Identifier
Identifier
Images
[1]
=>
1
[1,1]
=>
11
[2]
=>
10
[1,1,1]
=>
111
[1,2]
=>
110
[2,1]
=>
101
[3]
=>
100
[1,1,1,1]
=>
1111
[1,1,2]
=>
1110
[1,2,1]
=>
1101
[1,3]
=>
1100
[2,1,1]
=>
1011
[2,2]
=>
1010
[3,1]
=>
1001
[4]
=>
1000
[1,1,1,1,1]
=>
11111
[1,1,1,2]
=>
11110
[1,1,2,1]
=>
11101
[1,1,3]
=>
11100
[1,2,1,1]
=>
11011
[1,2,2]
=>
11010
[1,3,1]
=>
11001
[1,4]
=>
11000
[2,1,1,1]
=>
10111
[2,1,2]
=>
10110
[2,2,1]
=>
10101
[2,3]
=>
10100
[3,1,1]
=>
10011
[3,2]
=>
10010
[4,1]
=>
10001
[5]
=>
10000
[1,1,1,1,1,1]
=>
111111
[1,1,1,1,2]
=>
111110
[1,1,1,2,1]
=>
111101
[1,1,1,3]
=>
111100
[1,1,2,1,1]
=>
111011
[1,1,2,2]
=>
111010
[1,1,3,1]
=>
111001
[1,1,4]
=>
111000
[1,2,1,1,1]
=>
110111
[1,2,1,2]
=>
110110
[1,2,2,1]
=>
110101
[1,2,3]
=>
110100
[1,3,1,1]
=>
110011
[1,3,2]
=>
110010
[1,4,1]
=>
110001
[1,5]
=>
110000
[2,1,1,1,1]
=>
101111
[2,1,1,2]
=>
101110
[2,1,2,1]
=>
101101
[2,1,3]
=>
101100
[2,2,1,1]
=>
101011
[2,2,2]
=>
101010
[2,3,1]
=>
101001
[2,4]
=>
101000
[3,1,1,1]
=>
100111
[3,1,2]
=>
100110
[3,2,1]
=>
100101
[3,3]
=>
100100
[4,1,1]
=>
100011
[4,2]
=>
100010
[5,1]
=>
100001
[6]
=>
100000
[1,1,1,1,1,1,1]
=>
1111111
[1,1,1,1,1,2]
=>
1111110
[1,1,1,1,2,1]
=>
1111101
[1,1,1,1,3]
=>
1111100
[1,1,1,2,1,1]
=>
1111011
[1,1,1,2,2]
=>
1111010
[1,1,1,3,1]
=>
1111001
[1,1,1,4]
=>
1111000
[1,1,2,1,1,1]
=>
1110111
[1,1,2,1,2]
=>
1110110
[1,1,2,2,1]
=>
1110101
[1,1,2,3]
=>
1110100
[1,1,3,1,1]
=>
1110011
[1,1,3,2]
=>
1110010
[1,1,4,1]
=>
1110001
[1,1,5]
=>
1110000
[1,2,1,1,1,1]
=>
1101111
[1,2,1,1,2]
=>
1101110
[1,2,1,2,1]
=>
1101101
[1,2,1,3]
=>
1101100
[1,2,2,1,1]
=>
1101011
[1,2,2,2]
=>
1101010
[1,2,3,1]
=>
1101001
[1,2,4]
=>
1101000
[1,3,1,1,1]
=>
1100111
[1,3,1,2]
=>
1100110
[1,3,2,1]
=>
1100101
[1,3,3]
=>
1100100
[1,4,1,1]
=>
1100011
[1,4,2]
=>
1100010
[1,5,1]
=>
1100001
[1,6]
=>
1100000
[2,1,1,1,1,1]
=>
1011111
[2,1,1,1,2]
=>
1011110
[2,1,1,2,1]
=>
1011101
[2,1,1,3]
=>
1011100
[2,1,2,1,1]
=>
1011011
[2,1,2,2]
=>
1011010
[2,1,3,1]
=>
1011001
[2,1,4]
=>
1011000
[2,2,1,1,1]
=>
1010111
[2,2,1,2]
=>
1010110
[2,2,2,1]
=>
1010101
[2,2,3]
=>
1010100
[2,3,1,1]
=>
1010011
[2,3,2]
=>
1010010
[2,4,1]
=>
1010001
[2,5]
=>
1010000
[3,1,1,1,1]
=>
1001111
[3,1,1,2]
=>
1001110
[3,1,2,1]
=>
1001101
[3,1,3]
=>
1001100
[3,2,1,1]
=>
1001011
[3,2,2]
=>
1001010
[3,3,1]
=>
1001001
[3,4]
=>
1001000
[4,1,1,1]
=>
1000111
[4,1,2]
=>
1000110
[4,2,1]
=>
1000101
[4,3]
=>
1000100
[5,1,1]
=>
1000011
[5,2]
=>
1000010
[6,1]
=>
1000001
[7]
=>
1000000
[1,1,1,1,1,1,1,1]
=>
11111111
[1,1,1,1,1,1,2]
=>
11111110
[1,1,1,1,1,2,1]
=>
11111101
[1,1,1,1,1,3]
=>
11111100
[1,1,1,1,2,1,1]
=>
11111011
[1,1,1,1,2,2]
=>
11111010
[1,1,1,1,3,1]
=>
11111001
[1,1,1,1,4]
=>
11111000
[1,1,1,2,1,1,1]
=>
11110111
[1,1,1,2,1,2]
=>
11110110
[1,1,1,2,2,1]
=>
11110101
[1,1,1,2,3]
=>
11110100
[1,1,1,3,1,1]
=>
11110011
[1,1,1,3,2]
=>
11110010
[1,1,1,4,1]
=>
11110001
[1,1,1,5]
=>
11110000
[1,1,2,1,1,1,1]
=>
11101111
[1,1,2,1,1,2]
=>
11101110
[1,1,2,1,2,1]
=>
11101101
[1,1,2,1,3]
=>
11101100
[1,1,2,2,1,1]
=>
11101011
[1,1,2,2,2]
=>
11101010
[1,1,2,3,1]
=>
11101001
[1,1,2,4]
=>
11101000
[1,1,3,1,1,1]
=>
11100111
[1,1,3,1,2]
=>
11100110
[1,1,3,2,1]
=>
11100101
[1,1,3,3]
=>
11100100
[1,1,4,1,1]
=>
11100011
[1,1,4,2]
=>
11100010
[1,1,5,1]
=>
11100001
[1,1,6]
=>
11100000
[1,2,1,1,1,1,1]
=>
11011111
[1,2,1,1,1,2]
=>
11011110
[1,2,1,1,2,1]
=>
11011101
[1,2,1,1,3]
=>
11011100
[1,2,1,2,1,1]
=>
11011011
[1,2,1,2,2]
=>
11011010
[1,2,1,3,1]
=>
11011001
[1,2,1,4]
=>
11011000
[1,2,2,1,1,1]
=>
11010111
[1,2,2,1,2]
=>
11010110
[1,2,2,2,1]
=>
11010101
[1,2,2,3]
=>
11010100
[1,2,3,1,1]
=>
11010011
[1,2,3,2]
=>
11010010
[1,2,4,1]
=>
11010001
[1,2,5]
=>
11010000
[1,3,1,1,1,1]
=>
11001111
[1,3,1,1,2]
=>
11001110
[1,3,1,2,1]
=>
11001101
[1,3,1,3]
=>
11001100
[1,3,2,1,1]
=>
11001011
[1,3,2,2]
=>
11001010
[1,3,3,1]
=>
11001001
[1,3,4]
=>
11001000
[1,4,1,1,1]
=>
11000111
[1,4,1,2]
=>
11000110
[1,4,2,1]
=>
11000101
[1,4,3]
=>
11000100
[1,5,1,1]
=>
11000011
[1,5,2]
=>
11000010
[1,6,1]
=>
11000001
[1,7]
=>
11000000
[2,1,1,1,1,1,1]
=>
10111111
[2,1,1,1,1,2]
=>
10111110
[2,1,1,1,2,1]
=>
10111101
[2,1,1,1,3]
=>
10111100
[2,1,1,2,1,1]
=>
10111011
[2,1,1,2,2]
=>
10111010
[2,1,1,3,1]
=>
10111001
[2,1,1,4]
=>
10111000
[2,1,2,1,1,1]
=>
10110111
[2,1,2,1,2]
=>
10110110
[2,1,2,2,1]
=>
10110101
[2,1,2,3]
=>
10110100
[2,1,3,1,1]
=>
10110011
[2,1,3,2]
=>
10110010
[2,1,4,1]
=>
10110001
[2,1,5]
=>
10110000
[2,2,1,1,1,1]
=>
10101111
[2,2,1,1,2]
=>
10101110
[2,2,1,2,1]
=>
10101101
[2,2,1,3]
=>
10101100
[2,2,2,1,1]
=>
10101011
[2,2,2,2]
=>
10101010
[2,2,3,1]
=>
10101001
[2,2,4]
=>
10101000
[2,3,1,1,1]
=>
10100111
[2,3,1,2]
=>
10100110
[2,3,2,1]
=>
10100101
[2,3,3]
=>
10100100
[2,4,1,1]
=>
10100011
[2,4,2]
=>
10100010
[2,5,1]
=>
10100001
[2,6]
=>
10100000
[3,1,1,1,1,1]
=>
10011111
[3,1,1,1,2]
=>
10011110
[3,1,1,2,1]
=>
10011101
[3,1,1,3]
=>
10011100
[3,1,2,1,1]
=>
10011011
[3,1,2,2]
=>
10011010
[3,1,3,1]
=>
10011001
[3,1,4]
=>
10011000
[3,2,1,1,1]
=>
10010111
[3,2,1,2]
=>
10010110
[3,2,2,1]
=>
10010101
[3,2,3]
=>
10010100
[3,3,1,1]
=>
10010011
[3,3,2]
=>
10010010
[3,4,1]
=>
10010001
[3,5]
=>
10010000
[4,1,1,1,1]
=>
10001111
[4,1,1,2]
=>
10001110
[4,1,2,1]
=>
10001101
[4,1,3]
=>
10001100
[4,2,1,1]
=>
10001011
[4,2,2]
=>
10001010
[4,3,1]
=>
10001001
[4,4]
=>
10001000
[5,1,1,1]
=>
10000111
[5,1,2]
=>
10000110
[5,2,1]
=>
10000101
[5,3]
=>
10000100
[6,1,1]
=>
10000011
[6,2]
=>
10000010
[7,1]
=>
10000001
[8]
=>
10000000
[1,1,1,1,1,1,1,1,1]
=>
111111111
[1,1,1,1,1,1,1,2]
=>
111111110
[1,1,1,1,1,1,2,1]
=>
111111101
[1,1,1,1,1,1,3]
=>
111111100
[1,1,1,1,1,2,1,1]
=>
111111011
[1,1,1,1,1,2,2]
=>
111111010
[1,1,1,1,1,3,1]
=>
111111001
[1,1,1,1,1,4]
=>
111111000
[1,1,1,1,2,1,1,1]
=>
111110111
[1,1,1,1,2,1,2]
=>
111110110
[1,1,1,1,2,2,1]
=>
111110101
[1,1,1,1,2,3]
=>
111110100
[1,1,1,1,3,1,1]
=>
111110011
[1,1,1,1,3,2]
=>
111110010
[1,1,1,1,4,1]
=>
111110001
[1,1,1,1,5]
=>
111110000
[1,1,1,2,1,1,1,1]
=>
111101111
[1,1,1,2,1,1,2]
=>
111101110
[1,1,1,2,1,2,1]
=>
111101101
[1,1,1,2,1,3]
=>
111101100
[1,1,1,2,2,1,1]
=>
111101011
[1,1,1,2,2,2]
=>
111101010
[1,1,1,2,3,1]
=>
111101001
[1,1,1,2,4]
=>
111101000
[1,1,1,3,1,1,1]
=>
111100111
[1,1,1,3,1,2]
=>
111100110
[1,1,1,3,2,1]
=>
111100101
[1,1,1,3,3]
=>
111100100
[1,1,1,4,1,1]
=>
111100011
[1,1,1,4,2]
=>
111100010
[1,1,1,5,1]
=>
111100001
[1,1,1,6]
=>
111100000
[1,1,2,1,1,1,1,1]
=>
111011111
[1,1,2,1,1,1,2]
=>
111011110
[1,1,2,1,1,2,1]
=>
111011101
[1,1,2,1,1,3]
=>
111011100
[1,1,2,1,2,1,1]
=>
111011011
[1,1,2,1,2,2]
=>
111011010
[1,1,2,1,3,1]
=>
111011001
[1,1,2,1,4]
=>
111011000
[1,1,2,2,1,1,1]
=>
111010111
[1,1,2,2,1,2]
=>
111010110
[1,1,2,2,2,1]
=>
111010101
[1,1,2,2,3]
=>
111010100
[1,1,2,3,1,1]
=>
111010011
[1,1,2,3,2]
=>
111010010
[1,1,2,4,1]
=>
111010001
[1,1,2,5]
=>
111010000
[1,1,3,1,1,1,1]
=>
111001111
[1,1,3,1,1,2]
=>
111001110
[1,1,3,1,2,1]
=>
111001101
[1,1,3,1,3]
=>
111001100
[1,1,3,2,1,1]
=>
111001011
[1,1,3,2,2]
=>
111001010
[1,1,3,3,1]
=>
111001001
[1,1,3,4]
=>
111001000
[1,1,4,1,1,1]
=>
111000111
[1,1,4,1,2]
=>
111000110
[1,1,4,2,1]
=>
111000101
[1,1,4,3]
=>
111000100
[1,1,5,1,1]
=>
111000011
[1,1,5,2]
=>
111000010
[1,1,6,1]
=>
111000001
[1,1,7]
=>
111000000
[1,2,1,1,1,1,1,1]
=>
110111111
[1,2,1,1,1,1,2]
=>
110111110
[1,2,1,1,1,2,1]
=>
110111101
[1,2,1,1,1,3]
=>
110111100
[1,2,1,1,2,1,1]
=>
110111011
[1,2,1,1,2,2]
=>
110111010
[1,2,1,1,3,1]
=>
110111001
[1,2,1,1,4]
=>
110111000
[1,2,1,2,1,1,1]
=>
110110111
[1,2,1,2,1,2]
=>
110110110
[1,2,1,2,2,1]
=>
110110101
[1,2,1,2,3]
=>
110110100
[1,2,1,3,1,1]
=>
110110011
[1,2,1,3,2]
=>
110110010
[1,2,1,4,1]
=>
110110001
[1,2,1,5]
=>
110110000
[1,2,2,1,1,1,1]
=>
110101111
[1,2,2,1,1,2]
=>
110101110
[1,2,2,1,2,1]
=>
110101101
[1,2,2,1,3]
=>
110101100
[1,2,2,2,1,1]
=>
110101011
[1,2,2,2,2]
=>
110101010
[1,2,2,3,1]
=>
110101001
[1,2,2,4]
=>
110101000
[1,2,3,1,1,1]
=>
110100111
[1,2,3,1,2]
=>
110100110
[1,2,3,2,1]
=>
110100101
[1,2,3,3]
=>
110100100
[1,2,4,1,1]
=>
110100011
[1,2,4,2]
=>
110100010
[1,2,5,1]
=>
110100001
[1,2,6]
=>
110100000
[1,3,1,1,1,1,1]
=>
110011111
[1,3,1,1,1,2]
=>
110011110
[1,3,1,1,2,1]
=>
110011101
[1,3,1,1,3]
=>
110011100
[1,3,1,2,1,1]
=>
110011011
[1,3,1,2,2]
=>
110011010
[1,3,1,3,1]
=>
110011001
[1,3,1,4]
=>
110011000
[1,3,2,1,1,1]
=>
110010111
[1,3,2,1,2]
=>
110010110
[1,3,2,2,1]
=>
110010101
[1,3,2,3]
=>
110010100
[1,3,3,1,1]
=>
110010011
[1,3,3,2]
=>
110010010
[1,3,4,1]
=>
110010001
[1,3,5]
=>
110010000
[1,4,1,1,1,1]
=>
110001111
[1,4,1,1,2]
=>
110001110
[1,4,1,2,1]
=>
110001101
[1,4,1,3]
=>
110001100
[1,4,2,1,1]
=>
110001011
[1,4,2,2]
=>
110001010
[1,4,3,1]
=>
110001001
[1,4,4]
=>
110001000
[1,5,1,1,1]
=>
110000111
[1,5,1,2]
=>
110000110
[1,5,2,1]
=>
110000101
[1,5,3]
=>
110000100
[1,6,1,1]
=>
110000011
[1,6,2]
=>
110000010
[1,7,1]
=>
110000001
[1,8]
=>
110000000
[2,1,1,1,1,1,1,1]
=>
101111111
[2,1,1,1,1,1,2]
=>
101111110
[2,1,1,1,1,2,1]
=>
101111101
[2,1,1,1,1,3]
=>
101111100
[2,1,1,1,2,1,1]
=>
101111011
[2,1,1,1,2,2]
=>
101111010
[2,1,1,1,3,1]
=>
101111001
[2,1,1,1,4]
=>
101111000
[2,1,1,2,1,1,1]
=>
101110111
[2,1,1,2,1,2]
=>
101110110
[2,1,1,2,2,1]
=>
101110101
[2,1,1,2,3]
=>
101110100
[2,1,1,3,1,1]
=>
101110011
[2,1,1,3,2]
=>
101110010
[2,1,1,4,1]
=>
101110001
[2,1,1,5]
=>
101110000
[2,1,2,1,1,1,1]
=>
101101111
[2,1,2,1,1,2]
=>
101101110
[2,1,2,1,2,1]
=>
101101101
[2,1,2,1,3]
=>
101101100
[2,1,2,2,1,1]
=>
101101011
[2,1,2,2,2]
=>
101101010
[2,1,2,3,1]
=>
101101001
[2,1,2,4]
=>
101101000
[2,1,3,1,1,1]
=>
101100111
[2,1,3,1,2]
=>
101100110
[2,1,3,2,1]
=>
101100101
[2,1,3,3]
=>
101100100
[2,1,4,1,1]
=>
101100011
[2,1,4,2]
=>
101100010
[2,1,5,1]
=>
101100001
[2,1,6]
=>
101100000
[2,2,1,1,1,1,1]
=>
101011111
[2,2,1,1,1,2]
=>
101011110
[2,2,1,1,2,1]
=>
101011101
[2,2,1,1,3]
=>
101011100
[2,2,1,2,1,1]
=>
101011011
[2,2,1,2,2]
=>
101011010
[2,2,1,3,1]
=>
101011001
[2,2,1,4]
=>
101011000
[2,2,2,1,1,1]
=>
101010111
[2,2,2,1,2]
=>
101010110
[2,2,2,2,1]
=>
101010101
[2,2,2,3]
=>
101010100
[2,2,3,1,1]
=>
101010011
[2,2,3,2]
=>
101010010
[2,2,4,1]
=>
101010001
[2,2,5]
=>
101010000
[2,3,1,1,1,1]
=>
101001111
[2,3,1,1,2]
=>
101001110
[2,3,1,2,1]
=>
101001101
[2,3,1,3]
=>
101001100
[2,3,2,1,1]
=>
101001011
[2,3,2,2]
=>
101001010
[2,3,3,1]
=>
101001001
[2,3,4]
=>
101001000
[2,4,1,1,1]
=>
101000111
[2,4,1,2]
=>
101000110
[2,4,2,1]
=>
101000101
[2,4,3]
=>
101000100
[2,5,1,1]
=>
101000011
[2,5,2]
=>
101000010
[2,6,1]
=>
101000001
[2,7]
=>
101000000
[3,1,1,1,1,1,1]
=>
100111111
[3,1,1,1,1,2]
=>
100111110
[3,1,1,1,2,1]
=>
100111101
[3,1,1,1,3]
=>
100111100
[3,1,1,2,1,1]
=>
100111011
[3,1,1,2,2]
=>
100111010
[3,1,1,3,1]
=>
100111001
[3,1,1,4]
=>
100111000
[3,1,2,1,1,1]
=>
100110111
[3,1,2,1,2]
=>
100110110
[3,1,2,2,1]
=>
100110101
[3,1,2,3]
=>
100110100
[3,1,3,1,1]
=>
100110011
[3,1,3,2]
=>
100110010
[3,1,4,1]
=>
100110001
[3,1,5]
=>
100110000
[3,2,1,1,1,1]
=>
100101111
[3,2,1,1,2]
=>
100101110
[3,2,1,2,1]
=>
100101101
[3,2,1,3]
=>
100101100
[3,2,2,1,1]
=>
100101011
[3,2,2,2]
=>
100101010
[3,2,3,1]
=>
100101001
[3,2,4]
=>
100101000
[3,3,1,1,1]
=>
100100111
[3,3,1,2]
=>
100100110
[3,3,2,1]
=>
100100101
[3,3,3]
=>
100100100
[3,4,1,1]
=>
100100011
[3,4,2]
=>
100100010
[3,5,1]
=>
100100001
[3,6]
=>
100100000
[4,1,1,1,1,1]
=>
100011111
[4,1,1,1,2]
=>
100011110
[4,1,1,2,1]
=>
100011101
[4,1,1,3]
=>
100011100
[4,1,2,1,1]
=>
100011011
[4,1,2,2]
=>
100011010
[4,1,3,1]
=>
100011001
[4,1,4]
=>
100011000
[4,2,1,1,1]
=>
100010111
[4,2,1,2]
=>
100010110
[4,2,2,1]
=>
100010101
[4,2,3]
=>
100010100
[4,3,1,1]
=>
100010011
[4,3,2]
=>
100010010
[4,4,1]
=>
100010001
[4,5]
=>
100010000
[5,1,1,1,1]
=>
100001111
[5,1,1,2]
=>
100001110
[5,1,2,1]
=>
100001101
[5,1,3]
=>
100001100
[5,2,1,1]
=>
100001011
[5,2,2]
=>
100001010
[5,3,1]
=>
100001001
[5,4]
=>
100001000
[6,1,1,1]
=>
100000111
[6,1,2]
=>
100000110
[6,2,1]
=>
100000101
[6,3]
=>
100000100
[7,1,1]
=>
100000011
[7,2]
=>
100000010
[8,1]
=>
100000001
[9]
=>
100000000
[1,1,1,1,1,1,1,1,1,1]
=>
1111111111
[1,1,1,1,1,1,1,1,2]
=>
1111111110
[1,1,1,1,1,1,1,2,1]
=>
1111111101
[1,1,1,1,1,1,1,3]
=>
1111111100
[1,1,1,1,1,1,2,1,1]
=>
1111111011
[1,1,1,1,1,1,2,2]
=>
1111111010
[1,1,1,1,1,1,3,1]
=>
1111111001
[1,1,1,1,1,1,4]
=>
1111111000
[1,1,1,1,1,2,1,1,1]
=>
1111110111
[1,1,1,1,1,2,1,2]
=>
1111110110
[1,1,1,1,1,2,2,1]
=>
1111110101
[1,1,1,1,1,2,3]
=>
1111110100
[1,1,1,1,1,3,1,1]
=>
1111110011
[1,1,1,1,1,3,2]
=>
1111110010
[1,1,1,1,1,4,1]
=>
1111110001
[1,1,1,1,1,5]
=>
1111110000
[1,1,1,1,2,1,1,1,1]
=>
1111101111
[1,1,1,1,2,1,1,2]
=>
1111101110
[1,1,1,1,2,1,2,1]
=>
1111101101
[1,1,1,1,2,1,3]
=>
1111101100
[1,1,1,1,2,2,1,1]
=>
1111101011
[1,1,1,1,2,2,2]
=>
1111101010
[1,1,1,1,2,3,1]
=>
1111101001
[1,1,1,1,2,4]
=>
1111101000
[1,1,1,1,3,1,1,1]
=>
1111100111
[1,1,1,1,3,1,2]
=>
1111100110
[1,1,1,1,3,2,1]
=>
1111100101
[1,1,1,1,3,3]
=>
1111100100
[1,1,1,1,4,1,1]
=>
1111100011
[1,1,1,1,4,2]
=>
1111100010
[1,1,1,1,5,1]
=>
1111100001
[1,1,1,1,6]
=>
1111100000
[1,1,1,2,1,1,1,1,1]
=>
1111011111
[1,1,1,2,1,1,1,2]
=>
1111011110
[1,1,1,2,1,1,2,1]
=>
1111011101
[1,1,1,2,1,1,3]
=>
1111011100
[1,1,1,2,1,2,1,1]
=>
1111011011
[1,1,1,2,1,2,2]
=>
1111011010
[1,1,1,2,1,3,1]
=>
1111011001
[1,1,1,2,1,4]
=>
1111011000
[1,1,1,2,2,1,1,1]
=>
1111010111
[1,1,1,2,2,1,2]
=>
1111010110
[1,1,1,2,2,2,1]
=>
1111010101
[1,1,1,2,2,3]
=>
1111010100
[1,1,1,2,3,1,1]
=>
1111010011
[1,1,1,2,3,2]
=>
1111010010
[1,1,1,2,4,1]
=>
1111010001
[1,1,1,2,5]
=>
1111010000
[1,1,1,3,1,1,1,1]
=>
1111001111
[1,1,1,3,1,1,2]
=>
1111001110
[1,1,1,3,1,2,1]
=>
1111001101
[1,1,1,3,1,3]
=>
1111001100
[1,1,1,3,2,1,1]
=>
1111001011
[1,1,1,3,2,2]
=>
1111001010
[1,1,1,3,3,1]
=>
1111001001
[1,1,1,3,4]
=>
1111001000
[1,1,1,4,1,1,1]
=>
1111000111
[1,1,1,4,1,2]
=>
1111000110
[1,1,1,4,2,1]
=>
1111000101
[1,1,1,4,3]
=>
1111000100
[1,1,1,5,1,1]
=>
1111000011
[1,1,1,5,2]
=>
1111000010
[1,1,1,6,1]
=>
1111000001
[1,1,1,7]
=>
1111000000
[1,1,2,1,1,1,1,1,1]
=>
1110111111
[1,1,2,1,1,1,1,2]
=>
1110111110
[1,1,2,1,1,1,2,1]
=>
1110111101
[1,1,2,1,1,1,3]
=>
1110111100
[1,1,2,1,1,2,1,1]
=>
1110111011
[1,1,2,1,1,2,2]
=>
1110111010
[1,1,2,1,1,3,1]
=>
1110111001
[1,1,2,1,1,4]
=>
1110111000
[1,1,2,1,2,1,1,1]
=>
1110110111
[1,1,2,1,2,1,2]
=>
1110110110
[1,1,2,1,2,2,1]
=>
1110110101
[1,1,2,1,2,3]
=>
1110110100
[1,1,2,1,3,1,1]
=>
1110110011
[1,1,2,1,3,2]
=>
1110110010
[1,1,2,1,4,1]
=>
1110110001
[1,1,2,1,5]
=>
1110110000
[1,1,2,2,1,1,1,1]
=>
1110101111
[1,1,2,2,1,1,2]
=>
1110101110
[1,1,2,2,1,2,1]
=>
1110101101
[1,1,2,2,1,3]
=>
1110101100
[1,1,2,2,2,1,1]
=>
1110101011
[1,1,2,2,2,2]
=>
1110101010
[1,1,2,2,3,1]
=>
1110101001
[1,1,2,2,4]
=>
1110101000
[1,1,2,3,1,1,1]
=>
1110100111
[1,1,2,3,1,2]
=>
1110100110
[1,1,2,3,2,1]
=>
1110100101
[1,1,2,3,3]
=>
1110100100
[1,1,2,4,1,1]
=>
1110100011
[1,1,2,4,2]
=>
1110100010
[1,1,2,5,1]
=>
1110100001
[1,1,2,6]
=>
1110100000
[1,1,3,1,1,1,1,1]
=>
1110011111
[1,1,3,1,1,1,2]
=>
1110011110
[1,1,3,1,1,2,1]
=>
1110011101
[1,1,3,1,1,3]
=>
1110011100
[1,1,3,1,2,1,1]
=>
1110011011
[1,1,3,1,2,2]
=>
1110011010
[1,1,3,1,3,1]
=>
1110011001
[1,1,3,1,4]
=>
1110011000
[1,1,3,2,1,1,1]
=>
1110010111
[1,1,3,2,1,2]
=>
1110010110
[1,1,3,2,2,1]
=>
1110010101
[1,1,3,2,3]
=>
1110010100
[1,1,3,3,1,1]
=>
1110010011
[1,1,3,3,2]
=>
1110010010
[1,1,3,4,1]
=>
1110010001
[1,1,3,5]
=>
1110010000
[1,1,4,1,1,1,1]
=>
1110001111
[1,1,4,1,1,2]
=>
1110001110
[1,1,4,1,2,1]
=>
1110001101
[1,1,4,1,3]
=>
1110001100
[1,1,4,2,1,1]
=>
1110001011
[1,1,4,2,2]
=>
1110001010
[1,1,4,3,1]
=>
1110001001
[1,1,4,4]
=>
1110001000
[1,1,5,1,1,1]
=>
1110000111
[1,1,5,1,2]
=>
1110000110
[1,1,5,2,1]
=>
1110000101
[1,1,5,3]
=>
1110000100
[1,1,6,1,1]
=>
1110000011
[1,1,6,2]
=>
1110000010
[1,1,7,1]
=>
1110000001
[1,1,8]
=>
1110000000
[1,2,1,1,1,1,1,1,1]
=>
1101111111
[1,2,1,1,1,1,1,2]
=>
1101111110
[1,2,1,1,1,1,2,1]
=>
1101111101
[1,2,1,1,1,1,3]
=>
1101111100
[1,2,1,1,1,2,1,1]
=>
1101111011
[1,2,1,1,1,2,2]
=>
1101111010
[1,2,1,1,1,3,1]
=>
1101111001
[1,2,1,1,1,4]
=>
1101111000
[1,2,1,1,2,1,1,1]
=>
1101110111
[1,2,1,1,2,1,2]
=>
1101110110
[1,2,1,1,2,2,1]
=>
1101110101
[1,2,1,1,2,3]
=>
1101110100
[1,2,1,1,3,1,1]
=>
1101110011
[1,2,1,1,3,2]
=>
1101110010
[1,2,1,1,4,1]
=>
1101110001
[1,2,1,1,5]
=>
1101110000
[1,2,1,2,1,1,1,1]
=>
1101101111
[1,2,1,2,1,1,2]
=>
1101101110
[1,2,1,2,1,2,1]
=>
1101101101
[1,2,1,2,1,3]
=>
1101101100
[1,2,1,2,2,1,1]
=>
1101101011
[1,2,1,2,2,2]
=>
1101101010
[1,2,1,2,3,1]
=>
1101101001
[1,2,1,2,4]
=>
1101101000
[1,2,1,3,1,1,1]
=>
1101100111
[1,2,1,3,1,2]
=>
1101100110
[1,2,1,3,2,1]
=>
1101100101
[1,2,1,3,3]
=>
1101100100
[1,2,1,4,1,1]
=>
1101100011
[1,2,1,4,2]
=>
1101100010
[1,2,1,5,1]
=>
1101100001
[1,2,1,6]
=>
1101100000
[1,2,2,1,1,1,1,1]
=>
1101011111
[1,2,2,1,1,1,2]
=>
1101011110
[1,2,2,1,1,2,1]
=>
1101011101
[1,2,2,1,1,3]
=>
1101011100
[1,2,2,1,2,1,1]
=>
1101011011
[1,2,2,1,2,2]
=>
1101011010
[1,2,2,1,3,1]
=>
1101011001
[1,2,2,1,4]
=>
1101011000
[1,2,2,2,1,1,1]
=>
1101010111
[1,2,2,2,1,2]
=>
1101010110
[1,2,2,2,2,1]
=>
1101010101
[1,2,2,2,3]
=>
1101010100
[1,2,2,3,1,1]
=>
1101010011
[1,2,2,3,2]
=>
1101010010
[1,2,2,4,1]
=>
1101010001
[1,2,2,5]
=>
1101010000
[1,2,3,1,1,1,1]
=>
1101001111
[1,2,3,1,1,2]
=>
1101001110
[1,2,3,1,2,1]
=>
1101001101
[1,2,3,1,3]
=>
1101001100
[1,2,3,2,1,1]
=>
1101001011
[1,2,3,2,2]
=>
1101001010
[1,2,3,3,1]
=>
1101001001
[1,2,3,4]
=>
1101001000
[1,2,4,1,1,1]
=>
1101000111
[1,2,4,1,2]
=>
1101000110
[1,2,4,2,1]
=>
1101000101
[1,2,4,3]
=>
1101000100
[1,2,5,1,1]
=>
1101000011
[1,2,5,2]
=>
1101000010
[1,2,6,1]
=>
1101000001
[1,2,7]
=>
1101000000
[1,3,1,1,1,1,1,1]
=>
1100111111
[1,3,1,1,1,1,2]
=>
1100111110
[1,3,1,1,1,2,1]
=>
1100111101
[1,3,1,1,1,3]
=>
1100111100
[1,3,1,1,2,1,1]
=>
1100111011
[1,3,1,1,2,2]
=>
1100111010
[1,3,1,1,3,1]
=>
1100111001
[1,3,1,1,4]
=>
1100111000
[1,3,1,2,1,1,1]
=>
1100110111
[1,3,1,2,1,2]
=>
1100110110
[1,3,1,2,2,1]
=>
1100110101
[1,3,1,2,3]
=>
1100110100
[1,3,1,3,1,1]
=>
1100110011
[1,3,1,3,2]
=>
1100110010
[1,3,1,4,1]
=>
1100110001
[1,3,1,5]
=>
1100110000
[1,3,2,1,1,1,1]
=>
1100101111
[1,3,2,1,1,2]
=>
1100101110
[1,3,2,1,2,1]
=>
1100101101
[1,3,2,1,3]
=>
1100101100
[1,3,2,2,1,1]
=>
1100101011
[1,3,2,2,2]
=>
1100101010
[1,3,2,3,1]
=>
1100101001
[1,3,2,4]
=>
1100101000
[1,3,3,1,1,1]
=>
1100100111
[1,3,3,1,2]
=>
1100100110
[1,3,3,2,1]
=>
1100100101
[1,3,3,3]
=>
1100100100
[1,3,4,1,1]
=>
1100100011
[1,3,4,2]
=>
1100100010
[1,3,5,1]
=>
1100100001
[1,3,6]
=>
1100100000
[1,4,1,1,1,1,1]
=>
1100011111
[1,4,1,1,1,2]
=>
1100011110
[1,4,1,1,2,1]
=>
1100011101
[1,4,1,1,3]
=>
1100011100
[1,4,1,2,1,1]
=>
1100011011
[1,4,1,2,2]
=>
1100011010
[1,4,1,3,1]
=>
1100011001
[1,4,1,4]
=>
1100011000
[1,4,2,1,1,1]
=>
1100010111
[1,4,2,1,2]
=>
1100010110
[1,4,2,2,1]
=>
1100010101
[1,4,2,3]
=>
1100010100
[1,4,3,1,1]
=>
1100010011
[1,4,3,2]
=>
1100010010
[1,4,4,1]
=>
1100010001
[1,4,5]
=>
1100010000
[1,5,1,1,1,1]
=>
1100001111
[1,5,1,1,2]
=>
1100001110
[1,5,1,2,1]
=>
1100001101
[1,5,1,3]
=>
1100001100
[1,5,2,1,1]
=>
1100001011
[1,5,2,2]
=>
1100001010
[1,5,3,1]
=>
1100001001
[1,5,4]
=>
1100001000
[1,6,1,1,1]
=>
1100000111
[1,6,1,2]
=>
1100000110
[1,6,2,1]
=>
1100000101
[1,6,3]
=>
1100000100
[1,7,1,1]
=>
1100000011
[1,7,2]
=>
1100000010
[1,8,1]
=>
1100000001
[1,9]
=>
1100000000
[2,1,1,1,1,1,1,1,1]
=>
1011111111
[2,1,1,1,1,1,1,2]
=>
1011111110
[2,1,1,1,1,1,2,1]
=>
1011111101
[2,1,1,1,1,1,3]
=>
1011111100
[2,1,1,1,1,2,1,1]
=>
1011111011
[2,1,1,1,1,2,2]
=>
1011111010
[2,1,1,1,1,3,1]
=>
1011111001
[2,1,1,1,1,4]
=>
1011111000
[2,1,1,1,2,1,1,1]
=>
1011110111
[2,1,1,1,2,1,2]
=>
1011110110
[2,1,1,1,2,2,1]
=>
1011110101
[2,1,1,1,2,3]
=>
1011110100
[2,1,1,1,3,1,1]
=>
1011110011
[2,1,1,1,3,2]
=>
1011110010
[2,1,1,1,4,1]
=>
1011110001
[2,1,1,1,5]
=>
1011110000
[2,1,1,2,1,1,1,1]
=>
1011101111
[2,1,1,2,1,1,2]
=>
1011101110
[2,1,1,2,1,2,1]
=>
1011101101
[2,1,1,2,1,3]
=>
1011101100
[2,1,1,2,2,1,1]
=>
1011101011
[2,1,1,2,2,2]
=>
1011101010
[2,1,1,2,3,1]
=>
1011101001
[2,1,1,2,4]
=>
1011101000
[2,1,1,3,1,1,1]
=>
1011100111
[2,1,1,3,1,2]
=>
1011100110
[2,1,1,3,2,1]
=>
1011100101
[2,1,1,3,3]
=>
1011100100
[2,1,1,4,1,1]
=>
1011100011
[2,1,1,4,2]
=>
1011100010
[2,1,1,5,1]
=>
1011100001
[2,1,1,6]
=>
1011100000
[2,1,2,1,1,1,1,1]
=>
1011011111
[2,1,2,1,1,1,2]
=>
1011011110
[2,1,2,1,1,2,1]
=>
1011011101
[2,1,2,1,1,3]
=>
1011011100
[2,1,2,1,2,1,1]
=>
1011011011
[2,1,2,1,2,2]
=>
1011011010
[2,1,2,1,3,1]
=>
1011011001
[2,1,2,1,4]
=>
1011011000
[2,1,2,2,1,1,1]
=>
1011010111
[2,1,2,2,1,2]
=>
1011010110
[2,1,2,2,2,1]
=>
1011010101
[2,1,2,2,3]
=>
1011010100
[2,1,2,3,1,1]
=>
1011010011
[2,1,2,3,2]
=>
1011010010
[2,1,2,4,1]
=>
1011010001
[2,1,2,5]
=>
1011010000
[2,1,3,1,1,1,1]
=>
1011001111
[2,1,3,1,1,2]
=>
1011001110
[2,1,3,1,2,1]
=>
1011001101
[2,1,3,1,3]
=>
1011001100
[2,1,3,2,1,1]
=>
1011001011
[2,1,3,2,2]
=>
1011001010
[2,1,3,3,1]
=>
1011001001
[2,1,3,4]
=>
1011001000
[2,1,4,1,1,1]
=>
1011000111
[2,1,4,1,2]
=>
1011000110
[2,1,4,2,1]
=>
1011000101
[2,1,4,3]
=>
1011000100
[2,1,5,1,1]
=>
1011000011
[2,1,5,2]
=>
1011000010
[2,1,6,1]
=>
1011000001
[2,1,7]
=>
1011000000
[2,2,1,1,1,1,1,1]
=>
1010111111
[2,2,1,1,1,1,2]
=>
1010111110
[2,2,1,1,1,2,1]
=>
1010111101
[2,2,1,1,1,3]
=>
1010111100
[2,2,1,1,2,1,1]
=>
1010111011
[2,2,1,1,2,2]
=>
1010111010
[2,2,1,1,3,1]
=>
1010111001
[2,2,1,1,4]
=>
1010111000
[2,2,1,2,1,1,1]
=>
1010110111
[2,2,1,2,1,2]
=>
1010110110
[2,2,1,2,2,1]
=>
1010110101
[2,2,1,2,3]
=>
1010110100
[2,2,1,3,1,1]
=>
1010110011
[2,2,1,3,2]
=>
1010110010
[2,2,1,4,1]
=>
1010110001
[2,2,1,5]
=>
1010110000
[2,2,2,1,1,1,1]
=>
1010101111
[2,2,2,1,1,2]
=>
1010101110
[2,2,2,1,2,1]
=>
1010101101
[2,2,2,1,3]
=>
1010101100
[2,2,2,2,1,1]
=>
1010101011
[2,2,2,2,2]
=>
1010101010
[2,2,2,3,1]
=>
1010101001
[2,2,2,4]
=>
1010101000
[2,2,3,1,1,1]
=>
1010100111
[2,2,3,1,2]
=>
1010100110
[2,2,3,2,1]
=>
1010100101
[2,2,3,3]
=>
1010100100
[2,2,4,1,1]
=>
1010100011
[2,2,4,2]
=>
1010100010
[2,2,5,1]
=>
1010100001
[2,2,6]
=>
1010100000
[2,3,1,1,1,1,1]
=>
1010011111
[2,3,1,1,1,2]
=>
1010011110
[2,3,1,1,2,1]
=>
1010011101
[2,3,1,1,3]
=>
1010011100
[2,3,1,2,1,1]
=>
1010011011
[2,3,1,2,2]
=>
1010011010
[2,3,1,3,1]
=>
1010011001
[2,3,1,4]
=>
1010011000
[2,3,2,1,1,1]
=>
1010010111
[2,3,2,1,2]
=>
1010010110
[2,3,2,2,1]
=>
1010010101
[2,3,2,3]
=>
1010010100
[2,3,3,1,1]
=>
1010010011
[2,3,3,2]
=>
1010010010
[2,3,4,1]
=>
1010010001
[2,3,5]
=>
1010010000
[2,4,1,1,1,1]
=>
1010001111
[2,4,1,1,2]
=>
1010001110
[2,4,1,2,1]
=>
1010001101
[2,4,1,3]
=>
1010001100
[2,4,2,1,1]
=>
1010001011
[2,4,2,2]
=>
1010001010
[2,4,3,1]
=>
1010001001
[2,4,4]
=>
1010001000
[2,5,1,1,1]
=>
1010000111
[2,5,1,2]
=>
1010000110
[2,5,2,1]
=>
1010000101
[2,5,3]
=>
1010000100
[2,6,1,1]
=>
1010000011
[2,6,2]
=>
1010000010
[2,7,1]
=>
1010000001
[2,8]
=>
1010000000
[3,1,1,1,1,1,1,1]
=>
1001111111
[3,1,1,1,1,1,2]
=>
1001111110
[3,1,1,1,1,2,1]
=>
1001111101
[3,1,1,1,1,3]
=>
1001111100
[3,1,1,1,2,1,1]
=>
1001111011
[3,1,1,1,2,2]
=>
1001111010
[3,1,1,1,3,1]
=>
1001111001
[3,1,1,1,4]
=>
1001111000
[3,1,1,2,1,1,1]
=>
1001110111
[3,1,1,2,1,2]
=>
1001110110
[3,1,1,2,2,1]
=>
1001110101
[3,1,1,2,3]
=>
1001110100
[3,1,1,3,1,1]
=>
1001110011
[3,1,1,3,2]
=>
1001110010
[3,1,1,4,1]
=>
1001110001
[3,1,1,5]
=>
1001110000
[3,1,2,1,1,1,1]
=>
1001101111
[3,1,2,1,1,2]
=>
1001101110
[3,1,2,1,2,1]
=>
1001101101
[3,1,2,1,3]
=>
1001101100
[3,1,2,2,1,1]
=>
1001101011
[3,1,2,2,2]
=>
1001101010
[3,1,2,3,1]
=>
1001101001
[3,1,2,4]
=>
1001101000
[3,1,3,1,1,1]
=>
1001100111
[3,1,3,1,2]
=>
1001100110
[3,1,3,2,1]
=>
1001100101
[3,1,3,3]
=>
1001100100
[3,1,4,1,1]
=>
1001100011
[3,1,4,2]
=>
1001100010
[3,1,5,1]
=>
1001100001
[3,1,6]
=>
1001100000
[3,2,1,1,1,1,1]
=>
1001011111
[3,2,1,1,1,2]
=>
1001011110
[3,2,1,1,2,1]
=>
1001011101
[3,2,1,1,3]
=>
1001011100
[3,2,1,2,1,1]
=>
1001011011
[3,2,1,2,2]
=>
1001011010
[3,2,1,3,1]
=>
1001011001
[3,2,1,4]
=>
1001011000
[3,2,2,1,1,1]
=>
1001010111
[3,2,2,1,2]
=>
1001010110
[3,2,2,2,1]
=>
1001010101
[3,2,2,3]
=>
1001010100
[3,2,3,1,1]
=>
1001010011
[3,2,3,2]
=>
1001010010
[3,2,4,1]
=>
1001010001
[3,2,5]
=>
1001010000
[3,3,1,1,1,1]
=>
1001001111
[3,3,1,1,2]
=>
1001001110
[3,3,1,2,1]
=>
1001001101
[3,3,1,3]
=>
1001001100
[3,3,2,1,1]
=>
1001001011
[3,3,2,2]
=>
1001001010
[3,3,3,1]
=>
1001001001
[3,3,4]
=>
1001001000
[3,4,1,1,1]
=>
1001000111
[3,4,1,2]
=>
1001000110
[3,4,2,1]
=>
1001000101
[3,4,3]
=>
1001000100
[3,5,1,1]
=>
1001000011
[3,5,2]
=>
1001000010
[3,6,1]
=>
1001000001
[3,7]
=>
1001000000
[4,1,1,1,1,1,1]
=>
1000111111
[4,1,1,1,1,2]
=>
1000111110
[4,1,1,1,2,1]
=>
1000111101
[4,1,1,1,3]
=>
1000111100
[4,1,1,2,1,1]
=>
1000111011
[4,1,1,2,2]
=>
1000111010
[4,1,1,3,1]
=>
1000111001
[4,1,1,4]
=>
1000111000
[4,1,2,1,1,1]
=>
1000110111
[4,1,2,1,2]
=>
1000110110
[4,1,2,2,1]
=>
1000110101
[4,1,2,3]
=>
1000110100
[4,1,3,1,1]
=>
1000110011
[4,1,3,2]
=>
1000110010
[4,1,4,1]
=>
1000110001
[4,1,5]
=>
1000110000
[4,2,1,1,1,1]
=>
1000101111
[4,2,1,1,2]
=>
1000101110
[4,2,1,2,1]
=>
1000101101
[4,2,1,3]
=>
1000101100
[4,2,2,1,1]
=>
1000101011
[4,2,2,2]
=>
1000101010
[4,2,3,1]
=>
1000101001
[4,2,4]
=>
1000101000
[4,3,1,1,1]
=>
1000100111
[4,3,1,2]
=>
1000100110
[4,3,2,1]
=>
1000100101
[4,3,3]
=>
1000100100
[4,4,1,1]
=>
1000100011
[4,4,2]
=>
1000100010
[4,5,1]
=>
1000100001
[4,6]
=>
1000100000
[5,1,1,1,1,1]
=>
1000011111
[5,1,1,1,2]
=>
1000011110
[5,1,1,2,1]
=>
1000011101
[5,1,1,3]
=>
1000011100
[5,1,2,1,1]
=>
1000011011
[5,1,2,2]
=>
1000011010
[5,1,3,1]
=>
1000011001
[5,1,4]
=>
1000011000
[5,2,1,1,1]
=>
1000010111
[5,2,1,2]
=>
1000010110
[5,2,2,1]
=>
1000010101
[5,2,3]
=>
1000010100
[5,3,1,1]
=>
1000010011
[5,3,2]
=>
1000010010
[5,4,1]
=>
1000010001
[5,5]
=>
1000010000
[6,1,1,1,1]
=>
1000001111
[6,1,1,2]
=>
1000001110
[6,1,2,1]
=>
1000001101
[6,1,3]
=>
1000001100
[6,2,1,1]
=>
1000001011
[6,2,2]
=>
1000001010
[6,3,1]
=>
1000001001
[6,4]
=>
1000001000
[7,1,1,1]
=>
1000000111
[7,1,2]
=>
1000000110
[7,2,1]
=>
1000000101
[7,3]
=>
1000000100
[8,1,1]
=>
1000000011
[8,2]
=>
1000000010
[9,1]
=>
1000000001
[10]
=>
1000000000
[5,5,1,1]
=>
100001000011
[1,1,5,5]
=>
111000010000
[]
=>
0
[10,1]
=>
10000000001
[1,10]
=>
11000000000
[1,8,1,1]
=>
11000000011
[1,7,2,1]
=>
11000000101
[1,6,3,1]
=>
11000001001
[1,5,4,1]
=>
11000010001
[1,4,5,1]
=>
11000100001
[1,3,6,1]
=>
11001000001
[1,2,7,1]
=>
11010000001
[1,1,8,1]
=>
11100000001
[2,1,1,1,1,1,1,1,1,1]
=>
10111111111
[1,1,1,1,1,1,1,1,1,2]
=>
11111111110
[2,9]
=>
10100000000
[1,1,1,1,1,1,1,1,3]
=>
11111111100
[1,1,1,1,1,1,1,1,2,1]
=>
11111111101
[11]
=>
10000000000
[3,1,1,1,1,1,1,1,1]
=>
10011111111
[9,2]
=>
10000000010
[1,1,6,6]
=>
11100000100000
[1,1,4,1,1,4]
=>
111000111000
[4,1,1,4,1,1]
=>
100011100011
[6,6,1,1]
=>
10000010000011
[1,1,7,7]
=>
1110000001000000
[1,1,5,1,1,5]
=>
11100001110000
[1,1,3,1,2,4]
=>
111001101000
[1,1,4,2,1,3]
=>
111000101100
[3,1,2,4,1,1]
=>
100110100011
[4,2,1,3,1,1]
=>
100010110011
[5,1,1,5,1,1]
=>
10000111000011
[7,7,1,1]
=>
1000000100000011
[1,1,8,8]
=>
111000000010000000
[1,1,6,1,1,6]
=>
1110000011100000
[1,1,4,1,2,5]
=>
11100011010000
[1,1,5,2,1,4]
=>
11100001011000
[1,1,2,1,3,4]
=>
111011001000
[1,1,3,1,1,1,1,3]
=>
111001111100
[1,1,4,3,1,2]
=>
111000100110
[2,2,4,4]
=>
101010001000
[2,1,3,4,1,1]
=>
101100100011
[3,1,1,1,1,3,1,1]
=>
100111110011
[4,1,2,5,1,1]
=>
10001101000011
[4,4,2,2]
=>
100010001010
[4,3,1,2,1,1]
=>
100010011011
[5,2,1,4,1,1]
=>
10000101100011
[6,1,1,6,1,1]
=>
1000001110000011
[8,8,1,1]
=>
100000001000000011
[1,1,9,9]
=>
11100000000100000000
[1,1,7,1,1,7]
=>
111000000111000000
[1,1,5,1,2,6]
=>
1110000110100000
[1,1,6,2,1,5]
=>
1110000010110000
[1,1,3,1,3,5]
=>
11100110010000
[1,1,4,1,1,1,1,4]
=>
11100011111000
[1,1,5,3,1,3]
=>
11100001001100
[1,1,1,1,4,4]
=>
111110001000
[1,1,2,1,2,1,1,3]
=>
111011011100
[1,1,3,2,2,3]
=>
111001010100
[1,1,3,1,1,2,1,2]
=>
111001110110
[1,1,4,4,1,1]
=>
111000100011
[2,2,3,1,1,3]
=>
101010011100
[2,1,2,1,1,3,1,1]
=>
101101110011
[3,1,3,5,1,1]
=>
10011001000011
[3,3,3,3]
=>
100100100100
[3,2,2,3,1,1]
=>
100101010011
[3,1,1,3,2,2]
=>
100111001010
[3,1,1,2,1,2,1,1]
=>
100111011011
[4,1,1,1,1,4,1,1]
=>
10001111100011
[5,1,2,6,1,1]
=>
1000011010000011
[4,4,1,1,1,1]
=>
100010001111
[5,3,1,3,1,1]
=>
10000100110011
[6,2,1,5,1,1]
=>
1000001011000011
[7,1,1,7,1,1]
=>
100000011100000011
[9,9,1,1]
=>
10000000010000000011
[1,1,10,10]
=>
1110000000001000000000
[1,1,8,1,1,8]
=>
11100000001110000000
[1,1,6,1,2,7]
=>
111000001101000000
[1,1,7,2,1,6]
=>
111000000101100000
[1,1,4,1,3,6]
=>
1110001100100000
[1,1,5,1,1,1,1,5]
=>
1110000111110000
[1,1,6,3,1,4]
=>
1110000010011000
[1,1,2,1,4,5]
=>
11101100010000
[1,1,3,1,2,1,1,4]
=>
11100110111000
[1,1,4,2,2,4]
=>
11100010101000
[1,1,4,1,1,2,1,3]
=>
11100011101100
[1,1,5,4,1,2]
=>
11100001000110
[2,2,5,5]
=>
10101000010000
[1,1,1,1,3,1,1,3]
=>
111110011100
[1,1,2,1,1,1,2,3]
=>
111011110100
[1,1,2,1,2,2,1,2]
=>
111011010110
[1,1,3,2,1,1,1,2]
=>
111001011110
[1,1,3,1,1,3,1,1]
=>
111001110011
[2,1,4,5,1,1]
=>
10110001000011
[2,2,2,1,2,3]
=>
101010110100
[2,2,3,2,1,2]
=>
101010010110
[2,1,1,2,3,3]
=>
101110100100
[2,1,1,1,2,3,1,1]
=>
101111010011
[2,1,2,3,2,2]
=>
101101001010
[2,1,2,2,1,2,1,1]
=>
101101011011
[3,1,2,1,1,4,1,1]
=>
10011011100011
[4,1,3,6,1,1]
=>
1000110010000011
[3,3,2,1,1,2]
=>
100100101110
[3,2,1,2,2,2]
=>
100101101010
[3,2,1,1,1,2,1,1]
=>
100101111011
[4,2,2,4,1,1]
=>
10001010100011
[3,1,1,3,1,1,1,1]
=>
100111001111
[4,1,1,2,1,3,1,1]
=>
10001110110011
[5,1,1,1,1,5,1,1]
=>
1000011111000011
[6,1,2,7,1,1]
=>
100000110100000011
[5,5,2,2]
=>
10000100001010
[5,4,1,2,1,1]
=>
10000100011011
[6,3,1,4,1,1]
=>
1000001001100011
[7,2,1,6,1,1]
=>
100000010110000011
[8,1,1,8,1,1]
=>
10000000111000000011
[10,10,1,1]
=>
1000000000100000000011
[3,1,1,1,1,1,1,2]
=>
10011111110
[2,2,1,1,1,1,1,2]
=>
10101111110
[2,1,2,1,1,1,1,2]
=>
10110111110
[2,1,1,2,1,1,1,2]
=>
10111011110
[2,1,1,1,2,1,1,2]
=>
10111101110
[2,1,1,1,1,2,1,2]
=>
10111110110
[2,1,1,1,1,1,2,2]
=>
10111111010
[2,1,1,1,1,1,1,3]
=>
10111111100
[2,1,7,1]
=>
10110000001
[1,1,1,1,6,1]
=>
11111000001
[1,2,1,1,5,1]
=>
11011100001
[1,3,1,1,4,1]
=>
11001110001
[1,4,1,1,3,1]
=>
11000111001
[1,5,1,1,2,1]
=>
11000011101
[1,6,1,1,1,1]
=>
11000001111
[1,7,1,2]
=>
11000000110
[9,1,1]
=>
10000000011
[2,7,1,1]
=>
10100000011
[3,6,1,1]
=>
10010000011
[4,5,1,1]
=>
10001000011
[5,4,1,1]
=>
10000100011
[6,3,1,1]
=>
10000010011
[7,2,1,1]
=>
10000001011
[8,1,1,1]
=>
10000000111
[1,1,1,8]
=>
11110000000
[1,1,2,7]
=>
11101000000
[1,1,3,6]
=>
11100100000
[1,1,4,5]
=>
11100010000
[1,1,5,4]
=>
11100001000
[1,1,6,3]
=>
11100000100
[1,1,7,2]
=>
11100000010
[1,1,9]
=>
11100000000
[1,1,1,1,1,1,1,1,1,1,1]
=>
11111111111
[1,2,1,1,1,1,1,1,1,1]
=>
11011111111
[2,1,1,1,1,1,1,1,2]
=>
10111111110
[1,1,1,1,1,2,1,1,1,1]
=>
11111101111
[1,1,1,1,2,1,1,1,1,1]
=>
11111011111
[1,1,1,1,1,1,1,2,1,1]
=>
11111111011
[2,1,1,1,2,1,1,1,1]
=>
10111101111
[1,1,1,1,1,1,2,1,1,1]
=>
11111110111
[1,1,1,1,1,1,2,1,1,2]
=>
111111101110
[1,1,1,1,1,1,1,1,2,2]
=>
111111111010
[2,2,1,1,2,1,1,2]
=>
101011101110
[2,2,1,1,1,1,2,2]
=>
101011111010
[2,1,1,2,2,1,1,2]
=>
101110101110
[1,1,2,2,2,1,1,2]
=>
111010101110
[2,1,1,2,1,1,2,2]
=>
101110111010
[1,1,2,2,1,1,2,2]
=>
111010111010
[1,1,1,1,3,2,1,2]
=>
111110010110
[1,1,2,1,1,1,1,1,1,2]
=>
111011111110
[1,1,2,1,1,2,2,2]
=>
111011101010
[3,3,1,1,2,2]
=>
100100111010
[1,1,1,1,2,1,1,1,1,2]
=>
111110111110
[1,1,1,1,2,2,2,2]
=>
111110101010
[3,2,2,2,1,2]
=>
100101010110
[2,1,1,1,2,2,1,2]
=>
101111010110
[1,1,1,1,2,1,2,3]
=>
111110110100
[3,2,1,1,1,1,1,2]
=>
100101111110
[2,1,1,1,1,1,1,1,1,2]
=>
101111111110
[2,1,1,1,1,2,2,2]
=>
101111101010
[2,2,2,1,1,1,1,2]
=>
101010111110
[2,2,2,2,2,2]
=>
101010101010
[1,1,1,1,1,1,3,3]
=>
111111100100
[3,1,2,3,1,2]
=>
100110100110
[2,1,3,3,1,2]
=>
101100100110
[3,1,1,1,1,2,1,2]
=>
100111110110
[2,1,2,1,1,2,1,2]
=>
101101110110
[3,1,1,2,1,1,1,2]
=>
100111011110
[2,1,2,2,1,1,1,2]
=>
101101011110
[1,1,3,3,2,2]
=>
111001001010
[2,2,1,1,3,3]
=>
101011100100
[3,3,1,1,1,1,1,1]
=>
100100111111
[2,1,2,3,1,1,1,1]
=>
101101001111
[1,1,3,3,1,1,1,1]
=>
111001001111
[2,2,3,3,1,1]
=>
101010010011
[1,1,1,1,3,3,1,1]
=>
111110010011
[3,1,1,1,1,1,1,3]
=>
100111111100
[3,1,1,2,2,3]
=>
100111010100
[3,2,1,1,2,3]
=>
100101110100
[2,1,1,1,1,1,2,3]
=>
101111110100
[1,1,2,1,2,3,1,1]
=>
111011010011
[4,2,1,1,1,3]
=>
100010111100
[3,2,2,1,1,3]
=>
100101011100
[4,2,1,2,1,2]
=>
100010110110
[2,1,2,2,2,3]
=>
101101010100
[4,3,1,1,1,2]
=>
100010011110
[1,1,2,2,3,3]
=>
111010100100
[3,3,2,2,1,1]
=>
100100101011
[1,1,2,2,2,2,1,1]
=>
111010101011
[2,2,1,1,1,1,1,1,1,1]
=>
101011111111
[2,2,1,1,2,2,1,1]
=>
101011101011
[2,1,1,1,2,1,1,3]
=>
101111011100
[2,2,2,2,1,1,1,1]
=>
101010101111
[2,1,1,2,1,1,1,1,1,1]
=>
101110111111
[2,1,1,1,3,4]
=>
101111001000
[2,1,1,1,1,1,1,2,1,1]
=>
101111111011
[2,1,2,1,1,1,1,3]
=>
101101111100
[2,2,2,1,1,2,1,1]
=>
101010111011
[2,1,1,1,1,2,1,1,1,1]
=>
101111101111
[2,1,2,1,2,4]
=>
101101101000
[2,1,1,2,2,2,1,1]
=>
101110101011
[2,1,3,2,1,3]
=>
101100101100
[2,1,3,1,1,4]
=>
101100111000
[3,1,1,1,2,4]
=>
100111101000
[1,1,2,1,1,2,1,1,1,1]
=>
111011101111
[1,1,1,1,2,1,1,2,1,1]
=>
111110111011
[1,1,2,2,1,1,1,1,1,1]
=>
111010111111
[1,1,1,1,2,2,1,1,1,1]
=>
111110101111
[1,1,1,1,1,1,2,2,1,1]
=>
111111101011
[1,1,1,1,1,1,1,1,1,1,1,1]
=>
111111111111
[5,4,1,2]
=>
100001000110
[4,1,1,3,1,2]
=>
100011100110
[4,3,2,3]
=>
100010010100
[5,3,1,3]
=>
100001001100
[4,1,1,2,1,3]
=>
100011101100
[3,2,1,2,1,1,1,1]
=>
100101101111
[1,1,3,2,1,2,1,1]
=>
111001011011
[5,2,1,4]
=>
100001011000
[5,1,1,5]
=>
100001110000
[3,1,2,2,1,3]
=>
100110101100
[4,2,2,4]
=>
100010101000
[3,1,2,1,1,4]
=>
100110111000
[4,1,1,1,1,4]
=>
100011111000
[3,1,3,5]
=>
100110010000
[6,6]
=>
100000100000
[4,1,2,5]
=>
100011010000
[2,1,4,5]
=>
101100010000
[3,2,3,4]
=>
100101001000
[4,1,5,1]
=>
10001100001
[1,5,1,4]
=>
11000011000
[3,1,1,1,4,1]
=>
10011110001
[1,4,1,1,1,3]
=>
11000111100
[3,1,2,1,3,1]
=>
10011011001
[2,1,2,1,4,1]
=>
10110110001
[1,4,1,2,1,2]
=>
11000110110
[1,3,1,2,1,3]
=>
11001101100
[3,1,3,1,2,1]
=>
10011001101
[2,1,1,1,1,1,3,1]
=>
10111111001
[1,1,3,1,4,1]
=>
11100110001
[3,1,5,1,1]
=>
10011000011
[1,4,1,3,1,1]
=>
11000110011
[1,3,1,1,1,1,1,2]
=>
11001111110
[1,1,5,1,3]
=>
11100001100
[1,2,1,3,1,3]
=>
11011001100
[3,1,4,1,1,1]
=>
10011000111
[2,1,1,1,2,1,2,1]
=>
10111101101
[2,1,3,1,3,1]
=>
10110011001
[1,1,2,1,1,1,3,1]
=>
11101111001
[1,4,1,4,1]
=>
11000110001
[2,1,1,1,4,1,1]
=>
10111100011
[1,3,1,1,1,2,1,1]
=>
11001111011
[2,1,5,1,2]
=>
10110000110
[1,3,1,3,1,2]
=>
11001100110
[1,1,4,1,1,1,2]
=>
11100011110
[1,2,1,2,1,1,1,2]
=>
11011011110
[1,1,1,4,1,3]
=>
11110001100
[2,1,1,1,3,1,1,1]
=>
10111100111
[2,1,2,1,1,1,2,1]
=>
10110111101
[1,1,2,1,2,1,2,1]
=>
11101101101
[1,1,1,1,2,1,3,1]
=>
11111011001
[1,3,1,1,1,3,1]
=>
11001111001
[2,1,2,1,3,1,1]
=>
10110110011
[1,1,2,1,4,1,1]
=>
11101100011
[2,1,4,1,1,1,1]
=>
10110001111
[1,3,1,2,1,1,1,1]
=>
11001101111
[1,1,4,1,2,1,1]
=>
11100011011
[1,2,1,2,1,2,1,1]
=>
11011011011
[1,1,1,1,4,1,2]
=>
11111000110
[1,1,3,1,2,1,2]
=>
11100110110
[1,2,1,1,1,2,1,2]
=>
11011110110
[1,1,1,3,1,1,1,2]
=>
11110011110
[1,1,1,1,1,1,1,1,1,2,1]
=>
111111111101
[1,2,1,1,1,1,1,1,1,1,1]
=>
110111111111
[1,1,1,1,2,1,1,1,2,1]
=>
111110111101
[1,2,1,1,1,2,1,1,1,1]
=>
110111101111
[1,1,1,1,1,2,1,1,2,1]
=>
111111011101
[1,1,1,2,1,1,1,1,2,1]
=>
111101111101
[1,2,1,1,1,1,2,1,1,1]
=>
110111110111
[1,2,1,1,2,1,1,1,1,1]
=>
110111011111
[1,1,1,1,1,1,2,1,2,1]
=>
111111101101
[1,1,1,2,2,1,1,2,1]
=>
111101011101
[1,1,2,1,1,1,1,1,2,1]
=>
111011111101
[1,1,1,1,1,1,1,2,1,1,1]
=>
111111110111
[1,2,1,1,1,1,1,2,1,1]
=>
110111111011
[1,2,1,1,2,2,1,1,1]
=>
110111010111
[1,1,1,2,1,1,1,1,1,1,1]
=>
111101111111
[1,2,1,2,1,1,1,1,1,1]
=>
110110111111
[1,1,1,1,1,1,1,2,2,1]
=>
111111110101
[1,1,1,2,1,2,1,2,1]
=>
111101101101
[1,1,2,1,2,1,1,2,1]
=>
111011011101
[1,2,1,1,1,1,1,1,2,1]
=>
110111111101
[1,1,1,2,1,1,2,1,1,1]
=>
111101110111
[1,2,1,1,2,1,2,1,1]
=>
110111011011
[1,1,1,1,1,2,1,1,1,1,1]
=>
111111011111
[1,2,1,2,1,2,1,1,1]
=>
110110110111
[1,2,2,1,1,1,1,1,1,1]
=>
110101111111
[1,1,1,2,1,1,2,2,1]
=>
111101110101
[1,1,1,1,2,2,1,2,1]
=>
111110101101
[1,1,2,1,1,2,1,2,1]
=>
111011101101
[1,1,2,2,1,1,1,2,1]
=>
111010111101
[1,2,1,1,2,1,1,2,1]
=>
110111011101
[1,1,1,1,2,1,2,1,1,1]
=>
111110110111
[1,1,2,1,1,1,2,1,1,1]
=>
111011110111
[1,1,1,1,1,2,1,2,1,1]
=>
111111011011
[1,2,1,1,1,2,2,1,1]
=>
110111101011
[1,1,1,2,1,1,1,2,1,1]
=>
111101111011
[1,2,1,2,1,1,2,1,1]
=>
110110111011
[1,1,2,1,2,1,1,1,1,1]
=>
111011011111
[1,1,1,2,1,2,1,1,1,1]
=>
111101101111
[1,2,1,2,2,1,1,1,1]
=>
110110101111
[1,2,2,1,1,2,1,1,1]
=>
110101110111
[1,1,1,1,2,1,1,1,3]
=>
111110111100
[3,1,1,1,2,1,1,1,1]
=>
100111101111
[1,1,1,4,1,1,3]
=>
111100011100
[3,1,1,4,1,1,1]
=>
100111000111
[1,1,1,2,3,1,3]
=>
111101001100
[1,1,3,2,1,1,3]
=>
111001011100
[3,1,1,2,3,1,1]
=>
100111010011
[3,1,3,2,1,1,1]
=>
100110010111
[1,1,1,2,1,3,3]
=>
111101100100
[1,1,6,1,3]
=>
111000001100
[1,3,1,2,1,1,3]
=>
110011011100
[3,1,1,2,1,3,1]
=>
100111011001
[3,1,6,1,1]
=>
100110000011
[3,3,1,2,1,1,1]
=>
100100110111
[1,1,1,2,1,1,5]
=>
111101110000
[1,1,4,3,3]
=>
111000100100
[1,1,2,2,2,1,3]
=>
111010101100
[1,3,4,1,3]
=>
110010001100
[3,1,1,2,1,1,3]
=>
100111011100
[1,1,4,1,2,2,1]
=>
111000110101
[3,1,4,3,1]
=>
100110001001
[1,1,2,1,2,1,2,1,1]
=>
111011011011
[3,1,2,2,2,1,1]
=>
100110101011
[1,2,2,1,4,1,1]
=>
110101100011
[3,3,4,1,1]
=>
100100100011
[5,1,1,2,1,1,1]
=>
100001110111
[1,1,4,1,5]
=>
111000110000
[1,1,2,5,3]
=>
111010000100
[1,3,2,3,3]
=>
110010100100
[1,5,2,1,3]
=>
110000101100
[3,1,4,1,3]
=>
100110001100
[1,1,2,3,2,2,1]
=>
111010010101
[1,3,2,1,2,2,1]
=>
110010110101
[1,1,2,1,2,4,1]
=>
111011010001
[3,1,2,5,1]
=>
100110100001
[1,2,2,1,2,3,1]
=>
110101101001
[3,3,2,3,1]
=>
100100101001
[1,4,2,1,2,1,1]
=>
110001011011
[1,2,2,3,2,1,1]
=>
110101001011
[3,5,2,1,1]
=>
100100001011
[5,1,4,1,1]
=>
100001100011
[1,4,5,2]
=>
110001000010
[4,2,1,4,1]
=>
100010110001
[1,3,5,3]
=>
110010000100
[3,3,1,3,2]
=>
100100110010
[1,2,1,1,4,3]
=>
110111000100
[1,3,4,1,1,2]
=>
110010001110
[2,1,1,2,1,3,2]
=>
101110110010
[1,1,1,2,4,3]
=>
111101000100
[1,2,5,4]
=>
110100001000
[1,3,3,1,2,2]
=>
110010011010
[1,1,3,4,1,1,1]
=>
111001000111
[1,1,2,2,1,3,2]
=>
111010110010
[2,4,1,2,3]
=>
101000110100
[3,3,1,1,1,2,1]
=>
100100111101
[2,3,4,3]
=>
101001000100
[1,2,1,1,3,1,1,2]
=>
110111001110
[1,2,4,1,1,3]
=>
110100011100
[1,3,2,1,3,2]
=>
110010110010
[1,1,2,4,2,1,1]
=>
111010001011
[1,1,1,3,1,2,3]
=>
111100110100
[2,1,2,3,1,2,1]
=>
101101001101
[2,1,1,2,1,2,1,1,1]
=>
101110110111
[2,2,1,2,1,2,2]
=>
101011011010
[2,4,1,1,1,1,2]
=>
101000111110
[1,2,4,2,1,2]
=>
110100010110
[1,2,3,1,2,3]
=>
110100110100
[1,1,1,1,1,3,2,1,1]
=>
111111001011
[1,1,2,3,1,1,1,1,1]
=>
111010011111
[1,2,2,3,1,1,2]
=>
110101001110
[1,2,1,2,1,2,3]
=>
110110110100
[1,1,1,1,1,2,1,2,2]
=>
111111011010
[1,1,1,3,1,1,1,1,2]
=>
111100111110
[2,1,1,3,2,2,1]
=>
101110010101
[2,2,1,2,1,1,1,1,1]
=>
101011011111
[2,4,1,1,2,1,1]
=>
101000111011
[2,4,2,2,2]
=>
101000101010
[4,5,1,1,1]
=>
100010000111
[1,5,5,1]
=>
110000100001
[1,4,1,1,4,1]
=>
110001110001
[3,2,1,3,1,1,1]
=>
100101100111
[2,1,2,4,1,1,1]
=>
101101000111
[1,4,2,1,3,1]
=>
110001011001
[1,3,1,2,4,1]
=>
110011010001
[2,1,1,1,1,3,1,1,1]
=>
101111100111
[3,4,2,2,1]
=>
100100010101
[1,4,3,1,2,1]
=>
110001001101
[1,3,1,1,1,1,3,1]
=>
110011111001
[1,2,4,4,1]
=>
110100010001
[1,2,1,3,4,1]
=>
110110010001
[3,4,1,1,1,1,1]
=>
100100011111
[2,2,2,3,1,1,1]
=>
101010100111
[1,1,2,1,1,3,1,1,1]
=>
111011100111
[1,4,4,1,1,1]
=>
110001000111
[1,3,1,1,2,1,2,1]
=>
110011101101
[2,3,3,3,1]
=>
101001001001
[1,3,2,2,3,1]
=>
110010101001
[1,2,3,1,1,3,1]
=>
110100111001
[1,2,1,2,1,1,3,1]
=>
110110111001
[1,1,1,4,4,1]
=>
111100010001
[2,1,1,3,1,1,1,1,1]
=>
101110011111
[2,2,1,1,1,2,1,1,1]
=>
101011110111
[1,1,2,2,1,2,1,1,1]
=>
111010110111
[1,1,1,1,2,3,1,1,1]
=>
111110100111
[1,3,1,1,3,1,1,1]
=>
110011100111
[2,2,1,2,2,2,1]
=>
101011010101
[2,3,2,1,1,2,1]
=>
101001011101
[1,3,2,1,1,1,2,1]
=>
110010111101
[1,2,3,2,1,2,1]
=>
110100101101
[1,2,1,2,2,1,2,1]
=>
110110101101
[1,1,1,2,3,3,1]
=>
111101001001
[1,2,1,1,1,2,3,1]
=>
110111101001
[1,1,1,3,1,1,3,1]
=>
111100111001
[1,1,1,5,4]
=>
111100001000
[1,1,1,4,2,1,2]
=>
111100010110
[1,4,4,2,1]
=>
110001000101
[1,1,1,4,3,1,1]
=>
111100010011
[1,2,2,4,3]
=>
110101000100
[1,3,1,1,3,2,1]
=>
110011100101
[1,1,1,3,1,1,2,1,1]
=>
111100111011
[1,3,3,3,2]
=>
110010010010
[1,1,1,3,2,2,2]
=>
111100101010
[1,1,1,2,1,2,1,1,2]
=>
111101101110
[1,1,1,1,1,4,3]
=>
111111000100
[1,2,1,2,3,2,1]
=>
110110100101
[1,3,3,2,1,1,1]
=>
110010010111
[1,1,1,3,2,1,1,1,1]
=>
111100101111
[1,1,1,2,1,2,2,1,1]
=>
111101101011
[1,2,1,1,2,3,2]
=>
110111010010
[1,2,2,2,1,2,2]
=>
110101011010
[1,1,1,2,1,1,1,2,2]
=>
111101111010
[1,1,1,1,1,3,1,1,2]
=>
111111001110
[1,1,2,1,1,1,1,2,1,1]
=>
111011111011
[1,2,2,2,5]
=>
110101010000
[1,1,2,3,5]
=>
111010010000
[3,4,5]
=>
100100010000
[2,1,2,1,2,1,1,1]
=>
10110110111
[3,1,3,1,2,1,1]
=>
100110011011
[4,1,2,1,2,1,1]
=>
100011011011
[3,1,2,1,2,1,1]
=>
10011011011
[4,1,3,1,1,1,1]
=>
100011001111
[3,1,3,1,1,1,1]
=>
10011001111
[4,1,3,1,2]
=>
10001100110
[1,1,1,2,1,2,1,2]
=>
11110110110
[1,1,2,1,2,1,3]
=>
11101101100
[1,1,1,1,3,1,3]
=>
11111001100
[2,1,3,1,4]
=>
10110011000
[1,1,2,1,1,1,1,1,1,1]
=>
11101111111
[1,2,1,2,1,1,1,1,1]
=>
11011011111
[2,1,3,1,1,1,1,1]
=>
10110011111
[1,1,1,2,1,2,1,1,1]
=>
11110110111
[1,1,3,1,2,1,1,1]
=>
11100110111
[1,2,1,1,1,2,1,1,1]
=>
11011110111
[1,3,1,3,1,1,1]
=>
11001100111
[1,1,2,1,3,1,1,1]
=>
11101100111
[1,1,1,1,1,2,1,2,1]
=>
11111101101
[1,2,1,3,1,2,1]
=>
11011001101
[1,1,1,1,3,1,2,1]
=>
11111001101
[2,1,4,1,2,1]
=>
10110001101
[1,1,1,2,1,1,1,2,1]
=>
11110111101
[1,1,3,1,1,1,2,1]
=>
11100111101
[1,2,1,1,1,1,1,2,1]
=>
11011111101
[1,3,1,2,1,2,1]
=>
11001101101
[1,1,1,3,1,3,1]
=>
11110011001
[1,1,4,1,3,1]
=>
11100011001
[1,2,1,2,1,3,1]
=>
11011011001
[1,1,2,1,1,1,2,1,1]
=>
11101111011
[1,1,1,1,2,1,2,1,1]
=>
11111011011
[2,1,3,1,2,1,1]
=>
10110011011
[1,1,1,2,1,3,1,1]
=>
11110110011
[1,1,3,1,3,1,1]
=>
11100110011
[1,2,1,1,1,3,1,1]
=>
11011110011
[1,1,1,1,1,1,3,1,1]
=>
11111110011
[1,3,1,4,1,1]
=>
11001100011
[1,1,2,1,2,1,1,1,1]
=>
11101101111
[1,2,1,3,1,1,1,1]
=>
11011001111
[1,1,1,1,3,1,1,1,1]
=>
11111001111
[1,1,1,2,1,1,1,1,1,1]
=>
11110111111
[1,1,3,1,1,1,1,1,1]
=>
11100111111
[2,1,2,1,1,1,1,1,1]
=>
10110111111
[1,1,1,3,1,2,1,1]
=>
11110011011
[2,1,1,1,1,1,2,1,1]
=>
10111111011
[3,1,1,1,3,1,1]
=>
10011110011
[4,1,4,1,1]
=>
10001100011
[1,1,1,1,1,3,1,2]
=>
11111100110
[1,1,2,1,3,1,2]
=>
11101100110
[1,2,1,4,1,2]
=>
11011000110
[1,1,1,1,1,1,2,1,2]
=>
11111110110
[2,1,2,1,2,1,2]
=>
10110110110
[2,1,1,1,3,1,2]
=>
10111100110
[3,1,4,1,2]
=>
10011000110
[1,1,1,1,2,1,1,1,2]
=>
11111011110
[2,1,3,1,1,1,2]
=>
10110011110
[1,1,2,1,1,1,1,1,2]
=>
11101111110
[3,1,2,1,1,1,2]
=>
10011011110
[3,1,1,1,2,1,2]
=>
10011110110
[2,1,4,1,3]
=>
10110001100
[2,1,1,1,2,1,3]
=>
10111101100
[3,1,3,1,3]
=>
10011001100
[1,1,3,1,1,1,3]
=>
11100111100
[2,1,2,1,1,1,3]
=>
10110111100
[3,1,1,1,1,1,3]
=>
10011111100
[4,1,2,1,3]
=>
10001101100
[1,1,4,1,4]
=>
11100011000
[3,1,2,1,4]
=>
10011011000
[4,1,1,1,4]
=>
10001111000
[5,1,5]
=>
10000110000
[1,2,2,2,2,2,1]
=>
110101010101
[1,1,1,2,2,2,2,1]
=>
111101010101
[1,2,1,1,2,2,2,1]
=>
110111010101
[1,1,2,1,2,2,2,1]
=>
111011010101
[1,1,1,1,1,2,2,2,1]
=>
111111010101
[1,2,2,1,1,2,2,1]
=>
110101110101
[1,2,1,2,1,2,2,1]
=>
110110110101
[1,1,2,2,1,2,2,1]
=>
111010110101
[1,1,1,1,2,1,2,2,1]
=>
111110110101
[1,2,1,1,1,1,2,2,1]
=>
110111110101
[1,1,2,1,1,1,2,2,1]
=>
111011110101
[1,2,2,2,1,1,2,1]
=>
110101011101
[1,2,2,1,2,1,2,1]
=>
110101101101
[1,1,2,2,2,1,2,1]
=>
111010101101
[1,2,1,1,1,2,1,2,1]
=>
110111101101
[1,2,2,1,1,1,1,2,1]
=>
110101111101
[1,2,1,2,1,1,1,2,1]
=>
110110111101
[1,2,2,2,2,1,1,1]
=>
110101010111
[1,1,1,2,2,2,1,1,1]
=>
111101010111
[1,1,2,1,2,2,1,1,1]
=>
111011010111
[1,1,1,1,1,2,2,1,1,1]
=>
111111010111
[1,2,2,2,1,2,1,1]
=>
110101011011
[1,1,1,2,2,1,2,1,1]
=>
111101011011
[1,2,2,1,2,2,1,1]
=>
110101101011
[1,2,1,2,2,2,1,1]
=>
110110101011
[1,1,1,1,2,2,2,1,1]
=>
111110101011
[1,1,2,1,1,2,2,1,1]
=>
111011101011
[1,2,2,1,1,1,2,1,1]
=>
110101111011
[1,1,2,2,1,1,2,1,1]
=>
111010111011
[1,1,1,1,1,1,1,1,2,1,1]
=>
111111111011
[1,2,2,2,1,1,1,1,1]
=>
110101011111
[1,1,1,2,2,1,1,1,1,1]
=>
111101011111
[1,2,2,1,2,1,1,1,1]
=>
110101101111
[1,1,2,2,2,1,1,1,1]
=>
111010101111
[1,1,1,1,1,1,2,1,1,1,1]
=>
111111101111
[1,1,1,1,2,1,1,1,1,1,1]
=>
111110111111
[1,1,2,1,1,1,1,1,1,1,1]
=>
111011111111
[12]
=>
100000000000
[1,2,9]
=>
110100000000
[3,2,7]
=>
100101000000
[1,4,7]
=>
110001000000
[1,1,2,1,7]
=>
111011000000
[5,2,5]
=>
100001010000
[1,6,5]
=>
110000010000
[3,1,2,1,5]
=>
100110110000
[1,3,2,1,5]
=>
110010110000
[7,2,3]
=>
100000010100
[1,2,4,2,3]
=>
110100010100
[3,2,2,2,3]
=>
100101010100
[1,4,2,2,3]
=>
110001010100
[1,1,2,1,2,2,3]
=>
111011010100
[5,4,3]
=>
100001000100
[3,6,3]
=>
100100000100
[1,8,3]
=>
110000000100
[3,1,2,3,3]
=>
100110100100
[5,1,2,1,3]
=>
100001101100
[1,2,2,1,2,1,3]
=>
110101101100
[3,3,2,1,3]
=>
100100101100
[9,2,1]
=>
100000000101
[1,2,6,2,1]
=>
110100000101
[3,2,4,2,1]
=>
100101000101
[1,1,2,1,4,2,1]
=>
111011000101
[5,2,2,2,1]
=>
100001010101
[1,6,2,2,1]
=>
110000010101
[3,1,2,1,2,2,1]
=>
100110110101
[7,4,1]
=>
100000010001
[3,2,2,4,1]
=>
100101010001
[1,4,2,4,1]
=>
110001010001
[5,6,1]
=>
100001000001
[1,2,2,6,1]
=>
110101000001
[3,8,1]
=>
100100000001
[1,10,1]
=>
110000000001
[1,1,2,7,1]
=>
111010000001
[1,3,2,5,1]
=>
110010100001
[1,1,4,5,1]
=>
111000100001
[1,1,1,2,1,5,1]
=>
111101100001
[5,1,2,3,1]
=>
100001101001
[1,5,2,3,1]
=>
110000101001
[1,1,2,2,2,3,1]
=>
111010101001
[1,3,4,3,1]
=>
110010001001
[1,1,6,3,1]
=>
111000001001
[1,3,1,2,1,3,1]
=>
110011011001
[1,1,3,2,1,3,1]
=>
111001011001
[1,1,1,4,1,3,1]
=>
111100011001
[1,1,1,1,2,1,1,3,1]
=>
111110111001
[7,1,2,1,1]
=>
100000011011
[1,2,4,1,2,1,1]
=>
110100011011
[3,2,2,1,2,1,1]
=>
100101011011
[5,3,2,1,1]
=>
100001001011
[1,7,2,1,1]
=>
110000001011
[1,3,2,2,2,1,1]
=>
110010101011
[1,1,4,2,2,1,1]
=>
111000101011
[1,5,4,1,1]
=>
110000100011
[1,1,2,2,4,1,1]
=>
111010100011
[1,3,6,1,1]
=>
110010000011
[1,1,8,1,1]
=>
111000000011
[1,1,1,2,5,1,1]
=>
111101000011
[1,3,1,2,3,1,1]
=>
110011010011
[1,1,3,2,3,1,1]
=>
111001010011
[1,1,1,1,2,1,3,1,1]
=>
111110110011
[1,5,1,2,1,1,1]
=>
110000110111
[1,1,5,2,1,1,1]
=>
111000010111
[1,3,1,4,1,1,1]
=>
110011000111
[1,1,1,6,1,1,1]
=>
111100000111
[1,3,1,1,2,1,1,1,1]
=>
110011101111
[1,1,3,1,2,1,1,1,1]
=>
111001101111
[1,1,1,1,4,1,1,1,1]
=>
111110001111
[1,1,1,2,3,1,1,2]
=>
111101001110
[1,2,3,2,2,2]
=>
110100101010
[1,2,1,1,2,1,2,2]
=>
110111011010
[1,2,3,1,1,1,1,2]
=>
110100111110
[1,2,1,3,3,1,1]
=>
110110010011
[1,5,3,1,2]
=>
110000100110
[1,3,1,2,2,1,2]
=>
110011010110
[1,2,1,2,1,1,1,1,2]
=>
110110111110
[1,2,1,3,2,1,2]
=>
110110010110
[1,5,1,1,4]
=>
110000111000
[1,3,1,3,4]
=>
110011001000
[1,2,1,3,1,1,3]
=>
110110011100
[1,2,1,4,4]
=>
110110001000
[1,1,2,3,1,2,2]
=>
111010011010
[1,1,2,4,1,1,2]
=>
111010001110
[1,1,3,5,2]
=>
111001000010
[2,4,3,2,1]
=>
101000100101
[2,1,1,2,1,1,1,2,1]
=>
101110111101
[2,4,2,1,1,1,1]
=>
101000101111
[2,5,3,1,1]
=>
101000010011
[2,2,1,3,2,1,1]
=>
101011001011
[2,1,1,4,2,1,1]
=>
101110001011
[2,5,2,1,2]
=>
101000010110
[2,2,1,3,1,1,2]
=>
101011001110
[2,5,1,1,3]
=>
101000011100
[2,6,4]
=>
101000001000
[2,2,1,4,3]
=>
101011000100
[2,1,1,3,1,2,2]
=>
101110011010
[2,1,1,4,1,1,2]
=>
101110001110
[2,1,1,5,3]
=>
101110000100
[2,1,2,5,2]
=>
101101000010
[3,1,1,3,1,2,1]
=>
100111001101
[3,4,1,2,2]
=>
100100011010
[3,5,1,1,2]
=>
100100001110
[3,1,1,5,2]
=>
100111000010
[4,3,1,3,1]
=>
100010011001
[4,4,1,2,1]
=>
100010001101
[4,6,2]
=>
100010000010
[2,3,1,1,1,1,1,1,1]
=>
101001111111
[1,3,3,1,1,1,1,1]
=>
110010011111
[2,3,2,2,1,1,1]
=>
101001010111
[1,3,2,1,2,1,1,1]
=>
110010110111
[1,1,1,3,3,1,1,1]
=>
111100100111
[1,2,3,3,1,1,1]
=>
110100100111
[1,2,1,2,3,1,1,1]
=>
110110100111
[2,3,1,1,2,2,1]
=>
101001110101
[1,3,3,2,2,1]
=>
110010010101
[2,2,1,1,1,1,1,2,1]
=>
101011111101
[1,1,1,3,2,1,2,1]
=>
111100101101
[2,2,2,2,1,2,1]
=>
101010101101
[2,1,1,1,1,2,1,2,1]
=>
101111101101
[3,2,1,2,1,2,1]
=>
100101101101
[1,1,3,3,1,2,1]
=>
111001001101
[1,1,1,1,1,3,3,1]
=>
111111001001
[1,2,1,1,3,3,1]
=>
110111001001
[1,2,2,3,3,1]
=>
110101001001
[1,1,1,2,1,2,3,1]
=>
111101101001
[1,1,1,1,1,1,2,3,1]
=>
111111101001
[2,2,1,1,2,3,1]
=>
101011101001
[2,1,1,2,2,3,1]
=>
101110101001
[2,2,2,1,1,3,1]
=>
101010111001
[1,1,2,1,1,1,1,3,1]
=>
111011111001
[2,1,1,1,1,1,1,3,1]
=>
101111111001
[3,2,1,1,1,3,1]
=>
100101111001
[2,1,2,2,1,3,1]
=>
101101011001
[1,1,1,1,3,4,1]
=>
111110010001
[2,2,3,4,1]
=>
101010010001
[2,1,1,1,2,4,1]
=>
101111010001
[1,1,3,1,1,4,1]
=>
111001110001
[2,1,2,1,1,4,1]
=>
101101110001
[3,1,1,1,1,4,1]
=>
100111110001
[2,1,3,5,1]
=>
101100100001
[4,1,1,5,1]
=>
100011100001
[1,3,3,1,1,2,1]
=>
110010011101
[1,1,1,3,3,2,1]
=>
111100100101
[1,3,2,1,1,1,1,1,1]
=>
110010111111
[1,4,3,1,1,1,1]
=>
110001001111
[1,3,1,1,1,1,2,1,1]
=>
110011111011
[1,4,1,1,3,1,1]
=>
110001110011
[1,1,1,1,1,1,1,3,2]
=>
111111110010
[1,2,2,1,1,3,2]
=>
110101110010
[1,1,1,2,2,3,2]
=>
111101010010
[1,2,1,1,1,1,1,2,2]
=>
110111111010
[1,3,2,1,1,2,2]
=>
110010111010
[1,2,1,2,2,2,2]
=>
110110101010
[1,3,1,1,2,2,2]
=>
110011101010
[1,4,3,2,2]
=>
110001001010
[1,2,1,1,1,2,1,1,2]
=>
110111101110
[1,3,2,2,1,1,2]
=>
110010101110
[1,3,1,1,1,1,1,1,2]
=>
110011111110
[1,4,2,1,1,1,2]
=>
110001011110
[1,4,1,1,2,1,2]
=>
110001110110
[1,2,1,1,1,3,3]
=>
110111100100
[1,3,1,1,1,2,3]
=>
110011110100
[1,4,1,1,1,1,3]
=>
110001111100
[1,4,1,2,4]
=>
110001101000
[11,1]
=>
100000000001
[9,3]
=>
100000000100
[7,5]
=>
100000010000
[1,2,2,2,3,1,1]
=>
110101010011
[1,2,3,2,2,1,1]
=>
110100101011
[2,2,2,2,2,1,1]
=>
101010101011
[1,2,4,1,1,2,1]
=>
110100011101
[1,3,2,2,1,2,1]
=>
110010101101
[1,3,1,2,2,2,1]
=>
110011010101
[1,3,3,1,2,1,1]
=>
110010011011
[1,3,1,3,2,1,1]
=>
110011001011
[1,3,2,1,3,1,1]
=>
110010110011
[1,3,1,3,1,2,1]
=>
110011001101
[1,2,3,1,2,2,1]
=>
110100110101
[1,2,3,1,3,1,1]
=>
110100110011
[1,2,2,3,1,2,1]
=>
110101001101
[5,7]
=>
100001000000
[3,9]
=>
100100000000
[1,11]
=>
110000000000
[6,1,1,1,1,1,1]
=>
100000111111
[5,1,1,1,1,2,1]
=>
100001111101
[5,1,1,1,2,1,1]
=>
100001111011
[4,1,1,1,3,1,1]
=>
100011110011
[4,1,1,1,2,2,1]
=>
100011110101
[4,1,1,2,1,2,1]
=>
100011101101
[4,1,1,3,1,1,1]
=>
100011100111
[4,1,1,2,2,1,1]
=>
100011101011
[3,1,1,3,2,1,1]
=>
100111001011
[3,1,1,2,2,2,1]
=>
100111010101
[5,1,2,1,1,1,1]
=>
100001101111
[4,1,2,1,1,2,1]
=>
100011011101
[3,1,2,1,3,1,1]
=>
100110110011
[3,1,3,1,1,2,1]
=>
100110011101
[3,1,4,1,1,1,1]
=>
100110001111
[2,1,5,1,1,1,1]
=>
101100001111
[2,1,4,1,1,2,1]
=>
101100011101
[2,1,4,1,2,1,1]
=>
101100011011
[2,1,3,1,3,1,1]
=>
101100110011
[2,1,3,1,2,2,1]
=>
101100110101
[4,1,2,2,1,1,1]
=>
100011010111
[3,1,2,2,1,2,1]
=>
100110101101
[2,1,4,2,1,1,1]
=>
101100010111
[2,1,3,2,1,2,1]
=>
101100101101
[3,1,2,3,1,1,1]
=>
100110100111
[2,1,3,3,1,1,1]
=>
101100100111
[2,1,3,2,2,1,1]
=>
101100101011
[2,1,2,3,2,1,1]
=>
101101001011
[2,1,2,2,3,1,1]
=>
101101010011
[2,1,2,2,2,2,1]
=>
101101010101
[5,2,1,1,1,1,1]
=>
100001011111
[4,2,1,1,1,2,1]
=>
100010111101
[4,2,1,1,2,1,1]
=>
100010111011
[3,2,1,1,3,1,1]
=>
100101110011
[3,2,1,1,2,2,1]
=>
100101110101
[4,2,1,2,1,1,1]
=>
100010110111
[2,2,1,4,1,1,1]
=>
101011000111
[2,2,1,3,1,2,1]
=>
101011001101
[3,2,1,2,2,1,1]
=>
100101101011
[2,2,1,2,3,1,1]
=>
101011010011
[4,3,1,1,1,1,1]
=>
100010011111
[3,3,1,1,2,1,1]
=>
100100111011
[2,3,1,1,3,1,1]
=>
101001110011
[2,4,1,1,1,2,1]
=>
101000111101
[2,5,1,1,1,1,1]
=>
101000011111
[1,6,1,1,1,1,1]
=>
110000011111
[1,5,1,1,1,2,1]
=>
110000111101
[1,5,1,1,2,1,1]
=>
110000111011
[1,4,1,1,2,2,1]
=>
110001110101
[2,3,1,2,1,2,1]
=>
101001101101
[2,4,1,2,1,1,1]
=>
101000110111
[1,4,1,2,1,2,1]
=>
110001101101
[2,3,1,3,1,1,1]
=>
101001100111
[1,4,1,3,1,1,1]
=>
110001100111
[2,3,1,2,2,1,1]
=>
101001101011
[1,4,1,2,2,1,1]
=>
110001101011
[4,2,2,1,1,1,1]
=>
100010101111
[3,2,2,1,1,2,1]
=>
100101011101
[2,2,2,1,3,1,1]
=>
101010110011
[2,2,2,1,2,2,1]
=>
101010110101
[3,3,2,1,1,1,1]
=>
100100101111
[1,5,2,1,1,1,1]
=>
110000101111
[1,4,2,1,1,2,1]
=>
110001011101
[2,3,2,1,2,1,1]
=>
101001011011
[3,2,3,1,1,1,1]
=>
100101001111
[2,2,3,1,1,2,1]
=>
101010011101
[2,3,3,1,1,1,1]
=>
101001001111
[2,2,4,1,1,1,1]
=>
101010001111
[1,3,4,1,1,1,1]
=>
110010001111
[1,2,5,1,1,1,1]
=>
110100001111
[2,2,3,1,2,1,1]
=>
101010011011
[3,2,2,2,1,1,1]
=>
100101010111
[1,4,2,2,1,1,1]
=>
110001010111
[2,2,3,2,1,1,1]
=>
101010010111
[1,2,4,2,1,1,1]
=>
110100010111
[1,3,2,3,1,1,1]
=>
110010100111
[1,2,2,4,1,1,1]
=>
110101000111
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 $i_1,\dots,i_k$.
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 $i_1,\dots,i_k$.
Properties
injective, graded
Sage code
def mapping(w):
return Words([0,1])(w.to_code())
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
Jan 29, 2020 at 13:25 by Martin Rubey
searching the database
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