001=>[1,3,1]=>[1,3,1]
[-4,5,2,-1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,5,2,-1,-3]=>10011=>[1,2,2]=>[2,2,1]
[-4,5,-2,1,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,5,-2,1,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,5,-2,-1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,5,-2,-1,-3]=>10111=>[1,1,3]=>[3,1,1]
[-4,-5,2,1,3]=>11000=>[2,3]=>[3,2]
[-4,-5,2,1,-3]=>11001=>[2,2,1]=>[1,2,2]
[-4,-5,2,-1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-5,2,-1,-3]=>11011=>[2,1,2]=>[2,1,2]
[-4,-5,-2,1,3]=>11100=>[3,2]=>[2,3]
[-4,-5,-2,1,-3]=>11101=>[3,1,1]=>[1,1,3]
[-4,-5,-2,-1,3]=>11110=>[4,1]=>[1,4]
[-4,-5,-2,-1,-3]=>11111=>[5]=>[5]
[4,5,2,3,1]=>00000=>[5]=>[5]
[4,5,2,3,-1]=>00001=>[4,1]=>[1,4]
[4,5,2,-3,1]=>00010=>[3,1,1]=>[1,1,3]
[4,5,2,-3,-1]=>00011=>[3,2]=>[2,3]
[4,5,-2,3,1]=>00100=>[2,1,2]=>[2,1,2]
[4,5,-2,3,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,-2,-3,1]=>00110=>[2,2,1]=>[1,2,2]
[4,5,-2,-3,-1]=>00111=>[2,3]=>[3,2]
[4,-5,2,3,1]=>01000=>[1,1,3]=>[3,1,1]
[4,-5,2,3,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-5,2,-3,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-5,2,-3,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-5,-2,3,1]=>01100=>[1,2,2]=>[2,2,1]
[4,-5,-2,3,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-5,-2,-3,1]=>01110=>[1,3,1]=>[1,3,1]
[4,-5,-2,-3,-1]=>01111=>[1,4]=>[4,1]
[-4,5,2,3,1]=>10000=>[1,4]=>[4,1]
[-4,5,2,3,-1]=>10001=>[1,3,1]=>[1,3,1]
[-4,5,2,-3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,5,2,-3,-1]=>10011=>[1,2,2]=>[2,2,1]
[-4,5,-2,3,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,5,-2,3,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,5,-2,-3,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,5,-2,-3,-1]=>10111=>[1,1,3]=>[3,1,1]
[-4,-5,2,3,1]=>11000=>[2,3]=>[3,2]
[-4,-5,2,3,-1]=>11001=>[2,2,1]=>[1,2,2]
[-4,-5,2,-3,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-5,2,-3,-1]=>11011=>[2,1,2]=>[2,1,2]
[-4,-5,-2,3,1]=>11100=>[3,2]=>[2,3]
[-4,-5,-2,3,-1]=>11101=>[3,1,1]=>[1,1,3]
[-4,-5,-2,-3,1]=>11110=>[4,1]=>[1,4]
[-4,-5,-2,-3,-1]=>11111=>[5]=>[5]
[4,5,3,1,2]=>00000=>[5]=>[5]
[4,5,3,1,-2]=>00001=>[4,1]=>[1,4]
[4,5,3,-1,2]=>00010=>[3,1,1]=>[1,1,3]
[4,5,3,-1,-2]=>00011=>[3,2]=>[2,3]
[4,5,-3,1,2]=>00100=>[2,1,2]=>[2,1,2]
[4,5,-3,1,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,-3,-1,2]=>00110=>[2,2,1]=>[1,2,2]
[4,5,-3,-1,-2]=>00111=>[2,3]=>[3,2]
[4,-5,3,1,2]=>01000=>[1,1,3]=>[3,1,1]
[4,-5,3,1,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-5,3,-1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-5,3,-1,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-5,-3,1,2]=>01100=>[1,2,2]=>[2,2,1]
[4,-5,-3,1,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-5,-3,-1,2]=>01110=>[1,3,1]=>[1,3,1]
[4,-5,-3,-1,-2]=>01111=>[1,4]=>[4,1]
[-4,5,3,1,2]=>10000=>[1,4]=>[4,1]
[-4,5,3,1,-2]=>10001=>[1,3,1]=>[1,3,1]
[-4,5,3,-1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,5,3,-1,-2]=>10011=>[1,2,2]=>[2,2,1]
[-4,5,-3,1,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,5,-3,1,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,5,-3,-1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,5,-3,-1,-2]=>10111=>[1,1,3]=>[3,1,1]
[-4,-5,3,1,2]=>11000=>[2,3]=>[3,2]
[-4,-5,3,1,-2]=>11001=>[2,2,1]=>[1,2,2]
[-4,-5,3,-1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-5,3,-1,-2]=>11011=>[2,1,2]=>[2,1,2]
[-4,-5,-3,1,2]=>11100=>[3,2]=>[2,3]
[-4,-5,-3,1,-2]=>11101=>[3,1,1]=>[1,1,3]
[-4,-5,-3,-1,2]=>11110=>[4,1]=>[1,4]
[-4,-5,-3,-1,-2]=>11111=>[5]=>[5]
[4,5,3,2,1]=>00000=>[5]=>[5]
[4,5,3,2,-1]=>00001=>[4,1]=>[1,4]
[4,5,3,-2,1]=>00010=>[3,1,1]=>[1,1,3]
[4,5,3,-2,-1]=>00011=>[3,2]=>[2,3]
[4,5,-3,2,1]=>00100=>[2,1,2]=>[2,1,2]
[4,5,-3,2,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,-3,-2,1]=>00110=>[2,2,1]=>[1,2,2]
[4,5,-3,-2,-1]=>00111=>[2,3]=>[3,2]
[4,-5,3,2,1]=>01000=>[1,1,3]=>[3,1,1]
[4,-5,3,2,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,-5,3,-2,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,-5,3,-2,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,-5,-3,2,1]=>01100=>[1,2,2]=>[2,2,1]
[4,-5,-3,2,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,-5,-3,-2,1]=>01110=>[1,3,1]=>[1,3,1]
[4,-5,-3,-2,-1]=>01111=>[1,4]=>[4,1]
[-4,5,3,2,1]=>10000=>[1,4]=>[4,1]
[-4,5,3,2,-1]=>10001=>[1,3,1]=>[1,3,1]
[-4,5,3,-2,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-4,5,3,-2,-1]=>10011=>[1,2,2]=>[2,2,1]
[-4,5,-3,2,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-4,5,-3,2,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-4,5,-3,-2,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-4,5,-3,-2,-1]=>10111=>[1,1,3]=>[3,1,1]
[-4,-5,3,2,1]=>11000=>[2,3]=>[3,2]
[-4,-5,3,2,-1]=>11001=>[2,2,1]=>[1,2,2]
[-4,-5,3,-2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-4,-5,3,-2,-1]=>11011=>[2,1,2]=>[2,1,2]
[-4,-5,-3,2,1]=>11100=>[3,2]=>[2,3]
[-4,-5,-3,2,-1]=>11101=>[3,1,1]=>[1,1,3]
[-4,-5,-3,-2,1]=>11110=>[4,1]=>[1,4]
[-4,-5,-3,-2,-1]=>11111=>[5]=>[5]
[5,1,2,3,4]=>00000=>[5]=>[5]
[5,1,2,3,-4]=>00001=>[4,1]=>[1,4]
[5,1,2,-3,4]=>00010=>[3,1,1]=>[1,1,3]
[5,1,2,-3,-4]=>00011=>[3,2]=>[2,3]
[5,1,-2,3,4]=>00100=>[2,1,2]=>[2,1,2]
[5,1,-2,3,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,1,-2,-3,4]=>00110=>[2,2,1]=>[1,2,2]
[5,1,-2,-3,-4]=>00111=>[2,3]=>[3,2]
[5,-1,2,3,4]=>01000=>[1,1,3]=>[3,1,1]
[5,-1,2,3,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-1,2,-3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-1,2,-3,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-1,-2,3,4]=>01100=>[1,2,2]=>[2,2,1]
[5,-1,-2,3,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-1,-2,-3,4]=>01110=>[1,3,1]=>[1,3,1]
[5,-1,-2,-3,-4]=>01111=>[1,4]=>[4,1]
[-5,1,2,3,4]=>10000=>[1,4]=>[4,1]
[-5,1,2,3,-4]=>10001=>[1,3,1]=>[1,3,1]
[-5,1,2,-3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,1,2,-3,-4]=>10011=>[1,2,2]=>[2,2,1]
[-5,1,-2,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,1,-2,3,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,1,-2,-3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,1,-2,-3,-4]=>10111=>[1,1,3]=>[3,1,1]
[-5,-1,2,3,4]=>11000=>[2,3]=>[3,2]
[-5,-1,2,3,-4]=>11001=>[2,2,1]=>[1,2,2]
[-5,-1,2,-3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-1,2,-3,-4]=>11011=>[2,1,2]=>[2,1,2]
[-5,-1,-2,3,4]=>11100=>[3,2]=>[2,3]
[-5,-1,-2,3,-4]=>11101=>[3,1,1]=>[1,1,3]
[-5,-1,-2,-3,4]=>11110=>[4,1]=>[1,4]
[-5,-1,-2,-3,-4]=>11111=>[5]=>[5]
[5,1,2,4,3]=>00000=>[5]=>[5]
[5,1,2,4,-3]=>00001=>[4,1]=>[1,4]
[5,1,2,-4,3]=>00010=>[3,1,1]=>[1,1,3]
[5,1,2,-4,-3]=>00011=>[3,2]=>[2,3]
[5,1,-2,4,3]=>00100=>[2,1,2]=>[2,1,2]
[5,1,-2,4,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,1,-2,-4,3]=>00110=>[2,2,1]=>[1,2,2]
[5,1,-2,-4,-3]=>00111=>[2,3]=>[3,2]
[5,-1,2,4,3]=>01000=>[1,1,3]=>[3,1,1]
[5,-1,2,4,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-1,2,-4,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-1,2,-4,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-1,-2,4,3]=>01100=>[1,2,2]=>[2,2,1]
[5,-1,-2,4,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-1,-2,-4,3]=>01110=>[1,3,1]=>[1,3,1]
[5,-1,-2,-4,-3]=>01111=>[1,4]=>[4,1]
[-5,1,2,4,3]=>10000=>[1,4]=>[4,1]
[-5,1,2,4,-3]=>10001=>[1,3,1]=>[1,3,1]
[-5,1,2,-4,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,1,2,-4,-3]=>10011=>[1,2,2]=>[2,2,1]
[-5,1,-2,4,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,1,-2,4,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,1,-2,-4,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,1,-2,-4,-3]=>10111=>[1,1,3]=>[3,1,1]
[-5,-1,2,4,3]=>11000=>[2,3]=>[3,2]
[-5,-1,2,4,-3]=>11001=>[2,2,1]=>[1,2,2]
[-5,-1,2,-4,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-1,2,-4,-3]=>11011=>[2,1,2]=>[2,1,2]
[-5,-1,-2,4,3]=>11100=>[3,2]=>[2,3]
[-5,-1,-2,4,-3]=>11101=>[3,1,1]=>[1,1,3]
[-5,-1,-2,-4,3]=>11110=>[4,1]=>[1,4]
[-5,-1,-2,-4,-3]=>11111=>[5]=>[5]
[5,1,3,2,4]=>00000=>[5]=>[5]
[5,1,3,2,-4]=>00001=>[4,1]=>[1,4]
[5,1,3,-2,4]=>00010=>[3,1,1]=>[1,1,3]
[5,1,3,-2,-4]=>00011=>[3,2]=>[2,3]
[5,1,-3,2,4]=>00100=>[2,1,2]=>[2,1,2]
[5,1,-3,2,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,1,-3,-2,4]=>00110=>[2,2,1]=>[1,2,2]
[5,1,-3,-2,-4]=>00111=>[2,3]=>[3,2]
[5,-1,3,2,4]=>01000=>[1,1,3]=>[3,1,1]
[5,-1,3,2,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-1,3,-2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-1,3,-2,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-1,-3,2,4]=>01100=>[1,2,2]=>[2,2,1]
[5,-1,-3,2,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-1,-3,-2,4]=>01110=>[1,3,1]=>[1,3,1]
[5,-1,-3,-2,-4]=>01111=>[1,4]=>[4,1]
[-5,1,3,2,4]=>10000=>[1,4]=>[4,1]
[-5,1,3,2,-4]=>10001=>[1,3,1]=>[1,3,1]
[-5,1,3,-2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,1,3,-2,-4]=>10011=>[1,2,2]=>[2,2,1]
[-5,1,-3,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,1,-3,2,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,1,-3,-2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,1,-3,-2,-4]=>10111=>[1,1,3]=>[3,1,1]
[-5,-1,3,2,4]=>11000=>[2,3]=>[3,2]
[-5,-1,3,2,-4]=>11001=>[2,2,1]=>[1,2,2]
[-5,-1,3,-2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-1,3,-2,-4]=>11011=>[2,1,2]=>[2,1,2]
[-5,-1,-3,2,4]=>11100=>[3,2]=>[2,3]
[-5,-1,-3,2,-4]=>11101=>[3,1,1]=>[1,1,3]
[-5,-1,-3,-2,4]=>11110=>[4,1]=>[1,4]
[-5,-1,-3,-2,-4]=>11111=>[5]=>[5]
[5,1,3,4,2]=>00000=>[5]=>[5]
[5,1,3,4,-2]=>00001=>[4,1]=>[1,4]
[5,1,3,-4,2]=>00010=>[3,1,1]=>[1,1,3]
[5,1,3,-4,-2]=>00011=>[3,2]=>[2,3]
[5,1,-3,4,2]=>00100=>[2,1,2]=>[2,1,2]
[5,1,-3,4,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,1,-3,-4,2]=>00110=>[2,2,1]=>[1,2,2]
[5,1,-3,-4,-2]=>00111=>[2,3]=>[3,2]
[5,-1,3,4,2]=>01000=>[1,1,3]=>[3,1,1]
[5,-1,3,4,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-1,3,-4,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-1,3,-4,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-1,-3,4,2]=>01100=>[1,2,2]=>[2,2,1]
[5,-1,-3,4,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-1,-3,-4,2]=>01110=>[1,3,1]=>[1,3,1]
[5,-1,-3,-4,-2]=>01111=>[1,4]=>[4,1]
[-5,1,3,4,2]=>10000=>[1,4]=>[4,1]
[-5,1,3,4,-2]=>10001=>[1,3,1]=>[1,3,1]
[-5,1,3,-4,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,1,3,-4,-2]=>10011=>[1,2,2]=>[2,2,1]
[-5,1,-3,4,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,1,-3,4,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,1,-3,-4,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,1,-3,-4,-2]=>10111=>[1,1,3]=>[3,1,1]
[-5,-1,3,4,2]=>11000=>[2,3]=>[3,2]
[-5,-1,3,4,-2]=>11001=>[2,2,1]=>[1,2,2]
[-5,-1,3,-4,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-1,3,-4,-2]=>11011=>[2,1,2]=>[2,1,2]
[-5,-1,-3,4,2]=>11100=>[3,2]=>[2,3]
[-5,-1,-3,4,-2]=>11101=>[3,1,1]=>[1,1,3]
[-5,-1,-3,-4,2]=>11110=>[4,1]=>[1,4]
[-5,-1,-3,-4,-2]=>11111=>[5]=>[5]
[5,1,4,2,3]=>00000=>[5]=>[5]
[5,1,4,2,-3]=>00001=>[4,1]=>[1,4]
[5,1,4,-2,3]=>00010=>[3,1,1]=>[1,1,3]
[5,1,4,-2,-3]=>00011=>[3,2]=>[2,3]
[5,1,-4,2,3]=>00100=>[2,1,2]=>[2,1,2]
[5,1,-4,2,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,1,-4,-2,3]=>00110=>[2,2,1]=>[1,2,2]
[5,1,-4,-2,-3]=>00111=>[2,3]=>[3,2]
[5,-1,4,2,3]=>01000=>[1,1,3]=>[3,1,1]
[5,-1,4,2,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-1,4,-2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-1,4,-2,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-1,-4,2,3]=>01100=>[1,2,2]=>[2,2,1]
[5,-1,-4,2,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-1,-4,-2,3]=>01110=>[1,3,1]=>[1,3,1]
[5,-1,-4,-2,-3]=>01111=>[1,4]=>[4,1]
[-5,1,4,2,3]=>10000=>[1,4]=>[4,1]
[-5,1,4,2,-3]=>10001=>[1,3,1]=>[1,3,1]
[-5,1,4,-2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,1,4,-2,-3]=>10011=>[1,2,2]=>[2,2,1]
[-5,1,-4,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,1,-4,2,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,1,-4,-2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,1,-4,-2,-3]=>10111=>[1,1,3]=>[3,1,1]
[-5,-1,4,2,3]=>11000=>[2,3]=>[3,2]
[-5,-1,4,2,-3]=>11001=>[2,2,1]=>[1,2,2]
[-5,-1,4,-2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-1,4,-2,-3]=>11011=>[2,1,2]=>[2,1,2]
[-5,-1,-4,2,3]=>11100=>[3,2]=>[2,3]
[-5,-1,-4,2,-3]=>11101=>[3,1,1]=>[1,1,3]
[-5,-1,-4,-2,3]=>11110=>[4,1]=>[1,4]
[-5,-1,-4,-2,-3]=>11111=>[5]=>[5]
[5,1,4,3,2]=>00000=>[5]=>[5]
[5,1,4,3,-2]=>00001=>[4,1]=>[1,4]
[5,1,4,-3,2]=>00010=>[3,1,1]=>[1,1,3]
[5,1,4,-3,-2]=>00011=>[3,2]=>[2,3]
[5,1,-4,3,2]=>00100=>[2,1,2]=>[2,1,2]
[5,1,-4,3,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,1,-4,-3,2]=>00110=>[2,2,1]=>[1,2,2]
[5,1,-4,-3,-2]=>00111=>[2,3]=>[3,2]
[5,-1,4,3,2]=>01000=>[1,1,3]=>[3,1,1]
[5,-1,4,3,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-1,4,-3,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-1,4,-3,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-1,-4,3,2]=>01100=>[1,2,2]=>[2,2,1]
[5,-1,-4,3,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-1,-4,-3,2]=>01110=>[1,3,1]=>[1,3,1]
[5,-1,-4,-3,-2]=>01111=>[1,4]=>[4,1]
[-5,1,4,3,2]=>10000=>[1,4]=>[4,1]
[-5,1,4,3,-2]=>10001=>[1,3,1]=>[1,3,1]
[-5,1,4,-3,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,1,4,-3,-2]=>10011=>[1,2,2]=>[2,2,1]
[-5,1,-4,3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,1,-4,3,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,1,-4,-3,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,1,-4,-3,-2]=>10111=>[1,1,3]=>[3,1,1]
[-5,-1,4,3,2]=>11000=>[2,3]=>[3,2]
[-5,-1,4,3,-2]=>11001=>[2,2,1]=>[1,2,2]
[-5,-1,4,-3,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-1,4,-3,-2]=>11011=>[2,1,2]=>[2,1,2]
[-5,-1,-4,3,2]=>11100=>[3,2]=>[2,3]
[-5,-1,-4,3,-2]=>11101=>[3,1,1]=>[1,1,3]
[-5,-1,-4,-3,2]=>11110=>[4,1]=>[1,4]
[-5,-1,-4,-3,-2]=>11111=>[5]=>[5]
[5,2,1,3,4]=>00000=>[5]=>[5]
[5,2,1,3,-4]=>00001=>[4,1]=>[1,4]
[5,2,1,-3,4]=>00010=>[3,1,1]=>[1,1,3]
[5,2,1,-3,-4]=>00011=>[3,2]=>[2,3]
[5,2,-1,3,4]=>00100=>[2,1,2]=>[2,1,2]
[5,2,-1,3,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,2,-1,-3,4]=>00110=>[2,2,1]=>[1,2,2]
[5,2,-1,-3,-4]=>00111=>[2,3]=>[3,2]
[5,-2,1,3,4]=>01000=>[1,1,3]=>[3,1,1]
[5,-2,1,3,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-2,1,-3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-2,1,-3,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-2,-1,3,4]=>01100=>[1,2,2]=>[2,2,1]
[5,-2,-1,3,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-2,-1,-3,4]=>01110=>[1,3,1]=>[1,3,1]
[5,-2,-1,-3,-4]=>01111=>[1,4]=>[4,1]
[-5,2,1,3,4]=>10000=>[1,4]=>[4,1]
[-5,2,1,3,-4]=>10001=>[1,3,1]=>[1,3,1]
[-5,2,1,-3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,2,1,-3,-4]=>10011=>[1,2,2]=>[2,2,1]
[-5,2,-1,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,2,-1,3,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,2,-1,-3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,2,-1,-3,-4]=>10111=>[1,1,3]=>[3,1,1]
[-5,-2,1,3,4]=>11000=>[2,3]=>[3,2]
[-5,-2,1,3,-4]=>11001=>[2,2,1]=>[1,2,2]
[-5,-2,1,-3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-2,1,-3,-4]=>11011=>[2,1,2]=>[2,1,2]
[-5,-2,-1,3,4]=>11100=>[3,2]=>[2,3]
[-5,-2,-1,3,-4]=>11101=>[3,1,1]=>[1,1,3]
[-5,-2,-1,-3,4]=>11110=>[4,1]=>[1,4]
[-5,-2,-1,-3,-4]=>11111=>[5]=>[5]
[5,2,1,4,3]=>00000=>[5]=>[5]
[5,2,1,4,-3]=>00001=>[4,1]=>[1,4]
[5,2,1,-4,3]=>00010=>[3,1,1]=>[1,1,3]
[5,2,1,-4,-3]=>00011=>[3,2]=>[2,3]
[5,2,-1,4,3]=>00100=>[2,1,2]=>[2,1,2]
[5,2,-1,4,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,2,-1,-4,3]=>00110=>[2,2,1]=>[1,2,2]
[5,2,-1,-4,-3]=>00111=>[2,3]=>[3,2]
[5,-2,1,4,3]=>01000=>[1,1,3]=>[3,1,1]
[5,-2,1,4,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-2,1,-4,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-2,1,-4,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-2,-1,4,3]=>01100=>[1,2,2]=>[2,2,1]
[5,-2,-1,4,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-2,-1,-4,3]=>01110=>[1,3,1]=>[1,3,1]
[5,-2,-1,-4,-3]=>01111=>[1,4]=>[4,1]
[-5,2,1,4,3]=>10000=>[1,4]=>[4,1]
[-5,2,1,4,-3]=>10001=>[1,3,1]=>[1,3,1]
[-5,2,1,-4,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,2,1,-4,-3]=>10011=>[1,2,2]=>[2,2,1]
[-5,2,-1,4,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,2,-1,4,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,2,-1,-4,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,2,-1,-4,-3]=>10111=>[1,1,3]=>[3,1,1]
[-5,-2,1,4,3]=>11000=>[2,3]=>[3,2]
[-5,-2,1,4,-3]=>11001=>[2,2,1]=>[1,2,2]
[-5,-2,1,-4,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-2,1,-4,-3]=>11011=>[2,1,2]=>[2,1,2]
[-5,-2,-1,4,3]=>11100=>[3,2]=>[2,3]
[-5,-2,-1,4,-3]=>11101=>[3,1,1]=>[1,1,3]
[-5,-2,-1,-4,3]=>11110=>[4,1]=>[1,4]
[-5,-2,-1,-4,-3]=>11111=>[5]=>[5]
[5,2,3,1,4]=>00000=>[5]=>[5]
[5,2,3,1,-4]=>00001=>[4,1]=>[1,4]
[5,2,3,-1,4]=>00010=>[3,1,1]=>[1,1,3]
[5,2,3,-1,-4]=>00011=>[3,2]=>[2,3]
[5,2,-3,1,4]=>00100=>[2,1,2]=>[2,1,2]
[5,2,-3,1,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,2,-3,-1,4]=>00110=>[2,2,1]=>[1,2,2]
[5,2,-3,-1,-4]=>00111=>[2,3]=>[3,2]
[5,-2,3,1,4]=>01000=>[1,1,3]=>[3,1,1]
[5,-2,3,1,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-2,3,-1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-2,3,-1,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-2,-3,1,4]=>01100=>[1,2,2]=>[2,2,1]
[5,-2,-3,1,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-2,-3,-1,4]=>01110=>[1,3,1]=>[1,3,1]
[5,-2,-3,-1,-4]=>01111=>[1,4]=>[4,1]
[-5,2,3,1,4]=>10000=>[1,4]=>[4,1]
[-5,2,3,1,-4]=>10001=>[1,3,1]=>[1,3,1]
[-5,2,3,-1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,2,3,-1,-4]=>10011=>[1,2,2]=>[2,2,1]
[-5,2,-3,1,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,2,-3,1,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,2,-3,-1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,2,-3,-1,-4]=>10111=>[1,1,3]=>[3,1,1]
[-5,-2,3,1,4]=>11000=>[2,3]=>[3,2]
[-5,-2,3,1,-4]=>11001=>[2,2,1]=>[1,2,2]
[-5,-2,3,-1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-2,3,-1,-4]=>11011=>[2,1,2]=>[2,1,2]
[-5,-2,-3,1,4]=>11100=>[3,2]=>[2,3]
[-5,-2,-3,1,-4]=>11101=>[3,1,1]=>[1,1,3]
[-5,-2,-3,-1,4]=>11110=>[4,1]=>[1,4]
[-5,-2,-3,-1,-4]=>11111=>[5]=>[5]
[5,2,3,4,1]=>00000=>[5]=>[5]
[5,2,3,4,-1]=>00001=>[4,1]=>[1,4]
[5,2,3,-4,1]=>00010=>[3,1,1]=>[1,1,3]
[5,2,3,-4,-1]=>00011=>[3,2]=>[2,3]
[5,2,-3,4,1]=>00100=>[2,1,2]=>[2,1,2]
[5,2,-3,4,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,2,-3,-4,1]=>00110=>[2,2,1]=>[1,2,2]
[5,2,-3,-4,-1]=>00111=>[2,3]=>[3,2]
[5,-2,3,4,1]=>01000=>[1,1,3]=>[3,1,1]
[5,-2,3,4,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-2,3,-4,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-2,3,-4,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-2,-3,4,1]=>01100=>[1,2,2]=>[2,2,1]
[5,-2,-3,4,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-2,-3,-4,1]=>01110=>[1,3,1]=>[1,3,1]
[5,-2,-3,-4,-1]=>01111=>[1,4]=>[4,1]
[-5,2,3,4,1]=>10000=>[1,4]=>[4,1]
[-5,2,3,4,-1]=>10001=>[1,3,1]=>[1,3,1]
[-5,2,3,-4,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,2,3,-4,-1]=>10011=>[1,2,2]=>[2,2,1]
[-5,2,-3,4,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,2,-3,4,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,2,-3,-4,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,2,-3,-4,-1]=>10111=>[1,1,3]=>[3,1,1]
[-5,-2,3,4,1]=>11000=>[2,3]=>[3,2]
[-5,-2,3,4,-1]=>11001=>[2,2,1]=>[1,2,2]
[-5,-2,3,-4,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-2,3,-4,-1]=>11011=>[2,1,2]=>[2,1,2]
[-5,-2,-3,4,1]=>11100=>[3,2]=>[2,3]
[-5,-2,-3,4,-1]=>11101=>[3,1,1]=>[1,1,3]
[-5,-2,-3,-4,1]=>11110=>[4,1]=>[1,4]
[-5,-2,-3,-4,-1]=>11111=>[5]=>[5]
[5,2,4,1,3]=>00000=>[5]=>[5]
[5,2,4,1,-3]=>00001=>[4,1]=>[1,4]
[5,2,4,-1,3]=>00010=>[3,1,1]=>[1,1,3]
[5,2,4,-1,-3]=>00011=>[3,2]=>[2,3]
[5,2,-4,1,3]=>00100=>[2,1,2]=>[2,1,2]
[5,2,-4,1,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,2,-4,-1,3]=>00110=>[2,2,1]=>[1,2,2]
[5,2,-4,-1,-3]=>00111=>[2,3]=>[3,2]
[5,-2,4,1,3]=>01000=>[1,1,3]=>[3,1,1]
[5,-2,4,1,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-2,4,-1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-2,4,-1,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-2,-4,1,3]=>01100=>[1,2,2]=>[2,2,1]
[5,-2,-4,1,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-2,-4,-1,3]=>01110=>[1,3,1]=>[1,3,1]
[5,-2,-4,-1,-3]=>01111=>[1,4]=>[4,1]
[-5,2,4,1,3]=>10000=>[1,4]=>[4,1]
[-5,2,4,1,-3]=>10001=>[1,3,1]=>[1,3,1]
[-5,2,4,-1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,2,4,-1,-3]=>10011=>[1,2,2]=>[2,2,1]
[-5,2,-4,1,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,2,-4,1,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,2,-4,-1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,2,-4,-1,-3]=>10111=>[1,1,3]=>[3,1,1]
[-5,-2,4,1,3]=>11000=>[2,3]=>[3,2]
[-5,-2,4,1,-3]=>11001=>[2,2,1]=>[1,2,2]
[-5,-2,4,-1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-2,4,-1,-3]=>11011=>[2,1,2]=>[2,1,2]
[-5,-2,-4,1,3]=>11100=>[3,2]=>[2,3]
[-5,-2,-4,1,-3]=>11101=>[3,1,1]=>[1,1,3]
[-5,-2,-4,-1,3]=>11110=>[4,1]=>[1,4]
[-5,-2,-4,-1,-3]=>11111=>[5]=>[5]
[5,2,4,3,1]=>00000=>[5]=>[5]
[5,2,4,3,-1]=>00001=>[4,1]=>[1,4]
[5,2,4,-3,1]=>00010=>[3,1,1]=>[1,1,3]
[5,2,4,-3,-1]=>00011=>[3,2]=>[2,3]
[5,2,-4,3,1]=>00100=>[2,1,2]=>[2,1,2]
[5,2,-4,3,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,2,-4,-3,1]=>00110=>[2,2,1]=>[1,2,2]
[5,2,-4,-3,-1]=>00111=>[2,3]=>[3,2]
[5,-2,4,3,1]=>01000=>[1,1,3]=>[3,1,1]
[5,-2,4,3,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-2,4,-3,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-2,4,-3,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-2,-4,3,1]=>01100=>[1,2,2]=>[2,2,1]
[5,-2,-4,3,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-2,-4,-3,1]=>01110=>[1,3,1]=>[1,3,1]
[5,-2,-4,-3,-1]=>01111=>[1,4]=>[4,1]
[-5,2,4,3,1]=>10000=>[1,4]=>[4,1]
[-5,2,4,3,-1]=>10001=>[1,3,1]=>[1,3,1]
[-5,2,4,-3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,2,4,-3,-1]=>10011=>[1,2,2]=>[2,2,1]
[-5,2,-4,3,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,2,-4,3,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,2,-4,-3,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,2,-4,-3,-1]=>10111=>[1,1,3]=>[3,1,1]
[-5,-2,4,3,1]=>11000=>[2,3]=>[3,2]
[-5,-2,4,3,-1]=>11001=>[2,2,1]=>[1,2,2]
[-5,-2,4,-3,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-2,4,-3,-1]=>11011=>[2,1,2]=>[2,1,2]
[-5,-2,-4,3,1]=>11100=>[3,2]=>[2,3]
[-5,-2,-4,3,-1]=>11101=>[3,1,1]=>[1,1,3]
[-5,-2,-4,-3,1]=>11110=>[4,1]=>[1,4]
[-5,-2,-4,-3,-1]=>11111=>[5]=>[5]
[5,3,1,2,4]=>00000=>[5]=>[5]
[5,3,1,2,-4]=>00001=>[4,1]=>[1,4]
[5,3,1,-2,4]=>00010=>[3,1,1]=>[1,1,3]
[5,3,1,-2,-4]=>00011=>[3,2]=>[2,3]
[5,3,-1,2,4]=>00100=>[2,1,2]=>[2,1,2]
[5,3,-1,2,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,3,-1,-2,4]=>00110=>[2,2,1]=>[1,2,2]
[5,3,-1,-2,-4]=>00111=>[2,3]=>[3,2]
[5,-3,1,2,4]=>01000=>[1,1,3]=>[3,1,1]
[5,-3,1,2,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-3,1,-2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-3,1,-2,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-3,-1,2,4]=>01100=>[1,2,2]=>[2,2,1]
[5,-3,-1,2,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-3,-1,-2,4]=>01110=>[1,3,1]=>[1,3,1]
[5,-3,-1,-2,-4]=>01111=>[1,4]=>[4,1]
[-5,3,1,2,4]=>10000=>[1,4]=>[4,1]
[-5,3,1,2,-4]=>10001=>[1,3,1]=>[1,3,1]
[-5,3,1,-2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,3,1,-2,-4]=>10011=>[1,2,2]=>[2,2,1]
[-5,3,-1,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,3,-1,2,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,3,-1,-2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,3,-1,-2,-4]=>10111=>[1,1,3]=>[3,1,1]
[-5,-3,1,2,4]=>11000=>[2,3]=>[3,2]
[-5,-3,1,2,-4]=>11001=>[2,2,1]=>[1,2,2]
[-5,-3,1,-2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-3,1,-2,-4]=>11011=>[2,1,2]=>[2,1,2]
[-5,-3,-1,2,4]=>11100=>[3,2]=>[2,3]
[-5,-3,-1,2,-4]=>11101=>[3,1,1]=>[1,1,3]
[-5,-3,-1,-2,4]=>11110=>[4,1]=>[1,4]
[-5,-3,-1,-2,-4]=>11111=>[5]=>[5]
[5,3,1,4,2]=>00000=>[5]=>[5]
[5,3,1,4,-2]=>00001=>[4,1]=>[1,4]
[5,3,1,-4,2]=>00010=>[3,1,1]=>[1,1,3]
[5,3,1,-4,-2]=>00011=>[3,2]=>[2,3]
[5,3,-1,4,2]=>00100=>[2,1,2]=>[2,1,2]
[5,3,-1,4,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,3,-1,-4,2]=>00110=>[2,2,1]=>[1,2,2]
[5,3,-1,-4,-2]=>00111=>[2,3]=>[3,2]
[5,-3,1,4,2]=>01000=>[1,1,3]=>[3,1,1]
[5,-3,1,4,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-3,1,-4,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-3,1,-4,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-3,-1,4,2]=>01100=>[1,2,2]=>[2,2,1]
[5,-3,-1,4,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-3,-1,-4,2]=>01110=>[1,3,1]=>[1,3,1]
[5,-3,-1,-4,-2]=>01111=>[1,4]=>[4,1]
[-5,3,1,4,2]=>10000=>[1,4]=>[4,1]
[-5,3,1,4,-2]=>10001=>[1,3,1]=>[1,3,1]
[-5,3,1,-4,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,3,1,-4,-2]=>10011=>[1,2,2]=>[2,2,1]
[-5,3,-1,4,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,3,-1,4,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,3,-1,-4,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,3,-1,-4,-2]=>10111=>[1,1,3]=>[3,1,1]
[-5,-3,1,4,2]=>11000=>[2,3]=>[3,2]
[-5,-3,1,4,-2]=>11001=>[2,2,1]=>[1,2,2]
[-5,-3,1,-4,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-3,1,-4,-2]=>11011=>[2,1,2]=>[2,1,2]
[-5,-3,-1,4,2]=>11100=>[3,2]=>[2,3]
[-5,-3,-1,4,-2]=>11101=>[3,1,1]=>[1,1,3]
[-5,-3,-1,-4,2]=>11110=>[4,1]=>[1,4]
[-5,-3,-1,-4,-2]=>11111=>[5]=>[5]
[5,3,2,1,4]=>00000=>[5]=>[5]
[5,3,2,1,-4]=>00001=>[4,1]=>[1,4]
[5,3,2,-1,4]=>00010=>[3,1,1]=>[1,1,3]
[5,3,2,-1,-4]=>00011=>[3,2]=>[2,3]
[5,3,-2,1,4]=>00100=>[2,1,2]=>[2,1,2]
[5,3,-2,1,-4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,3,-2,-1,4]=>00110=>[2,2,1]=>[1,2,2]
[5,3,-2,-1,-4]=>00111=>[2,3]=>[3,2]
[5,-3,2,1,4]=>01000=>[1,1,3]=>[3,1,1]
[5,-3,2,1,-4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-3,2,-1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-3,2,-1,-4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-3,-2,1,4]=>01100=>[1,2,2]=>[2,2,1]
[5,-3,-2,1,-4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-3,-2,-1,4]=>01110=>[1,3,1]=>[1,3,1]
[5,-3,-2,-1,-4]=>01111=>[1,4]=>[4,1]
[-5,3,2,1,4]=>10000=>[1,4]=>[4,1]
[-5,3,2,1,-4]=>10001=>[1,3,1]=>[1,3,1]
[-5,3,2,-1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,3,2,-1,-4]=>10011=>[1,2,2]=>[2,2,1]
[-5,3,-2,1,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,3,-2,1,-4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,3,-2,-1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,3,-2,-1,-4]=>10111=>[1,1,3]=>[3,1,1]
[-5,-3,2,1,4]=>11000=>[2,3]=>[3,2]
[-5,-3,2,1,-4]=>11001=>[2,2,1]=>[1,2,2]
[-5,-3,2,-1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-3,2,-1,-4]=>11011=>[2,1,2]=>[2,1,2]
[-5,-3,-2,1,4]=>11100=>[3,2]=>[2,3]
[-5,-3,-2,1,-4]=>11101=>[3,1,1]=>[1,1,3]
[-5,-3,-2,-1,4]=>11110=>[4,1]=>[1,4]
[-5,-3,-2,-1,-4]=>11111=>[5]=>[5]
[5,3,2,4,1]=>00000=>[5]=>[5]
[5,3,2,4,-1]=>00001=>[4,1]=>[1,4]
[5,3,2,-4,1]=>00010=>[3,1,1]=>[1,1,3]
[5,3,2,-4,-1]=>00011=>[3,2]=>[2,3]
[5,3,-2,4,1]=>00100=>[2,1,2]=>[2,1,2]
[5,3,-2,4,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,3,-2,-4,1]=>00110=>[2,2,1]=>[1,2,2]
[5,3,-2,-4,-1]=>00111=>[2,3]=>[3,2]
[5,-3,2,4,1]=>01000=>[1,1,3]=>[3,1,1]
[5,-3,2,4,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-3,2,-4,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-3,2,-4,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-3,-2,4,1]=>01100=>[1,2,2]=>[2,2,1]
[5,-3,-2,4,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-3,-2,-4,1]=>01110=>[1,3,1]=>[1,3,1]
[5,-3,-2,-4,-1]=>01111=>[1,4]=>[4,1]
[-5,3,2,4,1]=>10000=>[1,4]=>[4,1]
[-5,3,2,4,-1]=>10001=>[1,3,1]=>[1,3,1]
[-5,3,2,-4,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,3,2,-4,-1]=>10011=>[1,2,2]=>[2,2,1]
[-5,3,-2,4,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,3,-2,4,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,3,-2,-4,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,3,-2,-4,-1]=>10111=>[1,1,3]=>[3,1,1]
[-5,-3,2,4,1]=>11000=>[2,3]=>[3,2]
[-5,-3,2,4,-1]=>11001=>[2,2,1]=>[1,2,2]
[-5,-3,2,-4,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-3,2,-4,-1]=>11011=>[2,1,2]=>[2,1,2]
[-5,-3,-2,4,1]=>11100=>[3,2]=>[2,3]
[-5,-3,-2,4,-1]=>11101=>[3,1,1]=>[1,1,3]
[-5,-3,-2,-4,1]=>11110=>[4,1]=>[1,4]
[-5,-3,-2,-4,-1]=>11111=>[5]=>[5]
[5,3,4,1,2]=>00000=>[5]=>[5]
[5,3,4,1,-2]=>00001=>[4,1]=>[1,4]
[5,3,4,-1,2]=>00010=>[3,1,1]=>[1,1,3]
[5,3,4,-1,-2]=>00011=>[3,2]=>[2,3]
[5,3,-4,1,2]=>00100=>[2,1,2]=>[2,1,2]
[5,3,-4,1,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,3,-4,-1,2]=>00110=>[2,2,1]=>[1,2,2]
[5,3,-4,-1,-2]=>00111=>[2,3]=>[3,2]
[5,-3,4,1,2]=>01000=>[1,1,3]=>[3,1,1]
[5,-3,4,1,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-3,4,-1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-3,4,-1,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-3,-4,1,2]=>01100=>[1,2,2]=>[2,2,1]
[5,-3,-4,1,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-3,-4,-1,2]=>01110=>[1,3,1]=>[1,3,1]
[5,-3,-4,-1,-2]=>01111=>[1,4]=>[4,1]
[-5,3,4,1,2]=>10000=>[1,4]=>[4,1]
[-5,3,4,1,-2]=>10001=>[1,3,1]=>[1,3,1]
[-5,3,4,-1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,3,4,-1,-2]=>10011=>[1,2,2]=>[2,2,1]
[-5,3,-4,1,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,3,-4,1,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,3,-4,-1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,3,-4,-1,-2]=>10111=>[1,1,3]=>[3,1,1]
[-5,-3,4,1,2]=>11000=>[2,3]=>[3,2]
[-5,-3,4,1,-2]=>11001=>[2,2,1]=>[1,2,2]
[-5,-3,4,-1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-3,4,-1,-2]=>11011=>[2,1,2]=>[2,1,2]
[-5,-3,-4,1,2]=>11100=>[3,2]=>[2,3]
[-5,-3,-4,1,-2]=>11101=>[3,1,1]=>[1,1,3]
[-5,-3,-4,-1,2]=>11110=>[4,1]=>[1,4]
[-5,-3,-4,-1,-2]=>11111=>[5]=>[5]
[5,3,4,2,1]=>00000=>[5]=>[5]
[5,3,4,2,-1]=>00001=>[4,1]=>[1,4]
[5,3,4,-2,1]=>00010=>[3,1,1]=>[1,1,3]
[5,3,4,-2,-1]=>00011=>[3,2]=>[2,3]
[5,3,-4,2,1]=>00100=>[2,1,2]=>[2,1,2]
[5,3,-4,2,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,3,-4,-2,1]=>00110=>[2,2,1]=>[1,2,2]
[5,3,-4,-2,-1]=>00111=>[2,3]=>[3,2]
[5,-3,4,2,1]=>01000=>[1,1,3]=>[3,1,1]
[5,-3,4,2,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-3,4,-2,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-3,4,-2,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-3,-4,2,1]=>01100=>[1,2,2]=>[2,2,1]
[5,-3,-4,2,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-3,-4,-2,1]=>01110=>[1,3,1]=>[1,3,1]
[5,-3,-4,-2,-1]=>01111=>[1,4]=>[4,1]
[-5,3,4,2,1]=>10000=>[1,4]=>[4,1]
[-5,3,4,2,-1]=>10001=>[1,3,1]=>[1,3,1]
[-5,3,4,-2,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,3,4,-2,-1]=>10011=>[1,2,2]=>[2,2,1]
[-5,3,-4,2,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,3,-4,2,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,3,-4,-2,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,3,-4,-2,-1]=>10111=>[1,1,3]=>[3,1,1]
[-5,-3,4,2,1]=>11000=>[2,3]=>[3,2]
[-5,-3,4,2,-1]=>11001=>[2,2,1]=>[1,2,2]
[-5,-3,4,-2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-3,4,-2,-1]=>11011=>[2,1,2]=>[2,1,2]
[-5,-3,-4,2,1]=>11100=>[3,2]=>[2,3]
[-5,-3,-4,2,-1]=>11101=>[3,1,1]=>[1,1,3]
[-5,-3,-4,-2,1]=>11110=>[4,1]=>[1,4]
[-5,-3,-4,-2,-1]=>11111=>[5]=>[5]
[5,4,1,2,3]=>00000=>[5]=>[5]
[5,4,1,2,-3]=>00001=>[4,1]=>[1,4]
[5,4,1,-2,3]=>00010=>[3,1,1]=>[1,1,3]
[5,4,1,-2,-3]=>00011=>[3,2]=>[2,3]
[5,4,-1,2,3]=>00100=>[2,1,2]=>[2,1,2]
[5,4,-1,2,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,4,-1,-2,3]=>00110=>[2,2,1]=>[1,2,2]
[5,4,-1,-2,-3]=>00111=>[2,3]=>[3,2]
[5,-4,1,2,3]=>01000=>[1,1,3]=>[3,1,1]
[5,-4,1,2,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-4,1,-2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-4,1,-2,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-4,-1,2,3]=>01100=>[1,2,2]=>[2,2,1]
[5,-4,-1,2,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-4,-1,-2,3]=>01110=>[1,3,1]=>[1,3,1]
[5,-4,-1,-2,-3]=>01111=>[1,4]=>[4,1]
[-5,4,1,2,3]=>10000=>[1,4]=>[4,1]
[-5,4,1,2,-3]=>10001=>[1,3,1]=>[1,3,1]
[-5,4,1,-2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,4,1,-2,-3]=>10011=>[1,2,2]=>[2,2,1]
[-5,4,-1,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,4,-1,2,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,4,-1,-2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,4,-1,-2,-3]=>10111=>[1,1,3]=>[3,1,1]
[-5,-4,1,2,3]=>11000=>[2,3]=>[3,2]
[-5,-4,1,2,-3]=>11001=>[2,2,1]=>[1,2,2]
[-5,-4,1,-2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-4,1,-2,-3]=>11011=>[2,1,2]=>[2,1,2]
[-5,-4,-1,2,3]=>11100=>[3,2]=>[2,3]
[-5,-4,-1,2,-3]=>11101=>[3,1,1]=>[1,1,3]
[-5,-4,-1,-2,3]=>11110=>[4,1]=>[1,4]
[-5,-4,-1,-2,-3]=>11111=>[5]=>[5]
[5,4,1,3,2]=>00000=>[5]=>[5]
[5,4,1,3,-2]=>00001=>[4,1]=>[1,4]
[5,4,1,-3,2]=>00010=>[3,1,1]=>[1,1,3]
[5,4,1,-3,-2]=>00011=>[3,2]=>[2,3]
[5,4,-1,3,2]=>00100=>[2,1,2]=>[2,1,2]
[5,4,-1,3,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,4,-1,-3,2]=>00110=>[2,2,1]=>[1,2,2]
[5,4,-1,-3,-2]=>00111=>[2,3]=>[3,2]
[5,-4,1,3,2]=>01000=>[1,1,3]=>[3,1,1]
[5,-4,1,3,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-4,1,-3,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-4,1,-3,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-4,-1,3,2]=>01100=>[1,2,2]=>[2,2,1]
[5,-4,-1,3,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-4,-1,-3,2]=>01110=>[1,3,1]=>[1,3,1]
[5,-4,-1,-3,-2]=>01111=>[1,4]=>[4,1]
[-5,4,1,3,2]=>10000=>[1,4]=>[4,1]
[-5,4,1,3,-2]=>10001=>[1,3,1]=>[1,3,1]
[-5,4,1,-3,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,4,1,-3,-2]=>10011=>[1,2,2]=>[2,2,1]
[-5,4,-1,3,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,4,-1,3,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,4,-1,-3,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,4,-1,-3,-2]=>10111=>[1,1,3]=>[3,1,1]
[-5,-4,1,3,2]=>11000=>[2,3]=>[3,2]
[-5,-4,1,3,-2]=>11001=>[2,2,1]=>[1,2,2]
[-5,-4,1,-3,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-4,1,-3,-2]=>11011=>[2,1,2]=>[2,1,2]
[-5,-4,-1,3,2]=>11100=>[3,2]=>[2,3]
[-5,-4,-1,3,-2]=>11101=>[3,1,1]=>[1,1,3]
[-5,-4,-1,-3,2]=>11110=>[4,1]=>[1,4]
[-5,-4,-1,-3,-2]=>11111=>[5]=>[5]
[5,4,2,1,3]=>00000=>[5]=>[5]
[5,4,2,1,-3]=>00001=>[4,1]=>[1,4]
[5,4,2,-1,3]=>00010=>[3,1,1]=>[1,1,3]
[5,4,2,-1,-3]=>00011=>[3,2]=>[2,3]
[5,4,-2,1,3]=>00100=>[2,1,2]=>[2,1,2]
[5,4,-2,1,-3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,4,-2,-1,3]=>00110=>[2,2,1]=>[1,2,2]
[5,4,-2,-1,-3]=>00111=>[2,3]=>[3,2]
[5,-4,2,1,3]=>01000=>[1,1,3]=>[3,1,1]
[5,-4,2,1,-3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-4,2,-1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-4,2,-1,-3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-4,-2,1,3]=>01100=>[1,2,2]=>[2,2,1]
[5,-4,-2,1,-3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-4,-2,-1,3]=>01110=>[1,3,1]=>[1,3,1]
[5,-4,-2,-1,-3]=>01111=>[1,4]=>[4,1]
[-5,4,2,1,3]=>10000=>[1,4]=>[4,1]
[-5,4,2,1,-3]=>10001=>[1,3,1]=>[1,3,1]
[-5,4,2,-1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,4,2,-1,-3]=>10011=>[1,2,2]=>[2,2,1]
[-5,4,-2,1,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,4,-2,1,-3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,4,-2,-1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,4,-2,-1,-3]=>10111=>[1,1,3]=>[3,1,1]
[-5,-4,2,1,3]=>11000=>[2,3]=>[3,2]
[-5,-4,2,1,-3]=>11001=>[2,2,1]=>[1,2,2]
[-5,-4,2,-1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-4,2,-1,-3]=>11011=>[2,1,2]=>[2,1,2]
[-5,-4,-2,1,3]=>11100=>[3,2]=>[2,3]
[-5,-4,-2,1,-3]=>11101=>[3,1,1]=>[1,1,3]
[-5,-4,-2,-1,3]=>11110=>[4,1]=>[1,4]
[-5,-4,-2,-1,-3]=>11111=>[5]=>[5]
[5,4,2,3,1]=>00000=>[5]=>[5]
[5,4,2,3,-1]=>00001=>[4,1]=>[1,4]
[5,4,2,-3,1]=>00010=>[3,1,1]=>[1,1,3]
[5,4,2,-3,-1]=>00011=>[3,2]=>[2,3]
[5,4,-2,3,1]=>00100=>[2,1,2]=>[2,1,2]
[5,4,-2,3,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,4,-2,-3,1]=>00110=>[2,2,1]=>[1,2,2]
[5,4,-2,-3,-1]=>00111=>[2,3]=>[3,2]
[5,-4,2,3,1]=>01000=>[1,1,3]=>[3,1,1]
[5,-4,2,3,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-4,2,-3,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-4,2,-3,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-4,-2,3,1]=>01100=>[1,2,2]=>[2,2,1]
[5,-4,-2,3,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-4,-2,-3,1]=>01110=>[1,3,1]=>[1,3,1]
[5,-4,-2,-3,-1]=>01111=>[1,4]=>[4,1]
[-5,4,2,3,1]=>10000=>[1,4]=>[4,1]
[-5,4,2,3,-1]=>10001=>[1,3,1]=>[1,3,1]
[-5,4,2,-3,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,4,2,-3,-1]=>10011=>[1,2,2]=>[2,2,1]
[-5,4,-2,3,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,4,-2,3,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,4,-2,-3,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,4,-2,-3,-1]=>10111=>[1,1,3]=>[3,1,1]
[-5,-4,2,3,1]=>11000=>[2,3]=>[3,2]
[-5,-4,2,3,-1]=>11001=>[2,2,1]=>[1,2,2]
[-5,-4,2,-3,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-4,2,-3,-1]=>11011=>[2,1,2]=>[2,1,2]
[-5,-4,-2,3,1]=>11100=>[3,2]=>[2,3]
[-5,-4,-2,3,-1]=>11101=>[3,1,1]=>[1,1,3]
[-5,-4,-2,-3,1]=>11110=>[4,1]=>[1,4]
[-5,-4,-2,-3,-1]=>11111=>[5]=>[5]
[5,4,3,1,2]=>00000=>[5]=>[5]
[5,4,3,1,-2]=>00001=>[4,1]=>[1,4]
[5,4,3,-1,2]=>00010=>[3,1,1]=>[1,1,3]
[5,4,3,-1,-2]=>00011=>[3,2]=>[2,3]
[5,4,-3,1,2]=>00100=>[2,1,2]=>[2,1,2]
[5,4,-3,1,-2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,4,-3,-1,2]=>00110=>[2,2,1]=>[1,2,2]
[5,4,-3,-1,-2]=>00111=>[2,3]=>[3,2]
[5,-4,3,1,2]=>01000=>[1,1,3]=>[3,1,1]
[5,-4,3,1,-2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-4,3,-1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-4,3,-1,-2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-4,-3,1,2]=>01100=>[1,2,2]=>[2,2,1]
[5,-4,-3,1,-2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-4,-3,-1,2]=>01110=>[1,3,1]=>[1,3,1]
[5,-4,-3,-1,-2]=>01111=>[1,4]=>[4,1]
[-5,4,3,1,2]=>10000=>[1,4]=>[4,1]
[-5,4,3,1,-2]=>10001=>[1,3,1]=>[1,3,1]
[-5,4,3,-1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,4,3,-1,-2]=>10011=>[1,2,2]=>[2,2,1]
[-5,4,-3,1,2]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,4,-3,1,-2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,4,-3,-1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,4,-3,-1,-2]=>10111=>[1,1,3]=>[3,1,1]
[-5,-4,3,1,2]=>11000=>[2,3]=>[3,2]
[-5,-4,3,1,-2]=>11001=>[2,2,1]=>[1,2,2]
[-5,-4,3,-1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-4,3,-1,-2]=>11011=>[2,1,2]=>[2,1,2]
[-5,-4,-3,1,2]=>11100=>[3,2]=>[2,3]
[-5,-4,-3,1,-2]=>11101=>[3,1,1]=>[1,1,3]
[-5,-4,-3,-1,2]=>11110=>[4,1]=>[1,4]
[-5,-4,-3,-1,-2]=>11111=>[5]=>[5]
[5,4,3,2,1]=>00000=>[5]=>[5]
[5,4,3,2,-1]=>00001=>[4,1]=>[1,4]
[5,4,3,-2,1]=>00010=>[3,1,1]=>[1,1,3]
[5,4,3,-2,-1]=>00011=>[3,2]=>[2,3]
[5,4,-3,2,1]=>00100=>[2,1,2]=>[2,1,2]
[5,4,-3,2,-1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[5,4,-3,-2,1]=>00110=>[2,2,1]=>[1,2,2]
[5,4,-3,-2,-1]=>00111=>[2,3]=>[3,2]
[5,-4,3,2,1]=>01000=>[1,1,3]=>[3,1,1]
[5,-4,3,2,-1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,-4,3,-2,1]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,-4,3,-2,-1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,-4,-3,2,1]=>01100=>[1,2,2]=>[2,2,1]
[5,-4,-3,2,-1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,-4,-3,-2,1]=>01110=>[1,3,1]=>[1,3,1]
[5,-4,-3,-2,-1]=>01111=>[1,4]=>[4,1]
[-5,4,3,2,1]=>10000=>[1,4]=>[4,1]
[-5,4,3,2,-1]=>10001=>[1,3,1]=>[1,3,1]
[-5,4,3,-2,1]=>10010=>[1,2,1,1]=>[1,1,2,1]
[-5,4,3,-2,-1]=>10011=>[1,2,2]=>[2,2,1]
[-5,4,-3,2,1]=>10100=>[1,1,1,2]=>[2,1,1,1]
[-5,4,-3,2,-1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[-5,4,-3,-2,1]=>10110=>[1,1,2,1]=>[1,2,1,1]
[-5,4,-3,-2,-1]=>10111=>[1,1,3]=>[3,1,1]
[-5,-4,3,2,1]=>11000=>[2,3]=>[3,2]
[-5,-4,3,2,-1]=>11001=>[2,2,1]=>[1,2,2]
[-5,-4,3,-2,1]=>11010=>[2,1,1,1]=>[1,1,1,2]
[-5,-4,3,-2,-1]=>11011=>[2,1,2]=>[2,1,2]
[-5,-4,-3,2,1]=>11100=>[3,2]=>[2,3]
[-5,-4,-3,2,-1]=>11101=>[3,1,1]=>[1,1,3]
[-5,-4,-3,-2,1]=>11110=>[4,1]=>[1,4]
[-5,-4,-3,-2,-1]=>11111=>[5]=>[5]
[1,2,3,4,5,6]=>000000=>[6]=>[6]
[1,2,3,6,4,5]=>000000=>[6]=>[6]
[1,2,5,3,4,6]=>000000=>[6]=>[6]
[1,2,5,6,3,4]=>000000=>[6]=>[6]
[1,4,2,3,5,6]=>000000=>[6]=>[6]
[1,4,2,6,3,5]=>000000=>[6]=>[6]
[1,4,5,2,3,6]=>000000=>[6]=>[6]
[1,4,5,6,2,3]=>000000=>[6]=>[6]
[1,5,2,3,4,6]=>000000=>[6]=>[6]
[1,5,6,2,3,4]=>000000=>[6]=>[6]
[1,6,2,3,4,5]=>000000=>[6]=>[6]
[1,6,2,5,3,4]=>000000=>[6]=>[6]
[1,6,4,2,3,5]=>000000=>[6]=>[6]
[1,6,4,5,2,3]=>000000=>[6]=>[6]
[3,1,2,4,5,6]=>000000=>[6]=>[6]
[3,1,2,6,4,5]=>000000=>[6]=>[6]
[3,1,5,2,4,6]=>000000=>[6]=>[6]
[3,1,5,6,2,4]=>000000=>[6]=>[6]
[3,4,1,2,5,6]=>000000=>[6]=>[6]
[3,4,1,6,2,5]=>000000=>[6]=>[6]
[3,4,5,1,2,6]=>000000=>[6]=>[6]
[3,4,5,6,1,2]=>000000=>[6]=>[6]
[3,4,6,1,2,5]=>000000=>[6]=>[6]
[3,5,1,2,4,6]=>000000=>[6]=>[6]
[3,5,6,1,2,4]=>000000=>[6]=>[6]
[3,6,1,2,4,5]=>000000=>[6]=>[6]
[3,6,1,5,2,4]=>000000=>[6]=>[6]
[3,6,4,1,2,5]=>000000=>[6]=>[6]
[3,6,4,5,1,2]=>000000=>[6]=>[6]
[4,1,2,3,5,6]=>000000=>[6]=>[6]
[4,5,1,2,3,6]=>000000=>[6]=>[6]
[4,5,6,1,2,3]=>000000=>[6]=>[6]
[4,6,1,2,3,5]=>000000=>[6]=>[6]
[4,6,5,1,2,3]=>000000=>[6]=>[6]
[5,1,2,3,4,6]=>000000=>[6]=>[6]
[5,1,2,6,3,4]=>000000=>[6]=>[6]
[5,1,4,2,3,6]=>000000=>[6]=>[6]
[5,1,4,6,2,3]=>000000=>[6]=>[6]
[5,1,6,2,3,4]=>000000=>[6]=>[6]
[5,3,1,2,4,6]=>000000=>[6]=>[6]
[5,3,1,6,2,4]=>000000=>[6]=>[6]
[5,3,4,1,2,6]=>000000=>[6]=>[6]
[5,3,4,6,1,2]=>000000=>[6]=>[6]
[5,6,1,2,3,4]=>000000=>[6]=>[6]
[5,6,1,4,2,3]=>000000=>[6]=>[6]
[5,6,3,1,2,4]=>000000=>[6]=>[6]
[5,6,3,4,1,2]=>000000=>[6]=>[6]
[6,1,2,3,4,5]=>000000=>[6]=>[6]
[6,2,1,5,3,4]=>000000=>[6]=>[6]
[6,2,4,1,3,5]=>000000=>[6]=>[6]
[6,3,1,2,4,5]=>000000=>[6]=>[6]
[1,2,3,4,7,5,6]=>0000000=>[7]=>[7]
[1,2,5,3,7,4,6]=>0000000=>[7]=>[7]
[1,2,7,3,4,5,6]=>0000000=>[7]=>[7]
[1,2,7,3,6,4,5]=>0000000=>[7]=>[7]
[1,4,7,2,3,5,6]=>0000000=>[7]=>[7]
[1,5,7,2,3,4,6]=>0000000=>[7]=>[7]
[1,6,7,2,3,4,5]=>0000000=>[7]=>[7]
[1,6,7,2,5,3,4]=>0000000=>[7]=>[7]
[1,6,7,4,2,3,5]=>0000000=>[7]=>[7]
[3,1,7,2,4,5,6]=>0000000=>[7]=>[7]
[3,1,7,5,2,4,6]=>0000000=>[7]=>[7]
[3,4,7,1,2,5,6]=>0000000=>[7]=>[7]
[3,4,7,1,6,2,5]=>0000000=>[7]=>[7]
[3,4,7,5,1,2,6]=>0000000=>[7]=>[7]
[3,4,7,5,6,1,2]=>0000000=>[7]=>[7]
[3,5,7,1,2,4,6]=>0000000=>[7]=>[7]
[3,6,1,2,7,4,5]=>0000000=>[7]=>[7]
[3,7,4,1,2,5,6]=>0000000=>[7]=>[7]
[3,7,4,5,1,2,6]=>0000000=>[7]=>[7]
[3,7,4,5,6,1,2]=>0000000=>[7]=>[7]
[3,7,4,6,1,2,5]=>0000000=>[7]=>[7]
[3,7,5,1,2,4,6]=>0000000=>[7]=>[7]
[3,7,5,6,1,2,4]=>0000000=>[7]=>[7]
[3,7,6,1,2,4,5]=>0000000=>[7]=>[7]
[4,7,5,6,1,2,3]=>0000000=>[7]=>[7]
[5,3,4,7,1,2,6]=>0000000=>[7]=>[7]
[5,3,7,1,2,4,6]=>0000000=>[7]=>[7]
[5,4,7,1,2,3,6]=>0000000=>[7]=>[7]
[7,1,2,5,3,4,6]=>0000000=>[7]=>[7]
[7,1,3,2,4,5,6]=>0000000=>[7]=>[7]
[7,1,4,2,3,5,6]=>0000000=>[7]=>[7]
[7,1,4,2,6,3,5]=>0000000=>[7]=>[7]
[7,1,4,5,2,3,6]=>0000000=>[7]=>[7]
[7,1,4,6,2,3,5]=>0000000=>[7]=>[7]
[7,1,5,2,3,4,6]=>0000000=>[7]=>[7]
[7,1,5,6,2,3,4]=>0000000=>[7]=>[7]
[7,1,6,2,3,4,5]=>0000000=>[7]=>[7]
[7,1,6,4,5,2,3]=>0000000=>[7]=>[7]
[7,2,4,1,3,5,6]=>0000000=>[7]=>[7]
[7,2,5,1,3,4,6]=>0000000=>[7]=>[7]
[7,2,6,1,3,4,5]=>0000000=>[7]=>[7]
[7,3,1,2,4,5,6]=>0000000=>[7]=>[7]
[7,3,5,1,2,4,6]=>0000000=>[7]=>[7]
[7,3,5,6,1,2,4]=>0000000=>[7]=>[7]
[7,3,6,1,2,4,5]=>0000000=>[7]=>[7]
[7,5,1,4,2,3,6]=>0000000=>[7]=>[7]
[5,6,7,8,3,4,1,2]=>00000000=>[8]=>[8]
[5,6,7,8,3,1,2,4]=>00000000=>[8]=>[8]
[5,6,7,8,4,1,2,3]=>00000000=>[8]=>[8]
[5,6,7,8,1,4,2,3]=>00000000=>[8]=>[8]
[7,8,5,6,3,4,1,2]=>00000000=>[8]=>[8]
[-6,-4,-2,1,3,5]=>111000=>[3,3]=>[3,3]
[4,6,-3,1,2,5]=>001000=>[2,1,3]=>[3,1,2]
[-3,2,-6,-4,1,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,6,-5,1,4]=>000100=>[3,1,2]=>[2,1,3]
[-5,-3,2,4,-6,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,5,2,3,-6,1]=>000010=>[4,1,1]=>[1,1,4]
[2,-6,-4,-5,1,3]=>011100=>[1,3,2]=>[2,3,1]
[-6,-5,1,-4,2,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-5,3,6,1,2,4]=>100000=>[1,5]=>[5,1]
[2,6,-5,1,3,4]=>001000=>[2,1,3]=>[3,1,2]
[-5,4,-6,-2,1,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,-5,-6,-3,1,2]=>011100=>[1,3,2]=>[2,3,1]
[3,6,5,-4,1,2]=>000100=>[3,1,2]=>[2,1,3]
[4,6,-5,3,1,2]=>001000=>[2,1,3]=>[3,1,2]
[-4,3,-5,2,-6,1]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[-8,-6,-4,-2,1,3,5,7]=>11110000=>[4,4]=>[4,4]
[6,8,-4,-3,1,2,5,7]=>00110000=>[2,2,4]=>[4,2,2]
[-3,2,-8,-6,-4,1,5,7]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[3,2,8,-6,-5,1,4,7]=>00011000=>[3,2,3]=>[3,2,3]
[-5,-3,2,4,-8,-6,1,7]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[5,-3,2,4,8,-7,1,6]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[-7,-5,-3,2,4,6,-8,1]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[5,7,-4,2,3,6,-8,1]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[-4,5,2,3,8,-7,1,6]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[4,5,2,3,-8,-6,1,7]=>00001100=>[4,2,2]=>[2,2,4]
[2,-8,-4,-6,-5,1,3,7]=>01111000=>[1,4,3]=>[3,4,1]
[-8,-6,1,-5,-4,2,3,7]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[-3,6,8,-5,1,2,4,7]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[2,8,-6,-5,1,3,4,7]=>00110000=>[2,2,4]=>[4,2,2]
[-5,4,-8,-6,-2,1,3,7]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[4,-5,-8,-6,-3,1,2,7]=>01111000=>[1,4,3]=>[3,4,1]
[3,-8,-5,-6,-4,1,2,7]=>01111000=>[1,4,3]=>[3,4,1]
[-6,4,3,8,-5,1,2,7]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[-4,3,-5,2,-8,-6,1,7]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[4,3,-5,2,8,-7,1,6]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[-4,3,-7,-5,2,6,-8,1]=>10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
[4,3,7,-6,2,5,-8,1]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[3,-4,-8,-6,2,-7,1,5]=>01110100=>[1,3,1,1,2]=>[2,1,1,3,1]
[8,4,-7,-6,3,1,2,5]=>00110000=>[2,2,4]=>[4,2,2]
[-5,4,-7,3,8,1,2,6]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[5,8,-4,3,-7,1,2,6]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[5,-3,4,8,-7,1,2,6]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[-5,2,4,8,-7,1,3,6]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[-7,-5,4,6,-8,-2,1,3]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[4,-7,-5,6,-8,-3,1,2]=>01101100=>[1,2,1,2,2]=>[2,2,1,2,1]
[-7,3,-5,6,-8,-4,1,2]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[-4,3,6,-7,-8,-5,1,2]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[-4,3,5,8,7,-6,1,2]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[4,-8,6,-7,3,5,1,2]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[-6,-4,3,5,-7,2,-8,1]=>11001010=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]
[5,6,3,4,-7,2,-8,1]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[3,-8,5,7,4,-6,1,2]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[-7,-6,3,-8,4,-5,1,2]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[-7,-6,5,3,-8,-4,1,2]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[-7,4,-6,5,-8,-3,1,2]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[6,7,4,5,-8,-2,1,3]=>00001100=>[4,2,2]=>[2,2,4]
[8,-6,2,4,-7,1,3,5]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[4,-8,-6,-3,-7,1,2,5]=>01111000=>[1,4,3]=>[3,4,1]
[-4,3,-8,-6,-7,1,2,5]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[-7,6,8,1,3,-5,2,4]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[-7,-6,5,8,3,1,2,4]=>11000000=>[2,6]=>[6,2]
[5,-6,3,8,2,-7,1,4]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[3,-7,-5,-6,2,4,-8,1]=>01110010=>[1,3,2,1,1]=>[1,1,2,3,1]
[-7,-6,2,-5,3,4,-8,1]=>11010010=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]
[-5,2,6,8,3,-7,1,4]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[-5,7,8,-6,2,1,3,4]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[5,6,7,1,8,2,3,4]=>00000000=>[8]=>[8]
[-4,-8,-7,1,-6,2,3,5]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[8,-7,-6,3,1,2,4,5]=>01100000=>[1,2,5]=>[5,2,1]
[2,-7,8,-6,1,3,4,5]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[-5,2,8,-7,1,3,4,6]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[-7,-5,3,8,1,2,4,6]=>11000000=>[2,6]=>[6,2]
[5,-7,-4,8,1,2,3,6]=>01100000=>[1,2,5]=>[5,2,1]
[-4,-8,-7,2,-5,1,3,6]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[4,2,-7,8,-6,1,3,5]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[-8,-4,-6,2,3,-7,1,5]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[-6,4,7,2,3,5,-8,1]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[3,7,-6,2,4,5,-8,1]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[6,8,-3,2,4,-7,1,5]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[2,-8,-7,-3,-6,1,4,5]=>01111000=>[1,4,3]=>[3,4,1]
[3,-7,2,8,-5,1,4,6]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[-3,2,7,8,-4,1,5,6]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[3,4,7,8,1,2,5,6]=>00000000=>[8]=>[8]
[4,8,-7,-2,1,3,5,6]=>00110000=>[2,2,4]=>[4,2,2]
[-7,6,-8,-4,-2,1,3,5]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[6,-7,-8,-4,-3,1,2,5]=>01111000=>[1,4,3]=>[3,4,1]
[-7,-3,2,6,-8,-4,1,5]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[3,7,2,6,-8,-5,1,4]=>00001100=>[4,2,2]=>[2,2,4]
[-7,-8,-3,2,5,-6,1,4]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[-8,5,-6,-3,2,-7,1,4]=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
[-6,5,-7,-3,2,4,-8,1]=>10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
[5,-6,-7,-4,2,3,-8,1]=>01110010=>[1,3,2,1,1]=>[1,1,2,3,1]
[-8,-6,5,-4,2,-7,1,3]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[-8,4,7,2,5,-6,1,3]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[-7,2,-4,6,-8,-5,1,3]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[-7,6,1,-8,-5,-4,2,3]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[6,-7,-3,-8,-5,1,2,4]=>01111000=>[1,4,3]=>[3,4,1]
[7,2,6,-8,-5,1,3,4]=>00011000=>[3,2,3]=>[3,2,3]
[7,-8,2,5,-6,1,3,4]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[7,-8,-5,-3,-6,1,2,4]=>01111000=>[1,4,3]=>[3,4,1]
[-8,6,7,5,-4,1,2,3]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[-8,6,7,1,4,-5,2,3]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[-8,2,5,7,4,-6,1,3]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[-8,-6,-5,4,2,-7,1,3]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[4,7,6,-5,2,3,-8,1]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[5,7,-6,4,2,3,-8,1]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[4,-8,-5,2,-6,-7,1,3]=>01101100=>[1,2,1,2,2]=>[2,2,1,2,1]
[4,-8,-5,-7,1,-6,2,3]=>01110100=>[1,3,1,1,2]=>[2,1,1,3,1]
[-8,-7,5,6,4,1,2,3]=>11000000=>[2,6]=>[6,2]
[8,6,-7,-4,5,1,2,3]=>00110000=>[2,2,4]=>[4,2,2]
[-8,6,-7,3,5,1,2,4]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[5,8,-6,2,-7,1,3,4]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[-6,5,-7,4,-8,-2,1,3]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[5,-6,-7,4,-8,-3,1,2]=>01101100=>[1,2,1,2,2]=>[2,2,1,2,1]
[7,-8,6,3,5,-4,1,2]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[6,-7,-4,-8,3,-5,1,2]=>01110100=>[1,3,1,1,2]=>[2,1,1,3,1]
[5,7,-8,4,3,-6,1,2]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[5,8,-6,4,-7,3,1,2]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[-5,4,-6,3,-7,2,-8,1]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[6,2,3,4,5,-1]=>000001=>[5,1]=>[1,5]
[5,2,3,4,6,-1]=>000001=>[5,1]=>[1,5]
[4,2,3,6,5,-1]=>000001=>[5,1]=>[1,5]
[5,2,3,6,4,-1]=>000001=>[5,1]=>[1,5]
[4,2,3,5,6,-1]=>000001=>[5,1]=>[1,5]
[3,2,6,4,5,-1]=>000001=>[5,1]=>[1,5]
[3,2,5,4,6,-1]=>000001=>[5,1]=>[1,5]
[4,2,6,3,5,-1]=>000001=>[5,1]=>[1,5]
[5,2,6,3,4,-1]=>000001=>[5,1]=>[1,5]
[4,2,5,3,6,-1]=>000001=>[5,1]=>[1,5]
[3,2,4,6,5,-1]=>000001=>[5,1]=>[1,5]
[3,2,5,6,4,-1]=>000001=>[5,1]=>[1,5]
[4,2,5,6,3,-1]=>000001=>[5,1]=>[1,5]
[3,2,4,5,6,-1]=>000001=>[5,1]=>[1,5]
[2,6,3,4,5,-1]=>000001=>[5,1]=>[1,5]
[2,5,3,4,6,-1]=>000001=>[5,1]=>[1,5]
[2,4,3,6,5,-1]=>000001=>[5,1]=>[1,5]
[2,5,3,6,4,-1]=>000001=>[5,1]=>[1,5]
[2,4,3,5,6,-1]=>000001=>[5,1]=>[1,5]
[3,6,2,4,5,-1]=>000001=>[5,1]=>[1,5]
[3,5,2,4,6,-1]=>000001=>[5,1]=>[1,5]
[4,6,2,3,5,-1]=>000001=>[5,1]=>[1,5]
[5,6,2,3,4,-1]=>000001=>[5,1]=>[1,5]
[4,5,2,3,6,-1]=>000001=>[5,1]=>[1,5]
[3,4,2,6,5,-1]=>000001=>[5,1]=>[1,5]
[3,5,2,6,4,-1]=>000001=>[5,1]=>[1,5]
[4,5,2,6,3,-1]=>000001=>[5,1]=>[1,5]
[3,4,2,5,6,-1]=>000001=>[5,1]=>[1,5]
[2,3,6,4,5,-1]=>000001=>[5,1]=>[1,5]
[2,3,5,4,6,-1]=>000001=>[5,1]=>[1,5]
[2,4,6,3,5,-1]=>000001=>[5,1]=>[1,5]
[2,5,6,3,4,-1]=>000001=>[5,1]=>[1,5]
[2,4,5,3,6,-1]=>000001=>[5,1]=>[1,5]
[3,4,6,2,5,-1]=>000001=>[5,1]=>[1,5]
[3,5,6,2,4,-1]=>000001=>[5,1]=>[1,5]
[4,5,6,2,3,-1]=>000001=>[5,1]=>[1,5]
[3,4,5,2,6,-1]=>000001=>[5,1]=>[1,5]
[2,3,4,6,5,-1]=>000001=>[5,1]=>[1,5]
[2,3,5,6,4,-1]=>000001=>[5,1]=>[1,5]
[2,4,5,6,3,-1]=>000001=>[5,1]=>[1,5]
[3,4,5,6,2,-1]=>000001=>[5,1]=>[1,5]
[2,3,4,5,6,-1]=>000001=>[5,1]=>[1,5]
[2,-6,-4,1,3,5]=>011000=>[1,2,3]=>[3,2,1]
[4,-6,-2,1,3,5]=>011000=>[1,2,3]=>[3,2,1]
[2,6,-4,1,3,5]=>001000=>[2,1,3]=>[3,1,2]
[-4,2,-6,1,3,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-4,-2,1,3,5,6]=>110000=>[2,4]=>[4,2]
[2,-4,1,3,5,6]=>010000=>[1,1,4]=>[4,1,1]
[-5,-4,-2,1,3,6]=>111000=>[3,3]=>[3,3]
[2,-5,-4,1,3,6]=>011000=>[1,2,3]=>[3,2,1]
[2,5,-4,1,3,6]=>001000=>[2,1,3]=>[3,1,2]
[-6,-5,-4,-2,1,3]=>111100=>[4,2]=>[2,4]
[2,-6,-5,-4,1,3]=>011100=>[1,3,2]=>[2,3,1]
[2,6,-5,-4,1,3]=>001100=>[2,2,2]=>[2,2,2]
[2,5,6,-4,1,3]=>000100=>[3,1,2]=>[2,1,3]
[2,-6,-5,1,3,4]=>011000=>[1,2,3]=>[3,2,1]
[-2,-6,-5,1,3,4]=>111000=>[3,3]=>[3,3]
[-6,2,-5,1,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,2,-5,1,3,4]=>001000=>[2,1,3]=>[3,1,2]
[2,-5,1,3,4,6]=>010000=>[1,1,4]=>[4,1,1]
[-2,-5,1,3,4,6]=>110000=>[2,4]=>[4,2]
[-5,-2,1,3,4,6]=>110000=>[2,4]=>[4,2]
[-5,-3,-2,1,4,6]=>111000=>[3,3]=>[3,3]
[3,-5,-2,1,4,6]=>011000=>[1,2,3]=>[3,2,1]
[-6,-5,-2,1,3,4]=>111000=>[3,3]=>[3,3]
[-6,-5,-3,-2,1,4]=>111100=>[4,2]=>[2,4]
[3,-6,-5,-2,1,4]=>011100=>[1,3,2]=>[2,3,1]
[3,6,-5,-2,1,4]=>001100=>[2,2,2]=>[2,2,2]
[-2,-6,1,3,4,5]=>110000=>[2,4]=>[4,2]
[-6,2,1,3,4,5]=>100000=>[1,5]=>[5,1]
[2,-6,1,3,4,5]=>010000=>[1,1,4]=>[4,1,1]
[3,-6,-2,1,4,5]=>011000=>[1,2,3]=>[3,2,1]
[2,3,-6,1,4,5]=>001000=>[2,1,3]=>[3,1,2]
[-6,-2,1,3,4,5]=>110000=>[2,4]=>[4,2]
[-6,-3,-2,1,4,5]=>111000=>[3,3]=>[3,3]
[-6,-4,-3,-2,1,5]=>111100=>[4,2]=>[2,4]
[4,-6,-3,-2,1,5]=>011100=>[1,3,2]=>[2,3,1]
[-2,1,3,4,5,6]=>100000=>[1,5]=>[5,1]
[-3,-2,1,4,5,6]=>110000=>[2,4]=>[4,2]
[-4,-3,-2,1,5,6]=>111000=>[3,3]=>[3,3]
[-5,-4,-3,-2,1,6]=>111100=>[4,2]=>[2,4]
[-6,-5,-4,-3,-2,1]=>111110=>[5,1]=>[1,5]
[6,-4,-3,1,2,5]=>011000=>[1,2,3]=>[3,2,1]
[-4,-6,-3,1,2,5]=>111000=>[3,3]=>[3,3]
[-6,3,4,1,2,5]=>100000=>[1,5]=>[5,1]
[4,-3,1,2,5,6]=>010000=>[1,1,4]=>[4,1,1]
[5,-4,-3,1,2,6]=>011000=>[1,2,3]=>[3,2,1]
[4,5,-3,1,2,6]=>001000=>[2,1,3]=>[3,1,2]
[6,-5,-4,-3,1,2]=>011100=>[1,3,2]=>[2,3,1]
[5,6,-4,-3,1,2]=>001100=>[2,2,2]=>[2,2,2]
[4,5,6,-3,1,2]=>000100=>[3,1,2]=>[2,1,3]
[5,6,-3,1,2,4]=>001000=>[2,1,3]=>[3,1,2]
[-3,6,-5,1,2,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-6,-5,3,1,2,4]=>110000=>[2,4]=>[4,2]
[-5,3,1,2,4,6]=>100000=>[1,5]=>[5,1]
[5,-3,1,2,4,6]=>010000=>[1,1,4]=>[4,1,1]
[-5,-3,1,2,4,6]=>110000=>[2,4]=>[4,2]
[3,-5,1,2,4,6]=>010000=>[1,1,4]=>[4,1,1]
[6,-5,-3,1,2,4]=>011000=>[1,2,3]=>[3,2,1]
[-6,-5,-3,1,2,4]=>111000=>[3,3]=>[3,3]
[3,-6,-5,1,2,4]=>011000=>[1,2,3]=>[3,2,1]
[3,6,-5,1,2,4]=>001000=>[2,1,3]=>[3,1,2]
[-6,3,1,2,4,5]=>100000=>[1,5]=>[5,1]
[3,-6,1,2,4,5]=>010000=>[1,1,4]=>[4,1,1]
[-3,-6,1,2,4,5]=>110000=>[2,4]=>[4,2]
[6,-3,1,2,4,5]=>010000=>[1,1,4]=>[4,1,1]
[-6,-3,1,2,4,5]=>110000=>[2,4]=>[4,2]
[-6,-4,-3,1,2,5]=>111000=>[3,3]=>[3,3]
[4,-6,-3,1,2,5]=>011000=>[1,2,3]=>[3,2,1]
[-3,1,2,4,5,6]=>100000=>[1,5]=>[5,1]
[-4,-3,1,2,5,6]=>110000=>[2,4]=>[4,2]
[-5,-4,-3,1,2,6]=>111000=>[3,3]=>[3,3]
[-6,-5,-4,-3,1,2]=>111100=>[4,2]=>[2,4]
[-5,6,-4,1,2,3]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-6,1,-5,-4,2,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-4,5,6,1,2,3]=>100000=>[1,5]=>[5,1]
[-5,-4,6,1,2,3]=>110000=>[2,4]=>[4,2]
[-4,5,1,2,3,6]=>100000=>[1,5]=>[5,1]
[-5,1,-4,2,3,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[1,-5,-4,2,3,6]=>011000=>[1,2,3]=>[3,2,1]
[5,-4,1,2,3,6]=>010000=>[1,1,4]=>[4,1,1]
[1,-6,-5,-4,2,3]=>011100=>[1,3,2]=>[2,3,1]
[6,-5,-4,1,2,3]=>011000=>[1,2,3]=>[3,2,1]
[5,6,-4,1,2,3]=>001000=>[2,1,3]=>[3,1,2]
[-6,1,-4,2,3,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,1,-6,2,3,5]=>001000=>[2,1,3]=>[3,1,2]
[-4,6,1,2,3,5]=>100000=>[1,5]=>[5,1]
[-6,4,1,2,3,5]=>100000=>[1,5]=>[5,1]
[1,-6,-4,2,3,5]=>011000=>[1,2,3]=>[3,2,1]
[6,-4,1,2,3,5]=>010000=>[1,1,4]=>[4,1,1]
[-6,-4,1,2,3,5]=>110000=>[2,4]=>[4,2]
[4,-6,1,2,3,5]=>010000=>[1,1,4]=>[4,1,1]
[1,-4,2,3,5,6]=>010000=>[1,1,4]=>[4,1,1]
[-4,1,2,3,5,6]=>100000=>[1,5]=>[5,1]
[-5,-4,1,2,3,6]=>110000=>[2,4]=>[4,2]
[-6,-5,-4,1,2,3]=>111000=>[3,3]=>[3,3]
[6,1,-5,2,3,4]=>001000=>[2,1,3]=>[3,1,2]
[-5,6,1,2,3,4]=>100000=>[1,5]=>[5,1]
[-6,1,-5,2,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[1,6,-5,2,3,4]=>001000=>[2,1,3]=>[3,1,2]
[1,-6,-5,2,3,4]=>011000=>[1,2,3]=>[3,2,1]
[6,-5,1,2,3,4]=>010000=>[1,1,4]=>[4,1,1]
[1,-5,2,3,4,6]=>010000=>[1,1,4]=>[4,1,1]
[-5,1,2,3,4,6]=>100000=>[1,5]=>[5,1]
[-6,-5,1,2,3,4]=>110000=>[2,4]=>[4,2]
[1,2,-6,3,4,5]=>001000=>[2,1,3]=>[3,1,2]
[1,-6,2,3,4,5]=>010000=>[1,1,4]=>[4,1,1]
[-6,1,2,3,4,5]=>100000=>[1,5]=>[5,1]
[2,-3,1,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[-2,-4,1,3,5,6]=>110000=>[2,4]=>[4,2]
[-4,3,1,2,5,6]=>100000=>[1,5]=>[5,1]
[-5,2,1,3,4,6]=>100000=>[1,5]=>[5,1]
[4,1,-5,2,3,6]=>001000=>[2,1,3]=>[3,1,2]
[-2,1,-6,3,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,1,-6,2,4,5]=>001000=>[2,1,3]=>[3,1,2]
[1,-4,-6,2,3,5]=>011000=>[1,2,3]=>[3,2,1]
[1,-6,5,2,3,4]=>010000=>[1,1,4]=>[4,1,1]
[2,5,-3,1,4,6]=>001000=>[2,1,3]=>[3,1,2]
[-5,2,-4,1,3,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-4,3,5,1,2,6]=>100000=>[1,5]=>[5,1]
[4,2,-5,1,3,6]=>001000=>[2,1,3]=>[3,1,2]
[-3,2,-6,1,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,2,-4,1,3,5]=>001000=>[2,1,3]=>[3,1,2]
[-6,-4,3,1,2,5]=>110000=>[2,4]=>[4,2]
[6,-2,-5,1,3,4]=>011000=>[1,2,3]=>[3,2,1]
[6,-5,3,1,2,4]=>010000=>[1,1,4]=>[4,1,1]
[6,-4,1,-5,2,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,-6,4,1,2,5]=>010000=>[1,1,4]=>[4,1,1]
[-2,-5,-6,1,3,4]=>111000=>[3,3]=>[3,3]
[-5,-6,3,1,2,4]=>110000=>[2,4]=>[4,2]
[4,5,1,-6,2,3]=>000100=>[3,1,2]=>[2,1,3]
[-3,2,-4,1,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,2,-5,1,4,6]=>001000=>[2,1,3]=>[3,1,2]
[2,-4,-5,1,3,6]=>011000=>[1,2,3]=>[3,2,1]
[4,-5,3,1,2,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-3,-6,1,4,5]=>011000=>[1,2,3]=>[3,2,1]
[-2,-4,-6,1,3,5]=>111000=>[3,3]=>[3,3]
[-4,-6,3,1,2,5]=>110000=>[2,4]=>[4,2]
[-5,-6,2,1,3,4]=>110000=>[2,4]=>[4,2]
[-6,5,3,1,2,4]=>100000=>[1,5]=>[5,1]
[-5,4,1,-6,2,3]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-5,-3,2,-6,1,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,-6,2,-4,1,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,-6,3,5,1,2]=>010000=>[1,1,4]=>[4,1,1]
[-4,-6,2,-5,1,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-3,2,6,-4,1,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,-4,2,-5,1,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,-5,3,6,1,2]=>010000=>[1,1,4]=>[4,1,1]
[5,-3,2,-6,1,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,2,-6,1,3]=>000100=>[3,1,2]=>[2,1,3]
[-4,-6,3,5,1,2]=>110000=>[2,4]=>[4,2]
[-5,4,2,-6,1,3]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-6,5,3,4,1,2]=>100000=>[1,5]=>[5,1]
[3,-4,2,-5,1,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-3,-4,2,-6,1,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-5,3,2,-6,1,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-4,2,-5,-6,1,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-5,4,-6,3,1,2]=>101000=>[1,1,1,3]=>[3,1,1,1]
[2,3,4,5,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,3,4,-1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[2,3,4,-1,6,5]=>000100=>[3,1,2]=>[2,1,3]
[2,3,5,4,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,3,-1,4,5,6]=>001000=>[2,1,3]=>[3,1,2]
[2,3,-1,4,6,5]=>001000=>[2,1,3]=>[3,1,2]
[2,3,6,5,4,-1]=>000001=>[5,1]=>[1,5]
[2,3,-1,5,4,6]=>001000=>[2,1,3]=>[3,1,2]
[2,3,-1,6,4,5]=>001000=>[2,1,3]=>[3,1,2]
[2,3,-1,6,5,4]=>001000=>[2,1,3]=>[3,1,2]
[2,4,3,5,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,4,3,-1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[2,4,3,-1,6,5]=>000100=>[3,1,2]=>[2,1,3]
[2,5,3,4,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,-1,3,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,3,4,6,5]=>010000=>[1,1,4]=>[4,1,1]
[2,6,3,5,4,-1]=>000001=>[5,1]=>[1,5]
[2,-1,3,5,4,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,3,6,4,5]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,3,6,5,4]=>010000=>[1,1,4]=>[4,1,1]
[2,5,4,3,6,-1]=>000001=>[5,1]=>[1,5]
[2,5,4,3,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,6,4,3,5,-1]=>000001=>[5,1]=>[1,5]
[2,-1,4,3,5,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,4,3,6,5]=>010000=>[1,1,4]=>[4,1,1]
[2,6,5,3,4,-1]=>000001=>[5,1]=>[1,5]
[2,-1,5,3,4,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,6,3,4,5]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,6,3,5,4]=>010000=>[1,1,4]=>[4,1,1]
[2,6,5,4,3,-1]=>000001=>[5,1]=>[1,5]
[2,-1,5,4,3,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,6,4,3,5]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,6,5,3,4]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,6,5,4,3]=>010000=>[1,1,4]=>[4,1,1]
[3,2,4,5,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[3,2,4,-1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[3,2,4,-1,6,5]=>000100=>[3,1,2]=>[2,1,3]
[3,2,5,4,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[3,2,-1,4,5,6]=>001000=>[2,1,3]=>[3,1,2]
[3,2,-1,4,6,5]=>001000=>[2,1,3]=>[3,1,2]
[3,2,6,5,4,-1]=>000001=>[5,1]=>[1,5]
[3,2,-1,5,4,6]=>001000=>[2,1,3]=>[3,1,2]
[3,2,-1,6,4,5]=>001000=>[2,1,3]=>[3,1,2]
[3,2,-1,6,5,4]=>001000=>[2,1,3]=>[3,1,2]
[4,2,3,5,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[4,2,3,-1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[4,2,3,-1,6,5]=>000100=>[3,1,2]=>[2,1,3]
[5,2,3,4,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[-1,2,3,4,5,6]=>100000=>[1,5]=>[5,1]
[-1,2,3,4,6,5]=>100000=>[1,5]=>[5,1]
[6,2,3,5,4,-1]=>000001=>[5,1]=>[1,5]
[-1,2,3,5,4,6]=>100000=>[1,5]=>[5,1]
[-1,2,3,6,4,5]=>100000=>[1,5]=>[5,1]
[-1,2,3,6,5,4]=>100000=>[1,5]=>[5,1]
[5,2,4,3,6,-1]=>000001=>[5,1]=>[1,5]
[5,2,4,3,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[6,2,4,3,5,-1]=>000001=>[5,1]=>[1,5]
[-1,2,4,3,5,6]=>100000=>[1,5]=>[5,1]
[-1,2,4,3,6,5]=>100000=>[1,5]=>[5,1]
[6,2,5,3,4,-1]=>000001=>[5,1]=>[1,5]
[-1,2,5,3,4,6]=>100000=>[1,5]=>[5,1]
[-1,2,6,3,4,5]=>100000=>[1,5]=>[5,1]
[-1,2,6,3,5,4]=>100000=>[1,5]=>[5,1]
[6,2,5,4,3,-1]=>000001=>[5,1]=>[1,5]
[-1,2,5,4,3,6]=>100000=>[1,5]=>[5,1]
[-1,2,6,4,3,5]=>100000=>[1,5]=>[5,1]
[-1,2,6,5,3,4]=>100000=>[1,5]=>[5,1]
[-1,2,6,5,4,3]=>100000=>[1,5]=>[5,1]
[4,3,2,5,6,-1]=>000001=>[5,1]=>[1,5]
[4,3,2,5,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[4,3,2,6,5,-1]=>000001=>[5,1]=>[1,5]
[4,3,2,-1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[4,3,2,-1,6,5]=>000100=>[3,1,2]=>[2,1,3]
[5,3,2,4,6,-1]=>000001=>[5,1]=>[1,5]
[5,3,2,4,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[6,3,2,4,5,-1]=>000001=>[5,1]=>[1,5]
[-1,3,2,4,5,6]=>100000=>[1,5]=>[5,1]
[-1,3,2,4,6,5]=>100000=>[1,5]=>[5,1]
[6,3,2,5,4,-1]=>000001=>[5,1]=>[1,5]
[-1,3,2,5,4,6]=>100000=>[1,5]=>[5,1]
[-1,3,2,6,4,5]=>100000=>[1,5]=>[5,1]
[-1,3,2,6,5,4]=>100000=>[1,5]=>[5,1]
[5,4,2,3,6,-1]=>000001=>[5,1]=>[1,5]
[5,4,2,3,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[6,4,2,3,5,-1]=>000001=>[5,1]=>[1,5]
[-1,4,2,3,5,6]=>100000=>[1,5]=>[5,1]
[-1,4,2,3,6,5]=>100000=>[1,5]=>[5,1]
[6,5,2,3,4,-1]=>000001=>[5,1]=>[1,5]
[-1,5,2,3,4,6]=>100000=>[1,5]=>[5,1]
[-1,6,2,3,4,5]=>100000=>[1,5]=>[5,1]
[-1,6,2,3,5,4]=>100000=>[1,5]=>[5,1]
[6,5,2,4,3,-1]=>000001=>[5,1]=>[1,5]
[-1,5,2,4,3,6]=>100000=>[1,5]=>[5,1]
[-1,6,2,4,3,5]=>100000=>[1,5]=>[5,1]
[-1,6,2,5,3,4]=>100000=>[1,5]=>[5,1]
[-1,6,2,5,4,3]=>100000=>[1,5]=>[5,1]
[5,4,3,2,6,-1]=>000001=>[5,1]=>[1,5]
[5,4,3,2,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[6,4,3,2,5,-1]=>000001=>[5,1]=>[1,5]
[-1,4,3,2,5,6]=>100000=>[1,5]=>[5,1]
[-1,4,3,2,6,5]=>100000=>[1,5]=>[5,1]
[6,5,3,2,4,-1]=>000001=>[5,1]=>[1,5]
[-1,5,3,2,4,6]=>100000=>[1,5]=>[5,1]
[-1,6,3,2,4,5]=>100000=>[1,5]=>[5,1]
[-1,6,3,2,5,4]=>100000=>[1,5]=>[5,1]
[6,5,4,2,3,-1]=>000001=>[5,1]=>[1,5]
[-1,5,4,2,3,6]=>100000=>[1,5]=>[5,1]
[-1,6,4,2,3,5]=>100000=>[1,5]=>[5,1]
[-1,6,5,2,3,4]=>100000=>[1,5]=>[5,1]
[-1,6,5,2,4,3]=>100000=>[1,5]=>[5,1]
[6,5,4,3,2,-1]=>000001=>[5,1]=>[1,5]
[-1,5,4,3,2,6]=>100000=>[1,5]=>[5,1]
[-1,6,4,3,2,5]=>100000=>[1,5]=>[5,1]
[-1,6,5,3,2,4]=>100000=>[1,5]=>[5,1]
[-1,6,5,4,2,3]=>100000=>[1,5]=>[5,1]
[-1,6,5,4,3,2]=>100000=>[1,5]=>[5,1]
[3,4,5,6,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[3,4,5,-1,2,6]=>000100=>[3,1,2]=>[2,1,3]
[3,4,6,2,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[3,4,6,-1,5,2]=>000100=>[3,1,2]=>[2,1,3]
[3,4,-1,2,5,6]=>001000=>[2,1,3]=>[3,1,2]
[3,5,2,6,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[3,5,2,-1,4,6]=>000100=>[3,1,2]=>[2,1,3]
[3,5,6,4,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[3,5,6,-1,4,2]=>000100=>[3,1,2]=>[2,1,3]
[3,5,-1,4,2,6]=>001000=>[2,1,3]=>[3,1,2]
[3,6,2,4,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[3,6,2,-1,5,4]=>000100=>[3,1,2]=>[2,1,3]
[3,6,-1,4,5,2]=>001000=>[2,1,3]=>[3,1,2]
[3,-1,2,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[4,2,5,6,-1,3]=>000010=>[4,1,1]=>[1,1,4]
[4,2,5,-1,3,6]=>000100=>[3,1,2]=>[2,1,3]
[4,2,6,3,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[4,2,6,-1,5,3]=>000100=>[3,1,2]=>[2,1,3]
[4,2,-1,3,5,6]=>001000=>[2,1,3]=>[3,1,2]
[4,5,3,6,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[4,5,3,-1,2,6]=>000100=>[3,1,2]=>[2,1,3]
[4,5,6,3,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[4,5,6,-1,2,3]=>000100=>[3,1,2]=>[2,1,3]
[4,5,-1,3,2,6]=>001000=>[2,1,3]=>[3,1,2]
[4,6,3,2,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[4,6,3,-1,5,2]=>000100=>[3,1,2]=>[2,1,3]
[4,6,-1,3,5,2]=>001000=>[2,1,3]=>[3,1,2]
[4,-1,3,2,5,6]=>010000=>[1,1,4]=>[4,1,1]
[5,2,3,6,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[5,2,3,-1,4,6]=>000100=>[3,1,2]=>[2,1,3]
[5,2,6,4,-1,3]=>000010=>[4,1,1]=>[1,1,4]
[5,2,6,-1,4,3]=>000100=>[3,1,2]=>[2,1,3]
[5,2,-1,4,3,6]=>001000=>[2,1,3]=>[3,1,2]
[5,6,3,4,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[5,6,3,-1,4,2]=>000100=>[3,1,2]=>[2,1,3]
[5,6,-1,4,3,2]=>001000=>[2,1,3]=>[3,1,2]
[5,-1,3,4,2,6]=>010000=>[1,1,4]=>[4,1,1]
[6,2,3,4,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[6,2,3,-1,5,4]=>000100=>[3,1,2]=>[2,1,3]
[6,2,-1,4,5,3]=>001000=>[2,1,3]=>[3,1,2]
[6,-1,3,4,5,2]=>010000=>[1,1,4]=>[4,1,1]
[3,4,5,6,7,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[3,4,5,6,-1,2,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,4,5,7,2,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[3,4,5,7,-1,6,2]=>0000100=>[4,1,2]=>[2,1,4]
[3,4,5,-1,2,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,4,6,2,7,-1,5]=>0000010=>[5,1,1]=>[1,1,5]
[3,4,6,2,-1,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,4,6,7,5,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[3,4,6,7,-1,5,2]=>0000100=>[4,1,2]=>[2,1,4]
[3,4,6,-1,5,2,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,4,7,2,5,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[3,4,7,2,-1,6,5]=>0000100=>[4,1,2]=>[2,1,4]
[3,4,7,-1,5,6,2]=>0001000=>[3,1,3]=>[3,1,3]
[3,4,-1,2,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[3,5,2,6,7,-1,4]=>0000010=>[5,1,1]=>[1,1,5]
[3,5,2,6,-1,4,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,5,2,7,4,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[3,5,2,7,-1,6,4]=>0000100=>[4,1,2]=>[2,1,4]
[3,5,2,-1,4,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,5,6,4,7,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[3,5,6,4,-1,2,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,5,6,7,4,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[3,5,6,7,-1,2,4]=>0000100=>[4,1,2]=>[2,1,4]
[3,5,6,-1,4,2,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,5,7,4,2,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[3,5,7,4,-1,6,2]=>0000100=>[4,1,2]=>[2,1,4]
[3,5,7,-1,4,6,2]=>0001000=>[3,1,3]=>[3,1,3]
[3,5,-1,4,2,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[3,6,2,4,7,-1,5]=>0000010=>[5,1,1]=>[1,1,5]
[3,6,2,4,-1,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,6,2,7,5,-1,4]=>0000010=>[5,1,1]=>[1,1,5]
[3,6,2,7,-1,5,4]=>0000100=>[4,1,2]=>[2,1,4]
[3,6,2,-1,5,4,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,6,7,4,5,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[3,6,7,4,-1,5,2]=>0000100=>[4,1,2]=>[2,1,4]
[3,6,7,-1,5,4,2]=>0001000=>[3,1,3]=>[3,1,3]
[3,6,-1,4,5,2,7]=>0010000=>[2,1,4]=>[4,1,2]
[3,7,2,4,5,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[3,7,2,4,-1,6,5]=>0000100=>[4,1,2]=>[2,1,4]
[3,7,2,-1,5,6,4]=>0001000=>[3,1,3]=>[3,1,3]
[3,7,-1,4,5,6,2]=>0010000=>[2,1,4]=>[4,1,2]
[3,-1,2,4,5,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[4,2,5,6,7,-1,3]=>0000010=>[5,1,1]=>[1,1,5]
[4,2,5,6,-1,3,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,2,5,7,3,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[4,2,5,7,-1,6,3]=>0000100=>[4,1,2]=>[2,1,4]
[4,2,5,-1,3,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,2,6,3,7,-1,5]=>0000010=>[5,1,1]=>[1,1,5]
[4,2,6,3,-1,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,2,6,7,5,-1,3]=>0000010=>[5,1,1]=>[1,1,5]
[4,2,6,7,-1,5,3]=>0000100=>[4,1,2]=>[2,1,4]
[4,2,6,-1,5,3,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,2,7,3,5,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[4,2,7,3,-1,6,5]=>0000100=>[4,1,2]=>[2,1,4]
[4,2,7,-1,5,6,3]=>0001000=>[3,1,3]=>[3,1,3]
[4,2,-1,3,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[4,5,3,6,7,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[4,5,3,6,-1,2,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,5,3,7,2,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[4,5,3,7,-1,6,2]=>0000100=>[4,1,2]=>[2,1,4]
[4,5,3,-1,2,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,5,6,3,7,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[4,5,6,3,-1,2,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,5,6,7,2,-1,3]=>0000010=>[5,1,1]=>[1,1,5]
[4,5,6,7,-1,3,2]=>0000100=>[4,1,2]=>[2,1,4]
[4,5,6,-1,2,3,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,5,7,3,2,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[4,5,7,3,-1,6,2]=>0000100=>[4,1,2]=>[2,1,4]
[4,5,7,-1,2,6,3]=>0001000=>[3,1,3]=>[3,1,3]
[4,5,-1,3,2,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[4,6,3,2,7,-1,5]=>0000010=>[5,1,1]=>[1,1,5]
[4,6,3,2,-1,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,6,3,7,5,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[4,6,3,7,-1,5,2]=>0000100=>[4,1,2]=>[2,1,4]
[4,6,3,-1,5,2,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,6,7,3,5,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[4,6,7,3,-1,5,2]=>0000100=>[4,1,2]=>[2,1,4]
[4,6,7,-1,5,2,3]=>0001000=>[3,1,3]=>[3,1,3]
[4,6,-1,3,5,2,7]=>0010000=>[2,1,4]=>[4,1,2]
[4,7,3,2,5,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[4,7,3,2,-1,6,5]=>0000100=>[4,1,2]=>[2,1,4]
[4,7,3,-1,5,6,2]=>0001000=>[3,1,3]=>[3,1,3]
[4,7,-1,3,5,6,2]=>0010000=>[2,1,4]=>[4,1,2]
[4,-1,3,2,5,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[5,2,3,6,7,-1,4]=>0000010=>[5,1,1]=>[1,1,5]
[5,2,3,6,-1,4,7]=>0000100=>[4,1,2]=>[2,1,4]
[5,2,3,7,4,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[5,2,3,7,-1,6,4]=>0000100=>[4,1,2]=>[2,1,4]
[5,2,3,-1,4,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[5,2,6,4,7,-1,3]=>0000010=>[5,1,1]=>[1,1,5]
[5,2,6,4,-1,3,7]=>0000100=>[4,1,2]=>[2,1,4]
[5,2,6,7,4,-1,3]=>0000010=>[5,1,1]=>[1,1,5]
[5,2,6,7,-1,3,4]=>0000100=>[4,1,2]=>[2,1,4]
[5,2,6,-1,4,3,7]=>0001000=>[3,1,3]=>[3,1,3]
[5,2,7,4,3,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[5,2,7,4,-1,6,3]=>0000100=>[4,1,2]=>[2,1,4]
[5,2,7,-1,4,6,3]=>0001000=>[3,1,3]=>[3,1,3]
[5,2,-1,4,3,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[5,6,3,4,7,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[5,6,3,4,-1,2,7]=>0000100=>[4,1,2]=>[2,1,4]
[5,6,3,7,4,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[5,6,3,7,-1,2,4]=>0000100=>[4,1,2]=>[2,1,4]
[5,6,3,-1,4,2,7]=>0001000=>[3,1,3]=>[3,1,3]
[5,6,7,4,3,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[5,6,7,4,-1,2,3]=>0000100=>[4,1,2]=>[2,1,4]
[5,6,7,-1,4,2,3]=>0001000=>[3,1,3]=>[3,1,3]
[5,6,-1,4,3,2,7]=>0010000=>[2,1,4]=>[4,1,2]
[5,7,3,4,2,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[5,7,3,4,-1,6,2]=>0000100=>[4,1,2]=>[2,1,4]
[5,7,3,-1,4,6,2]=>0001000=>[3,1,3]=>[3,1,3]
[5,7,-1,4,3,6,2]=>0010000=>[2,1,4]=>[4,1,2]
[5,-1,3,4,2,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[6,2,3,4,7,-1,5]=>0000010=>[5,1,1]=>[1,1,5]
[6,2,3,4,-1,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[6,2,3,7,5,-1,4]=>0000010=>[5,1,1]=>[1,1,5]
[6,2,3,7,-1,5,4]=>0000100=>[4,1,2]=>[2,1,4]
[6,2,3,-1,5,4,7]=>0001000=>[3,1,3]=>[3,1,3]
[6,2,7,4,5,-1,3]=>0000010=>[5,1,1]=>[1,1,5]
[6,2,7,4,-1,5,3]=>0000100=>[4,1,2]=>[2,1,4]
[6,2,7,-1,5,4,3]=>0001000=>[3,1,3]=>[3,1,3]
[6,2,-1,4,5,3,7]=>0010000=>[2,1,4]=>[4,1,2]
[6,7,3,4,5,-1,2]=>0000010=>[5,1,1]=>[1,1,5]
[6,7,3,4,-1,5,2]=>0000100=>[4,1,2]=>[2,1,4]
[6,7,3,-1,5,4,2]=>0001000=>[3,1,3]=>[3,1,3]
[6,7,-1,4,5,3,2]=>0010000=>[2,1,4]=>[4,1,2]
[6,-1,3,4,5,2,7]=>0100000=>[1,1,5]=>[5,1,1]
[7,2,3,4,5,-1,6]=>0000010=>[5,1,1]=>[1,1,5]
[7,2,3,4,-1,6,5]=>0000100=>[4,1,2]=>[2,1,4]
[7,2,3,-1,5,6,4]=>0001000=>[3,1,3]=>[3,1,3]
[7,2,-1,4,5,6,3]=>0010000=>[2,1,4]=>[4,1,2]
[7,-1,3,4,5,6,2]=>0100000=>[1,1,5]=>[5,1,1]
[-1,2,3,4,5,6,7]=>1000000=>[1,6]=>[6,1]
[-2,-3,-4,-5,-6,1]=>111110=>[5,1]=>[1,5]
[2,-3,-4,-6,-5,1]=>011110=>[1,4,1]=>[1,4,1]
[3,2,-5,-4,-6,1]=>001110=>[2,3,1]=>[1,3,2]
[-3,2,-6,-4,-5,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,2,-6,-5,-4,1]=>001110=>[2,3,1]=>[1,3,2]
[-3,4,2,-5,-6,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,4,2,-6,-5,1]=>000110=>[3,2,1]=>[1,2,3]
[-5,-3,2,-6,-4,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,5,2,-6,-3,1]=>000110=>[3,2,1]=>[1,2,3]
[-6,-3,2,-4,-5,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,-3,2,-5,-4,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,2,-3,-5,1]=>000110=>[3,2,1]=>[1,2,3]
[-5,6,2,-3,-4,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,6,2,-4,-3,1]=>000110=>[3,2,1]=>[1,2,3]
[-4,-5,2,3,-6,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,-6,2,3,-5,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[-4,6,2,3,-5,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,6,2,3,-4,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,-5,-6,4,-3,1]=>111010=>[3,1,1,1]=>[1,1,1,3]
[-3,-6,2,4,-5,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[2,5,3,4,-6,1]=>000010=>[4,1,1]=>[1,1,4]
[5,6,3,4,-2,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,-3,-6,5,-4,1]=>111010=>[3,1,1,1]=>[1,1,1,3]
[4,-3,2,5,-6,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,3,5,-6,1]=>000010=>[4,1,1]=>[1,1,4]
[2,-6,4,5,-3,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,4,5,-2,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,-3,-4,6,-5,1]=>111010=>[3,1,1,1]=>[1,1,1,3]
[2,-3,-5,6,-4,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,-3,6,-5,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[-5,2,-3,6,-4,1]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,-4,6,-3,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[-4,2,3,6,-5,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,2,3,6,-4,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,-5,4,6,-3,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,4,6,-2,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,-3,5,6,-4,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[2,-4,5,6,-3,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,3,5,6,-4,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,4,5,6,-3,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,4,5,6,-2,1]=>000010=>[4,1,1]=>[1,1,4]
[-4,-5,-6,3,1,2]=>111000=>[3,3]=>[3,3]
[4,-6,-5,3,1,2]=>011000=>[1,2,3]=>[3,2,1]
[4,5,-6,3,1,2]=>001000=>[2,1,3]=>[3,1,2]
[-4,6,-5,3,1,2]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,6,-4,3,1,2]=>001000=>[2,1,3]=>[3,1,2]
[-6,-4,3,5,1,2]=>110000=>[2,4]=>[4,2]
[-4,-5,3,6,1,2]=>110000=>[2,4]=>[4,2]
[5,-4,3,6,1,2]=>010000=>[1,1,4]=>[4,1,1]
[-4,3,5,6,1,2]=>100000=>[1,5]=>[5,1]
[-4,-5,-6,-2,1,3]=>111100=>[4,2]=>[2,4]
[-4,-6,-5,2,1,3]=>111000=>[3,3]=>[3,3]
[2,-4,-6,5,1,3]=>011000=>[1,2,3]=>[3,2,1]
[6,-4,-5,2,1,3]=>011000=>[1,2,3]=>[3,2,1]
[2,-5,-4,6,1,3]=>011000=>[1,2,3]=>[3,2,1]
[-6,5,1,4,2,3]=>100000=>[1,5]=>[5,1]
[-2,-5,-6,-3,1,4]=>111100=>[4,2]=>[2,4]
[2,-6,-5,-3,1,4]=>011100=>[1,3,2]=>[2,3,1]
[5,2,-6,3,1,4]=>001000=>[2,1,3]=>[3,1,2]
[2,6,-5,3,1,4]=>001000=>[2,1,3]=>[3,1,2]
[-6,5,-2,1,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-5,6,2,1,3,4]=>100000=>[1,5]=>[5,1]
[-2,-3,-6,-4,1,5]=>111100=>[4,2]=>[2,4]
[4,2,-6,-3,1,5]=>001100=>[2,2,2]=>[2,2,2]
[-4,2,-6,3,1,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-6,-2,4,-3,1,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[3,6,4,-2,1,5]=>000100=>[3,1,2]=>[2,1,3]
[-6,-2,-3,1,4,5]=>111000=>[3,3]=>[3,3]
[-6,2,3,1,4,5]=>100000=>[1,5]=>[5,1]
[-2,6,1,3,4,5]=>100000=>[1,5]=>[5,1]
[-2,-3,-4,-5,1,6]=>111100=>[4,2]=>[2,4]
[2,-3,-5,-4,1,6]=>011100=>[1,3,2]=>[2,3,1]
[4,2,-3,-5,1,6]=>001100=>[2,2,2]=>[2,2,2]
[-5,2,-3,-4,1,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,-4,-3,1,6]=>001100=>[2,2,2]=>[2,2,2]
[-4,2,3,-5,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,3,-4,1,6]=>000100=>[3,1,2]=>[2,1,3]
[-2,-5,4,-3,1,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,4,-2,1,6]=>000100=>[3,1,2]=>[2,1,3]
[-2,-3,5,-4,1,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[2,-4,5,-3,1,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,3,5,-4,1,6]=>000100=>[3,1,2]=>[2,1,3]
[-2,4,5,-3,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,4,5,-2,1,6]=>000100=>[3,1,2]=>[2,1,3]
[-4,-5,3,1,2,6]=>110000=>[2,4]=>[4,2]
[5,-4,3,1,2,6]=>010000=>[1,1,4]=>[4,1,1]
[-4,-5,-2,1,3,6]=>111000=>[3,3]=>[3,3]
[-5,-4,2,1,3,6]=>110000=>[2,4]=>[4,2]
[-2,-5,-3,1,4,6]=>111000=>[3,3]=>[3,3]
[2,-5,3,1,4,6]=>010000=>[1,1,4]=>[4,1,1]
[5,-2,1,3,4,6]=>010000=>[1,1,4]=>[4,1,1]
[-2,-3,-4,1,5,6]=>111000=>[3,3]=>[3,3]
[2,-4,-3,1,5,6]=>011000=>[1,2,3]=>[3,2,1]
[2,3,-4,1,5,6]=>001000=>[2,1,3]=>[3,1,2]
[-2,4,-3,1,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,4,-2,1,5,6]=>001000=>[2,1,3]=>[3,1,2]
[-2,-3,1,4,5,6]=>110000=>[2,4]=>[4,2]
[3,-2,1,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[5,-6,1,2,3,4]=>010000=>[1,1,4]=>[4,1,1]
[5,-6,-4,1,2,3]=>011000=>[1,2,3]=>[3,2,1]
[4,-5,1,2,3,6]=>010000=>[1,1,4]=>[4,1,1]
[4,-6,-5,1,2,3]=>011000=>[1,2,3]=>[3,2,1]
[4,6,-5,1,2,3]=>001000=>[2,1,3]=>[3,1,2]
[-5,4,-6,1,2,3]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,-6,-3,1,2,4]=>011000=>[1,2,3]=>[3,2,1]
[5,-6,-4,-3,1,2]=>011100=>[1,3,2]=>[2,3,1]
[4,-5,-3,1,2,6]=>011000=>[1,2,3]=>[3,2,1]
[4,-6,-5,-3,1,2]=>011100=>[1,3,2]=>[2,3,1]
[4,6,-5,-3,1,2]=>001100=>[2,2,2]=>[2,2,2]
[-5,4,-6,-3,1,2]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,-4,1,2,5,6]=>010000=>[1,1,4]=>[4,1,1]
[3,-6,-4,1,2,5]=>011000=>[1,2,3]=>[3,2,1]
[3,-5,-4,1,2,6]=>011000=>[1,2,3]=>[3,2,1]
[3,-6,-5,-4,1,2]=>011100=>[1,3,2]=>[2,3,1]
[3,5,-6,-4,1,2]=>001100=>[2,2,2]=>[2,2,2]
[3,5,-4,1,2,6]=>001000=>[2,1,3]=>[3,1,2]
[3,6,-5,-4,1,2]=>001100=>[2,2,2]=>[2,2,2]
[3,5,6,-4,1,2]=>000100=>[3,1,2]=>[2,1,3]
[-6,3,5,-4,1,2]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-4,3,-5,1,2,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-4,3,-6,-5,1,2]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-4,3,6,-5,1,2]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-6,-4,3,-5,1,2]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,-5,3,-6,1,2]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,-6,-2,1,3,4]=>011000=>[1,2,3]=>[3,2,1]
[5,-6,-4,-2,1,3]=>011100=>[1,3,2]=>[2,3,1]
[4,-5,-2,1,3,6]=>011000=>[1,2,3]=>[3,2,1]
[4,-6,-5,-2,1,3]=>011100=>[1,3,2]=>[2,3,1]
[4,6,-5,-2,1,3]=>001100=>[2,2,2]=>[2,2,2]
[5,-6,-3,-2,1,4]=>011100=>[1,3,2]=>[2,3,1]
[5,-6,-4,-3,-2,1]=>011110=>[1,4,1]=>[1,4,1]
[4,-5,-3,-2,1,6]=>011100=>[1,3,2]=>[2,3,1]
[4,-6,-5,-3,-2,1]=>011110=>[1,4,1]=>[1,4,1]
[4,6,-5,-3,-2,1]=>001110=>[2,3,1]=>[1,3,2]
[-5,4,-6,-3,-2,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,-4,-2,1,5,6]=>011000=>[1,2,3]=>[3,2,1]
[3,-6,-4,-2,1,5]=>011100=>[1,3,2]=>[2,3,1]
[3,-5,-4,-2,1,6]=>011100=>[1,3,2]=>[2,3,1]
[3,-6,-5,-4,-2,1]=>011110=>[1,4,1]=>[1,4,1]
[3,5,-6,-4,-2,1]=>001110=>[2,3,1]=>[1,3,2]
[3,5,-4,-2,1,6]=>001100=>[2,2,2]=>[2,2,2]
[3,6,-5,-4,-2,1]=>001110=>[2,3,1]=>[1,3,2]
[3,5,6,-4,-2,1]=>000110=>[3,2,1]=>[1,2,3]
[-6,3,5,-4,-2,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-4,3,-5,-2,1,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-4,3,-6,-5,-2,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[-4,3,6,-5,-2,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-6,-4,3,-5,-2,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,-5,3,-6,-2,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,-6,-3,1,4,5]=>011000=>[1,2,3]=>[3,2,1]
[2,-5,-3,1,4,6]=>011000=>[1,2,3]=>[3,2,1]
[2,5,-6,-3,1,4]=>001100=>[2,2,2]=>[2,2,2]
[2,-6,-4,-3,1,5]=>011100=>[1,3,2]=>[2,3,1]
[2,-5,-4,-3,1,6]=>011100=>[1,3,2]=>[2,3,1]
[2,-6,-5,-4,-3,1]=>011110=>[1,4,1]=>[1,4,1]
[2,5,-6,-4,-3,1]=>001110=>[2,3,1]=>[1,3,2]
[2,4,-5,-3,1,6]=>001100=>[2,2,2]=>[2,2,2]
[2,4,-6,-5,-3,1]=>001110=>[2,3,1]=>[1,3,2]
[2,4,6,-5,-3,1]=>000110=>[3,2,1]=>[1,2,3]
[-5,2,4,-6,-3,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,4,-3,1,5,6]=>001000=>[2,1,3]=>[3,1,2]
[2,6,-4,-3,1,5]=>001100=>[2,2,2]=>[2,2,2]
[2,5,-4,-3,1,6]=>001100=>[2,2,2]=>[2,2,2]
[2,6,-5,-4,-3,1]=>001110=>[2,3,1]=>[1,3,2]
[-5,2,-6,-4,-3,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[2,4,5,-3,1,6]=>000100=>[3,1,2]=>[2,1,3]
[2,5,6,-4,-3,1]=>000110=>[3,2,1]=>[1,2,3]
[2,4,5,6,-3,1]=>000010=>[4,1,1]=>[1,1,4]
[-6,2,4,5,-3,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-5,2,4,-3,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-4,2,6,-5,-3,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-5,2,4,6,-3,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-6,-5,2,4,-3,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,-6,2,4,-3,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[-3,2,-5,-4,1,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-3,2,-6,-5,-4,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[-3,2,5,-6,-4,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-3,2,5,-4,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-3,2,6,-5,-4,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-3,2,5,6,-4,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-6,-3,2,5,-4,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-5,-3,2,-4,1,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-6,-3,2,-5,-4,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[-5,-3,2,6,-4,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-6,-5,-3,2,-4,1]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,-6,-3,2,-4,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,-4,2,-6,-5,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,-4,2,6,-5,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,-6,-4,2,-5,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,-4,2,-5,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[-6,1,5,2,3,4]=>100000=>[1,5]=>[5,1]
[-6,1,4,2,3,5]=>100000=>[1,5]=>[5,1]
[1,-5,-6,2,3,4]=>011000=>[1,2,3]=>[3,2,1]
[-6,-4,-5,1,2,3]=>111000=>[3,3]=>[3,3]
[-6,3,5,1,2,4]=>100000=>[1,5]=>[5,1]
[4,-6,5,1,2,3]=>010000=>[1,1,4]=>[4,1,1]
[5,2,-6,1,3,4]=>001000=>[2,1,3]=>[3,1,2]
[-6,-3,-5,1,2,4]=>111000=>[3,3]=>[3,3]
[4,1,-6,-5,2,3]=>001100=>[2,2,2]=>[2,2,2]
[-4,3,6,1,2,5]=>100000=>[1,5]=>[5,1]
[3,-6,5,1,2,4]=>010000=>[1,1,4]=>[4,1,1]
[-3,6,-5,-4,1,2]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,-6,1,3,5]=>001000=>[2,1,3]=>[3,1,2]
[2,-5,-6,1,3,4]=>011000=>[1,2,3]=>[3,2,1]
[-4,2,-6,-5,1,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-4,-3,6,-5,1,2]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-5,3,-6,-2,1,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-5,-4,2,-6,1,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[3,-6,4,5,1,2]=>010000=>[1,1,4]=>[4,1,1]
[1,2,-7,-6,3,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[1,7,-6,-5,2,3,4]=>0011000=>[2,2,3]=>[3,2,2]
[-7,1,-4,2,3,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-6,7,-4,1,2,3,5]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,1,2,-7,3,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[-5,1,7,-6,2,3,4]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,5,-7,-4,2,3,6]=>0011000=>[2,2,3]=>[3,2,2]
[-7,-4,6,1,2,3,5]=>1100000=>[2,5]=>[5,2]
[1,-7,-6,-5,-4,2,3]=>0111100=>[1,4,2]=>[2,4,1]
[-3,7,-6,1,2,4,5]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,7,-5,-3,1,2,4]=>0011000=>[2,2,3]=>[3,2,2]
[-4,1,7,-6,2,3,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,1,2,-7,3,4,6]=>0001000=>[3,1,3]=>[3,1,3]
[1,-6,7,2,3,4,5]=>0100000=>[1,1,5]=>[5,1,1]
[1,-5,-7,-6,2,3,4]=>0111000=>[1,3,3]=>[3,3,1]
[-5,7,6,1,2,3,4]=>1000000=>[1,6]=>[6,1]
[-7,-4,-6,-5,1,2,3]=>1111000=>[4,3]=>[3,4]
[-7,4,-3,1,2,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-4,-7,-6,-3,1,2,5]=>1111000=>[4,3]=>[3,4]
[6,-7,3,1,2,4,5]=>0100000=>[1,1,5]=>[5,1,1]
[-6,5,7,-3,1,2,4]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,-7,1,4,2,3,5]=>0100000=>[1,1,5]=>[5,1,1]
[6,5,1,-7,2,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[5,-4,7,-6,1,2,3]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[-5,-7,-4,-3,1,2,6]=>1111000=>[4,3]=>[3,4]
[6,4,-7,-3,1,2,5]=>0011000=>[2,2,3]=>[3,2,2]
[7,-6,-5,-4,-3,1,2]=>0111100=>[1,4,2]=>[2,4,1]
[-2,1,-7,3,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-2,7,-6,1,3,4,5]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-7,2,-5,1,3,4,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-2,-7,-6,-5,1,3,4]=>1111000=>[4,3]=>[3,4]
[-4,2,-7,1,3,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[2,7,-6,-4,1,3,5]=>0011000=>[2,2,3]=>[3,2,2]
[-2,-6,-7,1,3,4,5]=>1110000=>[3,4]=>[4,3]
[5,2,-7,-6,1,3,4]=>0011000=>[2,2,3]=>[3,2,2]
[2,5,-7,-4,1,3,6]=>0011000=>[2,2,3]=>[3,2,2]
[-7,2,6,-4,1,3,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,-5,2,-7,1,3,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,-7,-6,-5,-4,1,3]=>0111100=>[1,4,2]=>[2,4,1]
[3,1,-7,-6,2,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[-7,-3,-6,-5,1,2,4]=>1111000=>[4,3]=>[3,4]
[1,-7,4,2,3,5,6]=>0100000=>[1,1,5]=>[5,1,1]
[1,-4,-7,-6,2,3,5]=>0111000=>[1,3,3]=>[3,3,1]
[1,-7,5,2,3,4,6]=>0100000=>[1,1,5]=>[5,1,1]
[1,6,2,-7,3,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[6,1,7,-5,2,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[4,-5,7,1,2,3,6]=>0100000=>[1,1,5]=>[5,1,1]
[-4,7,6,1,2,3,5]=>1000000=>[1,6]=>[6,1]
[7,-5,1,6,2,3,4]=>0100000=>[1,1,5]=>[5,1,1]
[4,1,-7,-6,-5,2,3]=>0011100=>[2,3,2]=>[2,3,2]
[-7,-4,3,1,2,5,6]=>1100000=>[2,5]=>[5,2]
[-3,6,7,-4,1,2,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,6,1,-7,2,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[5,-3,7,-6,1,2,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[-4,7,5,1,2,3,6]=>1000000=>[1,6]=>[6,1]
[-4,6,1,-7,2,3,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,5,1,-6,2,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[7,-5,-4,-6,1,2,3]=>0111000=>[1,3,3]=>[3,3,1]
[-5,-3,-7,-4,1,2,6]=>1111000=>[4,3]=>[3,4]
[-7,-4,3,6,1,2,5]=>1100000=>[2,5]=>[5,2]
[4,5,-7,6,1,2,3]=>0010000=>[2,1,4]=>[4,1,2]
[-3,7,-6,-5,-4,1,2]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[-2,3,-7,1,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[2,3,-7,-6,1,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[3,7,-5,-2,1,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[-6,2,3,-7,1,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,-7,-6,-5,-2,1,4]=>0111100=>[1,4,2]=>[2,4,1]
[4,2,-7,-6,1,3,5]=>0011000=>[2,2,3]=>[3,2,2]
[-2,-5,-7,1,3,4,6]=>1110000=>[3,4]=>[4,3]
[7,-6,2,1,3,4,5]=>0100000=>[1,1,5]=>[5,1,1]
[2,-5,-7,-6,1,3,4]=>0111000=>[1,3,3]=>[3,3,1]
[-4,2,7,-5,1,3,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,-4,2,-7,1,3,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,6,2,-7,1,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[-4,2,-7,-6,-5,1,3]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,-3,7,-6,1,2,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,5,1,-7,2,4,6]=>0001000=>[3,1,3]=>[3,1,3]
[-6,7,3,1,2,4,5]=>1000000=>[1,6]=>[6,1]
[-3,-5,7,-6,1,2,4]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,4,1,-7,2,3,6]=>0001000=>[3,1,3]=>[3,1,3]
[7,4,1,-6,2,3,5]=>0001000=>[3,1,3]=>[3,1,3]
[-7,1,-6,5,2,3,4]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-5,4,1,-7,-6,2,3]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[-7,5,3,6,1,2,4]=>1000000=>[1,6]=>[6,1]
[-5,4,7,6,1,2,3]=>1000000=>[1,6]=>[6,1]
[-4,-3,7,-6,-5,1,2]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,4,-7,-2,1,5,6]=>0011000=>[2,2,3]=>[3,2,2]
[4,-7,-6,-3,-2,1,5]=>0111100=>[1,4,2]=>[2,4,1]
[-5,2,3,-7,1,4,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,2,3,-7,1,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[-5,3,-7,-6,-2,1,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[5,-4,2,-7,1,3,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[-4,-6,2,-7,1,3,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[-5,2,-6,-7,1,3,4]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[-5,-4,2,-7,-6,1,3]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,6,-7,4,1,2,5]=>0010000=>[2,1,4]=>[4,1,2]
[6,5,-7,3,1,2,4]=>0010000=>[2,1,4]=>[4,1,2]
[6,4,5,1,-7,2,3]=>0000100=>[4,1,2]=>[2,1,4]
[-5,-4,-3,7,-6,1,2]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[5,-7,-4,-3,-2,1,6]=>0111100=>[1,4,2]=>[2,4,1]
[-6,4,-7,-3,-2,1,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[-6,-5,3,-7,-2,1,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[-6,-5,-4,2,-7,1,3]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[-7,-6,-5,-4,-3,-2,1]=>1111110=>[6,1]=>[1,6]
[5,6,-1,2,3,4]=>001000=>[2,1,3]=>[3,1,2]
[-2,1,-4,3,-6,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[-2,4,1,3,-6,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-2,1,-4,6,3,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-2,6,1,-4,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-2,4,1,6,3,5]=>100000=>[1,5]=>[5,1]
[-2,1,-4,3,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-2,4,1,3,5,6]=>100000=>[1,5]=>[5,1]
[-2,1,5,-4,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,-2,1,-4,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-2,4,5,1,3,6]=>100000=>[1,5]=>[5,1]
[-2,1,5,6,-4,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,-2,1,6,-4,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,-2,1,-4,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[-2,4,5,6,1,3]=>100000=>[1,5]=>[5,1]
[-2,1,-6,3,-5,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[-2,6,1,3,-5,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-2,-5,1,6,3,4]=>110000=>[2,4]=>[4,2]
[-2,6,-5,1,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-2,1,5,6,3,4]=>100000=>[1,5]=>[5,1]
[-2,1,5,3,4,6]=>100000=>[1,5]=>[5,1]
[-2,1,3,-5,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,-2,1,-5,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,-2,5,1,4,6]=>010000=>[1,1,4]=>[4,1,1]
[-2,1,3,6,-5,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,-2,1,6,-5,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,-2,1,-5,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,-2,5,6,1,4]=>010000=>[1,1,4]=>[4,1,1]
[-2,1,3,6,4,5]=>100000=>[1,5]=>[5,1]
[3,-2,-6,1,4,5]=>011000=>[1,2,3]=>[3,2,1]
[3,-2,1,6,4,5]=>010000=>[1,1,4]=>[4,1,1]
[-2,1,3,4,-6,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,-2,1,4,-6,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,-2,1,-6,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,-2,6,1,5]=>001000=>[2,1,3]=>[3,1,2]
[-4,1,-3,2,-6,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,1,2,-6,5]=>000010=>[4,1,1]=>[1,1,4]
[-4,1,-3,6,2,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-4,6,1,-3,2,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-4,1,-3,2,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-4,1,5,-3,2,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,-4,1,-3,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-4,1,5,6,-3,2]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,-4,1,6,-3,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,-4,1,-3,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[-6,1,-3,2,-5,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,1,2,-5,4]=>000010=>[4,1,1]=>[1,1,4]
[5,1,-3,6,2,4]=>001000=>[2,1,3]=>[3,1,2]
[5,6,1,-3,2,4]=>000100=>[3,1,2]=>[2,1,3]
[5,1,-3,2,4,6]=>001000=>[2,1,3]=>[3,1,2]
[3,1,2,-5,4,6]=>000100=>[3,1,2]=>[2,1,3]
[1,-3,2,-5,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,-3,5,2,4,6]=>010000=>[1,1,4]=>[4,1,1]
[3,1,2,6,-5,4]=>000010=>[4,1,1]=>[1,1,4]
[1,-3,2,6,-5,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,-3,2,-5,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,-3,5,6,2,4]=>010000=>[1,1,4]=>[4,1,1]
[1,6,-3,2,4,5]=>001000=>[2,1,3]=>[3,1,2]
[1,-3,-6,2,4,5]=>011000=>[1,2,3]=>[3,2,1]
[1,-3,2,6,4,5]=>010000=>[1,1,4]=>[4,1,1]
[3,1,2,4,-6,5]=>000010=>[4,1,1]=>[1,1,4]
[1,-3,2,4,-6,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,-3,2,-6,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,-3,6,2,5]=>001000=>[2,1,3]=>[3,1,2]
[1,-3,2,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[1,4,-3,2,5,6]=>001000=>[2,1,3]=>[3,1,2]
[1,4,5,-3,2,6]=>000100=>[3,1,2]=>[2,1,3]
[1,4,5,6,-3,2]=>000010=>[4,1,1]=>[1,1,4]
[-6,1,-5,2,-4,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,1,2,-4,3]=>000010=>[4,1,1]=>[1,1,4]
[5,-4,1,6,2,3]=>010000=>[1,1,4]=>[4,1,1]
[5,1,2,-4,3,6]=>000100=>[3,1,2]=>[2,1,3]
[1,-5,2,-4,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-4,1,5,2,3,6]=>100000=>[1,5]=>[5,1]
[5,1,2,6,-4,3]=>000010=>[4,1,1]=>[1,1,4]
[1,-5,2,6,-4,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,-5,2,-4,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[-4,1,5,6,2,3]=>100000=>[1,5]=>[5,1]
[1,6,2,-4,3,5]=>000100=>[3,1,2]=>[2,1,3]
[-6,1,2,-4,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-4,1,2,6,3,5]=>100000=>[1,5]=>[5,1]
[1,4,2,3,-6,5]=>000010=>[4,1,1]=>[1,1,4]
[-4,1,2,3,-6,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[1,2,-4,3,-6,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,-4,6,3,5]=>001000=>[2,1,3]=>[3,1,2]
[1,2,-4,3,5,6]=>001000=>[2,1,3]=>[3,1,2]
[1,2,5,-4,3,6]=>000100=>[3,1,2]=>[2,1,3]
[1,2,5,6,-4,3]=>000010=>[4,1,1]=>[1,1,4]
[1,6,2,3,-5,4]=>000010=>[4,1,1]=>[1,1,4]
[-6,1,2,3,-5,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[1,2,-6,3,-5,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,-5,2,6,3,4]=>010000=>[1,1,4]=>[4,1,1]
[1,2,3,-5,4,6]=>000100=>[3,1,2]=>[2,1,3]
[1,2,3,6,-5,4]=>000010=>[4,1,1]=>[1,1,4]
[1,2,3,4,-6,5]=>000010=>[4,1,1]=>[1,1,4]
[4,5,2,3,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[6,4,2,-1,3,5]=>000100=>[3,1,2]=>[2,1,3]
[-1,4,2,6,3,5]=>100000=>[1,5]=>[5,1]
[-1,5,6,2,3,4]=>100000=>[1,5]=>[5,1]
[6,5,-1,2,3,4]=>001000=>[2,1,3]=>[3,1,2]
[4,6,2,-1,3,5]=>000100=>[3,1,2]=>[2,1,3]
[3,2,6,-1,4,5]=>000100=>[3,1,2]=>[2,1,3]
[4,-1,2,6,3,5]=>010000=>[1,1,4]=>[4,1,1]
[5,-1,6,2,3,4]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,5,2,3,4]=>010000=>[1,1,4]=>[4,1,1]
[3,2,5,4,7,6,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[4,5,2,3,7,6,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[5,4,2,3,7,6,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[6,4,2,7,3,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[7,4,2,6,3,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[8,4,2,6,3,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[-1,4,2,6,3,8,5,7]=>10000000=>[1,7]=>[7,1]
[-1,5,6,2,3,8,4,7]=>10000000=>[1,7]=>[7,1]
[8,5,6,2,3,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[7,5,6,2,3,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[6,5,7,2,3,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[5,6,7,2,3,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[4,6,2,7,3,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[3,2,6,7,4,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[3,2,7,6,4,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[4,7,2,6,3,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[5,7,6,2,3,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[6,7,5,2,3,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[7,6,5,2,3,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[8,6,5,2,3,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[-1,6,5,2,3,8,4,7]=>10000000=>[1,7]=>[7,1]
[-1,7,5,2,8,3,4,6]=>10000000=>[1,7]=>[7,1]
[8,7,5,2,-1,3,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[7,8,5,2,-1,3,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,8,5,2,3,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[5,8,6,2,3,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[4,8,2,6,3,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,8,6,4,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,-1,6,4,8,5,7]=>00100000=>[2,1,5]=>[5,1,2]
[4,-1,2,6,3,8,5,7]=>01000000=>[1,1,6]=>[6,1,1]
[5,-1,6,2,3,8,4,7]=>01000000=>[1,1,6]=>[6,1,1]
[6,-1,5,2,3,8,4,7]=>01000000=>[1,1,6]=>[6,1,1]
[7,-1,5,2,8,3,4,6]=>01000000=>[1,1,6]=>[6,1,1]
[8,-1,5,2,7,3,4,6]=>01000000=>[1,1,6]=>[6,1,1]
[-1,8,5,2,7,3,4,6]=>10000000=>[1,7]=>[7,1]
[-1,8,6,7,2,3,4,5]=>10000000=>[1,7]=>[7,1]
[8,-1,6,7,2,3,4,5]=>01000000=>[1,1,6]=>[6,1,1]
[7,-1,6,8,2,3,4,5]=>01000000=>[1,1,6]=>[6,1,1]
[6,-1,7,8,2,3,4,5]=>01000000=>[1,1,6]=>[6,1,1]
[5,-1,7,2,8,3,4,6]=>01000000=>[1,1,6]=>[6,1,1]
[4,-1,2,7,8,3,5,6]=>01000000=>[1,1,6]=>[6,1,1]
[3,2,-1,7,8,4,5,6]=>00100000=>[2,1,5]=>[5,1,2]
[3,2,8,7,-1,4,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[4,8,2,7,-1,3,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[5,8,7,2,-1,3,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,8,7,-1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[7,8,6,-1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[8,7,6,-1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[-1,7,6,8,2,3,4,5]=>10000000=>[1,7]=>[7,1]
[-1,6,7,8,2,3,4,5]=>10000000=>[1,7]=>[7,1]
[8,6,7,-1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[7,6,8,-1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[6,7,8,-1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[5,7,8,2,-1,3,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[4,7,2,8,-1,3,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[3,2,7,8,-1,4,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[3,2,6,8,4,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[4,6,2,8,3,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[5,6,8,2,3,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[6,5,8,2,3,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[7,5,8,2,-1,3,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[8,5,7,2,-1,3,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[-1,5,7,2,8,3,4,6]=>10000000=>[1,7]=>[7,1]
[-1,4,2,7,8,3,5,6]=>10000000=>[1,7]=>[7,1]
[8,4,2,7,-1,3,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[7,4,2,8,-1,3,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,4,2,8,3,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[5,4,2,3,8,-1,6,7]=>00000100=>[5,1,2]=>[2,1,5]
[4,5,2,3,8,-1,6,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,5,4,8,-1,6,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,5,4,-1,8,6,7]=>00001000=>[4,1,3]=>[3,1,4]
[4,5,2,3,-1,8,6,7]=>00001000=>[4,1,3]=>[3,1,4]
[5,4,2,3,-1,8,6,7]=>00001000=>[4,1,3]=>[3,1,4]
[6,4,2,-1,3,8,5,7]=>00010000=>[3,1,4]=>[4,1,3]
[7,4,2,-1,8,3,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[8,4,2,-1,7,3,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[-1,4,2,8,7,3,5,6]=>10000000=>[1,7]=>[7,1]
[-1,5,8,2,7,3,4,6]=>10000000=>[1,7]=>[7,1]
[8,5,-1,2,7,3,4,6]=>00100000=>[2,1,5]=>[5,1,2]
[7,5,-1,2,8,3,4,6]=>00100000=>[2,1,5]=>[5,1,2]
[6,5,-1,2,3,8,4,7]=>00100000=>[2,1,5]=>[5,1,2]
[5,6,-1,2,3,8,4,7]=>00100000=>[2,1,5]=>[5,1,2]
[4,6,2,-1,3,8,5,7]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,6,-1,4,8,5,7]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,7,-1,8,4,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[4,7,2,-1,8,3,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[5,7,-1,2,8,3,4,6]=>00100000=>[2,1,5]=>[5,1,2]
[6,7,-1,8,2,3,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[7,6,-1,8,2,3,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[8,6,-1,7,2,3,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[-1,6,8,7,2,3,4,5]=>10000000=>[1,7]=>[7,1]
[-1,7,8,6,2,3,4,5]=>10000000=>[1,7]=>[7,1]
[8,7,-1,6,2,3,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[7,8,-1,6,2,3,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[6,8,-1,7,2,3,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[5,8,-1,2,7,3,4,6]=>00100000=>[2,1,5]=>[5,1,2]
[4,8,2,-1,7,3,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,8,-1,7,4,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,-1,8,7,4,5,6]=>00100000=>[2,1,5]=>[5,1,2]
[4,-1,2,8,7,3,5,6]=>01000000=>[1,1,6]=>[6,1,1]
[5,-1,8,2,7,3,4,6]=>01000000=>[1,1,6]=>[6,1,1]
[6,-1,8,7,2,3,4,5]=>01000000=>[1,1,6]=>[6,1,1]
[7,-1,8,6,2,3,4,5]=>01000000=>[1,1,6]=>[6,1,1]
[8,-1,7,6,2,3,4,5]=>01000000=>[1,1,6]=>[6,1,1]
[-1,8,7,6,2,3,4,5]=>10000000=>[1,7]=>[7,1]
[1,2,3,-5,-6,4]=>000110=>[3,2,1]=>[1,2,3]
[1,2,5,-4,-6,3]=>000110=>[3,2,1]=>[1,2,3]
[1,2,-4,-5,3,6]=>001100=>[2,2,2]=>[2,2,2]
[1,2,-4,6,-5,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,-4,2,5,-6,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,2,-4,-5,-6,3]=>001110=>[2,3,1]=>[1,3,2]
[1,-3,2,-5,-6,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,5,-3,-6,2]=>000110=>[3,2,1]=>[1,2,3]
[1,4,-3,-5,2,6]=>001100=>[2,2,2]=>[2,2,2]
[1,4,-3,6,-5,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,-3,4,5,-6,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,-3,-5,-6,2]=>001110=>[2,3,1]=>[1,3,2]
[1,-3,-4,2,5,6]=>011000=>[1,2,3]=>[3,2,1]
[1,-3,-4,2,-6,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,-3,5,-4,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,-3,5,6,-4,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,-3,5,-4,-6,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[-3,1,4,-5,2,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-3,1,4,6,-5,2]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,4,5,-6,2]=>000010=>[4,1,1]=>[1,1,4]
[-3,1,4,-5,-6,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[1,-3,-4,-5,2,6]=>011100=>[1,3,2]=>[2,3,1]
[1,-3,-4,6,-5,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,-3,-6,5,-4,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[-5,1,3,-4,-6,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[1,-3,-4,-5,-6,2]=>011110=>[1,4,1]=>[1,4,1]
[-2,1,3,-5,-6,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-2,1,5,-4,-6,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-2,1,-4,-5,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-2,1,-4,6,-5,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[-2,-4,1,5,-6,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-2,1,-4,-5,-6,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,-2,1,-5,-6,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,5,-2,-6,1]=>000110=>[3,2,1]=>[1,2,3]
[3,4,-2,-5,1,6]=>001100=>[2,2,2]=>[2,2,2]
[3,4,-2,6,-5,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,-2,4,5,-6,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,-2,-5,-6,1]=>001110=>[2,3,1]=>[1,3,2]
[3,-2,-4,1,5,6]=>011000=>[1,2,3]=>[3,2,1]
[3,-2,-4,1,-6,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,-2,5,-4,1,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,-2,5,6,-4,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,-2,5,-4,-6,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[-2,3,4,-5,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-2,3,4,6,-5,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,3,4,5,-6,1]=>000010=>[4,1,1]=>[1,1,4]
[-2,3,4,-5,-6,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,-2,-4,-5,1,6]=>011100=>[1,3,2]=>[2,3,1]
[3,-2,-4,6,-5,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,-2,-6,5,-4,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[-2,5,3,-4,-6,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,-2,-4,-5,-6,1]=>011110=>[1,4,1]=>[1,4,1]
[-2,-3,1,4,-6,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-2,-3,1,-5,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-2,-3,1,6,-5,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-2,-3,1,-5,-6,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[-2,4,-3,1,-6,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[-2,4,5,-3,-6,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-2,4,-3,-5,1,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[-2,4,-3,6,-5,1]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[-2,-3,4,5,-6,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-2,4,-3,-5,-6,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[2,3,-4,1,-6,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,5,-4,-6,1]=>000110=>[3,2,1]=>[1,2,3]
[5,3,4,-2,-6,1]=>000110=>[3,2,1]=>[1,2,3]
[2,3,-4,-5,1,6]=>001100=>[2,2,2]=>[2,2,2]
[2,3,-4,6,-5,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,-4,3,5,-6,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,3,-2,-6,1]=>000110=>[3,2,1]=>[1,2,3]
[2,3,-4,-5,-6,1]=>001110=>[2,3,1]=>[1,3,2]
[-2,-3,-4,1,-6,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[-2,-3,5,-4,-6,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[-2,-5,4,-3,-6,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,2,-3,-5,-6,1]=>001110=>[2,3,1]=>[1,3,2]
[-3,2,6,-5,1,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-6,2,4,-5,-3,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-6,-5,2,3,-4,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[2,-5,6,-4,1,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,-5,-3,1,2]=>001100=>[2,2,2]=>[2,2,2]
[3,-5,6,-4,1,2]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-6,-5,-4,3,1,2]=>111000=>[3,3]=>[3,3]
[2,8,-6,-4,-3,1,5,7]=>00111000=>[2,3,3]=>[3,3,2]
[-3,2,8,-6,-5,1,4,7]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[-8,2,4,-6,-5,-3,1,7]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[-8,-7,2,4,-5,-3,1,6]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[8,2,4,6,-7,-5,-3,1]=>00001110=>[4,3,1]=>[1,3,4]
[6,8,2,3,-7,-5,-4,1]=>00001110=>[4,3,1]=>[1,3,4]
[5,-7,2,3,8,-4,1,6]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[-8,-6,2,3,-5,-4,1,7]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[2,-6,8,-5,-4,1,3,7]=>01011000=>[1,1,1,2,3]=>[3,2,1,1,1]
[4,8,-6,-5,-2,1,3,7]=>00111000=>[2,3,3]=>[3,3,2]
[8,4,-6,-5,-3,1,2,7]=>00111000=>[2,3,3]=>[3,3,2]
[3,-6,8,-5,-4,1,2,7]=>01011000=>[1,1,1,2,3]=>[3,2,1,1,1]
[3,-5,6,8,-4,1,2,7]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[-8,-6,-3,2,-5,-4,1,7]=>11101100=>[3,1,2,2]=>[2,2,1,3]
[5,-7,-3,2,8,-4,1,6]=>01100100=>[1,2,2,1,2]=>[2,1,2,2,1]
[3,8,-6,2,-7,-5,-4,1]=>00101110=>[2,1,1,3,1]=>[1,3,1,1,2]
[5,8,-7,-3,2,-6,-4,1]=>00110110=>[2,2,1,2,1]=>[1,2,1,2,2]
[3,8,-7,-4,2,-6,1,5]=>00110100=>[2,2,1,1,2]=>[2,1,1,2,2]
[4,8,-7,-6,3,1,2,5]=>00110000=>[2,2,4]=>[4,2,2]
[5,-7,-4,3,8,1,2,6]=>01100000=>[1,2,5]=>[5,2,1]
[5,-8,-7,3,-4,1,2,6]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[4,-7,8,-5,-3,1,2,6]=>01011000=>[1,1,1,2,3]=>[3,2,1,1,1]
[-5,4,8,-7,-2,1,3,6]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[-8,4,6,-7,-5,-2,1,3]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[4,-8,6,-7,-5,-3,1,2]=>01011100=>[1,1,1,3,2]=>[2,3,1,1,1]
[-8,6,3,-7,-5,-4,1,2]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[3,8,-7,6,-5,-4,1,2]=>00101100=>[2,1,1,2,2]=>[2,2,1,1,2]
[3,8,-7,-6,5,-4,1,2]=>00110100=>[2,2,1,1,2]=>[2,1,1,2,2]
[4,8,-7,-6,3,5,1,2]=>00110000=>[2,2,4]=>[4,2,2]
[3,8,-7,-6,2,5,-4,1]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[4,7,8,-6,-3,2,-5,1]=>00011010=>[3,2,1,1,1]=>[1,1,1,2,3]
[3,6,7,8,4,-5,1,2]=>00000100=>[5,1,2]=>[2,1,5]
[3,7,8,-6,4,-5,1,2]=>00010100=>[3,1,1,1,2]=>[2,1,1,1,3]
[-5,8,-7,3,-6,-4,1,2]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[7,8,4,5,-6,-3,1,2]=>00001100=>[4,2,2]=>[2,2,4]
[-8,-7,4,5,-6,-2,1,3]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[-8,-7,2,4,-6,1,3,5]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[-8,-7,-4,-3,-6,1,2,5]=>11111000=>[5,3]=>[3,5]
[-4,3,-7,8,-6,1,2,5]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[6,7,8,1,3,-5,2,4]=>00000100=>[5,1,2]=>[2,1,5]
[-3,7,8,-6,2,-5,1,4]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[3,7,8,-6,2,4,-5,1]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[6,7,8,2,3,4,-5,1]=>00000010=>[6,1,1]=>[1,1,6]
[2,7,8,-6,3,-5,1,4]=>00010100=>[3,1,1,1,2]=>[2,1,1,1,3]
[6,7,8,-5,2,1,3,4]=>00010000=>[3,1,4]=>[4,1,3]
[5,-8,-7,2,-4,1,3,6]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[-4,2,-7,8,-6,1,3,5]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[7,8,-4,2,3,-6,1,5]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[5,8,-7,2,3,-6,-4,1]=>00100110=>[2,1,2,2,1]=>[1,2,2,1,2]
[8,-7,2,4,5,-6,-3,1]=>01000110=>[1,1,3,2,1]=>[1,2,3,1,1]
[-8,-7,-3,2,4,-6,1,5]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[3,-8,-7,2,-6,1,4,5]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[-7,-3,2,8,-5,1,4,6]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[2,4,7,8,-3,1,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,8,-7,-4,-2,1,3,5]=>00111000=>[2,3,3]=>[3,3,2]
[8,6,-7,-4,-3,1,2,5]=>00111000=>[2,3,3]=>[3,3,2]
[-8,2,6,-7,-4,-3,1,5]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[-8,-3,2,6,-7,-5,1,4]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[-8,-7,-3,2,5,-6,1,4]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[-8,-7,-5,-3,2,-6,1,4]=>11110100=>[4,1,1,2]=>[2,1,1,4]
[5,-8,-7,2,4,-6,-3,1]=>01100110=>[1,2,2,2,1]=>[1,2,2,2,1]
[7,8,-6,2,3,5,-4,1]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[6,7,8,2,5,-4,1,3]=>00000100=>[5,1,2]=>[2,1,5]
[-5,8,-7,2,-6,-4,1,3]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[-8,6,2,-7,-5,-4,1,3]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[-6,-8,1,-7,-5,-4,2,3]=>11011100=>[2,1,3,2]=>[2,3,1,2]
[-8,-6,-3,-7,-5,1,2,4]=>11111000=>[5,3]=>[3,5]
[-8,2,6,-7,-5,1,3,4]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[-8,-7,2,5,-6,1,3,4]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[-8,-7,-5,-3,-6,1,2,4]=>11111000=>[5,3]=>[3,5]
[6,7,8,5,-4,1,2,3]=>00001000=>[4,1,3]=>[3,1,4]
[6,7,8,1,4,-5,2,3]=>00000100=>[5,1,2]=>[2,1,5]
[2,7,8,-6,4,-5,1,3]=>00010100=>[3,1,1,1,2]=>[2,1,1,1,3]
[-4,7,8,-6,2,-5,1,3]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[4,7,8,-6,2,3,-5,1]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[4,6,7,8,2,3,-5,1]=>00000010=>[6,1,1]=>[1,1,6]
[-6,4,7,8,2,-5,1,3]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[-4,7,8,-6,1,-5,2,3]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[7,8,-6,-4,5,1,2,3]=>00110000=>[2,2,4]=>[4,2,2]
[8,-7,-6,3,5,1,2,4]=>01100000=>[1,2,5]=>[5,2,1]
[-8,-7,-5,2,-6,1,3,4]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[-8,-7,-5,4,-6,-2,1,3]=>11101100=>[3,1,2,2]=>[2,2,1,3]
[5,8,-7,4,-6,-3,1,2]=>00101100=>[2,1,1,2,2]=>[2,2,1,1,2]
[6,7,8,3,5,-4,1,2]=>00000100=>[5,1,2]=>[2,1,5]
[-4,7,8,-6,3,-5,1,2]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[-6,4,7,8,3,-5,1,2]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[4,6,7,8,-5,3,1,2]=>00001000=>[4,1,3]=>[3,1,4]
[3,6,7,8,-4,2,-5,1]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[-1,6,5,3,4,2]=>100000=>[1,5]=>[5,1]
[-1,6,4,5,3,2]=>100000=>[1,5]=>[5,1]
[-1,6,4,5,2,3]=>100000=>[1,5]=>[5,1]
[-1,6,4,3,5,2]=>100000=>[1,5]=>[5,1]
[-1,6,3,4,5,2]=>100000=>[1,5]=>[5,1]
[-1,6,3,4,2,5]=>100000=>[1,5]=>[5,1]
[-1,5,6,4,3,2]=>100000=>[1,5]=>[5,1]
[-1,5,6,4,2,3]=>100000=>[1,5]=>[5,1]
[-1,5,6,3,4,2]=>100000=>[1,5]=>[5,1]
[-1,5,6,3,2,4]=>100000=>[1,5]=>[5,1]
[-1,5,4,6,3,2]=>100000=>[1,5]=>[5,1]
[-1,5,4,6,2,3]=>100000=>[1,5]=>[5,1]
[-1,5,4,3,6,2]=>100000=>[1,5]=>[5,1]
[-1,5,3,4,6,2]=>100000=>[1,5]=>[5,1]
[-1,5,3,4,2,6]=>100000=>[1,5]=>[5,1]
[-1,4,5,6,3,2]=>100000=>[1,5]=>[5,1]
[-1,4,5,6,2,3]=>100000=>[1,5]=>[5,1]
[-1,4,5,3,6,2]=>100000=>[1,5]=>[5,1]
[-1,4,5,3,2,6]=>100000=>[1,5]=>[5,1]
[-1,4,5,2,3,6]=>100000=>[1,5]=>[5,1]
[-1,4,3,5,6,2]=>100000=>[1,5]=>[5,1]
[-1,4,3,5,2,6]=>100000=>[1,5]=>[5,1]
[-1,3,4,5,6,2]=>100000=>[1,5]=>[5,1]
[-1,3,4,5,2,6]=>100000=>[1,5]=>[5,1]
[-1,3,4,2,5,6]=>100000=>[1,5]=>[5,1]
[6,-1,5,4,3,2]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,5,4,2,3]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,5,3,4,2]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,5,3,2,4]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,4,5,3,2]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,4,5,2,3]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,4,3,5,2]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,4,3,2,5]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,4,2,3,5]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,3,4,2,5]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,3,2,4,5]=>010000=>[1,1,4]=>[4,1,1]
[6,-1,2,3,4,5]=>010000=>[1,1,4]=>[4,1,1]
[6,5,-1,4,3,2]=>001000=>[2,1,3]=>[3,1,2]
[6,5,-1,4,2,3]=>001000=>[2,1,3]=>[3,1,2]
[6,5,-1,3,4,2]=>001000=>[2,1,3]=>[3,1,2]
[6,5,-1,3,2,4]=>001000=>[2,1,3]=>[3,1,2]
[6,5,4,-1,3,2]=>000100=>[3,1,2]=>[2,1,3]
[6,5,4,-1,2,3]=>000100=>[3,1,2]=>[2,1,3]
[6,5,4,3,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[6,5,3,4,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[6,5,3,4,2,-1]=>000001=>[5,1]=>[1,5]
[6,4,5,-1,3,2]=>000100=>[3,1,2]=>[2,1,3]
[6,4,5,-1,2,3]=>000100=>[3,1,2]=>[2,1,3]
[6,4,5,3,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[6,4,5,3,2,-1]=>000001=>[5,1]=>[1,5]
[6,4,5,2,3,-1]=>000001=>[5,1]=>[1,5]
[6,4,3,5,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[6,4,3,5,2,-1]=>000001=>[5,1]=>[1,5]
[6,3,4,5,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[6,3,4,5,2,-1]=>000001=>[5,1]=>[1,5]
[6,3,4,2,5,-1]=>000001=>[5,1]=>[1,5]
[5,6,-1,4,2,3]=>001000=>[2,1,3]=>[3,1,2]
[5,6,-1,3,4,2]=>001000=>[2,1,3]=>[3,1,2]
[5,6,-1,3,2,4]=>001000=>[2,1,3]=>[3,1,2]
[5,6,4,-1,3,2]=>000100=>[3,1,2]=>[2,1,3]
[5,6,4,-1,2,3]=>000100=>[3,1,2]=>[2,1,3]
[5,6,4,3,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[5,6,4,3,2,-1]=>000001=>[5,1]=>[1,5]
[5,6,4,2,3,-1]=>000001=>[5,1]=>[1,5]
[5,6,3,4,2,-1]=>000001=>[5,1]=>[1,5]
[5,6,3,2,4,-1]=>000001=>[5,1]=>[1,5]
[5,4,6,-1,3,2]=>000100=>[3,1,2]=>[2,1,3]
[5,4,6,-1,2,3]=>000100=>[3,1,2]=>[2,1,3]
[5,4,6,3,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[5,4,6,3,2,-1]=>000001=>[5,1]=>[1,5]
[5,4,6,2,3,-1]=>000001=>[5,1]=>[1,5]
[5,4,3,6,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[5,4,3,6,2,-1]=>000001=>[5,1]=>[1,5]
[5,3,4,6,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[5,3,4,6,2,-1]=>000001=>[5,1]=>[1,5]
[5,3,4,2,6,-1]=>000001=>[5,1]=>[1,5]
[4,5,6,-1,3,2]=>000100=>[3,1,2]=>[2,1,3]
[4,5,6,3,2,-1]=>000001=>[5,1]=>[1,5]
[4,5,3,6,2,-1]=>000001=>[5,1]=>[1,5]
[4,5,3,2,6,-1]=>000001=>[5,1]=>[1,5]
[4,3,5,6,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[4,3,5,6,2,-1]=>000001=>[5,1]=>[1,5]
[4,3,5,2,6,-1]=>000001=>[5,1]=>[1,5]
[4,2,5,3,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[3,2,6,4,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[5,2,6,3,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[5,2,-1,3,4,6]=>001000=>[2,1,3]=>[3,1,2]
[6,2,-1,3,4,5]=>001000=>[2,1,3]=>[3,1,2]
[3,2,5,-1,4,6]=>000100=>[3,1,2]=>[2,1,3]
[4,2,6,-1,3,5]=>000100=>[3,1,2]=>[2,1,3]
[5,2,6,-1,3,4]=>000100=>[3,1,2]=>[2,1,3]
[6,2,3,-1,4,5]=>000100=>[3,1,2]=>[2,1,3]
[3,2,5,6,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[3,2,4,6,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[4,2,3,6,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[3,5,2,4,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[4,6,2,3,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[5,6,2,3,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[4,-1,2,3,5,6]=>010000=>[1,1,4]=>[4,1,1]
[5,-1,2,3,4,6]=>010000=>[1,1,4]=>[4,1,1]
[4,5,2,-1,3,6]=>000100=>[3,1,2]=>[2,1,3]
[3,6,2,-1,4,5]=>000100=>[3,1,2]=>[2,1,3]
[5,6,2,-1,3,4]=>000100=>[3,1,2]=>[2,1,3]
[3,4,2,-1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[2,5,3,-1,4,6]=>000100=>[3,1,2]=>[2,1,3]
[2,6,3,-1,4,5]=>000100=>[3,1,2]=>[2,1,3]
[4,5,2,6,-1,3]=>000010=>[4,1,1]=>[1,1,4]
[3,4,2,6,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[2,4,3,6,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[2,5,3,6,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[3,4,2,5,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,6,3,4,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[3,5,-1,2,4,6]=>001000=>[2,1,3]=>[3,1,2]
[4,5,-1,2,3,6]=>001000=>[2,1,3]=>[3,1,2]
[3,6,-1,2,4,5]=>001000=>[2,1,3]=>[3,1,2]
[4,6,-1,2,3,5]=>001000=>[2,1,3]=>[3,1,2]
[2,4,-1,3,5,6]=>001000=>[2,1,3]=>[3,1,2]
[2,5,-1,3,4,6]=>001000=>[2,1,3]=>[3,1,2]
[2,6,-1,3,4,5]=>001000=>[2,1,3]=>[3,1,2]
[3,5,6,2,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[4,5,6,2,-1,3]=>000010=>[4,1,1]=>[1,1,4]
[2,4,6,3,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[2,5,6,3,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[3,4,5,2,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,4,5,3,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,3,6,4,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[3,5,6,-1,2,4]=>000100=>[3,1,2]=>[2,1,3]
[3,4,6,-1,2,5]=>000100=>[3,1,2]=>[2,1,3]
[2,4,6,-1,3,5]=>000100=>[3,1,2]=>[2,1,3]
[2,5,6,-1,3,4]=>000100=>[3,1,2]=>[2,1,3]
[2,4,5,-1,3,6]=>000100=>[3,1,2]=>[2,1,3]
[2,3,5,-1,4,6]=>000100=>[3,1,2]=>[2,1,3]
[2,3,6,-1,4,5]=>000100=>[3,1,2]=>[2,1,3]
[2,4,5,6,-1,3]=>000010=>[4,1,1]=>[1,1,4]
[2,3,5,6,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[2,3,4,6,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[2,3,-1,5,6,4]=>001000=>[2,1,3]=>[3,1,2]
[2,-1,3,5,6,4]=>010000=>[1,1,4]=>[4,1,1]
[2,6,4,5,3,-1]=>000001=>[5,1]=>[1,5]
[2,-1,4,5,3,6]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,4,5,6,3]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,4,6,5,3]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,5,4,6,3]=>010000=>[1,1,4]=>[4,1,1]
[2,-1,6,4,5,3]=>010000=>[1,1,4]=>[4,1,1]
[3,2,-1,5,6,4]=>001000=>[2,1,3]=>[3,1,2]
[-1,2,3,5,6,4]=>100000=>[1,5]=>[5,1]
[6,2,4,5,3,-1]=>000001=>[5,1]=>[1,5]
[-1,2,4,5,3,6]=>100000=>[1,5]=>[5,1]
[-1,2,4,5,6,3]=>100000=>[1,5]=>[5,1]
[-1,2,4,6,5,3]=>100000=>[1,5]=>[5,1]
[-1,2,5,4,6,3]=>100000=>[1,5]=>[5,1]
[-1,2,6,4,5,3]=>100000=>[1,5]=>[5,1]
[-1,3,2,5,6,4]=>100000=>[1,5]=>[5,1]
[5,3,4,2,-1,6]=>000010=>[4,1,1]=>[1,1,4]
[-1,3,4,2,6,5]=>100000=>[1,5]=>[5,1]
[-1,3,4,6,5,2]=>100000=>[1,5]=>[5,1]
[6,3,5,4,2,-1]=>000001=>[5,1]=>[1,5]
[-1,3,5,4,2,6]=>100000=>[1,5]=>[5,1]
[-1,3,5,4,6,2]=>100000=>[1,5]=>[5,1]
[-1,3,6,4,5,2]=>100000=>[1,5]=>[5,1]
[-1,3,6,5,4,2]=>100000=>[1,5]=>[5,1]
[-1,4,3,6,5,2]=>100000=>[1,5]=>[5,1]
[-1,6,3,5,4,2]=>100000=>[1,5]=>[5,1]
[1,2,-6,5,3,4]=>001000=>[2,1,3]=>[3,1,2]
[-6,1,2,5,3,4]=>100000=>[1,5]=>[5,1]
[6,1,-4,2,-5,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,1,-6,-3,2,4]=>001100=>[2,2,2]=>[2,2,2]
[-6,1,4,5,2,3]=>100000=>[1,5]=>[5,1]
[-2,1,-6,5,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-6,3,1,2,-5,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-4,6,1,2,-5,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,-3,1,-4,2,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-6,5,1,-3,2,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-6,5,-4,1,2,3]=>101000=>[1,1,1,3]=>[3,1,1,1]
[-5,-3,1,6,-4,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-6,-2,4,1,3,5]=>110000=>[2,4]=>[4,2]
[-6,-2,1,5,3,4]=>110000=>[2,4]=>[4,2]
[6,-2,-4,1,-5,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,-3,1,-5,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,-2,-6,5,1,4]=>011000=>[1,2,3]=>[3,2,1]
[-6,-2,4,5,1,3]=>110000=>[2,4]=>[4,2]
[1,2,7,3,4,-6,5]=>0000010=>[5,1,1]=>[1,1,5]
[1,2,7,3,-5,4,6]=>0000100=>[4,1,2]=>[2,1,4]
[1,2,3,-7,6,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[1,6,2,3,7,-5,4]=>0000010=>[5,1,1]=>[1,1,5]
[1,2,7,-4,3,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[7,1,2,-4,3,-6,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,-7,2,5,3,4,6]=>0100000=>[1,1,5]=>[5,1,1]
[1,-7,2,3,6,4,5]=>0100000=>[1,1,5]=>[5,1,1]
[1,7,2,-5,3,-6,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,1,2,-4,7,3,6]=>0001000=>[3,1,3]=>[3,1,3]
[1,6,2,-7,-4,3,5]=>0001100=>[3,2,2]=>[2,2,3]
[1,-7,2,5,6,3,4]=>0100000=>[1,1,5]=>[5,1,1]
[5,1,2,6,7,-4,3]=>0000010=>[5,1,1]=>[1,1,5]
[1,-3,7,2,4,5,6]=>0100000=>[1,1,5]=>[5,1,1]
[7,1,-3,2,4,-6,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,1,-3,2,-5,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,6,-3,-7,2,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[-6,1,-3,2,7,-5,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,-7,4,2,3,-6,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,-5,7,2,3,-6,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,7,-4,2,-5,3,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,1,-7,2,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[6,1,-4,2,7,-5,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[-4,1,-3,2,7,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[-4,1,7,-3,2,-6,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,-7,1,-3,2,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,-7,6,-3,2,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[-7,1,-3,-5,2,-6,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[-6,-7,1,2,5,3,4]=>1100000=>[2,5]=>[5,2]
[1,5,7,-4,2,-6,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[-4,1,5,-3,7,2,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[-4,1,-3,-7,6,2,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,-3,-7,1,6,2,4]=>0110000=>[1,2,4]=>[4,2,1]
[-4,1,7,5,6,2,3]=>1000000=>[1,6]=>[6,1]
[-4,1,5,6,7,-3,2]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[-2,1,3,4,7,5,6]=>1000000=>[1,6]=>[6,1]
[-2,1,7,3,4,-6,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[-2,1,7,3,-5,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[-2,1,3,-7,6,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[-2,6,1,3,7,-5,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[-2,1,7,-4,3,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,-2,1,-4,3,-6,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[-2,-7,1,5,3,4,6]=>1100000=>[2,5]=>[5,2]
[-2,-7,1,3,6,4,5]=>1100000=>[2,5]=>[5,2]
[-2,7,1,-5,3,-6,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,-2,1,-4,7,3,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[-2,6,1,-7,-4,3,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[-2,-7,1,5,6,3,4]=>1100000=>[2,5]=>[5,2]
[5,-2,1,6,7,-4,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,3,1,2,4,-6,5]=>0000010=>[5,1,1]=>[1,1,5]
[7,3,1,2,-5,4,6]=>0000100=>[4,1,2]=>[2,1,4]
[-6,3,1,2,7,-5,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[7,1,4,2,3,-6,5]=>0000010=>[5,1,1]=>[1,1,5]
[1,6,7,2,3,-5,4]=>0000010=>[5,1,1]=>[1,1,5]
[-4,1,7,2,-5,3,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,1,6,-7,2,3,5]=>0001000=>[3,1,3]=>[3,1,3]
[1,7,2,-5,6,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[-4,6,1,2,7,-5,3]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[-3,7,1,-4,2,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[-7,-3,1,-4,2,-6,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,1,-3,2,4,6]=>0001000=>[3,1,3]=>[3,1,3]
[7,1,6,-3,2,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[-7,-5,1,-3,2,-6,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,-4,1,2,3,6]=>0010000=>[2,1,4]=>[4,1,2]
[7,-4,6,1,2,3,5]=>0100000=>[1,1,5]=>[5,1,1]
[-6,1,7,2,5,3,4]=>1000000=>[1,6]=>[6,1]
[-7,-5,1,-6,2,-4,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[-5,-3,1,-4,7,2,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,-3,1,-7,-4,2,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,1,-3,6,2,4]=>0001000=>[3,1,3]=>[3,1,3]
[7,5,-4,1,6,2,3]=>0010000=>[2,1,4]=>[4,1,2]
[-5,-3,1,6,7,-4,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[3,-2,1,4,7,5,6]=>0100000=>[1,1,5]=>[5,1,1]
[3,-2,7,1,4,-6,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,-2,7,1,-5,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,-2,1,-7,6,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,6,-2,1,7,-5,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,-2,4,1,3,5,6]=>0100000=>[1,1,5]=>[5,1,1]
[-2,-7,4,1,3,-6,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,-2,1,5,3,4,6]=>0100000=>[1,1,5]=>[5,1,1]
[-2,1,3,6,7,4,5]=>1000000=>[1,6]=>[6,1]
[-2,-5,7,1,3,-6,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[-2,7,-4,1,-5,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[-4,6,-2,-7,1,3,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,6,-2,-7,1,3,4]=>0011000=>[2,2,3]=>[3,2,2]
[6,-2,-4,1,7,-5,3]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,4,1,2,-6,5]=>0000010=>[5,1,1]=>[1,1,5]
[5,3,7,1,2,-6,4]=>0000010=>[5,1,1]=>[1,1,5]
[-4,-5,7,1,2,-6,3]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,-3,7,1,-5,2,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,-3,1,-7,6,2,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[-3,5,1,-7,6,2,4]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[-4,-7,6,-5,1,2,3]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,6,-3,1,7,-5,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,-2,1,7,5,6]=>0010000=>[2,1,4]=>[4,1,2]
[3,4,7,-2,1,-6,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,-7,-2,5,1,4,6]=>0110000=>[1,2,4]=>[4,2,1]
[3,-7,-2,1,6,4,5]=>0110000=>[1,2,4]=>[4,2,1]
[3,7,-2,-5,1,-6,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,-2,4,5,1,3,6]=>0100000=>[1,1,5]=>[5,1,1]
[7,-2,4,1,6,3,5]=>0100000=>[1,1,5]=>[5,1,1]
[-6,-7,-2,1,5,3,4]=>1110000=>[3,4]=>[4,3]
[-2,5,7,-4,1,-6,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,-7,6,1,5,2,4]=>0100000=>[1,1,5]=>[5,1,1]
[4,5,7,-6,1,-3,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,5,-2,7,1,6]=>0001000=>[3,1,3]=>[3,1,3]
[3,4,-2,-7,6,1,5]=>0011000=>[2,2,3]=>[3,2,2]
[3,-7,-2,5,6,1,4]=>0110000=>[1,2,4]=>[4,2,1]
[-7,2,4,5,6,1,3]=>1000000=>[1,6]=>[6,1]
[3,4,5,6,7,-2,1]=>0000010=>[5,1,1]=>[1,1,5]
[3,5,-4,2,-6,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,-5,2,-6,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,-6,-3,2,-5,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,-5,-4,2,-6,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[-5,-4,-3,2,-6,1]=>111010=>[3,1,1,1]=>[1,1,1,3]
[-4,-3,2,6,-5,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-5,4,2,3,-6,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,6,2,3,-5,1]=>000010=>[4,1,1]=>[1,1,4]
[6,-4,2,3,-5,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[-3,-5,2,4,-6,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,-6,2,4,-5,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,-4,2,5,-6,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[-4,-3,2,5,-6,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[-4,-3,2,-6,-5,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[2,-5,3,4,-6,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,3,4,-5,1]=>000010=>[4,1,1]=>[1,1,4]
[4,2,3,-6,-5,1]=>000110=>[3,2,1]=>[1,2,3]
[-6,2,3,-5,-4,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-3,2,4,5,-6,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-3,2,4,-6,-5,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,3,4,-6,-5,1]=>000110=>[3,2,1]=>[1,2,3]
[2,3,-6,-5,-4,1]=>001110=>[2,3,1]=>[1,3,2]
[-5,-4,3,6,1,2]=>110000=>[2,4]=>[4,2]
[-6,4,2,-5,1,3]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,5,-4,-6,1,3]=>001100=>[2,2,2]=>[2,2,2]
[-3,-6,2,-5,1,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,-3,2,-6,1,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[-4,-3,2,-5,1,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[2,5,3,-6,1,4]=>000100=>[3,1,2]=>[2,1,3]
[2,-6,3,-5,1,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,-4,3,-6,1,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,3,-5,1,6]=>000100=>[3,1,2]=>[2,1,3]
[-5,2,3,-4,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,4,-6,1,5]=>000100=>[3,1,2]=>[2,1,3]
[-3,2,4,-5,1,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-2,3,4,-6,1,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,3,4,-5,1,6]=>000100=>[3,1,2]=>[2,1,3]
[2,3,-5,-4,1,6]=>001100=>[2,2,2]=>[2,2,2]
[-4,-6,1,-5,2,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[-5,-4,3,1,2,6]=>110000=>[2,4]=>[4,2]
[6,-5,2,1,3,4]=>010000=>[1,1,4]=>[4,1,1]
[5,2,-4,1,3,6]=>001000=>[2,1,3]=>[3,1,2]
[-3,-2,-6,1,4,5]=>111000=>[3,3]=>[3,3]
[-2,3,-5,1,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,5,-6,1,2,3]=>001000=>[2,1,3]=>[3,1,2]
[4,5,-6,-3,1,2]=>001100=>[2,2,2]=>[2,2,2]
[3,4,-5,1,2,6]=>001000=>[2,1,3]=>[3,1,2]
[3,4,-6,-5,1,2]=>001100=>[2,2,2]=>[2,2,2]
[3,4,5,-6,1,2]=>000100=>[3,1,2]=>[2,1,3]
[-5,3,4,-6,1,2]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-4,3,5,-6,1,2]=>100100=>[1,2,1,2]=>[2,1,2,1]
[-5,-4,3,-6,1,2]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,5,-6,-2,1,3]=>001100=>[2,2,2]=>[2,2,2]
[4,5,-6,-3,-2,1]=>001110=>[2,3,1]=>[1,3,2]
[3,4,-5,-2,1,6]=>001100=>[2,2,2]=>[2,2,2]
[3,4,-6,-5,-2,1]=>001110=>[2,3,1]=>[1,3,2]
[3,4,5,-6,-2,1]=>000110=>[3,2,1]=>[1,2,3]
[-5,3,4,-6,-2,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-4,3,5,-6,-2,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-5,-4,3,-6,-2,1]=>110110=>[2,1,2,1]=>[1,2,1,2]
[2,4,5,-6,-3,1]=>000110=>[3,2,1]=>[1,2,3]
[2,3,-6,-4,1,5]=>001100=>[2,2,2]=>[2,2,2]
[2,3,5,-6,-4,1]=>000110=>[3,2,1]=>[1,2,3]
[-5,2,3,4,-6,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-4,2,3,-6,-5,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[-4,2,3,5,-6,1]=>100010=>[1,3,1,1]=>[1,1,3,1]
[-5,-4,2,3,-6,1]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,-5,2,3,-6,1]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,-5,-3,2,-6,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,2,5,6,7,8,3,4]=>00000000=>[8]=>[8]
[2,-4,-3,1,-6,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[-5,2,-3,6,1,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[2,-6,4,-3,-5,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[-2,1,4,-6,-5,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,-6,1,-3,-5,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,3,1,-4,2]=>000010=>[4,1,1]=>[1,1,4]
[-2,1,-4,3,-6,5,-8,7]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[3,4,1,2,-6,5,-8,7]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[2,-4,-3,1,-6,5,-8,7]=>01101010=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]
[-5,2,-3,6,1,4,-8,7]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[2,-6,4,-3,-5,1,-8,7]=>01011010=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]
[-7,2,4,-3,-5,8,1,6]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[2,-8,4,-3,6,-5,-7,1]=>01010110=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
[5,8,2,3,6,-4,-7,1]=>00000110=>[5,2,1]=>[1,2,5]
[5,2,7,3,-4,8,1,6]=>00001000=>[4,1,3]=>[3,1,4]
[5,6,2,3,-4,1,-8,7]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[2,-5,-4,6,1,3,-8,7]=>01100010=>[1,2,3,1,1]=>[1,1,3,2,1]
[1,4,5,6,2,3,-8,7]=>00000010=>[6,1,1]=>[1,1,6]
[5,6,1,-3,2,4,-8,7]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[-2,-5,1,6,3,4,-8,7]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[-2,1,4,-6,-5,3,-8,7]=>10011010=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]
[4,-6,1,-3,-5,2,-8,7]=>01011010=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]
[5,6,3,1,-4,2,-8,7]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[5,6,-4,3,1,2,-8,7]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[3,2,-6,-5,-4,1,-8,7]=>00111010=>[2,3,1,1,1]=>[1,1,1,3,2]
[3,-7,2,-5,-4,8,1,6]=>01011000=>[1,1,1,2,3]=>[3,2,1,1,1]
[3,2,-8,-5,6,-4,-7,1]=>00110110=>[2,2,1,2,1]=>[1,2,1,2,2]
[7,-3,8,-6,2,5,-4,1]=>01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
[-7,3,8,-6,2,-4,1,5]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[-4,6,7,3,1,8,2,5]=>10000000=>[1,7]=>[7,1]
[-7,3,8,-5,1,-4,2,6]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[5,3,7,1,-4,8,2,6]=>00001000=>[4,1,3]=>[3,1,4]
[-7,4,1,-3,-5,8,2,6]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[-2,1,-7,4,-5,8,3,6]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[-2,1,4,-8,6,-5,-7,3]=>10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
[4,-8,1,-3,6,-5,-7,2]=>01010110=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
[5,8,3,1,6,-4,-7,2]=>00000110=>[5,2,1]=>[1,2,5]
[3,6,-8,-5,1,-4,-7,2]=>00110110=>[2,2,1,2,1]=>[1,2,1,2,2]
[7,-3,8,-6,5,1,-4,2]=>01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
[7,8,-4,3,-6,5,1,2]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[3,5,-8,2,-7,-4,-6,1]=>00101110=>[2,1,1,3,1]=>[1,3,1,1,2]
[7,8,3,4,2,-6,-5,1]=>00000110=>[5,2,1]=>[1,2,5]
[7,8,-3,-6,4,1,-5,2]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[1,6,7,8,3,4,-5,2]=>00000010=>[6,1,1]=>[1,1,6]
[7,8,3,1,-6,5,-4,2]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[-7,8,-3,1,4,5,-6,2]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[-2,-7,1,8,4,5,-6,3]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[-2,1,4,-7,-6,8,3,5]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[7,8,1,4,-6,-3,2,5]=>00001100=>[4,2,2]=>[2,2,4]
[3,-7,8,-6,1,-4,2,5]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[3,6,7,8,-5,1,2,4]=>00001000=>[4,1,3]=>[3,1,4]
[3,8,-7,-6,-5,2,1,4]=>00111000=>[2,3,3]=>[3,3,2]
[7,8,-3,-6,2,4,-5,1]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[5,6,7,8,3,4,-2,1]=>00000010=>[6,1,1]=>[1,1,6]
[2,6,7,8,-5,3,1,4]=>00001000=>[4,1,3]=>[3,1,4]
[-6,2,-5,7,1,8,3,4]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[-4,6,7,8,1,2,3,5]=>10000000=>[1,7]=>[7,1]
[1,6,7,-3,2,8,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[-6,-2,1,3,7,8,4,5]=>11000000=>[2,6]=>[6,2]
[-2,-7,1,8,3,-5,4,6]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[7,8,1,-3,2,-5,4,6]=>00010100=>[3,1,1,1,2]=>[2,1,1,1,3]
[5,1,7,8,2,-4,3,6]=>00000100=>[5,1,2]=>[2,1,5]
[2,-7,8,-5,1,-4,3,6]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[-6,2,-4,1,7,8,3,5]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[2,-7,8,-6,3,-4,1,5]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[7,8,2,3,-6,5,-4,1]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[-7,2,-3,8,4,5,-6,1]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[-7,2,4,8,-6,-3,1,5]=>10001100=>[1,3,2,2]=>[2,2,3,1]
[6,2,-3,1,7,8,4,5]=>00100000=>[2,1,5]=>[5,1,2]
[-7,2,-3,8,1,-5,4,6]=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[2,-4,-3,-7,1,8,5,6]=>01110000=>[1,3,4]=>[4,3,1]
[3,4,1,-7,2,8,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[-2,1,-4,-7,3,8,5,6]=>10110000=>[1,1,2,4]=>[4,2,1,1]
[-2,1,-4,3,6,-8,-7,5]=>10100110=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]
[3,4,1,2,6,-8,-7,5]=>00000110=>[5,2,1]=>[1,2,5]
[2,-4,-3,1,6,-8,-7,5]=>01100110=>[1,2,2,2,1]=>[1,2,2,2,1]
[2,-8,6,-3,1,-5,-7,4]=>01010110=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
[-7,2,-3,8,5,1,-6,4]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[-7,2,-3,8,-6,5,1,4]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[2,-8,5,4,-3,-7,-6,1]=>01001110=>[1,1,2,3,1]=>[1,3,2,1,1]
[5,2,-8,3,-7,-4,-6,1]=>00101110=>[2,1,1,3,1]=>[1,3,1,1,2]
[2,-7,-4,8,-6,5,1,3]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[2,-7,8,-6,5,1,-4,3]=>01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
[6,2,-8,-5,1,-4,-7,3]=>00110110=>[2,2,1,2,1]=>[1,2,1,2,2]
[5,8,6,1,2,-4,-7,3]=>00000110=>[5,2,1]=>[1,2,5]
[6,-8,1,-3,2,-5,-7,4]=>01010110=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
[-2,1,6,-8,3,-5,-7,4]=>10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
[-2,-7,1,8,5,3,-6,4]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[7,8,1,-3,5,2,-6,4]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[7,8,5,1,-6,2,-4,3]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[1,6,7,8,4,2,-5,3]=>00000010=>[6,1,1]=>[1,1,6]
[2,8,-7,-6,4,1,-5,3]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[2,6,7,-5,8,4,1,3]=>00010000=>[3,1,4]=>[4,1,3]
[7,8,4,2,3,-6,-5,1]=>00000110=>[5,2,1]=>[1,2,5]
[7,8,4,-6,2,3,-5,1]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[2,8,-7,-6,-5,4,1,3]=>00111000=>[2,3,3]=>[3,3,2]
[1,6,7,8,-5,4,2,3]=>00001000=>[4,1,3]=>[3,1,4]
[7,8,5,-4,-6,1,2,3]=>00011000=>[3,2,3]=>[3,2,3]
[7,8,1,-3,-6,5,2,4]=>00011000=>[3,2,3]=>[3,2,3]
[-2,-7,1,8,-6,5,3,4]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[-2,1,5,4,-8,-7,-6,3]=>10001110=>[1,3,3,1]=>[1,3,3,1]
[5,-8,1,4,-3,-7,-6,2]=>01001110=>[1,1,2,3,1]=>[1,3,2,1,1]
[5,3,-8,1,-7,-4,-6,2]=>00101110=>[2,1,1,3,1]=>[1,3,1,1,2]
[7,8,4,3,1,-6,-5,2]=>00000110=>[5,2,1]=>[1,2,5]
[7,8,4,-6,3,1,-5,2]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[7,8,4,-6,-5,3,1,2]=>00011000=>[3,2,3]=>[3,2,3]
[4,3,2,-8,-7,-6,-5,1]=>00011110=>[3,4,1]=>[1,4,3]
[2,-3,-5,-4,-6,1]=>011110=>[1,4,1]=>[1,4,1]
[2,-4,-3,-5,-6,1]=>011110=>[1,4,1]=>[1,4,1]
[4,2,-6,-3,-5,1]=>001110=>[2,3,1]=>[1,3,2]
[-5,2,-3,-4,-6,1]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,2,-4,-3,-6,1]=>001110=>[2,3,1]=>[1,3,2]
[6,-4,2,-3,-5,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,-2,-6,-5,1]=>001110=>[2,3,1]=>[1,3,2]
[5,3,-2,-4,-6,1]=>001110=>[2,3,1]=>[1,3,2]
[6,-2,3,-4,-5,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,3,-2,-4,1]=>000110=>[3,2,1]=>[1,2,3]
[-2,6,4,-3,-5,1]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,6,4,-2,-5,1]=>000110=>[3,2,1]=>[1,2,3]
[2,-4,5,-3,-6,1]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,-4,-3,6,-5,1]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,-2,6,-4,1]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,-4,-6,-5,2]=>001110=>[2,3,1]=>[1,3,2]
[1,3,-5,-4,-6,2]=>001110=>[2,3,1]=>[1,3,2]
[1,-6,3,-4,-5,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,3,-5,-4,2]=>000110=>[3,2,1]=>[1,2,3]
[1,6,4,-3,-5,2]=>000110=>[3,2,1]=>[1,2,3]
[1,3,-5,6,-4,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,4,-6,-5,3]=>000110=>[3,2,1]=>[1,2,3]
[2,-4,-3,-5,1,6]=>011100=>[1,3,2]=>[2,3,1]
[5,3,-2,-4,1,6]=>001100=>[2,2,2]=>[2,2,2]
[1,3,-5,-4,2,6]=>001100=>[2,2,2]=>[2,2,2]
[-2,-5,-3,6,1,4]=>111000=>[3,3]=>[3,3]
[-5,4,1,-3,-6,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,-4,3,1,-6,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[-2,-3,-4,1,-6,5,-8,7]=>11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
[-2,-5,-3,6,1,4,-8,7]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[-2,-5,4,-3,-6,1,-8,7]=>11011010=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]
[-2,-5,4,-7,-3,8,1,6]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[-2,-5,-3,4,6,-7,-8,1]=>11100110=>[3,2,2,1]=>[1,2,2,3]
[7,5,2,3,6,-4,-8,1]=>00000110=>[5,2,1]=>[1,2,5]
[4,5,2,-7,3,8,1,6]=>00010000=>[3,1,4]=>[4,1,3]
[4,5,2,3,-6,1,-8,7]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[6,-4,-5,2,1,3,-8,7]=>01100010=>[1,2,3,1,1]=>[1,1,3,2,1]
[-2,1,-4,-5,-6,3,-8,7]=>10111010=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]
[-5,4,1,-3,-6,2,-8,7]=>10011010=>[1,2,2,1,1,1]=>[1,1,1,2,2,1]
[5,-4,3,1,-6,2,-8,7]=>01001010=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]
[4,-6,-5,3,1,2,-8,7]=>01100010=>[1,2,3,1,1]=>[1,1,3,2,1]
[-2,-3,-4,-5,-6,1,-8,7]=>11111010=>[5,1,1,1]=>[1,1,1,5]
[-2,-3,-4,-7,-5,8,1,6]=>11111000=>[5,3]=>[3,5]
[-2,-3,-4,-7,6,-5,-8,1]=>11110110=>[4,1,2,1]=>[1,2,1,4]
[-7,-3,-8,-6,2,5,-4,1]=>11110010=>[4,2,1,1]=>[1,1,2,4]
[8,-3,-4,-6,-7,2,1,5]=>01111000=>[1,4,3]=>[3,4,1]
[-7,-6,4,3,1,8,2,5]=>11000000=>[2,6]=>[6,2]
[-3,8,-7,-4,1,-5,2,6]=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
[5,-4,3,-7,1,8,2,6]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[-5,4,1,-7,-3,8,2,6]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[-2,1,-4,-7,-5,8,3,6]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[-2,1,-4,-7,6,-5,-8,3]=>10110110=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]
[-5,4,-3,1,6,-7,-8,2]=>10100110=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]
[-4,5,3,1,6,-7,-8,2]=>10000110=>[1,4,2,1]=>[1,2,4,1]
[6,-3,-7,-4,1,-5,-8,2]=>01110110=>[1,3,1,2,1]=>[1,2,1,3,1]
[-3,-4,-8,7,5,1,-6,2]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[-6,-8,4,3,-7,5,1,2]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[-5,-3,-6,2,-7,-4,-8,1]=>11101110=>[3,1,3,1]=>[1,3,1,3]
[-5,6,3,4,2,-7,-8,1]=>10000110=>[1,4,2,1]=>[1,2,4,1]
[3,7,-5,-8,4,1,-6,2]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[5,1,6,7,3,4,-8,2]=>00000010=>[6,1,1]=>[1,1,6]
[7,-6,3,1,-8,5,-4,2]=>01001010=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]
[-6,-3,1,7,4,5,-8,2]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[-7,-2,-6,1,4,5,-8,3]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[-2,-8,1,-6,-7,4,3,5]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[6,1,8,4,-7,-3,2,5]=>00001100=>[4,2,2]=>[2,2,4]
[-8,-6,3,1,-7,-4,2,5]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[5,6,3,8,-7,1,2,4]=>00001000=>[4,1,3]=>[3,1,4]
[7,-6,5,8,3,1,2,4]=>01000000=>[1,1,6]=>[6,1,1]
[-8,-3,-5,-6,-7,2,1,4]=>11111000=>[5,3]=>[3,5]
[-7,3,-5,-8,2,4,-6,1]=>10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1]
[5,8,6,7,3,4,-2,1]=>00000010=>[6,1,1]=>[1,1,6]
[2,5,6,8,-7,3,1,4]=>00001000=>[4,1,3]=>[3,1,4]
[2,-5,-6,7,1,8,3,4]=>01100000=>[1,2,5]=>[5,2,1]
[8,-7,2,-4,1,-5,3,6]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[-4,-6,7,2,1,8,3,5]=>11000000=>[2,6]=>[6,2]
[2,-6,8,3,-7,-4,1,5]=>01001100=>[1,1,2,2,2]=>[2,2,2,1,1]
[-6,2,7,-4,3,5,-8,1]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[-6,2,-3,7,4,5,-8,1]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[-6,-2,4,8,-7,-3,1,5]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[-6,-2,-3,1,7,8,4,5]=>11100000=>[3,5]=>[5,3]
[-2,-7,-3,8,1,-5,4,6]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[-2,-3,-4,-7,1,8,5,6]=>11110000=>[4,4]=>[4,4]
[-2,1,-4,3,-6,-7,-8,5]=>10101110=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[3,4,1,2,-6,-7,-8,5]=>00001110=>[4,3,1]=>[1,3,4]
[-2,-3,-4,1,-6,-7,-8,5]=>11101110=>[3,1,3,1]=>[1,3,1,3]
[-2,-3,-7,6,1,-5,-8,4]=>11100110=>[3,2,2,1]=>[1,2,2,3]
[-2,-7,-3,-6,5,1,-8,4]=>11110010=>[4,2,1,1]=>[1,1,2,4]
[-2,-6,-3,-8,-7,5,1,4]=>11111000=>[5,3]=>[3,5]
[-2,-5,4,-3,-6,-7,-8,1]=>11011110=>[2,1,4,1]=>[1,4,1,2]
[-6,5,2,3,-4,-7,-8,1]=>10001110=>[1,3,3,1]=>[1,3,3,1]
[-8,6,-4,2,-7,5,1,3]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[7,-8,-4,2,5,1,-6,3]=>01100010=>[1,2,3,1,1]=>[1,1,3,2,1]
[6,2,-7,-4,1,-5,-8,3]=>00110110=>[2,2,1,2,1]=>[1,2,1,2,2]
[5,7,1,6,2,-4,-8,3]=>00000110=>[5,2,1]=>[1,2,5]
[-7,6,1,-3,2,-5,-8,4]=>10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
[-2,1,-7,6,3,-5,-8,4]=>10100110=>[1,1,1,2,2,1]=>[1,2,2,1,1,1]
[-2,-7,1,-6,5,3,-8,4]=>11010010=>[2,1,1,2,1,1]=>[1,1,2,1,1,2]
[7,5,1,-6,-3,2,-8,4]=>00011010=>[3,2,1,1,1]=>[1,1,1,2,3]
[8,7,1,5,-6,2,-4,3]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[5,6,7,1,4,2,-8,3]=>00000010=>[6,1,1]=>[1,1,6]
[4,-7,-5,-6,2,1,-8,3]=>01110010=>[1,3,2,1,1]=>[1,1,2,3,1]
[-8,5,6,-7,2,4,1,3]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[6,4,-5,2,3,-7,-8,1]=>00100110=>[2,1,2,2,1]=>[1,2,2,1,2]
[5,4,-7,-6,2,3,-8,1]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[4,-5,-8,-6,-7,2,1,3]=>01111000=>[1,4,3]=>[3,4,1]
[7,8,-6,5,1,4,2,3]=>00100000=>[2,1,5]=>[5,1,2]
[5,8,6,1,-7,4,2,3]=>00001000=>[4,1,3]=>[3,1,4]
[8,1,6,-4,-7,5,2,3]=>00011000=>[3,2,3]=>[3,2,3]
[6,5,1,-8,-7,-3,2,4]=>00011100=>[3,3,2]=>[2,3,3]
[-2,-6,1,-8,-7,5,3,4]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[-2,1,-4,-5,-6,-7,-8,3]=>10111110=>[1,1,5,1]=>[1,5,1,1]
[-5,4,1,-3,-6,-7,-8,2]=>10011110=>[1,2,4,1]=>[1,4,2,1]
[-5,-6,3,1,-4,-7,-8,2]=>11001110=>[2,2,3,1]=>[1,3,2,2]
[4,-6,-5,3,1,-7,-8,2]=>01100110=>[1,2,2,2,1]=>[1,2,2,2,1]
[4,-5,-7,-6,3,1,-8,2]=>01110010=>[1,3,2,1,1]=>[1,1,2,3,1]
[4,-5,-6,-8,-7,3,1,2]=>01111000=>[1,4,3]=>[3,4,1]
[-2,-3,-4,-5,-6,-7,-8,1]=>11111110=>[7,1]=>[1,7]
[-2,-3,5,1,4,6]=>110000=>[2,4]=>[4,2]
[-4,-2,5,1,3,6]=>110000=>[2,4]=>[4,2]
[-5,2,4,1,3,6]=>100000=>[1,5]=>[5,1]
[-2,-3,1,6,4,5]=>110000=>[2,4]=>[4,2]
[-4,-2,1,6,3,5]=>110000=>[2,4]=>[4,2]
[-4,3,1,6,2,5]=>100000=>[1,5]=>[5,1]
[5,-2,1,6,3,4]=>010000=>[1,1,4]=>[4,1,1]
[6,2,-3,5,1,4]=>001000=>[2,1,3]=>[3,1,2]
[6,-4,2,5,1,3]=>010000=>[1,1,4]=>[4,1,1]
[-4,6,3,5,1,2]=>100000=>[1,5]=>[5,1]
[2,-5,6,4,1,3]=>010000=>[1,1,4]=>[4,1,1]
[-2,-3,-4,6,1,5]=>111000=>[3,3]=>[3,3]
[-4,-5,-2,6,1,3]=>111000=>[3,3]=>[3,3]
[-6,-2,-3,5,1,4]=>111000=>[3,3]=>[3,3]
[-6,-4,-2,5,1,3]=>111000=>[3,3]=>[3,3]
[5,-6,2,4,1,3]=>010000=>[1,1,4]=>[4,1,1]
[6,4,3,-1,2,5]=>000100=>[3,1,2]=>[2,1,3]
[4,-1,2,6,5,3]=>010000=>[1,1,4]=>[4,1,1]
[5,-1,6,2,4,3]=>010000=>[1,1,4]=>[4,1,1]
[5,4,3,2,7,6,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[6,4,3,7,2,5,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[7,4,3,6,5,2,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[8,4,3,6,5,-1,2,7]=>00000100=>[5,1,2]=>[2,1,5]
[-1,4,3,6,5,8,7,2]=>10000000=>[1,7]=>[7,1]
[-1,5,6,3,4,8,7,2]=>10000000=>[1,7]=>[7,1]
[8,5,6,3,4,-1,2,7]=>00000100=>[5,1,2]=>[2,1,5]
[7,5,6,3,4,2,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[6,5,7,3,2,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[3,2,7,6,5,4,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[4,7,2,6,5,3,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[5,7,6,2,4,3,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[6,7,5,4,2,3,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[7,6,5,4,3,2,-1,8]=>00000010=>[6,1,1]=>[1,1,6]
[8,6,5,4,3,-1,2,7]=>00000100=>[5,1,2]=>[2,1,5]
[-1,6,5,4,3,8,7,2]=>10000000=>[1,7]=>[7,1]
[-1,7,5,4,8,3,6,2]=>10000000=>[1,7]=>[7,1]
[8,7,5,4,-1,3,2,6]=>00001000=>[4,1,3]=>[3,1,4]
[7,8,5,4,-1,2,3,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,8,5,4,2,-1,3,7]=>00000100=>[5,1,2]=>[2,1,5]
[5,8,6,2,4,-1,3,7]=>00000100=>[5,1,2]=>[2,1,5]
[4,8,2,6,5,-1,3,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,8,6,5,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,-1,6,5,8,7,4]=>00100000=>[2,1,5]=>[5,1,2]
[4,-1,2,6,5,8,7,3]=>01000000=>[1,1,6]=>[6,1,1]
[5,-1,6,2,4,8,7,3]=>01000000=>[1,1,6]=>[6,1,1]
[6,-1,5,4,2,8,7,3]=>01000000=>[1,1,6]=>[6,1,1]
[7,-1,5,4,8,2,6,3]=>01000000=>[1,1,6]=>[6,1,1]
[8,-1,5,4,7,6,2,3]=>01000000=>[1,1,6]=>[6,1,1]
[-1,8,5,4,7,6,3,2]=>10000000=>[1,7]=>[7,1]
[-1,8,6,7,4,5,3,2]=>10000000=>[1,7]=>[7,1]
[8,-1,6,7,4,5,2,3]=>01000000=>[1,1,6]=>[6,1,1]
[7,-1,6,8,4,2,5,3]=>01000000=>[1,1,6]=>[6,1,1]
[6,-1,7,8,2,4,5,3]=>01000000=>[1,1,6]=>[6,1,1]
[5,-1,7,2,8,4,6,3]=>01000000=>[1,1,6]=>[6,1,1]
[4,-1,2,7,8,5,6,3]=>01000000=>[1,1,6]=>[6,1,1]
[3,2,-1,7,8,5,6,4]=>00100000=>[2,1,5]=>[5,1,2]
[3,2,8,7,-1,5,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[4,8,2,7,-1,5,3,6]=>00001000=>[4,1,3]=>[3,1,4]
[5,8,7,2,-1,4,3,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,8,7,-1,2,4,3,5]=>00010000=>[3,1,4]=>[4,1,3]
[7,8,6,-1,4,2,3,5]=>00010000=>[3,1,4]=>[4,1,3]
[8,7,6,-1,4,3,2,5]=>00010000=>[3,1,4]=>[4,1,3]
[-1,7,6,8,4,3,5,2]=>10000000=>[1,7]=>[7,1]
[-1,6,7,8,3,4,5,2]=>10000000=>[1,7]=>[7,1]
[8,6,7,-1,3,4,2,5]=>00010000=>[3,1,4]=>[4,1,3]
[7,6,8,-1,3,2,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[6,5,8,3,2,-1,4,7]=>00000100=>[5,1,2]=>[2,1,5]
[7,5,8,3,-1,2,4,6]=>00001000=>[4,1,3]=>[3,1,4]
[8,5,7,3,-1,4,2,6]=>00001000=>[4,1,3]=>[3,1,4]
[-1,5,7,3,8,4,6,2]=>10000000=>[1,7]=>[7,1]
[-1,4,3,7,8,5,6,2]=>10000000=>[1,7]=>[7,1]
[8,4,3,7,-1,5,2,6]=>00001000=>[4,1,3]=>[3,1,4]
[7,4,3,8,-1,2,5,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,4,3,8,2,-1,5,7]=>00000100=>[5,1,2]=>[2,1,5]
[5,4,3,2,8,-1,6,7]=>00000100=>[5,1,2]=>[2,1,5]
[3,2,5,4,-1,8,7,6]=>00001000=>[4,1,3]=>[3,1,4]
[4,5,2,3,-1,8,7,6]=>00001000=>[4,1,3]=>[3,1,4]
[5,4,3,2,-1,8,7,6]=>00001000=>[4,1,3]=>[3,1,4]
[6,4,3,-1,2,8,7,5]=>00010000=>[3,1,4]=>[4,1,3]
[7,4,3,-1,8,2,6,5]=>00010000=>[3,1,4]=>[4,1,3]
[8,4,3,-1,7,6,2,5]=>00010000=>[3,1,4]=>[4,1,3]
[-1,4,3,8,7,6,5,2]=>10000000=>[1,7]=>[7,1]
[-1,5,8,3,7,6,4,2]=>10000000=>[1,7]=>[7,1]
[8,5,-1,3,7,6,2,4]=>00100000=>[2,1,5]=>[5,1,2]
[7,5,-1,3,8,2,6,4]=>00100000=>[2,1,5]=>[5,1,2]
[6,5,-1,3,2,8,7,4]=>00100000=>[2,1,5]=>[5,1,2]
[5,6,-1,2,3,8,7,4]=>00100000=>[2,1,5]=>[5,1,2]
[4,6,2,-1,3,8,7,5]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,6,-1,4,8,7,5]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,7,-1,8,4,6,5]=>00010000=>[3,1,4]=>[4,1,3]
[4,7,2,-1,8,3,6,5]=>00010000=>[3,1,4]=>[4,1,3]
[5,7,-1,2,8,3,6,4]=>00100000=>[2,1,5]=>[5,1,2]
[6,7,-1,8,2,3,5,4]=>00100000=>[2,1,5]=>[5,1,2]
[7,6,-1,8,3,2,5,4]=>00100000=>[2,1,5]=>[5,1,2]
[8,6,-1,7,3,5,2,4]=>00100000=>[2,1,5]=>[5,1,2]
[-1,6,8,7,3,5,4,2]=>10000000=>[1,7]=>[7,1]
[-1,7,8,6,5,3,4,2]=>10000000=>[1,7]=>[7,1]
[8,7,-1,6,5,3,2,4]=>00100000=>[2,1,5]=>[5,1,2]
[7,8,-1,6,5,2,3,4]=>00100000=>[2,1,5]=>[5,1,2]
[6,8,-1,7,2,5,3,4]=>00100000=>[2,1,5]=>[5,1,2]
[5,8,-1,2,7,6,3,4]=>00100000=>[2,1,5]=>[5,1,2]
[4,8,2,-1,7,6,3,5]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,8,-1,7,6,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[3,2,-1,8,7,6,5,4]=>00100000=>[2,1,5]=>[5,1,2]
[4,-1,2,8,7,6,5,3]=>01000000=>[1,1,6]=>[6,1,1]
[5,-1,8,2,7,6,4,3]=>01000000=>[1,1,6]=>[6,1,1]
[6,-1,8,7,2,5,4,3]=>01000000=>[1,1,6]=>[6,1,1]
[7,-1,8,6,5,2,4,3]=>01000000=>[1,1,6]=>[6,1,1]
[8,-1,7,6,5,4,2,3]=>01000000=>[1,1,6]=>[6,1,1]
[-1,8,7,6,5,4,3,2]=>10000000=>[1,7]=>[7,1]
[5,3,2,6,4,-1]=>000001=>[5,1]=>[1,5]
[5,3,6,2,4,-1]=>000001=>[5,1]=>[1,5]
[5,3,6,4,2,-1]=>000001=>[5,1]=>[1,5]
[5,3,2,6,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[5,3,6,2,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[5,6,3,2,-1,4]=>000010=>[4,1,1]=>[1,1,4]
[5,3,6,-1,2,4]=>000100=>[3,1,2]=>[2,1,3]
[5,6,3,-1,2,4]=>000100=>[3,1,2]=>[2,1,3]
[5,3,6,4,-1,2]=>000010=>[4,1,1]=>[1,1,4]
[5,3,6,-1,4,2]=>000100=>[3,1,2]=>[2,1,3]
[6,4,2,-1,5,3]=>000100=>[3,1,2]=>[2,1,3]
[6,4,-1,2,5,3]=>001000=>[2,1,3]=>[3,1,2]
[6,-1,4,2,5,3]=>010000=>[1,1,4]=>[4,1,1]
[6,4,-1,5,2,3]=>001000=>[2,1,3]=>[3,1,2]
[6,4,3,2,-1,5]=>000010=>[4,1,1]=>[1,1,4]
[6,4,-1,3,2,5]=>001000=>[2,1,3]=>[3,1,2]
[6,4,3,-1,5,2]=>000100=>[3,1,2]=>[2,1,3]
[6,4,-1,3,5,2]=>001000=>[2,1,3]=>[3,1,2]
[6,4,-1,5,3,2]=>001000=>[2,1,3]=>[3,1,2]
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 $w$.
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
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