************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 The FindStatCrew * * * * This information is distributed in the hope that it will be * * useful, but WITHOUT ANY WARRANTY; without even the implied * * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ************************************************************************ ------------------------------------------------------------------------ Map identifier: Mp00094 ------------------------------------------------------------------------ Map name: to binary word ------------------------------------------------------------------------ Domain: Integer compositions ------------------------------------------------------------------------ Codomain: Binary words ------------------------------------------------------------------------ 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 $0$. ------------------------------------------------------------------------ References: ------------------------------------------------------------------------ Code: def mapping(w): # we diverge from the SageMath convention for the empty # composition to make the map graded in the strict sense if w: return Words([0,1])(w.to_code()) return Words([0,1])([]) ------------------------------------------------------------------------ Map 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 [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 [10,1] => 10000000001 [1,1,1,1,1,1,1,1,1,1,1,1] => 111111111111 [1,1,1,1,1,1,1,1,2,2] => 111111111010 [1,1,1,1,1,1,2,2,1,1] => 111111101011 [1,1,1,1,1,1,2,1,1,2] => 111111101110 [1,1,1,1,1,1,3,3] => 111111100100 [1,1,1,1,2,2,1,1,1,1] => 111110101111 [1,1,1,1,2,2,2,2] => 111110101010 [1,1,1,1,2,1,1,2,1,1] => 111110111011 [1,1,1,1,2,1,1,1,1,2] => 111110111110 [1,1,1,1,2,1,2,3] => 111110110100 [1,1,1,1,3,3,1,1] => 111110010011 [1,1,1,1,3,2,1,2] => 111110010110 [1,1,1,1,3,1,1,3] => 111110011100 [1,1,1,1,4,4] => 111110001000 [1,1,2,2,1,1,1,1,1,1] => 111010111111 [1,1,2,2,1,1,2,2] => 111010111010 [1,1,2,2,2,2,1,1] => 111010101011 [1,1,2,2,2,1,1,2] => 111010101110 [1,1,2,2,3,3] => 111010100100 [1,1,2,1,1,2,1,1,1,1] => 111011101111 [1,1,2,1,1,2,2,2] => 111011101010 [1,1,2,1,1,1,1,2,1,1] => 111011111011 [1,1,2,1,1,1,1,1,1,2] => 111011111110 [1,1,2,1,1,1,2,3] => 111011110100 [1,1,2,1,2,3,1,1] => 111011010011 [1,1,2,1,2,2,1,2] => 111011010110 [1,1,2,1,2,1,1,3] => 111011011100 [1,1,2,1,3,4] => 111011001000 [1,1,3,3,1,1,1,1] => 111001001111 [1,1,3,3,2,2] => 111001001010 [1,1,3,2,1,2,1,1] => 111001011011 [1,1,3,2,1,1,1,2] => 111001011110 [1,1,3,2,2,3] => 111001010100 [1,1,3,1,1,3,1,1] => 111001110011 [1,1,3,1,1,2,1,2] => 111001110110 [1,1,3,1,1,1,1,3] => 111001111100 [1,1,3,1,2,4] => 111001101000 [1,1,4,4,1,1] => 111000100011 [1,1,4,3,1,2] => 111000100110 [1,1,4,2,1,3] => 111000101100 [1,1,4,1,1,4] => 111000111000 [1,1,5,5] => 111000010000 [2,2,1,1,1,1,1,1,1,1] => 101011111111 [2,2,1,1,1,1,2,2] => 101011111010 [2,2,1,1,2,2,1,1] => 101011101011 [2,2,1,1,2,1,1,2] => 101011101110 [2,2,1,1,3,3] => 101011100100 [2,2,2,2,1,1,1,1] => 101010101111 [2,2,2,2,2,2] => 101010101010 [2,2,2,1,1,2,1,1] => 101010111011 [2,2,2,1,1,1,1,2] => 101010111110 [2,2,2,1,2,3] => 101010110100 [2,2,3,3,1,1] => 101010010011 [2,2,3,2,1,2] => 101010010110 [2,2,3,1,1,3] => 101010011100 [2,2,4,4] => 101010001000 [2,1,1,2,1,1,1,1,1,1] => 101110111111 [2,1,1,2,1,1,2,2] => 101110111010 [2,1,1,2,2,2,1,1] => 101110101011 [2,1,1,2,2,1,1,2] => 101110101110 [2,1,1,2,3,3] => 101110100100 [2,1,1,1,1,2,1,1,1,1] => 101111101111 [2,1,1,1,1,2,2,2] => 101111101010 [2,1,1,1,1,1,1,2,1,1] => 101111111011 [2,1,1,1,1,1,1,1,1,2] => 101111111110 [2,1,1,1,1,1,2,3] => 101111110100 [2,1,1,1,2,3,1,1] => 101111010011 [2,1,1,1,2,2,1,2] => 101111010110 [2,1,1,1,2,1,1,3] => 101111011100 [2,1,1,1,3,4] => 101111001000 [2,1,2,3,1,1,1,1] => 101101001111 [2,1,2,3,2,2] => 101101001010 [2,1,2,2,1,2,1,1] => 101101011011 [2,1,2,2,1,1,1,2] => 101101011110 [2,1,2,2,2,3] => 101101010100 [2,1,2,1,1,3,1,1] => 101101110011 [2,1,2,1,1,2,1,2] => 101101110110 [2,1,2,1,1,1,1,3] => 101101111100 [2,1,2,1,2,4] => 101101101000 [2,1,3,4,1,1] => 101100100011 [2,1,3,3,1,2] => 101100100110 [2,1,3,2,1,3] => 101100101100 [2,1,3,1,1,4] => 101100111000 [2,1,4,5] => 101100010000 [3,3,1,1,1,1,1,1] => 100100111111 [3,3,1,1,2,2] => 100100111010 [3,3,2,2,1,1] => 100100101011 [3,3,2,1,1,2] => 100100101110 [3,3,3,3] => 100100100100 [3,2,1,2,1,1,1,1] => 100101101111 [3,2,1,2,2,2] => 100101101010 [3,2,1,1,1,2,1,1] => 100101111011 [3,2,1,1,1,1,1,2] => 100101111110 [3,2,1,1,2,3] => 100101110100 [3,2,2,3,1,1] => 100101010011 [3,2,2,2,1,2] => 100101010110 [3,2,2,1,1,3] => 100101011100 [3,2,3,4] => 100101001000 [3,1,1,3,1,1,1,1] => 100111001111 [3,1,1,3,2,2] => 100111001010 [3,1,1,2,1,2,1,1] => 100111011011 [3,1,1,2,1,1,1,2] => 100111011110 [3,1,1,2,2,3] => 100111010100 [3,1,1,1,1,3,1,1] => 100111110011 [3,1,1,1,1,2,1,2] => 100111110110 [3,1,1,1,1,1,1,3] => 100111111100 [3,1,1,1,2,4] => 100111101000 [3,1,2,4,1,1] => 100110100011 [3,1,2,3,1,2] => 100110100110 [3,1,2,2,1,3] => 100110101100 [3,1,2,1,1,4] => 100110111000 [3,1,3,5] => 100110010000 [4,4,1,1,1,1] => 100010001111 [4,4,2,2] => 100010001010 [4,3,1,2,1,1] => 100010011011 [4,3,1,1,1,2] => 100010011110 [4,3,2,3] => 100010010100 [4,2,1,3,1,1] => 100010110011 [4,2,1,2,1,2] => 100010110110 [4,2,1,1,1,3] => 100010111100 [4,2,2,4] => 100010101000 [4,1,1,4,1,1] => 100011100011 [4,1,1,3,1,2] => 100011100110 [4,1,1,2,1,3] => 100011101100 [4,1,1,1,1,4] => 100011111000 [4,1,2,5] => 100011010000 [5,5,1,1] => 100001000011 [5,4,1,2] => 100001000110 [5,3,1,3] => 100001001100 [5,2,1,4] => 100001011000 [5,1,1,5] => 100001110000 [6,6] => 100000100000 [1,2,2,2,2,2,1] => 110101010101 [1,2,2,2,3,2] => 110101010010 [1,2,2,3,3,1] => 110101001001 [1,2,2,3,2,2] => 110101001010 [1,2,2,4,3] => 110101000100 [1,2,3,3,2,1] => 110100100101 [1,2,3,4,2] => 110100100010 [1,2,3,2,3,1] => 110100101001 [1,2,3,2,2,2] => 110100101010 [1,2,3,3,3] => 110100100100 [1,2,4,4,1] => 110100010001 [1,2,4,3,2] => 110100010010 [1,2,4,2,3] => 110100010100 [1,2,5,4] => 110100001000 [1,3,3,2,2,1] => 110010010101 [1,3,3,3,2] => 110010010010 [1,3,4,3,1] => 110010001001 [1,3,4,2,2] => 110010001010 [1,3,5,3] => 110010000100 [1,3,2,3,2,1] => 110010100101 [1,3,2,4,2] => 110010100010 [1,3,2,2,3,1] => 110010101001 [1,3,2,2,2,2] => 110010101010 [1,3,2,3,3] => 110010100100 [1,3,3,4,1] => 110010010001 [1,3,3,2,3] => 110010010100 [1,3,4,4] => 110010001000 [1,4,4,2,1] => 110001000101 [1,4,5,2] => 110001000010 [1,4,3,3,1] => 110001001001 [1,4,3,2,2] => 110001001010 [1,4,4,3] => 110001000100 [1,4,2,4,1] => 110001010001 [1,4,2,3,2] => 110001010010 [1,4,2,2,3] => 110001010100 ----------------------------------------------------------------------------- Created: Sep 22, 2020 at 11:07 by FindStatCrew ----------------------------------------------------------------------------- Last Updated: Sep 22, 2020 at 11:07 by Martin Rubey