Identifier
Mp00094: Integer compositions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-3
[1]=>1=>[1,1]=>[1,0,1,0] [1,1]=>11=>[1,1,1]=>[1,0,1,0,1,0] [2]=>10=>[1,2]=>[1,0,1,1,0,0] [1,1,1]=>111=>[1,1,1,1]=>[1,0,1,0,1,0,1,0] [1,2]=>110=>[1,1,2]=>[1,0,1,0,1,1,0,0] [2,1]=>101=>[1,2,1]=>[1,0,1,1,0,0,1,0] [3]=>100=>[1,3]=>[1,0,1,1,1,0,0,0] [1,1,1,1]=>1111=>[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0] [1,1,2]=>1110=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0] [1,2,1]=>1101=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0] [1,3]=>1100=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [2,1,1]=>1011=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0] [2,2]=>1010=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0] [3,1]=>1001=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0] [4]=>1000=>[1,4]=>[1,0,1,1,1,1,0,0,0,0] [1,1,1,1,1]=>11111=>[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,2]=>11110=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0] [1,1,2,1]=>11101=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0] [1,1,3]=>11100=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [1,2,1,1]=>11011=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0] [1,2,2]=>11010=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [1,3,1]=>11001=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [1,4]=>11000=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [2,1,1,1]=>10111=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0] [2,1,2]=>10110=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [2,2,1]=>10101=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [2,3]=>10100=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [3,1,1]=>10011=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0] [3,2]=>10010=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [4,1]=>10001=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0] [5]=>10000=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0] [1,1,1,1,1,1]=>111111=>[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,2]=>111110=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,1,2,1]=>111101=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,1,3]=>111100=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [1,1,2,1,1]=>111011=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,2,2]=>111010=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,1,3,1]=>111001=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [1,1,4]=>111000=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [1,2,1,1,1]=>110111=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,2,1,2]=>110110=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,2,2,1]=>110101=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [1,2,3]=>110100=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [1,3,1,1]=>110011=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [1,3,2]=>110010=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [1,4,1]=>110001=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [1,5]=>110000=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [2,1,1,1,1]=>101111=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0] [2,1,1,2]=>101110=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [2,1,2,1]=>101101=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [2,1,3]=>101100=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [2,2,1,1]=>101011=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [2,2,2]=>101010=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [2,3,1]=>101001=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [2,4]=>101000=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [3,1,1,1]=>100111=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0] [3,1,2]=>100110=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [3,2,1]=>100101=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [3,3]=>100100=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [4,1,1]=>100011=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0] [4,2]=>100010=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [5,1]=>100001=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0] [6]=>100000=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [1,1,1,1,1,1,1]=>1111111=>[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,2]=>1111110=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,1,1,2,1]=>1111101=>[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,1,1,3]=>1111100=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [1,1,1,2,1,1]=>1111011=>[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,2,2]=>1111010=>[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,1,1,3,1]=>1111001=>[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] [1,1,1,4]=>1111000=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [1,1,2,1,1,1]=>1110111=>[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,1,2,1,2]=>1110110=>[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,1,2,2,1]=>1110101=>[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] [1,1,2,3]=>1110100=>[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [1,1,3,1,1]=>1110011=>[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] [1,1,3,2]=>1110010=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] [1,1,4,1]=>1110001=>[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] [1,1,5]=>1110000=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [1,2,1,1,1,1]=>1101111=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,2,1,1,2]=>1101110=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] [1,2,1,2,1]=>1101101=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] [1,2,1,3]=>1101100=>[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] [1,2,2,1,1]=>1101011=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] [1,2,2,2]=>1101010=>[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [1,2,3,1]=>1101001=>[1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] [1,2,4]=>1101000=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [1,3,1,1,1]=>1100111=>[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] [1,3,1,2]=>1100110=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] [1,3,2,1]=>1100101=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] [1,3,3]=>1100100=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [1,4,1,1]=>1100011=>[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] [1,4,2]=>1100010=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] [1,5,1]=>1100001=>[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] [1,6]=>1100000=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [2,1,1,1,1,1]=>1011111=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [2,1,1,1,2]=>1011110=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] [2,1,1,2,1]=>1011101=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] [2,1,1,3]=>1011100=>[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] [2,1,2,1,1]=>1011011=>[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] [2,1,2,2]=>1011010=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] [2,1,3,1]=>1011001=>[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] [2,1,4]=>1011000=>[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] [2,2,1,1,1]=>1010111=>[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] [2,2,1,2]=>1010110=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] [2,2,2,1]=>1010101=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] [2,2,3]=>1010100=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [2,3,1,1]=>1010011=>[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] [2,3,2]=>1010010=>[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] [2,4,1]=>1010001=>[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] [2,5]=>1010000=>[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [3,1,1,1,1]=>1001111=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] [3,1,1,2]=>1001110=>[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] [3,1,2,1]=>1001101=>[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] [3,1,3]=>1001100=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] [3,2,1,1]=>1001011=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] [3,2,2]=>1001010=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] [3,3,1]=>1001001=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] [3,4]=>1001000=>[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [4,1,1,1]=>1000111=>[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] [4,1,2]=>1000110=>[1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] [4,2,1]=>1000101=>[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] [4,3]=>1000100=>[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] [5,1,1]=>1000011=>[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] [5,2]=>1000010=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [6,1]=>1000001=>[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] [7]=>1000000=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1]=>11111111=>[1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,2]=>11111110=>[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,1,1,1,2,1]=>11111101=>[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,1,1,1,3]=>11111100=>[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [1,1,1,1,2,1,1]=>11111011=>[1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,1,2,2]=>11111010=>[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,1,1,1,3,1]=>11111001=>[1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] [1,1,1,1,4]=>11111000=>[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [1,1,1,2,1,1,1]=>11110111=>[1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,1,1,2,1,2]=>11110110=>[1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,1,1,2,2,1]=>11110101=>[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] [1,1,1,2,3]=>11110100=>[1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [1,1,1,3,1,1]=>11110011=>[1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] [1,1,1,3,2]=>11110010=>[1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] [1,1,1,4,1]=>11110001=>[1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] [1,1,1,5]=>11110000=>[1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [1,1,2,1,1,1,1]=>11101111=>[1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,1,2,1,1,2]=>11101110=>[1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] [1,1,2,1,2,1]=>11101101=>[1,1,1,2,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] [1,1,2,1,3]=>11101100=>[1,1,1,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] [1,1,2,2,1,1]=>11101011=>[1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] [1,1,2,2,2]=>11101010=>[1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [1,1,2,3,1]=>11101001=>[1,1,1,2,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] [1,1,2,4]=>11101000=>[1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [1,1,3,1,1,1]=>11100111=>[1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] [1,1,3,1,2]=>11100110=>[1,1,1,3,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] [1,1,3,2,1]=>11100101=>[1,1,1,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] [1,1,3,3]=>11100100=>[1,1,1,3,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [1,1,4,1,1]=>11100011=>[1,1,1,4,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] [1,1,4,2]=>11100010=>[1,1,1,4,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] [1,1,5,1]=>11100001=>[1,1,1,5,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] [1,1,6]=>11100000=>[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [1,2,1,1,1,1,1]=>11011111=>[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,2,1,1,1,2]=>11011110=>[1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] [1,2,1,1,2,1]=>11011101=>[1,1,2,1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] [1,2,1,1,3]=>11011100=>[1,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] [1,2,1,2,1,1]=>11011011=>[1,1,2,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] [1,2,1,2,2]=>11011010=>[1,1,2,1,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] [1,2,1,3,1]=>11011001=>[1,1,2,1,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] [1,2,1,4]=>11011000=>[1,1,2,1,4]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] [1,2,2,1,1,1]=>11010111=>[1,1,2,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] [1,2,2,1,2]=>11010110=>[1,1,2,2,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] [1,2,2,2,1]=>11010101=>[1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] [1,2,2,3]=>11010100=>[1,1,2,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [1,2,3,1,1]=>11010011=>[1,1,2,3,1,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] [1,2,3,2]=>11010010=>[1,1,2,3,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] [1,2,4,1]=>11010001=>[1,1,2,4,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] [1,2,5]=>11010000=>[1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [1,3,1,1,1,1]=>11001111=>[1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] [1,3,1,1,2]=>11001110=>[1,1,3,1,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] [1,3,1,2,1]=>11001101=>[1,1,3,1,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] [1,3,1,3]=>11001100=>[1,1,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] [1,3,2,1,1]=>11001011=>[1,1,3,2,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] [1,3,2,2]=>11001010=>[1,1,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] [1,3,3,1]=>11001001=>[1,1,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] [1,3,4]=>11001000=>[1,1,3,4]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [1,4,1,1,1]=>11000111=>[1,1,4,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] [1,4,1,2]=>11000110=>[1,1,4,1,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] [1,4,2,1]=>11000101=>[1,1,4,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] [1,4,3]=>11000100=>[1,1,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] [1,5,1,1]=>11000011=>[1,1,5,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] [1,5,2]=>11000010=>[1,1,5,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [1,6,1]=>11000001=>[1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] [1,7]=>11000000=>[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [2,1,1,1,1,1,1]=>10111111=>[1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,1,1,1,1,2]=>10111110=>[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [2,1,1,1,2,1]=>10111101=>[1,2,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] [2,1,1,1,3]=>10111100=>[1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] [2,1,1,2,1,1]=>10111011=>[1,2,1,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] [2,1,1,2,2]=>10111010=>[1,2,1,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] [2,1,1,3,1]=>10111001=>[1,2,1,1,3,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] [2,1,1,4]=>10111000=>[1,2,1,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] [2,1,2,1,1,1]=>10110111=>[1,2,1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] [2,1,2,1,2]=>10110110=>[1,2,1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] [2,1,2,2,1]=>10110101=>[1,2,1,2,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] [2,1,2,3]=>10110100=>[1,2,1,2,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] [2,1,3,1,1]=>10110011=>[1,2,1,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] [2,1,3,2]=>10110010=>[1,2,1,3,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] [2,1,4,1]=>10110001=>[1,2,1,4,1]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] [2,1,5]=>10110000=>[1,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] [2,2,1,1,1,1]=>10101111=>[1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] [2,2,1,1,2]=>10101110=>[1,2,2,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] [2,2,1,2,1]=>10101101=>[1,2,2,1,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] [2,2,1,3]=>10101100=>[1,2,2,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] [2,2,2,1,1]=>10101011=>[1,2,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] [2,2,2,2]=>10101010=>[1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [2,2,3,1]=>10101001=>[1,2,2,3,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] [2,2,4]=>10101000=>[1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [2,3,1,1,1]=>10100111=>[1,2,3,1,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] [2,3,1,2]=>10100110=>[1,2,3,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] [2,3,2,1]=>10100101=>[1,2,3,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] [2,3,3]=>10100100=>[1,2,3,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [2,4,1,1]=>10100011=>[1,2,4,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] [2,4,2]=>10100010=>[1,2,4,2]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] [2,5,1]=>10100001=>[1,2,5,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] [2,6]=>10100000=>[1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [3,1,1,1,1,1]=>10011111=>[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [3,1,1,1,2]=>10011110=>[1,3,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] [3,1,1,2,1]=>10011101=>[1,3,1,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] [3,1,1,3]=>10011100=>[1,3,1,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] [3,1,2,1,1]=>10011011=>[1,3,1,2,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] [3,1,2,2]=>10011010=>[1,3,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] [3,1,3,1]=>10011001=>[1,3,1,3,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] [3,1,4]=>10011000=>[1,3,1,4]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] [3,2,1,1,1]=>10010111=>[1,3,2,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] [3,2,1,2]=>10010110=>[1,3,2,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] [3,2,2,1]=>10010101=>[1,3,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] [3,2,3]=>10010100=>[1,3,2,3]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] [3,3,1,1]=>10010011=>[1,3,3,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] [3,3,2]=>10010010=>[1,3,3,2]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] [3,4,1]=>10010001=>[1,3,4,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] [3,5]=>10010000=>[1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [4,1,1,1,1]=>10001111=>[1,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] [4,1,1,2]=>10001110=>[1,4,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] [4,1,2,1]=>10001101=>[1,4,1,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] [4,1,3]=>10001100=>[1,4,1,3]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] [4,2,1,1]=>10001011=>[1,4,2,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] [4,2,2]=>10001010=>[1,4,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] [4,3,1]=>10001001=>[1,4,3,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] [4,4]=>10001000=>[1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [5,1,1,1]=>10000111=>[1,5,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] [5,1,2]=>10000110=>[1,5,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] [5,2,1]=>10000101=>[1,5,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] [5,3]=>10000100=>[1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] [6,1,1]=>10000011=>[1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] [6,2]=>10000010=>[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] [7,1]=>10000001=>[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] [8]=>10000000=>[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [1,1,1,1,1,1,1,1,1]=>111111111=>[1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,1,1,1,1,1,1,2]=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,1,1,1,1,1,2,1]=>111111101=>[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,1,1,1,1,1,3]=>111111100=>[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [1,1,1,1,1,2,1,1]=>111111011=>[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,1,1,1,1,2,2]=>111111010=>[1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,1,1,1,1,3,1]=>111111001=>[1,1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] [1,1,1,1,1,4]=>111111000=>[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [1,1,1,1,2,1,1,1]=>111110111=>[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,1,1,1,2,1,2]=>111110110=>[1,1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,1,1,1,2,2,1]=>111110101=>[1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] [1,1,1,1,2,3]=>111110100=>[1,1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [1,1,1,1,3,1,1]=>111110011=>[1,1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] [1,1,1,1,3,2]=>111110010=>[1,1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] [1,1,1,1,4,1]=>111110001=>[1,1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] [1,1,1,1,5]=>111110000=>[1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [1,1,1,2,1,1,1,1]=>111101111=>[1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,1,1,2,1,1,2]=>111101110=>[1,1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] [1,1,1,2,1,2,1]=>111101101=>[1,1,1,1,2,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] [1,1,1,2,1,3]=>111101100=>[1,1,1,1,2,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] [1,1,1,2,2,1,1]=>111101011=>[1,1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] [1,1,1,2,2,2]=>111101010=>[1,1,1,1,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [1,1,1,2,3,1]=>111101001=>[1,1,1,1,2,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] [1,1,1,2,4]=>111101000=>[1,1,1,1,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [1,1,1,3,1,1,1]=>111100111=>[1,1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] [1,1,1,3,1,2]=>111100110=>[1,1,1,1,3,1,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] [1,1,1,3,2,1]=>111100101=>[1,1,1,1,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] [1,1,1,3,3]=>111100100=>[1,1,1,1,3,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [1,1,1,4,1,1]=>111100011=>[1,1,1,1,4,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] [1,1,1,4,2]=>111100010=>[1,1,1,1,4,2]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] [1,1,1,5,1]=>111100001=>[1,1,1,1,5,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] [1,1,1,6]=>111100000=>[1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [1,1,2,1,1,1,1,1]=>111011111=>[1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [1,1,2,1,1,1,2]=>111011110=>[1,1,1,2,1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] [1,1,2,1,1,2,1]=>111011101=>[1,1,1,2,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] [1,1,2,1,1,3]=>111011100=>[1,1,1,2,1,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] [1,1,2,1,2,1,1]=>111011011=>[1,1,1,2,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] [1,1,2,1,2,2]=>111011010=>[1,1,1,2,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] [1,1,2,1,3,1]=>111011001=>[1,1,1,2,1,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] [1,1,2,1,4]=>111011000=>[1,1,1,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] [1,1,2,2,1,1,1]=>111010111=>[1,1,1,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] [1,1,2,2,1,2]=>111010110=>[1,1,1,2,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] [1,1,2,2,2,1]=>111010101=>[1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] [1,1,2,2,3]=>111010100=>[1,1,1,2,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [1,1,2,3,1,1]=>111010011=>[1,1,1,2,3,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] [1,1,2,3,2]=>111010010=>[1,1,1,2,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] [1,1,2,4,1]=>111010001=>[1,1,1,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] [1,1,2,5]=>111010000=>[1,1,1,2,5]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [1,1,3,1,1,1,1]=>111001111=>[1,1,1,3,1,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] [1,1,3,1,1,2]=>111001110=>[1,1,1,3,1,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] [1,1,3,1,2,1]=>111001101=>[1,1,1,3,1,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] [1,1,3,1,3]=>111001100=>[1,1,1,3,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] [1,1,3,2,1,1]=>111001011=>[1,1,1,3,2,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] [1,1,3,2,2]=>111001010=>[1,1,1,3,2,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] [1,1,3,3,1]=>111001001=>[1,1,1,3,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] [1,1,3,4]=>111001000=>[1,1,1,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [1,1,4,1,1,1]=>111000111=>[1,1,1,4,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] [1,1,4,1,2]=>111000110=>[1,1,1,4,1,2]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] [1,1,4,2,1]=>111000101=>[1,1,1,4,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] [1,1,4,3]=>111000100=>[1,1,1,4,3]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] [1,1,5,1,1]=>111000011=>[1,1,1,5,1,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] [1,1,5,2]=>111000010=>[1,1,1,5,2]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [1,1,6,1]=>111000001=>[1,1,1,6,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] [1,1,7]=>111000000=>[1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [1,2,1,1,1,1,1,1]=>110111111=>[1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [1,2,1,1,1,1,2]=>110111110=>[1,1,2,1,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [1,2,1,1,1,2,1]=>110111101=>[1,1,2,1,1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] [1,2,1,1,1,3]=>110111100=>[1,1,2,1,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] [1,2,1,1,2,1,1]=>110111011=>[1,1,2,1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] [1,2,1,1,2,2]=>110111010=>[1,1,2,1,1,2,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] [1,2,1,1,3,1]=>110111001=>[1,1,2,1,1,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] [1,2,1,1,4]=>110111000=>[1,1,2,1,1,4]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] [1,2,1,2,1,1,1]=>110110111=>[1,1,2,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] [1,2,1,2,1,2]=>110110110=>[1,1,2,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] [1,2,1,2,2,1]=>110110101=>[1,1,2,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] [1,2,1,2,3]=>110110100=>[1,1,2,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] [1,2,1,3,1,1]=>110110011=>[1,1,2,1,3,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] [1,2,1,3,2]=>110110010=>[1,1,2,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] [1,2,1,4,1]=>110110001=>[1,1,2,1,4,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] [1,2,1,5]=>110110000=>[1,1,2,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] [1,2,2,1,1,1,1]=>110101111=>[1,1,2,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] [1,2,2,1,1,2]=>110101110=>[1,1,2,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] [1,2,2,1,2,1]=>110101101=>[1,1,2,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] [1,2,2,1,3]=>110101100=>[1,1,2,2,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] [1,2,2,2,1,1]=>110101011=>[1,1,2,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] [1,2,2,2,2]=>110101010=>[1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [1,2,2,3,1]=>110101001=>[1,1,2,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] [1,2,2,4]=>110101000=>[1,1,2,2,4]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [1,2,3,1,1,1]=>110100111=>[1,1,2,3,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] [1,2,3,1,2]=>110100110=>[1,1,2,3,1,2]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] [1,2,3,2,1]=>110100101=>[1,1,2,3,2,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] [1,2,3,3]=>110100100=>[1,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [1,2,4,1,1]=>110100011=>[1,1,2,4,1,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] [1,2,4,2]=>110100010=>[1,1,2,4,2]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] [1,2,5,1]=>110100001=>[1,1,2,5,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] [1,2,6]=>110100000=>[1,1,2,6]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [1,3,1,1,1,1,1]=>110011111=>[1,1,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [1,3,1,1,1,2]=>110011110=>[1,1,3,1,1,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] [1,3,1,1,2,1]=>110011101=>[1,1,3,1,1,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] [1,3,1,1,3]=>110011100=>[1,1,3,1,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] [1,3,1,2,1,1]=>110011011=>[1,1,3,1,2,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] [1,3,1,2,2]=>110011010=>[1,1,3,1,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] [1,3,1,3,1]=>110011001=>[1,1,3,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] [1,3,1,4]=>110011000=>[1,1,3,1,4]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] [1,3,2,1,1,1]=>110010111=>[1,1,3,2,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] [1,3,2,1,2]=>110010110=>[1,1,3,2,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] [1,3,2,2,1]=>110010101=>[1,1,3,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] [1,3,2,3]=>110010100=>[1,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] [1,3,3,1,1]=>110010011=>[1,1,3,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] [1,3,3,2]=>110010010=>[1,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] [1,3,4,1]=>110010001=>[1,1,3,4,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] [1,3,5]=>110010000=>[1,1,3,5]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [1,4,1,1,1,1]=>110001111=>[1,1,4,1,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] [1,4,1,1,2]=>110001110=>[1,1,4,1,1,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] [1,4,1,2,1]=>110001101=>[1,1,4,1,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] [1,4,1,3]=>110001100=>[1,1,4,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] [1,4,2,1,1]=>110001011=>[1,1,4,2,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] [1,4,2,2]=>110001010=>[1,1,4,2,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] [1,4,3,1]=>110001001=>[1,1,4,3,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] [1,4,4]=>110001000=>[1,1,4,4]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [1,5,1,1,1]=>110000111=>[1,1,5,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] [1,5,1,2]=>110000110=>[1,1,5,1,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] [1,5,2,1]=>110000101=>[1,1,5,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] [1,5,3]=>110000100=>[1,1,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] [1,6,1,1]=>110000011=>[1,1,6,1,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] [1,6,2]=>110000010=>[1,1,6,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] [1,7,1]=>110000001=>[1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] [1,8]=>110000000=>[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [2,1,1,1,1,1,1,1]=>101111111=>[1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [2,1,1,1,1,1,2]=>101111110=>[1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [2,1,1,1,1,2,1]=>101111101=>[1,2,1,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] [2,1,1,1,1,3]=>101111100=>[1,2,1,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [2,1,1,1,2,1,1]=>101111011=>[1,2,1,1,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] [2,1,1,1,2,2]=>101111010=>[1,2,1,1,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [2,1,1,1,3,1]=>101111001=>[1,2,1,1,1,3,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] [2,1,1,1,4]=>101111000=>[1,2,1,1,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [2,1,1,2,1,1,1]=>101110111=>[1,2,1,1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] [2,1,1,2,1,2]=>101110110=>[1,2,1,1,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] [2,1,1,2,2,1]=>101110101=>[1,2,1,1,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] [2,1,1,2,3]=>101110100=>[1,2,1,1,2,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [2,1,1,3,1,1]=>101110011=>[1,2,1,1,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] [2,1,1,3,2]=>101110010=>[1,2,1,1,3,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] [2,1,1,4,1]=>101110001=>[1,2,1,1,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] [2,1,1,5]=>101110000=>[1,2,1,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [2,1,2,1,1,1,1]=>101101111=>[1,2,1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] [2,1,2,1,1,2]=>101101110=>[1,2,1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] [2,1,2,1,2,1]=>101101101=>[1,2,1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] [2,1,2,1,3]=>101101100=>[1,2,1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] [2,1,2,2,1,1]=>101101011=>[1,2,1,2,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] [2,1,2,2,2]=>101101010=>[1,2,1,2,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [2,1,2,3,1]=>101101001=>[1,2,1,2,3,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] [2,1,2,4]=>101101000=>[1,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [2,1,3,1,1,1]=>101100111=>[1,2,1,3,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] [2,1,3,1,2]=>101100110=>[1,2,1,3,1,2]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] [2,1,3,2,1]=>101100101=>[1,2,1,3,2,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] [2,1,3,3]=>101100100=>[1,2,1,3,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [2,1,4,1,1]=>101100011=>[1,2,1,4,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] [2,1,4,2]=>101100010=>[1,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] [2,1,5,1]=>101100001=>[1,2,1,5,1]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] [2,1,6]=>101100000=>[1,2,1,6]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [2,2,1,1,1,1,1]=>101011111=>[1,2,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [2,2,1,1,1,2]=>101011110=>[1,2,2,1,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] [2,2,1,1,2,1]=>101011101=>[1,2,2,1,1,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] [2,2,1,1,3]=>101011100=>[1,2,2,1,1,3]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] [2,2,1,2,1,1]=>101011011=>[1,2,2,1,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] [2,2,1,2,2]=>101011010=>[1,2,2,1,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] [2,2,1,3,1]=>101011001=>[1,2,2,1,3,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] [2,2,1,4]=>101011000=>[1,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] [2,2,2,1,1,1]=>101010111=>[1,2,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] [2,2,2,1,2]=>101010110=>[1,2,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] [2,2,2,2,1]=>101010101=>[1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] [2,2,2,3]=>101010100=>[1,2,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [2,2,3,1,1]=>101010011=>[1,2,2,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] [2,2,3,2]=>101010010=>[1,2,2,3,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] [2,2,4,1]=>101010001=>[1,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] [2,2,5]=>101010000=>[1,2,2,5]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [2,3,1,1,1,1]=>101001111=>[1,2,3,1,1,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] [2,3,1,1,2]=>101001110=>[1,2,3,1,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] [2,3,1,2,1]=>101001101=>[1,2,3,1,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] [2,3,1,3]=>101001100=>[1,2,3,1,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] [2,3,2,1,1]=>101001011=>[1,2,3,2,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] [2,3,2,2]=>101001010=>[1,2,3,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] [2,3,3,1]=>101001001=>[1,2,3,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] [2,3,4]=>101001000=>[1,2,3,4]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [2,4,1,1,1]=>101000111=>[1,2,4,1,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] [2,4,1,2]=>101000110=>[1,2,4,1,2]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] [2,4,2,1]=>101000101=>[1,2,4,2,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] [2,4,3]=>101000100=>[1,2,4,3]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] [2,5,1,1]=>101000011=>[1,2,5,1,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] [2,5,2]=>101000010=>[1,2,5,2]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [2,6,1]=>101000001=>[1,2,6,1]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] [2,7]=>101000000=>[1,2,7]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [3,1,1,1,1,1,1]=>100111111=>[1,3,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [3,1,1,1,1,2]=>100111110=>[1,3,1,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [3,1,1,1,2,1]=>100111101=>[1,3,1,1,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] [3,1,1,1,3]=>100111100=>[1,3,1,1,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] [3,1,1,2,1,1]=>100111011=>[1,3,1,1,2,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0] [3,1,1,2,2]=>100111010=>[1,3,1,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0] [3,1,1,3,1]=>100111001=>[1,3,1,1,3,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,1,0] [3,1,1,4]=>100111000=>[1,3,1,1,4]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] [3,1,2,1,1,1]=>100110111=>[1,3,1,2,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,1,0] [3,1,2,1,2]=>100110110=>[1,3,1,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] [3,1,2,2,1]=>100110101=>[1,3,1,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] [3,1,2,3]=>100110100=>[1,3,1,2,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] [3,1,3,1,1]=>100110011=>[1,3,1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0] [3,1,3,2]=>100110010=>[1,3,1,3,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] [3,1,4,1]=>100110001=>[1,3,1,4,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] [3,1,5]=>100110000=>[1,3,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] [3,2,1,1,1,1]=>100101111=>[1,3,2,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] [3,2,1,1,2]=>100101110=>[1,3,2,1,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0] [3,2,1,2,1]=>100101101=>[1,3,2,1,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,0] [3,2,1,3]=>100101100=>[1,3,2,1,3]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] [3,2,2,1,1]=>100101011=>[1,3,2,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0] [3,2,2,2]=>100101010=>[1,3,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [3,2,3,1]=>100101001=>[1,3,2,3,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] [3,2,4]=>100101000=>[1,3,2,4]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [3,3,1,1,1]=>100100111=>[1,3,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] [3,3,1,2]=>100100110=>[1,3,3,1,2]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] [3,3,2,1]=>100100101=>[1,3,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] [3,3,3]=>100100100=>[1,3,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [3,4,1,1]=>100100011=>[1,3,4,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] [3,4,2]=>100100010=>[1,3,4,2]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] [3,5,1]=>100100001=>[1,3,5,1]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] [3,6]=>100100000=>[1,3,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [4,1,1,1,1,1]=>100011111=>[1,4,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] [4,1,1,1,2]=>100011110=>[1,4,1,1,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] [4,1,1,2,1]=>100011101=>[1,4,1,1,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0] [4,1,1,3]=>100011100=>[1,4,1,1,3]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] [4,1,2,1,1]=>100011011=>[1,4,1,2,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,1,0] [4,1,2,2]=>100011010=>[1,4,1,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] [4,1,3,1]=>100011001=>[1,4,1,3,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] [4,1,4]=>100011000=>[1,4,1,4]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] [4,2,1,1,1]=>100010111=>[1,4,2,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] [4,2,1,2]=>100010110=>[1,4,2,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0] [4,2,2,1]=>100010101=>[1,4,2,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] [4,2,3]=>100010100=>[1,4,2,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] [4,3,1,1]=>100010011=>[1,4,3,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] [4,3,2]=>100010010=>[1,4,3,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] [4,4,1]=>100010001=>[1,4,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] [4,5]=>100010000=>[1,4,5]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] [5,1,1,1,1]=>100001111=>[1,5,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] [5,1,1,2]=>100001110=>[1,5,1,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] [5,1,2,1]=>100001101=>[1,5,1,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] [5,1,3]=>100001100=>[1,5,1,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] [5,2,1,1]=>100001011=>[1,5,2,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] [5,2,2]=>100001010=>[1,5,2,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0] [5,3,1]=>100001001=>[1,5,3,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] [5,4]=>100001000=>[1,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] [6,1,1,1]=>100000111=>[1,6,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] [6,1,2]=>100000110=>[1,6,1,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] [6,2,1]=>100000101=>[1,6,2,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] [6,3]=>100000100=>[1,6,3]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] [7,1,1]=>100000011=>[1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] [7,2]=>100000010=>[1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] [8,1]=>100000001=>[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] [9]=>100000000=>[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
bounce path
Description
The bounce path determined by an integer composition.