***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 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. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000293 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The number of inversions of a binary word. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(x): return len(x.inversions()) ----------------------------------------------------------------------------- Statistic values: 0 => 0 1 => 0 00 => 0 01 => 0 10 => 1 11 => 0 000 => 0 001 => 0 010 => 1 011 => 0 100 => 2 101 => 1 110 => 2 111 => 0 0000 => 0 0001 => 0 0010 => 1 0011 => 0 0100 => 2 0101 => 1 0110 => 2 0111 => 0 1000 => 3 1001 => 2 1010 => 3 1011 => 1 1100 => 4 1101 => 2 1110 => 3 1111 => 0 00000 => 0 00001 => 0 00010 => 1 00011 => 0 00100 => 2 00101 => 1 00110 => 2 00111 => 0 01000 => 3 01001 => 2 01010 => 3 01011 => 1 01100 => 4 01101 => 2 01110 => 3 01111 => 0 10000 => 4 10001 => 3 10010 => 4 10011 => 2 10100 => 5 10101 => 3 10110 => 4 10111 => 1 11000 => 6 11001 => 4 11010 => 5 11011 => 2 11100 => 6 11101 => 3 11110 => 4 11111 => 0 000000 => 0 000001 => 0 000010 => 1 000011 => 0 000100 => 2 000101 => 1 000110 => 2 000111 => 0 001000 => 3 001001 => 2 001010 => 3 001011 => 1 001100 => 4 001101 => 2 001110 => 3 001111 => 0 010000 => 4 010001 => 3 010010 => 4 010011 => 2 010100 => 5 010101 => 3 010110 => 4 010111 => 1 011000 => 6 011001 => 4 011010 => 5 011011 => 2 011100 => 6 011101 => 3 011110 => 4 011111 => 0 100000 => 5 100001 => 4 100010 => 5 100011 => 3 100100 => 6 100101 => 4 100110 => 5 100111 => 2 101000 => 7 101001 => 5 101010 => 6 101011 => 3 101100 => 7 101101 => 4 101110 => 5 101111 => 1 110000 => 8 110001 => 6 110010 => 7 110011 => 4 110100 => 8 110101 => 5 110110 => 6 110111 => 2 111000 => 9 111001 => 6 111010 => 7 111011 => 3 111100 => 8 111101 => 4 111110 => 5 111111 => 0 0000000 => 0 0000001 => 0 0000010 => 1 0000011 => 0 0000100 => 2 0000101 => 1 0000110 => 2 0000111 => 0 0001000 => 3 0001001 => 2 0001010 => 3 0001011 => 1 0001100 => 4 0001101 => 2 0001110 => 3 0001111 => 0 0010000 => 4 0010001 => 3 0010010 => 4 0010011 => 2 0010100 => 5 0010101 => 3 0010110 => 4 0010111 => 1 0011000 => 6 0011001 => 4 0011010 => 5 0011011 => 2 0011100 => 6 0011101 => 3 0011110 => 4 0011111 => 0 0100000 => 5 0100001 => 4 0100010 => 5 0100011 => 3 0100100 => 6 0100101 => 4 0100110 => 5 0100111 => 2 0101000 => 7 0101001 => 5 0101010 => 6 0101011 => 3 0101100 => 7 0101101 => 4 0101110 => 5 0101111 => 1 0110000 => 8 0110001 => 6 0110010 => 7 0110011 => 4 0110100 => 8 0110101 => 5 0110110 => 6 0110111 => 2 0111000 => 9 0111001 => 6 0111010 => 7 0111011 => 3 0111100 => 8 0111101 => 4 0111110 => 5 0111111 => 0 1000000 => 6 1000001 => 5 1000010 => 6 1000011 => 4 1000100 => 7 1000101 => 5 1000110 => 6 1000111 => 3 1001000 => 8 1001001 => 6 1001010 => 7 1001011 => 4 1001100 => 8 1001101 => 5 1001110 => 6 1001111 => 2 1010000 => 9 1010001 => 7 1010010 => 8 1010011 => 5 1010100 => 9 1010101 => 6 1010110 => 7 1010111 => 3 1011000 => 10 1011001 => 7 1011010 => 8 1011011 => 4 1011100 => 9 1011101 => 5 1011110 => 6 1011111 => 1 1100000 => 10 1100001 => 8 1100010 => 9 1100011 => 6 1100100 => 10 1100101 => 7 1100110 => 8 1100111 => 4 1101000 => 11 1101001 => 8 1101010 => 9 1101011 => 5 1101100 => 10 1101101 => 6 1101110 => 7 1101111 => 2 1110000 => 12 1110001 => 9 1110010 => 10 1110011 => 6 1110100 => 11 1110101 => 7 1110110 => 8 1110111 => 3 1111000 => 12 1111001 => 8 1111010 => 9 1111011 => 4 1111100 => 10 1111101 => 5 1111110 => 6 1111111 => 0 00000000 => 0 00000001 => 0 00000010 => 1 00000011 => 0 00000100 => 2 00000101 => 1 00000110 => 2 00000111 => 0 00001000 => 3 00001001 => 2 00001010 => 3 00001011 => 1 00001100 => 4 00001101 => 2 00001110 => 3 00001111 => 0 00010000 => 4 00010001 => 3 00010010 => 4 00010011 => 2 00010100 => 5 00010101 => 3 00010110 => 4 00010111 => 1 00011000 => 6 00011001 => 4 00011010 => 5 00011011 => 2 00011100 => 6 00011101 => 3 00011110 => 4 00011111 => 0 00100000 => 5 00100001 => 4 00100010 => 5 00100011 => 3 00100100 => 6 00100101 => 4 00100110 => 5 00100111 => 2 00101000 => 7 00101001 => 5 00101010 => 6 00101011 => 3 00101100 => 7 00101101 => 4 00101110 => 5 00101111 => 1 00110000 => 8 00110001 => 6 00110010 => 7 00110011 => 4 00110100 => 8 00110101 => 5 00110110 => 6 00110111 => 2 00111000 => 9 00111001 => 6 00111010 => 7 00111011 => 3 00111100 => 8 00111101 => 4 00111110 => 5 00111111 => 0 01000000 => 6 01000001 => 5 01000010 => 6 01000011 => 4 01000100 => 7 01000101 => 5 01000110 => 6 01000111 => 3 01001000 => 8 01001001 => 6 01001010 => 7 01001011 => 4 01001100 => 8 01001101 => 5 01001110 => 6 01001111 => 2 01010000 => 9 01010001 => 7 01010010 => 8 01010011 => 5 01010100 => 9 01010101 => 6 01010110 => 7 01010111 => 3 01011000 => 10 01011001 => 7 01011010 => 8 01011011 => 4 01011100 => 9 01011101 => 5 01011110 => 6 01011111 => 1 01100000 => 10 01100001 => 8 01100010 => 9 01100011 => 6 01100100 => 10 01100101 => 7 01100110 => 8 01100111 => 4 01101000 => 11 01101001 => 8 01101010 => 9 01101011 => 5 01101100 => 10 01101101 => 6 01101110 => 7 01101111 => 2 01110000 => 12 01110001 => 9 01110010 => 10 01110011 => 6 01110100 => 11 01110101 => 7 01110110 => 8 01110111 => 3 01111000 => 12 01111001 => 8 01111010 => 9 01111011 => 4 01111100 => 10 01111101 => 5 01111110 => 6 01111111 => 0 10000000 => 7 10000001 => 6 10000010 => 7 10000011 => 5 10000100 => 8 10000101 => 6 10000110 => 7 10000111 => 4 10001000 => 9 10001001 => 7 10001010 => 8 10001011 => 5 10001100 => 9 10001101 => 6 10001110 => 7 10001111 => 3 10010000 => 10 10010001 => 8 10010010 => 9 10010011 => 6 10010100 => 10 10010101 => 7 10010110 => 8 10010111 => 4 10011000 => 11 10011001 => 8 10011010 => 9 10011011 => 5 10011100 => 10 10011101 => 6 10011110 => 7 10011111 => 2 10100000 => 11 10100001 => 9 10100010 => 10 10100011 => 7 10100100 => 11 10100101 => 8 10100110 => 9 10100111 => 5 10101000 => 12 10101001 => 9 10101010 => 10 10101011 => 6 10101100 => 11 10101101 => 7 10101110 => 8 10101111 => 3 10110000 => 13 10110001 => 10 10110010 => 11 10110011 => 7 10110100 => 12 10110101 => 8 10110110 => 9 10110111 => 4 10111000 => 13 10111001 => 9 10111010 => 10 10111011 => 5 10111100 => 11 10111101 => 6 10111110 => 7 10111111 => 1 11000000 => 12 11000001 => 10 11000010 => 11 11000011 => 8 11000100 => 12 11000101 => 9 11000110 => 10 11000111 => 6 11001000 => 13 11001001 => 10 11001010 => 11 11001011 => 7 11001100 => 12 11001101 => 8 11001110 => 9 11001111 => 4 11010000 => 14 11010001 => 11 11010010 => 12 11010011 => 8 11010100 => 13 11010101 => 9 11010110 => 10 11010111 => 5 11011000 => 14 11011001 => 10 11011010 => 11 11011011 => 6 11011100 => 12 11011101 => 7 11011110 => 8 11011111 => 2 11100000 => 15 11100001 => 12 11100010 => 13 11100011 => 9 11100100 => 14 11100101 => 10 11100110 => 11 11100111 => 6 11101000 => 15 11101001 => 11 11101010 => 12 11101011 => 7 11101100 => 13 11101101 => 8 11101110 => 9 11101111 => 3 11110000 => 16 11110001 => 12 11110010 => 13 11110011 => 8 11110100 => 14 11110101 => 9 11110110 => 10 11110111 => 4 11111000 => 15 11111001 => 10 11111010 => 11 11111011 => 5 11111100 => 12 11111101 => 6 11111110 => 7 11111111 => 0 000000000 => 0 000000001 => 0 000000010 => 1 000000011 => 0 000000100 => 2 000000101 => 1 000000110 => 2 000000111 => 0 000001000 => 3 000001001 => 2 000001010 => 3 000001011 => 1 000001100 => 4 000001101 => 2 000001110 => 3 000001111 => 0 000010000 => 4 000010001 => 3 000010010 => 4 000010011 => 2 000010100 => 5 000010101 => 3 000010110 => 4 000010111 => 1 000011000 => 6 000011001 => 4 000011010 => 5 000011011 => 2 000011100 => 6 000011101 => 3 000011110 => 4 000011111 => 0 000100000 => 5 000100001 => 4 000100010 => 5 000100011 => 3 000100100 => 6 000100101 => 4 000100110 => 5 000100111 => 2 000101000 => 7 000101001 => 5 000101010 => 6 000101011 => 3 000101100 => 7 000101101 => 4 000101110 => 5 000101111 => 1 000110000 => 8 000110001 => 6 000110010 => 7 000110011 => 4 000110100 => 8 000110101 => 5 000110110 => 6 000110111 => 2 000111000 => 9 000111001 => 6 000111010 => 7 000111011 => 3 000111100 => 8 000111101 => 4 000111110 => 5 000111111 => 0 001000000 => 6 001000001 => 5 001000010 => 6 001000011 => 4 001000100 => 7 001000101 => 5 001000110 => 6 001000111 => 3 001001000 => 8 001001001 => 6 001001010 => 7 001001011 => 4 001001100 => 8 001001101 => 5 001001110 => 6 001001111 => 2 001010000 => 9 001010001 => 7 001010010 => 8 001010011 => 5 001010100 => 9 001010101 => 6 001010110 => 7 001010111 => 3 001011000 => 10 001011001 => 7 001011010 => 8 001011011 => 4 001011100 => 9 001011101 => 5 001011110 => 6 001011111 => 1 001100000 => 10 001100001 => 8 001100010 => 9 001100011 => 6 001100100 => 10 001100101 => 7 001100110 => 8 001100111 => 4 001101000 => 11 001101001 => 8 001101010 => 9 001101011 => 5 001101100 => 10 001101101 => 6 001101110 => 7 001101111 => 2 001110000 => 12 001110001 => 9 001110010 => 10 001110011 => 6 001110100 => 11 001110101 => 7 001110110 => 8 001110111 => 3 001111000 => 12 001111001 => 8 001111010 => 9 001111011 => 4 001111100 => 10 001111101 => 5 001111110 => 6 001111111 => 0 010000000 => 7 010000001 => 6 010000010 => 7 010000011 => 5 010000100 => 8 010000101 => 6 010000110 => 7 010000111 => 4 010001000 => 9 010001001 => 7 010001010 => 8 010001011 => 5 010001100 => 9 010001101 => 6 010001110 => 7 010001111 => 3 010010000 => 10 010010001 => 8 010010010 => 9 010010011 => 6 010010100 => 10 010010101 => 7 010010110 => 8 010010111 => 4 010011000 => 11 010011001 => 8 010011010 => 9 010011011 => 5 010011100 => 10 010011101 => 6 010011110 => 7 010011111 => 2 010100000 => 11 010100001 => 9 010100010 => 10 010100011 => 7 010100100 => 11 010100101 => 8 010100110 => 9 010100111 => 5 010101000 => 12 010101001 => 9 010101010 => 10 010101011 => 6 010101100 => 11 010101101 => 7 010101110 => 8 010101111 => 3 010110000 => 13 010110001 => 10 010110010 => 11 010110011 => 7 010110100 => 12 010110101 => 8 010110110 => 9 010110111 => 4 010111000 => 13 010111001 => 9 010111010 => 10 010111011 => 5 010111100 => 11 010111101 => 6 010111110 => 7 010111111 => 1 011000000 => 12 011000001 => 10 011000010 => 11 011000011 => 8 011000100 => 12 011000101 => 9 011000110 => 10 011000111 => 6 011001000 => 13 011001001 => 10 011001010 => 11 011001011 => 7 011001100 => 12 011001101 => 8 011001110 => 9 011001111 => 4 011010000 => 14 011010001 => 11 011010010 => 12 011010011 => 8 011010100 => 13 011010101 => 9 011010110 => 10 011010111 => 5 011011000 => 14 011011001 => 10 011011010 => 11 011011011 => 6 011011100 => 12 011011101 => 7 011011110 => 8 011011111 => 2 011100000 => 15 011100001 => 12 011100010 => 13 011100011 => 9 011100100 => 14 011100101 => 10 011100110 => 11 011100111 => 6 011101000 => 15 011101001 => 11 011101010 => 12 011101011 => 7 011101100 => 13 011101101 => 8 011101110 => 9 011101111 => 3 011110000 => 16 011110001 => 12 011110010 => 13 011110011 => 8 011110100 => 14 011110101 => 9 011110110 => 10 011110111 => 4 011111000 => 15 011111001 => 10 011111010 => 11 011111011 => 5 011111100 => 12 011111101 => 6 011111110 => 7 011111111 => 0 100000000 => 8 100000001 => 7 100000010 => 8 100000011 => 6 100000100 => 9 100000101 => 7 100000110 => 8 100000111 => 5 100001000 => 10 100001001 => 8 100001010 => 9 100001011 => 6 100001100 => 10 100001101 => 7 100001110 => 8 100001111 => 4 100010000 => 11 100010001 => 9 100010010 => 10 100010011 => 7 100010100 => 11 100010101 => 8 100010110 => 9 100010111 => 5 100011000 => 12 100011001 => 9 100011010 => 10 100011011 => 6 100011100 => 11 100011101 => 7 100011110 => 8 100011111 => 3 100100000 => 12 100100001 => 10 100100010 => 11 100100011 => 8 100100100 => 12 100100101 => 9 100100110 => 10 100100111 => 6 100101000 => 13 100101001 => 10 100101010 => 11 100101011 => 7 100101100 => 12 100101101 => 8 100101110 => 9 100101111 => 4 100110000 => 14 100110001 => 11 100110010 => 12 100110011 => 8 100110100 => 13 100110101 => 9 100110110 => 10 100110111 => 5 100111000 => 14 100111001 => 10 100111010 => 11 100111011 => 6 100111100 => 12 100111101 => 7 100111110 => 8 100111111 => 2 101000000 => 13 101000001 => 11 101000010 => 12 101000011 => 9 101000100 => 13 101000101 => 10 101000110 => 11 101000111 => 7 101001000 => 14 101001001 => 11 101001010 => 12 101001011 => 8 101001100 => 13 101001101 => 9 101001110 => 10 101001111 => 5 101010000 => 15 101010001 => 12 101010010 => 13 101010011 => 9 101010100 => 14 101010101 => 10 101010110 => 11 101010111 => 6 101011000 => 15 101011001 => 11 101011010 => 12 101011011 => 7 101011100 => 13 101011101 => 8 101011110 => 9 101011111 => 3 101100000 => 16 101100001 => 13 101100010 => 14 101100011 => 10 101100100 => 15 101100101 => 11 101100110 => 12 101100111 => 7 101101000 => 16 101101001 => 12 101101010 => 13 101101011 => 8 101101100 => 14 101101101 => 9 101101110 => 10 101101111 => 4 101110000 => 17 101110001 => 13 101110010 => 14 101110011 => 9 101110100 => 15 101110101 => 10 101110110 => 11 101110111 => 5 101111000 => 16 101111001 => 11 101111010 => 12 101111011 => 6 101111100 => 13 101111101 => 7 101111110 => 8 101111111 => 1 110000000 => 14 110000001 => 12 110000010 => 13 110000011 => 10 110000100 => 14 110000101 => 11 110000110 => 12 110000111 => 8 110001000 => 15 110001001 => 12 110001010 => 13 110001011 => 9 110001100 => 14 110001101 => 10 110001110 => 11 110001111 => 6 110010000 => 16 110010001 => 13 110010010 => 14 110010011 => 10 110010100 => 15 110010101 => 11 110010110 => 12 110010111 => 7 110011000 => 16 110011001 => 12 110011010 => 13 110011011 => 8 110011100 => 14 110011101 => 9 110011110 => 10 110011111 => 4 110100000 => 17 110100001 => 14 110100010 => 15 110100011 => 11 110100100 => 16 110100101 => 12 110100110 => 13 110100111 => 8 110101000 => 17 110101001 => 13 110101010 => 14 110101011 => 9 110101100 => 15 110101101 => 10 110101110 => 11 110101111 => 5 110110000 => 18 110110001 => 14 110110010 => 15 110110011 => 10 110110100 => 16 110110101 => 11 110110110 => 12 110110111 => 6 110111000 => 17 110111001 => 12 110111010 => 13 110111011 => 7 110111100 => 14 110111101 => 8 110111110 => 9 110111111 => 2 111000000 => 18 111000001 => 15 111000010 => 16 111000011 => 12 111000100 => 17 111000101 => 13 111000110 => 14 111000111 => 9 111001000 => 18 111001001 => 14 111001010 => 15 111001011 => 10 111001100 => 16 111001101 => 11 111001110 => 12 111001111 => 6 111010000 => 19 111010001 => 15 111010010 => 16 111010011 => 11 111010100 => 17 111010101 => 12 111010110 => 13 111010111 => 7 111011000 => 18 111011001 => 13 111011010 => 14 111011011 => 8 111011100 => 15 111011101 => 9 111011110 => 10 111011111 => 3 111100000 => 20 111100001 => 16 111100010 => 17 111100011 => 12 111100100 => 18 111100101 => 13 111100110 => 14 111100111 => 8 111101000 => 19 111101001 => 14 111101010 => 15 111101011 => 9 111101100 => 16 111101101 => 10 111101110 => 11 111101111 => 4 111110000 => 20 111110001 => 15 111110010 => 16 111110011 => 10 111110100 => 17 111110101 => 11 111110110 => 12 111110111 => 5 111111000 => 18 111111001 => 12 111111010 => 13 111111011 => 6 111111100 => 14 111111101 => 7 111111110 => 8 111111111 => 0 1010101010 => 15 1010101100 => 16 1010110010 => 16 1010110100 => 17 1010111000 => 18 1011001010 => 16 1011001100 => 17 1011010010 => 17 1011010100 => 18 1011011000 => 19 1011100010 => 18 1011100100 => 19 1011101000 => 20 1011110000 => 21 1100101010 => 16 1100101100 => 17 1100110010 => 17 1100110100 => 18 1100111000 => 19 1101001010 => 17 1101001100 => 18 1101010010 => 18 1101010100 => 19 1101011000 => 20 1101100010 => 19 1101100100 => 20 1101101000 => 21 1101110000 => 22 1110001010 => 18 1110001100 => 19 1110010010 => 19 1110010100 => 20 1110011000 => 21 1110100010 => 20 1110100100 => 21 1110101000 => 22 1110110000 => 23 1111000010 => 21 1111000100 => 22 1111001000 => 23 1111010000 => 24 1111100000 => 25 1111111110 => 9 1111111101 => 8 1111000001 => 20 1110111110 => 11 1110100001 => 19 1110011110 => 13 1110010001 => 18 1110001001 => 17 1110000101 => 16 1101111110 => 10 1101100001 => 18 1101010001 => 17 1101001110 => 14 1101001001 => 16 1101000101 => 15 1100110001 => 16 1100101001 => 15 1100100110 => 15 1100100101 => 14 1100011001 => 14 1100010101 => 13 1100010010 => 16 1100001000 => 17 1011111110 => 9 1011111101 => 8 1011100001 => 17 1011010001 => 16 1011001001 => 15 1011000101 => 14 1010111110 => 10 1010110001 => 15 1010101001 => 14 1010100110 => 14 1010100101 => 13 1010011010 => 14 1010011001 => 13 1010010110 => 13 1010010101 => 12 1010001110 => 12 1001111110 => 9 1001111000 => 17 1001110100 => 16 1001110001 => 14 1001101100 => 15 1001101010 => 14 1001101001 => 13 1001100110 => 13 1001100101 => 12 1001011110 => 10 1001011010 => 13 1001011001 => 12 1001010110 => 12 1001010101 => 11 1001001110 => 11 1000111110 => 9 1000111100 => 13 1000111010 => 12 1000110110 => 11 1000101110 => 10 1000011110 => 9 1000010110 => 10 1000001110 => 9 1000001010 => 10 1000000110 => 9 1000000100 => 10 1000000010 => 9 1000000000 => 9 0111111111 => 0 0111111101 => 7 0111111001 => 12 0111110001 => 15 0111100001 => 16 0111000001 => 15 0110000001 => 12 0100000001 => 7 0000000001 => 0 0111111011 => 6 0111110101 => 11 0111101001 => 14 0111010001 => 15 0110100001 => 14 0101000001 => 11 0010000001 => 6 0101010101 => 10 0101010011 => 9 0101001101 => 9 0101001011 => 8 0101000111 => 7 0100110101 => 9 0100110011 => 8 0100101101 => 8 0100101011 => 7 0100100111 => 6 0100011101 => 7 0100011011 => 6 0100010111 => 5 0100001111 => 4 0011010101 => 9 0011010011 => 8 0011001101 => 8 0011001011 => 7 0011000111 => 6 0010110101 => 8 0010110011 => 7 0010101101 => 7 0010101011 => 6 0010100111 => 5 0010011101 => 6 0010011011 => 5 0010010111 => 4 0010001111 => 3 0001110101 => 7 0001110011 => 6 0001101101 => 6 0001101011 => 5 0001100111 => 4 0001011101 => 5 0001011011 => 4 0001010111 => 3 0001001111 => 2 0000111101 => 4 0000111011 => 3 0000110111 => 2 0000101111 => 1 0000011111 => 0 0000000000 => 0 0000000110 => 2 0000011000 => 6 0000011110 => 4 0000010010 => 4 0001100000 => 10 0001100110 => 8 0001111000 => 12 0001111110 => 6 0001110010 => 10 0001001000 => 8 0001001110 => 6 0001000010 => 6 0001011010 => 8 0100000010 => 8 0010101010 => 10 0010101000 => 12 0010101100 => 11 0010100100 => 11 0010010100 => 10 0001010100 => 9 0010101110 => 8 0010100000 => 11 0010111100 => 11 0010000100 => 8 0011110100 => 14 0000010100 => 5 0111010100 => 17 0000000010 => 1 0000001110 => 3 0000111110 => 5 0000000100 => 2 0000001010 => 3 0000010110 => 4 0000101110 => 5 0001011110 => 6 0100000000 => 8 0100000011 => 6 0100000111 => 5 0100011111 => 3 0100111111 => 2 0101111111 => 1 0100000101 => 7 0100001011 => 6 0100101111 => 4 0101011111 => 3 0110111111 => 2 0101010110 => 11 0101011001 => 11 0101011010 => 12 0101011100 => 13 0101100101 => 11 0101100110 => 12 0101101001 => 12 0101101010 => 13 0101101100 => 14 0101110001 => 13 0101110010 => 14 0101110100 => 15 0101111000 => 16 0110010101 => 11 0110010110 => 12 0110011001 => 12 0110011010 => 13 0110011100 => 14 0110100101 => 12 0110100110 => 13 0110101001 => 13 0110101010 => 14 0110101100 => 15 0110110001 => 14 0110110010 => 15 0110110100 => 16 0110111000 => 17 0111000101 => 13 0111000110 => 14 0111001001 => 14 0111001010 => 15 0111001100 => 16 0111010010 => 16 0111011000 => 18 0111100010 => 17 0111100100 => 18 0111101000 => 19 0111110000 => 20 0100000100 => 9 0011100110 => 11 0011101010 => 12 0011101100 => 13 0001101110 => 7 0010110110 => 9 0011110010 => 13 0001110110 => 8 0100111010 => 11 0010111010 => 10 0011111000 => 15 0001111010 => 9 0100111100 => 12 0001111100 => 10 0000000101 => 1 0000001101 => 2 0000011101 => 3 0001111101 => 5 0011111101 => 6 0000001001 => 2 0000010101 => 3 0000101101 => 4 0010111101 => 6 0101111101 => 7 0010110001 => 10 0001100001 => 8 0001000001 => 5 0000111111 => 0 0001110100 => 11 0001101100 => 10 0010011100 => 10 0001011100 => 9 0000111100 => 8 0001101010 => 9 0010011010 => 9 0000111010 => 7 0010100110 => 9 0010010110 => 8 0001010110 => 7 0000110110 => 6 0010001110 => 7 0001101001 => 8 0000110001 => 6 0000010001 => 3 0000001100 => 4 0000011001 => 4 0000110011 => 4 0000110100 => 8 0000000011 => 0 0000011011 => 2 0001101111 => 2 0000110101 => 5 0010000010 => 7 0001000011 => 4 0010011110 => 7 0001010000 => 9 0001000100 => 7 0001010101 => 6 0001001011 => 4 0001100011 => 6 0001110111 => 3 0010000000 => 7 0000000111 => 0 0000001111 => 0 0001111111 => 0 0000001011 => 1 0000010111 => 1 0001011111 => 1 0001111001 => 8 0000011010 => 5 0000101010 => 6 0000100101 => 4 0010010001 => 8 0010000101 => 6 0010010101 => 7 0010010011 => 6 0000101011 => 3 0001000111 => 3 0000100111 => 2 0010010010 => 9 0001001010 => 7 0001001001 => 6 0001000101 => 5 0000100011 => 3 0000100100 => 6 0000100010 => 5 0010110000 => 13 0000011100 => 6 0000001000 => 3 0000101100 => 7 0010101111 => 3 0000101000 => 7 0010001000 => 9 0001001100 => 8 0001000110 => 6 0001100100 => 10 0001100010 => 9 0000100110 => 5 0000110010 => 7 0010010000 => 10 0001010010 => 8 0001000000 => 6 0001011001 => 7 0001100101 => 7 0001110001 => 9 0010011001 => 8 0010100101 => 8 0010101001 => 9 0010011111 => 2 0000111001 => 6 0010001101 => 6 0001001101 => 5 0001010001 => 7 0001010011 => 5 0001111011 => 4 0010011000 => 11 0001011000 => 10 0000100000 => 5 0010001011 => 5 0010000111 => 4 0000010011 => 2 0010001100 => 9 0010000110 => 7 0000110000 => 8 0000100001 => 4 0010100011 => 7 0010100001 => 9 0000111000 => 9 0001101000 => 11 0000010000 => 4 0000101001 => 5 0010100010 => 10 0010001001 => 7 0010000011 => 5 0010001010 => 8 0001110000 => 12 10000000000 => 10 10000000010 => 10 10000000110 => 10 10000001110 => 10 10000011110 => 10 10000111110 => 10 10001111110 => 10 10011111110 => 10 10111111110 => 10 11111111110 => 10 10000000100 => 11 10000001010 => 11 10000010110 => 11 10000101110 => 11 10001011110 => 11 10010111110 => 11 10101111110 => 11 11011111110 => 11 10000010000 => 13 10000100010 => 13 10001000010 => 14 10000100100 => 14 10001001010 => 14 10001000100 => 15 10000101000 => 15 10010001010 => 15 10001010010 => 15 10010000100 => 16 10001001000 => 16 10010010010 => 16 10001010100 => 16 10010101010 => 16 10010001000 => 17 10100010010 => 17 10010100010 => 17 10010010100 => 17 10100101010 => 17 01111111111 => 0 01111111101 => 8 01111111001 => 14 01111110001 => 18 01111100001 => 20 01111000001 => 20 01110000001 => 18 01100000001 => 14 01000000001 => 8 00000000001 => 0 00000000010 => 1 10101010101 => 15 10101010010 => 19 10101001001 => 17 10101001010 => 18 10101000100 => 20 10100100101 => 15 10100100010 => 18 10100101001 => 16 10100100100 => 19 10100010001 => 16 10100010100 => 18 10100001000 => 18 10010010101 => 13 10010001001 => 14 10010100101 => 14 10010101001 => 15 10010100100 => 18 10010010001 => 15 10001000101 => 12 10001001001 => 13 10001010001 => 14 10000100001 => 12 01001010101 => 11 01001010010 => 14 01001001001 => 12 01001001010 => 13 01001000100 => 14 01000100101 => 10 01000100010 => 12 01000101001 => 11 01000101010 => 12 01000100100 => 13 01000010001 => 10 01000010010 => 11 01000010100 => 12 01000001000 => 11 01010010101 => 12 01010010010 => 15 01010001001 => 13 01010001010 => 14 01010000100 => 15 01010100101 => 13 01010100010 => 16 01010101001 => 14 01010101010 => 15 01010100100 => 17 01010010001 => 14 01010010100 => 16 01010001000 => 16 01001000101 => 11 01001000010 => 13 01001010001 => 13 01001010100 => 15 01001001000 => 15 01000100001 => 11 01000101000 => 14 01000010000 => 12 00100010101 => 8 00100010010 => 10 00100001001 => 8 00100001010 => 9 00100000100 => 9 00100100101 => 9 00100100010 => 11 00100101001 => 10 00100101010 => 11 00100100100 => 12 00100010001 => 9 00100010100 => 11 00100001000 => 10 00101000101 => 10 00101000010 => 12 00101001001 => 11 00101001010 => 12 00101000100 => 13 00101010001 => 12 00101010010 => 13 00101010100 => 14 00101001000 => 14 00100100001 => 10 00100101000 => 13 00100010000 => 11 00010000101 => 6 00010000010 => 7 00010001001 => 7 00010001010 => 8 00010000100 => 8 00010010001 => 8 00010010010 => 9 00010010100 => 10 00010001000 => 9 00010100001 => 9 00010100010 => 10 00010100100 => 11 00010101000 => 12 00010010000 => 10 00001000001 => 5 00001000010 => 6 00001000100 => 7 00001001000 => 8 00001010000 => 9 00000100000 => 5 01000000000 => 9 01000000011 => 7 01000000111 => 6 01000001111 => 5 01000011111 => 4 01000111111 => 3 01001111111 => 2 01011111111 => 1 00000000101 => 1 00000001101 => 2 00000011101 => 3 00000111101 => 4 00001111101 => 5 00011111101 => 6 00111111101 => 7 11111111101 => 9 101010101010 => 21 101010101100 => 22 101010110010 => 22 101010110100 => 23 101010111000 => 24 101011001010 => 22 101011001100 => 23 101011010010 => 23 101011010100 => 24 101011011000 => 25 101011100010 => 24 101011100100 => 25 101011101000 => 26 101011110000 => 27 101100101010 => 22 101100101100 => 23 101100110010 => 23 101100110100 => 24 101100111000 => 25 101101001010 => 23 101101001100 => 24 101101010010 => 24 101101010100 => 25 101101011000 => 26 101101100010 => 25 101101100100 => 26 101101101000 => 27 101101110000 => 28 101110001010 => 24 101110001100 => 25 101110010010 => 25 101110010100 => 26 101110011000 => 27 101110100010 => 26 101110100100 => 27 101110101000 => 28 101110110000 => 29 101111000010 => 27 101111000100 => 28 101111001000 => 29 101111010000 => 30 101111100000 => 31 110010101010 => 22 110010101100 => 23 110010110010 => 23 110010110100 => 24 110010111000 => 25 110011001010 => 23 110011001100 => 24 110011010010 => 24 110011010100 => 25 110011011000 => 26 110011100010 => 25 110011100100 => 26 110011101000 => 27 110011110000 => 28 110100101010 => 23 110100101100 => 24 110100110010 => 24 110100110100 => 25 110100111000 => 26 110101001010 => 24 110101001100 => 25 110101010010 => 25 110101010100 => 26 110101011000 => 27 110101100010 => 26 110101100100 => 27 110101101000 => 28 110101110000 => 29 110110001010 => 25 110110001100 => 26 110110010010 => 26 110110010100 => 27 110110011000 => 28 110110100010 => 27 110110100100 => 28 110110101000 => 29 110110110000 => 30 110111000010 => 28 110111000100 => 29 110111001000 => 30 110111010000 => 31 110111100000 => 32 111000101010 => 24 111000101100 => 25 111000110010 => 25 111000110100 => 26 111000111000 => 27 111001001010 => 25 111001001100 => 26 111001010010 => 26 111001010100 => 27 111001011000 => 28 111001100010 => 27 111001100100 => 28 111001101000 => 29 111001110000 => 30 111010001010 => 26 111010001100 => 27 111010010010 => 27 111010010100 => 28 111010011000 => 29 111010100010 => 28 111010100100 => 29 111010101000 => 30 111010110000 => 31 111011000010 => 29 111011000100 => 30 111011001000 => 31 111011010000 => 32 111011100000 => 33 111100001010 => 27 111100001100 => 28 111100010010 => 28 111100010100 => 29 111100011000 => 30 111100100010 => 29 111100100100 => 30 111100101000 => 31 111100110000 => 32 111101000010 => 30 111101000100 => 31 111101001000 => 32 111101010000 => 33 111101100000 => 34 111110000010 => 31 111110000100 => 32 111110001000 => 33 111110010000 => 34 111110100000 => 35 111111000000 => 36 100001111100 => 16 010101010101 => 15 010101010011 => 14 010101001101 => 14 010101001011 => 13 010101000111 => 12 010100110101 => 14 010100110011 => 13 010100101101 => 13 010100101011 => 12 010100100111 => 11 010100011101 => 12 010100011011 => 11 010100010111 => 10 010100001111 => 9 010011010101 => 14 010011010011 => 13 010011001101 => 13 010011001011 => 12 010011000111 => 11 010010110101 => 13 010010110011 => 12 010010101101 => 12 010010101011 => 11 010010100111 => 10 010010011101 => 11 010010011011 => 10 010010010111 => 9 010010001111 => 8 010001110101 => 12 010001110011 => 11 010001101101 => 11 010001101011 => 10 010001100111 => 9 010001011101 => 10 010001011011 => 9 010001010111 => 8 010001001111 => 7 010000111101 => 9 010000111011 => 8 010000110111 => 7 010000101111 => 6 010000011111 => 5 001101010101 => 14 001101010011 => 13 001101001101 => 13 001101001011 => 12 001101000111 => 11 001100110101 => 13 001100110011 => 12 001100101101 => 12 001100101011 => 11 001100100111 => 10 001100011101 => 11 001100011011 => 10 001100010111 => 9 001100001111 => 8 001011010101 => 13 001011010011 => 12 001011001101 => 12 001011001011 => 11 001011000111 => 10 001010110101 => 12 001010110011 => 11 001010101101 => 11 001010101011 => 10 001010100111 => 9 001010011101 => 10 001010011011 => 9 001010010111 => 8 001010001111 => 7 001001110101 => 11 001001110011 => 10 001001101101 => 10 001001101011 => 9 001001100111 => 8 001001011101 => 9 001001011011 => 8 001001010111 => 7 001001001111 => 6 001000111101 => 8 001000111011 => 7 001000110111 => 6 001000101111 => 5 001000011111 => 4 000111010101 => 12 000111010011 => 11 000111001101 => 11 000111001011 => 10 000111000111 => 9 000110110101 => 11 000110110011 => 10 000110101101 => 10 000110101011 => 9 000110100111 => 8 000110011101 => 9 000110011011 => 8 000110010111 => 7 000110001111 => 6 000101110101 => 10 000101110011 => 9 000101101101 => 9 000101101011 => 8 000101100111 => 7 000101011101 => 8 000101011011 => 7 000101010111 => 6 000101001111 => 5 000100111101 => 7 000100111011 => 6 000100110111 => 5 000100101111 => 4 000100011111 => 3 000011110101 => 9 000011110011 => 8 000011101101 => 8 000011101011 => 7 000011100111 => 6 000011011101 => 7 000011011011 => 6 000011010111 => 5 000011001111 => 4 000010111101 => 6 000010111011 => 5 000010110111 => 4 000010101111 => 3 000010011111 => 2 000001111101 => 5 000001111011 => 4 000001110111 => 3 000001101111 => 2 000001011111 => 1 000000111111 => 0 111110000001 => 30 111001100001 => 26 111000011001 => 22 111000110001 => 24 111000100101 => 22 111011000001 => 28 111010010001 => 26 111010000101 => 24 100111100001 => 22 100110011001 => 18 100110110001 => 20 100110100101 => 18 101101100001 => 24 101100011001 => 20 101100110001 => 22 101100100101 => 20 101111000001 => 26 101110010001 => 24 101110000101 => 22 101001011001 => 18 101001110001 => 20 101001100101 => 18 101011010001 => 22 101011000101 => 20 101010010101 => 18 000001111110 => 6 000111100110 => 14 000111111000 => 18 000111110010 => 16 000111001110 => 12 000111011010 => 14 000101101110 => 10 000101111010 => 12 011001100110 => 18 011001111000 => 22 011001110010 => 20 011001011010 => 18 011110000110 => 22 011110011000 => 26 011110010010 => 24 011111100000 => 30 011111001000 => 28 011111000010 => 26 011100100110 => 20 011100111000 => 24 011100110010 => 22 011100011010 => 20 011101101000 => 26 011101100010 => 24 011101001010 => 22 010011111000 => 20 010011110010 => 18 010011011010 => 16 010001111010 => 14 010110100110 => 18 010110111000 => 22 010110110010 => 20 010110011010 => 18 010111101000 => 24 010111100010 => 22 010111001010 => 20 010101101010 => 18 010101010110 => 16 010101011001 => 16 010101011010 => 17 010101011100 => 18 010101100101 => 16 010101100110 => 17 010101101001 => 17 010101101100 => 19 010101110001 => 18 010101110010 => 19 010101110100 => 20 010101111000 => 21 010110010101 => 16 010110010110 => 17 010110011001 => 17 010110011100 => 19 010110100101 => 17 010110101001 => 18 010110101010 => 19 010110101100 => 20 010110110001 => 19 010110110100 => 21 010111000101 => 18 010111000110 => 19 010111001001 => 19 010111001100 => 21 010111010001 => 20 010111010010 => 21 010111010100 => 22 010111011000 => 23 010111100001 => 21 010111100100 => 23 010111110000 => 25 011001010101 => 16 011001010110 => 17 011001011001 => 17 011001011100 => 19 011001100101 => 17 011001101001 => 18 011001101010 => 19 011001101100 => 20 011001110001 => 19 011001110100 => 21 011010010101 => 17 011010010110 => 18 011010011001 => 18 011010011010 => 19 011010011100 => 20 011010100101 => 18 011010100110 => 19 011010101001 => 19 011010101010 => 20 011010101100 => 21 011010110001 => 20 011010110010 => 21 011010110100 => 22 011010111000 => 23 011011000101 => 19 011011000110 => 20 011011001001 => 20 011011001010 => 21 011011001100 => 22 011011010001 => 21 011011010010 => 22 011011010100 => 23 011011011000 => 24 011011100001 => 22 011011100010 => 23 011011100100 => 24 011011101000 => 25 011011110000 => 26 011100010101 => 18 011100010110 => 19 011100011001 => 19 011100011100 => 21 011100100101 => 19 011100101001 => 20 011100101010 => 21 011100101100 => 22 011100110001 => 21 011100110100 => 23 011101000101 => 20 011101000110 => 21 011101001001 => 21 011101001100 => 23 011101010001 => 22 011101010010 => 23 011101010100 => 24 011101011000 => 25 011101100001 => 23 011101100100 => 25 011101110000 => 27 011110000101 => 21 011110001001 => 22 011110001010 => 23 011110001100 => 24 011110010001 => 23 011110010100 => 25 011110100001 => 24 011110100010 => 25 011110100100 => 26 011110101000 => 27 011110110000 => 28 011111000001 => 25 011111000100 => 27 011111010000 => 29 001111000110 => 18 001111001010 => 19 100111001100 => 22 001111001100 => 20 001011010110 => 14 001111010010 => 20 100111010100 => 23 001111010100 => 21 000111010110 => 13 001011011010 => 15 100111011000 => 24 001111011000 => 22 100011011100 => 18 010011011100 => 17 001011011100 => 16 000111011100 => 15 000011011110 => 8 001101100110 => 16 001101101010 => 17 100101101100 => 20 001101101100 => 18 001011100110 => 15 001111100010 => 21 100111100100 => 24 001111100100 => 22 010011101010 => 17 001011101010 => 16 100111101000 => 25 001111101000 => 23 000111101010 => 15 100011101100 => 19 010011101100 => 18 001011101100 => 17 000111101100 => 16 000011101110 => 9 101001110100 => 22 001001110110 => 12 001101110010 => 18 100101110100 => 21 001101110100 => 19 000101110110 => 11 001011110010 => 17 100111110000 => 26 001111110000 => 24 100011110100 => 20 010011110100 => 19 001011110100 => 18 000111110100 => 17 000011110110 => 10 110001111000 => 24 101001111000 => 23 001001111010 => 13 100101111000 => 22 001101111000 => 20 100011111000 => 21 001011111000 => 19 000011111010 => 11 010001111100 => 15 001001111100 => 14 000101111100 => 13 000011111100 => 12 100101010101 => 16 100101011001 => 17 100101100101 => 17 100101101001 => 18 100101110001 => 19 100110010101 => 17 100110101001 => 19 100111000101 => 19 100111001001 => 20 100111010001 => 21 101001010101 => 17 101001101001 => 19 101010011001 => 19 101010100101 => 19 101010101001 => 20 101010110001 => 21 101011001001 => 21 101011100001 => 23 101100010101 => 19 101100101001 => 21 101101000101 => 21 101101001001 => 22 101101010001 => 23 101110001001 => 23 101110100001 => 25 110001010101 => 18 110001011001 => 19 110001100101 => 19 110001101001 => 20 110001110001 => 21 110010010101 => 19 110010011001 => 20 110010100101 => 20 110010101001 => 21 110010110001 => 22 110011000101 => 21 110011001001 => 22 110011010001 => 23 110011100001 => 24 110100010101 => 20 110100011001 => 21 110100100101 => 21 110100101001 => 22 110100110001 => 23 110101000101 => 22 110101001001 => 23 110101010001 => 24 110101100001 => 25 110110000101 => 23 110110001001 => 24 110110010001 => 25 110110100001 => 26 110111000001 => 27 111000010101 => 21 111000101001 => 23 111001000101 => 23 111001001001 => 24 111001010001 => 25 111010001001 => 25 111010100001 => 27 111100000101 => 25 111100001001 => 26 111100010001 => 27 111100100001 => 28 111101000001 => 29 10110111100000 => 39 10111011010000 => 39 10111011100000 => 40 10111100110000 => 39 10111101001000 => 39 10111101010000 => 40 10111101100000 => 41 10111110000100 => 39 10111110001000 => 40 10111110010000 => 41 10111110100000 => 42 10111111000000 => 43 11001111100000 => 39 11011110000010 => 39 11101101000010 => 39 11101110000010 => 40 11110011000010 => 39 11110100100010 => 39 11110101000010 => 40 11110110000010 => 41 11111000001100 => 39 11111000010010 => 39 11111000100010 => 40 11111001000010 => 41 11111010000010 => 42 11111100000010 => 43 1011110111000000 => 54 1011111010100000 => 54 1011111011000000 => 55 1011111100010000 => 54 1011111100100000 => 55 1011111101000000 => 56 1011111110000000 => 57 1111011100000010 => 54 1111101010000010 => 54 1111101100000010 => 55 1111110001000010 => 54 1111110010000010 => 55 1111110100000010 => 56 1111111000000010 => 57 111111110000000010 => 73 101111111100000000 => 73 111111101000000010 => 72 101111111010000000 => 72 111111100100000010 => 71 111111011000000010 => 71 101111111001000000 => 71 101111110110000000 => 71 11111111100000000010 => 91 10111111111000000000 => 91 11111111010000000010 => 90 10111111110100000000 => 90 1111111111000000000010 => 111 1011111111110000000000 => 111 ----------------------------------------------------------------------------- Created: Nov 19, 2015 at 12:14 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 12, 2018 at 22:30 by Martin Rubey