***************************************************************************** * 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: St001372 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The length of a longest cyclic run of ones of a binary word. Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(w): if len(w) == 0: return 0 if w[0] == 1: c = Composition(w.delta())[::2] else: c = Composition(w.delta())[1::2] if len(c) > 1 and w[0] == w[-1]: c[-1] += c[0] c = c[1:] return max(c + [0]) ----------------------------------------------------------------------------- Statistic values: 0 => 0 1 => 1 00 => 0 01 => 1 10 => 1 11 => 2 000 => 0 001 => 1 010 => 1 011 => 2 100 => 1 101 => 2 110 => 2 111 => 3 0000 => 0 0001 => 1 0010 => 1 0011 => 2 0100 => 1 0101 => 1 0110 => 2 0111 => 3 1000 => 1 1001 => 2 1010 => 1 1011 => 3 1100 => 2 1101 => 3 1110 => 3 1111 => 4 00000 => 0 00001 => 1 00010 => 1 00011 => 2 00100 => 1 00101 => 1 00110 => 2 00111 => 3 01000 => 1 01001 => 1 01010 => 2 01011 => 2 01100 => 2 01101 => 2 01110 => 3 01111 => 4 10000 => 1 10001 => 2 10010 => 1 10011 => 3 10100 => 1 10101 => 2 10110 => 2 10111 => 4 11000 => 2 11001 => 3 11010 => 2 11011 => 4 11100 => 3 11101 => 4 11110 => 4 11111 => 5 000000 => 0 000001 => 1 000010 => 1 000011 => 2 000100 => 1 000101 => 1 000110 => 2 000111 => 3 001000 => 1 001001 => 1 001010 => 2 001011 => 2 001100 => 2 001101 => 2 001110 => 3 001111 => 4 010000 => 1 010001 => 1 010010 => 2 010011 => 2 010100 => 2 010101 => 1 010110 => 3 010111 => 3 011000 => 2 011001 => 2 011010 => 3 011011 => 2 011100 => 3 011101 => 3 011110 => 4 011111 => 5 100000 => 1 100001 => 2 100010 => 1 100011 => 3 100100 => 1 100101 => 2 100110 => 2 100111 => 4 101000 => 1 101001 => 2 101010 => 1 101011 => 3 101100 => 2 101101 => 2 101110 => 3 101111 => 5 110000 => 2 110001 => 3 110010 => 2 110011 => 4 110100 => 2 110101 => 3 110110 => 2 110111 => 5 111000 => 3 111001 => 4 111010 => 3 111011 => 5 111100 => 4 111101 => 5 111110 => 5 111111 => 6 0000000 => 0 0000001 => 1 0000010 => 1 0000011 => 2 0000100 => 1 0000101 => 1 0000110 => 2 0000111 => 3 0001000 => 1 0001001 => 1 0001010 => 2 0001011 => 2 0001100 => 2 0001101 => 2 0001110 => 3 0001111 => 4 0010000 => 1 0010001 => 1 0010010 => 2 0010011 => 2 0010100 => 2 0010101 => 1 0010110 => 3 0010111 => 3 0011000 => 2 0011001 => 2 0011010 => 3 0011011 => 2 0011100 => 3 0011101 => 3 0011110 => 4 0011111 => 5 0100000 => 1 0100001 => 1 0100010 => 2 0100011 => 2 0100100 => 2 0100101 => 1 0100110 => 3 0100111 => 3 0101000 => 2 0101001 => 1 0101010 => 2 0101011 => 2 0101100 => 3 0101101 => 2 0101110 => 4 0101111 => 4 0110000 => 2 0110001 => 2 0110010 => 3 0110011 => 2 0110100 => 3 0110101 => 2 0110110 => 4 0110111 => 3 0111000 => 3 0111001 => 3 0111010 => 4 0111011 => 3 0111100 => 4 0111101 => 4 0111110 => 5 0111111 => 6 1000000 => 1 1000001 => 2 1000010 => 1 1000011 => 3 1000100 => 1 1000101 => 2 1000110 => 2 1000111 => 4 1001000 => 1 1001001 => 2 1001010 => 1 1001011 => 3 1001100 => 2 1001101 => 2 1001110 => 3 1001111 => 5 1010000 => 1 1010001 => 2 1010010 => 1 1010011 => 3 1010100 => 1 1010101 => 2 1010110 => 2 1010111 => 4 1011000 => 2 1011001 => 2 1011010 => 2 1011011 => 3 1011100 => 3 1011101 => 3 1011110 => 4 1011111 => 6 1100000 => 2 1100001 => 3 1100010 => 2 1100011 => 4 1100100 => 2 1100101 => 3 1100110 => 2 1100111 => 5 1101000 => 2 1101001 => 3 1101010 => 2 1101011 => 4 1101100 => 2 1101101 => 3 1101110 => 3 1101111 => 6 1110000 => 3 1110001 => 4 1110010 => 3 1110011 => 5 1110100 => 3 1110101 => 4 1110110 => 3 1110111 => 6 1111000 => 4 1111001 => 5 1111010 => 4 1111011 => 6 1111100 => 5 1111101 => 6 1111110 => 6 1111111 => 7 00000000 => 0 00000001 => 1 00000010 => 1 00000011 => 2 00000100 => 1 00000101 => 1 00000110 => 2 00000111 => 3 00001000 => 1 00001001 => 1 00001010 => 2 00001011 => 2 00001100 => 2 00001101 => 2 00001110 => 3 00001111 => 4 00010000 => 1 00010001 => 1 00010010 => 2 00010011 => 2 00010100 => 2 00010101 => 1 00010110 => 3 00010111 => 3 00011000 => 2 00011001 => 2 00011010 => 3 00011011 => 2 00011100 => 3 00011101 => 3 00011110 => 4 00011111 => 5 00100000 => 1 00100001 => 1 00100010 => 2 00100011 => 2 00100100 => 2 00100101 => 1 00100110 => 3 00100111 => 3 00101000 => 2 00101001 => 1 00101010 => 2 00101011 => 2 00101100 => 3 00101101 => 2 00101110 => 4 00101111 => 4 00110000 => 2 00110001 => 2 00110010 => 3 00110011 => 2 00110100 => 3 00110101 => 2 00110110 => 4 00110111 => 3 00111000 => 3 00111001 => 3 00111010 => 4 00111011 => 3 00111100 => 4 00111101 => 4 00111110 => 5 00111111 => 6 01000000 => 1 01000001 => 1 01000010 => 2 01000011 => 2 01000100 => 2 01000101 => 1 01000110 => 3 01000111 => 3 01001000 => 2 01001001 => 1 01001010 => 2 01001011 => 2 01001100 => 3 01001101 => 2 01001110 => 4 01001111 => 4 01010000 => 2 01010001 => 1 01010010 => 2 01010011 => 2 01010100 => 2 01010101 => 1 01010110 => 3 01010111 => 3 01011000 => 3 01011001 => 2 01011010 => 2 01011011 => 2 01011100 => 4 01011101 => 3 01011110 => 5 01011111 => 5 01100000 => 2 01100001 => 2 01100010 => 3 01100011 => 2 01100100 => 3 01100101 => 2 01100110 => 4 01100111 => 3 01101000 => 3 01101001 => 2 01101010 => 3 01101011 => 2 01101100 => 4 01101101 => 2 01101110 => 5 01101111 => 4 01110000 => 3 01110001 => 3 01110010 => 4 01110011 => 3 01110100 => 4 01110101 => 3 01110110 => 5 01110111 => 3 01111000 => 4 01111001 => 4 01111010 => 5 01111011 => 4 01111100 => 5 01111101 => 5 01111110 => 6 01111111 => 7 10000000 => 1 10000001 => 2 10000010 => 1 10000011 => 3 10000100 => 1 10000101 => 2 10000110 => 2 10000111 => 4 10001000 => 1 10001001 => 2 10001010 => 1 10001011 => 3 10001100 => 2 10001101 => 2 10001110 => 3 10001111 => 5 10010000 => 1 10010001 => 2 10010010 => 1 10010011 => 3 10010100 => 1 10010101 => 2 10010110 => 2 10010111 => 4 10011000 => 2 10011001 => 2 10011010 => 2 10011011 => 3 10011100 => 3 10011101 => 3 10011110 => 4 10011111 => 6 10100000 => 1 10100001 => 2 10100010 => 1 10100011 => 3 10100100 => 1 10100101 => 2 10100110 => 2 10100111 => 4 10101000 => 1 10101001 => 2 10101010 => 1 10101011 => 3 10101100 => 2 10101101 => 2 10101110 => 3 10101111 => 5 10110000 => 2 10110001 => 2 10110010 => 2 10110011 => 3 10110100 => 2 10110101 => 2 10110110 => 2 10110111 => 4 10111000 => 3 10111001 => 3 10111010 => 3 10111011 => 3 10111100 => 4 10111101 => 4 10111110 => 5 10111111 => 7 11000000 => 2 11000001 => 3 11000010 => 2 11000011 => 4 11000100 => 2 11000101 => 3 11000110 => 2 11000111 => 5 11001000 => 2 11001001 => 3 11001010 => 2 11001011 => 4 11001100 => 2 11001101 => 3 11001110 => 3 11001111 => 6 11010000 => 2 11010001 => 3 11010010 => 2 11010011 => 4 11010100 => 2 11010101 => 3 11010110 => 2 11010111 => 5 11011000 => 2 11011001 => 3 11011010 => 2 11011011 => 4 11011100 => 3 11011101 => 3 11011110 => 4 11011111 => 7 11100000 => 3 11100001 => 4 11100010 => 3 11100011 => 5 11100100 => 3 11100101 => 4 11100110 => 3 11100111 => 6 11101000 => 3 11101001 => 4 11101010 => 3 11101011 => 5 11101100 => 3 11101101 => 4 11101110 => 3 11101111 => 7 11110000 => 4 11110001 => 5 11110010 => 4 11110011 => 6 11110100 => 4 11110101 => 5 11110110 => 4 11110111 => 7 11111000 => 5 11111001 => 6 11111010 => 5 11111011 => 7 11111100 => 6 11111101 => 7 11111110 => 7 11111111 => 8 000000000 => 0 000000001 => 1 000000010 => 1 000000011 => 2 000000100 => 1 000000101 => 1 000000110 => 2 000000111 => 3 000001000 => 1 000001001 => 1 000001010 => 2 000001011 => 2 000001100 => 2 000001101 => 2 000001110 => 3 000001111 => 4 000010000 => 1 000010001 => 1 000010010 => 2 000010011 => 2 000010100 => 2 000010101 => 1 000010110 => 3 000010111 => 3 000011000 => 2 000011001 => 2 000011010 => 3 000011011 => 2 000011100 => 3 000011101 => 3 000011110 => 4 000011111 => 5 000100000 => 1 000100001 => 1 000100010 => 2 000100011 => 2 000100100 => 2 000100101 => 1 000100110 => 3 000100111 => 3 000101000 => 2 000101001 => 1 000101010 => 2 000101011 => 2 000101100 => 3 000101101 => 2 000101110 => 4 000101111 => 4 000110000 => 2 000110001 => 2 000110010 => 3 000110011 => 2 000110100 => 3 000110101 => 2 000110110 => 4 000110111 => 3 000111000 => 3 000111001 => 3 000111010 => 4 000111011 => 3 000111100 => 4 000111101 => 4 000111110 => 5 000111111 => 6 001000000 => 1 001000001 => 1 001000010 => 2 001000011 => 2 001000100 => 2 001000101 => 1 001000110 => 3 001000111 => 3 001001000 => 2 001001001 => 1 001001010 => 2 001001011 => 2 001001100 => 3 001001101 => 2 001001110 => 4 001001111 => 4 001010000 => 2 001010001 => 1 001010010 => 2 001010011 => 2 001010100 => 2 001010101 => 1 001010110 => 3 001010111 => 3 001011000 => 3 001011001 => 2 001011010 => 2 001011011 => 2 001011100 => 4 001011101 => 3 001011110 => 5 001011111 => 5 001100000 => 2 001100001 => 2 001100010 => 3 001100011 => 2 001100100 => 3 001100101 => 2 001100110 => 4 001100111 => 3 001101000 => 3 001101001 => 2 001101010 => 3 001101011 => 2 001101100 => 4 001101101 => 2 001101110 => 5 001101111 => 4 001110000 => 3 001110001 => 3 001110010 => 4 001110011 => 3 001110100 => 4 001110101 => 3 001110110 => 5 001110111 => 3 001111000 => 4 001111001 => 4 001111010 => 5 001111011 => 4 001111100 => 5 001111101 => 5 001111110 => 6 001111111 => 7 010000000 => 1 010000001 => 1 010000010 => 2 010000011 => 2 010000100 => 2 010000101 => 1 010000110 => 3 010000111 => 3 010001000 => 2 010001001 => 1 010001010 => 2 010001011 => 2 010001100 => 3 010001101 => 2 010001110 => 4 010001111 => 4 010010000 => 2 010010001 => 1 010010010 => 2 010010011 => 2 010010100 => 2 010010101 => 1 010010110 => 3 010010111 => 3 010011000 => 3 010011001 => 2 010011010 => 2 010011011 => 2 010011100 => 4 010011101 => 3 010011110 => 5 010011111 => 5 010100000 => 2 010100001 => 1 010100010 => 2 010100011 => 2 010100100 => 2 010100101 => 1 010100110 => 3 010100111 => 3 010101000 => 2 010101001 => 1 010101010 => 2 010101011 => 2 010101100 => 3 010101101 => 2 010101110 => 4 010101111 => 4 010110000 => 3 010110001 => 2 010110010 => 2 010110011 => 2 010110100 => 2 010110101 => 2 010110110 => 3 010110111 => 3 010111000 => 4 010111001 => 3 010111010 => 3 010111011 => 3 010111100 => 5 010111101 => 4 010111110 => 6 010111111 => 6 011000000 => 2 011000001 => 2 011000010 => 3 011000011 => 2 011000100 => 3 011000101 => 2 011000110 => 4 011000111 => 3 011001000 => 3 011001001 => 2 011001010 => 3 011001011 => 2 011001100 => 4 011001101 => 2 011001110 => 5 011001111 => 4 011010000 => 3 011010001 => 2 011010010 => 3 011010011 => 2 011010100 => 3 011010101 => 2 011010110 => 4 011010111 => 3 011011000 => 4 011011001 => 2 011011010 => 3 011011011 => 2 011011100 => 5 011011101 => 3 011011110 => 6 011011111 => 5 011100000 => 3 011100001 => 3 011100010 => 4 011100011 => 3 011100100 => 4 011100101 => 3 011100110 => 5 011100111 => 3 011101000 => 4 011101001 => 3 011101010 => 4 011101011 => 3 011101100 => 5 011101101 => 3 011101110 => 6 011101111 => 4 011110000 => 4 011110001 => 4 011110010 => 5 011110011 => 4 011110100 => 5 011110101 => 4 011110110 => 6 011110111 => 4 011111000 => 5 011111001 => 5 011111010 => 6 011111011 => 5 011111100 => 6 011111101 => 6 011111110 => 7 011111111 => 8 100000000 => 1 100000001 => 2 100000010 => 1 100000011 => 3 100000100 => 1 100000101 => 2 100000110 => 2 100000111 => 4 100001000 => 1 100001001 => 2 100001010 => 1 100001011 => 3 100001100 => 2 100001101 => 2 100001110 => 3 100001111 => 5 100010000 => 1 100010001 => 2 100010010 => 1 100010011 => 3 100010100 => 1 100010101 => 2 100010110 => 2 100010111 => 4 100011000 => 2 100011001 => 2 100011010 => 2 100011011 => 3 100011100 => 3 100011101 => 3 100011110 => 4 100011111 => 6 100100000 => 1 100100001 => 2 100100010 => 1 100100011 => 3 100100100 => 1 100100101 => 2 100100110 => 2 100100111 => 4 100101000 => 1 100101001 => 2 100101010 => 1 100101011 => 3 100101100 => 2 100101101 => 2 100101110 => 3 100101111 => 5 100110000 => 2 100110001 => 2 100110010 => 2 100110011 => 3 100110100 => 2 100110101 => 2 100110110 => 2 100110111 => 4 100111000 => 3 100111001 => 3 100111010 => 3 100111011 => 3 100111100 => 4 100111101 => 4 100111110 => 5 100111111 => 7 101000000 => 1 101000001 => 2 101000010 => 1 101000011 => 3 101000100 => 1 101000101 => 2 101000110 => 2 101000111 => 4 101001000 => 1 101001001 => 2 101001010 => 1 101001011 => 3 101001100 => 2 101001101 => 2 101001110 => 3 101001111 => 5 101010000 => 1 101010001 => 2 101010010 => 1 101010011 => 3 101010100 => 1 101010101 => 2 101010110 => 2 101010111 => 4 101011000 => 2 101011001 => 2 101011010 => 2 101011011 => 3 101011100 => 3 101011101 => 3 101011110 => 4 101011111 => 6 101100000 => 2 101100001 => 2 101100010 => 2 101100011 => 3 101100100 => 2 101100101 => 2 101100110 => 2 101100111 => 4 101101000 => 2 101101001 => 2 101101010 => 2 101101011 => 3 101101100 => 2 101101101 => 2 101101110 => 3 101101111 => 5 101110000 => 3 101110001 => 3 101110010 => 3 101110011 => 3 101110100 => 3 101110101 => 3 101110110 => 3 101110111 => 4 101111000 => 4 101111001 => 4 101111010 => 4 101111011 => 4 101111100 => 5 101111101 => 5 101111110 => 6 101111111 => 8 110000000 => 2 110000001 => 3 110000010 => 2 110000011 => 4 110000100 => 2 110000101 => 3 110000110 => 2 110000111 => 5 110001000 => 2 110001001 => 3 110001010 => 2 110001011 => 4 110001100 => 2 110001101 => 3 110001110 => 3 110001111 => 6 110010000 => 2 110010001 => 3 110010010 => 2 110010011 => 4 110010100 => 2 110010101 => 3 110010110 => 2 110010111 => 5 110011000 => 2 110011001 => 3 110011010 => 2 110011011 => 4 110011100 => 3 110011101 => 3 110011110 => 4 110011111 => 7 110100000 => 2 110100001 => 3 110100010 => 2 110100011 => 4 110100100 => 2 110100101 => 3 110100110 => 2 110100111 => 5 110101000 => 2 110101001 => 3 110101010 => 2 110101011 => 4 110101100 => 2 110101101 => 3 110101110 => 3 110101111 => 6 110110000 => 2 110110001 => 3 110110010 => 2 110110011 => 4 110110100 => 2 110110101 => 3 110110110 => 2 110110111 => 5 110111000 => 3 110111001 => 3 110111010 => 3 110111011 => 4 110111100 => 4 110111101 => 4 110111110 => 5 110111111 => 8 111000000 => 3 111000001 => 4 111000010 => 3 111000011 => 5 111000100 => 3 111000101 => 4 111000110 => 3 111000111 => 6 111001000 => 3 111001001 => 4 111001010 => 3 111001011 => 5 111001100 => 3 111001101 => 4 111001110 => 3 111001111 => 7 111010000 => 3 111010001 => 4 111010010 => 3 111010011 => 5 111010100 => 3 111010101 => 4 111010110 => 3 111010111 => 6 111011000 => 3 111011001 => 4 111011010 => 3 111011011 => 5 111011100 => 3 111011101 => 4 111011110 => 4 111011111 => 8 111100000 => 4 111100001 => 5 111100010 => 4 111100011 => 6 111100100 => 4 111100101 => 5 111100110 => 4 111100111 => 7 111101000 => 4 111101001 => 5 111101010 => 4 111101011 => 6 111101100 => 4 111101101 => 5 111101110 => 4 111101111 => 8 111110000 => 5 111110001 => 6 111110010 => 5 111110011 => 7 111110100 => 5 111110101 => 6 111110110 => 5 111110111 => 8 111111000 => 6 111111001 => 7 111111010 => 6 111111011 => 8 111111100 => 7 111111101 => 8 111111110 => 8 111111111 => 9 1010101010 => 1 1010101100 => 2 1010110010 => 2 1010110100 => 2 1010111000 => 3 1011001010 => 2 1011001100 => 2 1011010010 => 2 1011010100 => 2 1011011000 => 2 1011100010 => 3 1011100100 => 3 1011101000 => 3 1011110000 => 4 1100101010 => 2 1100101100 => 2 1100110010 => 2 1100110100 => 2 1100111000 => 3 1101001010 => 2 1101001100 => 2 1101010010 => 2 1101010100 => 2 1101011000 => 2 1101100010 => 2 1101100100 => 2 1101101000 => 2 1101110000 => 3 1110001010 => 3 1110001100 => 3 1110010010 => 3 1110010100 => 3 1110011000 => 3 1110100010 => 3 1110100100 => 3 1110101000 => 3 1110110000 => 3 1111000010 => 4 1111000100 => 4 1111001000 => 4 1111010000 => 4 1111100000 => 5 1111111110 => 9 1111111101 => 9 1111000001 => 5 1110111110 => 5 1110100001 => 4 1110011110 => 4 1110010001 => 4 1110001001 => 4 1110000101 => 4 1101111110 => 6 1101100001 => 3 1101010001 => 3 1101001110 => 3 1101001001 => 3 1101000101 => 3 1100110001 => 3 1100101001 => 3 1100100110 => 2 1100100101 => 3 1100011001 => 3 1100010101 => 3 1100010010 => 2 1100001000 => 2 1011111110 => 7 1011111101 => 6 1011100001 => 3 1011010001 => 2 1011001001 => 2 1011000101 => 2 1010111110 => 5 1010110001 => 2 1010101001 => 2 1010100110 => 2 1010100101 => 2 1010011010 => 2 1010011001 => 2 1010010110 => 2 1010010101 => 2 1010001110 => 3 1001111110 => 6 1001111000 => 4 1001110100 => 3 1001110001 => 3 1001101100 => 2 1001101010 => 2 1001101001 => 2 1001100110 => 2 1001100101 => 2 1001011110 => 4 1001011010 => 2 1001011001 => 2 1001010110 => 2 1001010101 => 2 1001001110 => 3 1000111110 => 5 1000111100 => 4 1000111010 => 3 1000110110 => 2 1000101110 => 3 1000011110 => 4 1000010110 => 2 1000001110 => 3 1000001010 => 1 1000000110 => 2 1000000100 => 1 1000000010 => 1 1000000000 => 1 0111111111 => 9 0111111101 => 7 0111111001 => 6 0111110001 => 5 0111100001 => 4 0111000001 => 3 0110000001 => 2 0100000001 => 1 0000000001 => 1 0111111011 => 6 0111110101 => 5 0111101001 => 4 0111010001 => 3 0110100001 => 2 0101000001 => 1 0010000001 => 1 0101010101 => 1 0101010011 => 2 0101001101 => 2 0101001011 => 2 0101000111 => 3 0100110101 => 2 0100110011 => 2 0100101101 => 2 0100101011 => 2 0100100111 => 3 0100011101 => 3 0100011011 => 2 0100010111 => 3 0100001111 => 4 0011010101 => 2 0011010011 => 2 0011001101 => 2 0011001011 => 2 0011000111 => 3 0010110101 => 2 0010110011 => 2 0010101101 => 2 0010101011 => 2 0010100111 => 3 0010011101 => 3 0010011011 => 2 0010010111 => 3 0010001111 => 4 0001110101 => 3 0001110011 => 3 0001101101 => 2 0001101011 => 2 0001100111 => 3 0001011101 => 3 0001011011 => 2 0001010111 => 3 0001001111 => 4 0000111101 => 4 0000111011 => 3 0000110111 => 3 0000101111 => 4 0000011111 => 5 0100000010 => 2 0010111100 => 5 0011110100 => 5 0111010100 => 4 0000000010 => 1 0000111110 => 5 0100000000 => 1 0100000011 => 2 0100000111 => 3 0100011111 => 5 0100111111 => 6 0101111111 => 7 0100000101 => 1 0100001011 => 2 0100101111 => 4 0101011111 => 5 0110111111 => 6 0101010110 => 3 0101011001 => 2 0101011010 => 2 0101011100 => 4 0101100101 => 2 0101100110 => 3 0101101001 => 2 0101101010 => 2 0101101100 => 3 0101110001 => 3 0101110010 => 3 0101110100 => 3 0101111000 => 5 0110010101 => 2 0110010110 => 4 0110011001 => 2 0110011010 => 3 0110011100 => 5 0110100101 => 2 0110100110 => 4 0110101001 => 2 0110101010 => 3 0110101100 => 4 0110110001 => 2 0110110010 => 3 0110110100 => 3 0110111000 => 5 0111000101 => 3 0111000110 => 5 0111001001 => 3 0111001010 => 4 0111001100 => 5 0111010010 => 4 0111011000 => 5 0111100010 => 5 0111100100 => 5 0111101000 => 5 0111110000 => 5 0100000100 => 2 0011100110 => 5 0011101010 => 4 0011101100 => 5 0001101110 => 5 0010110110 => 3 0011110010 => 5 0001110110 => 5 0100111010 => 3 0010111010 => 3 0011111000 => 5 0001111010 => 5 0100111100 => 5 0001111100 => 5 0000000101 => 1 0000001101 => 2 0000011101 => 3 0001111101 => 5 0011111101 => 6 0000001001 => 1 0000010101 => 1 0000101101 => 2 0010111101 => 4 0101111101 => 5 10000000000 => 1 10000000010 => 1 10000000110 => 2 10000001110 => 3 10000011110 => 4 10000111110 => 5 10001111110 => 6 10011111110 => 7 10111111110 => 8 11111111110 => 10 10000000100 => 1 10000001010 => 1 10000010110 => 2 10000101110 => 3 10001011110 => 4 10010111110 => 5 10101111110 => 6 11011111110 => 7 10000010000 => 1 10000100010 => 1 10001000010 => 1 10000100100 => 1 10001001010 => 1 10001000100 => 1 10000101000 => 1 10010001010 => 1 10001010010 => 1 10010000100 => 1 10001001000 => 1 10010010010 => 1 10001010100 => 1 10010101010 => 1 10010001000 => 1 10100010010 => 1 10010100010 => 1 10010010100 => 1 10100101010 => 1 01111111111 => 10 01111111101 => 8 01111111001 => 7 01111110001 => 6 01111100001 => 5 01111000001 => 4 01110000001 => 3 01100000001 => 2 01000000001 => 1 00000000001 => 1 00000000010 => 1 10101010101 => 2 10101010010 => 1 10101001001 => 2 10101001010 => 1 10101000100 => 1 10100100101 => 2 10100100010 => 1 10100101001 => 2 10100100100 => 1 10100010001 => 2 10100010100 => 1 10100001000 => 1 10010010101 => 2 10010001001 => 2 10010100101 => 2 10010101001 => 2 10010100100 => 1 10010010001 => 2 10001000101 => 2 10001001001 => 2 10001010001 => 2 10000100001 => 2 01001010101 => 1 01001010010 => 2 01001001001 => 1 01001001010 => 2 01001000100 => 2 01000100101 => 1 01000100010 => 2 01000101001 => 1 01000101010 => 2 01000100100 => 2 01000010001 => 1 01000010010 => 2 01000010100 => 2 01000001000 => 2 01010010101 => 1 01010010010 => 2 01010001001 => 1 01010001010 => 2 01010000100 => 2 01010100101 => 1 01010100010 => 2 01010101001 => 1 01010101010 => 2 01010100100 => 2 01010010001 => 1 01010010100 => 2 01010001000 => 2 01001000101 => 1 01001000010 => 2 01001010001 => 1 01001010100 => 2 01001001000 => 2 01000100001 => 1 01000101000 => 2 01000010000 => 2 00100010101 => 1 00100010010 => 2 00100001001 => 1 00100001010 => 2 00100000100 => 2 00100100101 => 1 00100100010 => 2 00100101001 => 1 00100101010 => 2 00100100100 => 2 00100010001 => 1 00100010100 => 2 00100001000 => 2 00101000101 => 1 00101000010 => 2 00101001001 => 1 00101001010 => 2 00101000100 => 2 00101010001 => 1 00101010010 => 2 00101010100 => 2 00101001000 => 2 00100100001 => 1 00100101000 => 2 00100010000 => 2 00010000101 => 1 00010000010 => 2 00010001001 => 1 00010001010 => 2 00010000100 => 2 00010010001 => 1 00010010010 => 2 00010010100 => 2 00010001000 => 2 00010100001 => 1 00010100010 => 2 00010100100 => 2 00010101000 => 2 00010010000 => 2 00001000001 => 1 00001000010 => 2 00001000100 => 2 00001001000 => 2 00001010000 => 2 00000100000 => 1 01000000000 => 1 01000000011 => 2 01000000111 => 3 01000001111 => 4 01000011111 => 5 01000111111 => 6 01001111111 => 7 01011111111 => 8 00000000101 => 1 00000001101 => 2 00000011101 => 3 00000111101 => 4 00001111101 => 5 00011111101 => 6 00111111101 => 7 11111111101 => 10 101010101010 => 1 101010101100 => 2 101010110010 => 2 101010110100 => 2 101010111000 => 3 101011001010 => 2 101011001100 => 2 101011010010 => 2 101011010100 => 2 101011011000 => 2 101011100010 => 3 101011100100 => 3 101011101000 => 3 101011110000 => 4 101100101010 => 2 101100101100 => 2 101100110010 => 2 101100110100 => 2 101100111000 => 3 101101001010 => 2 101101001100 => 2 101101010010 => 2 101101010100 => 2 101101011000 => 2 101101100010 => 2 101101100100 => 2 101101101000 => 2 101101110000 => 3 101110001010 => 3 101110001100 => 3 101110010010 => 3 101110010100 => 3 101110011000 => 3 101110100010 => 3 101110100100 => 3 101110101000 => 3 101110110000 => 3 101111000010 => 4 101111000100 => 4 101111001000 => 4 101111010000 => 4 101111100000 => 5 110010101010 => 2 110010101100 => 2 110010110010 => 2 110010110100 => 2 110010111000 => 3 110011001010 => 2 110011001100 => 2 110011010010 => 2 110011010100 => 2 110011011000 => 2 110011100010 => 3 110011100100 => 3 110011101000 => 3 110011110000 => 4 110100101010 => 2 110100101100 => 2 110100110010 => 2 110100110100 => 2 110100111000 => 3 110101001010 => 2 110101001100 => 2 110101010010 => 2 110101010100 => 2 110101011000 => 2 110101100010 => 2 110101100100 => 2 110101101000 => 2 110101110000 => 3 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=> 8 1111111111000000000010 => 10 1011111111110000000000 => 10 ----------------------------------------------------------------------------- Created: Mar 19, 2019 at 22:50 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 22, 2019 at 13:50 by Martin Rubey