***************************************************************************** * 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: St000921 ----------------------------------------------------------------------------- Collection: Binary words ----------------------------------------------------------------------------- Description: The number of internal inversions of a binary word. Let $\bar w$ be the non-decreasing rearrangement of $w$, that is, $\bar w$ is sorted. An internal inversion is a pair $i < j$ such that $w_i > w_j$ and $\bar w_i = \bar w_j$. For example, the word $110$ has two inversions, but only the second is internal. ----------------------------------------------------------------------------- References: [1] Foata, D., Han, G.-N. Inverses of words [[MathSciNet:1611988]] [2] Hohlweg, C., Reutenauer, C. Inverses of words and the parabolic structure of the symmetric group [[MathSciNet:1861050]] ----------------------------------------------------------------------------- Code: def statistic(w): w_bar = sorted(w) return len([(i,j) for (i, j) in w.inversions() if w_bar[i] == w_bar[j]]) ----------------------------------------------------------------------------- Statistic values: 0 => 0 1 => 0 00 => 0 01 => 0 10 => 0 11 => 0 000 => 0 001 => 0 010 => 0 011 => 0 100 => 1 101 => 0 110 => 1 111 => 0 0000 => 0 0001 => 0 0010 => 0 0011 => 0 0100 => 1 0101 => 0 0110 => 1 0111 => 0 1000 => 2 1001 => 1 1010 => 2 1011 => 0 1100 => 0 1101 => 1 1110 => 2 1111 => 0 00000 => 0 00001 => 0 00010 => 0 00011 => 0 00100 => 1 00101 => 0 00110 => 1 00111 => 0 01000 => 2 01001 => 1 01010 => 2 01011 => 0 01100 => 0 01101 => 1 01110 => 2 01111 => 0 10000 => 3 10001 => 2 10010 => 3 10011 => 1 10100 => 1 10101 => 2 10110 => 3 10111 => 0 11000 => 2 11001 => 0 11010 => 1 11011 => 1 11100 => 2 11101 => 2 11110 => 3 11111 => 0 000000 => 0 000001 => 0 000010 => 0 000011 => 0 000100 => 1 000101 => 0 000110 => 1 000111 => 0 001000 => 2 001001 => 1 001010 => 2 001011 => 0 001100 => 0 001101 => 1 001110 => 2 001111 => 0 010000 => 3 010001 => 2 010010 => 3 010011 => 1 010100 => 1 010101 => 2 010110 => 3 010111 => 0 011000 => 2 011001 => 0 011010 => 1 011011 => 1 011100 => 2 011101 => 2 011110 => 3 011111 => 0 100000 => 4 100001 => 3 100010 => 4 100011 => 2 100100 => 2 100101 => 3 100110 => 4 100111 => 1 101000 => 3 101001 => 1 101010 => 2 101011 => 2 101100 => 3 101101 => 3 101110 => 4 101111 => 0 110000 => 4 110001 => 2 110010 => 3 110011 => 0 110100 => 4 110101 => 1 110110 => 2 110111 => 1 111000 => 0 111001 => 2 111010 => 3 111011 => 2 111100 => 4 111101 => 3 111110 => 4 111111 => 0 0000000 => 0 0000001 => 0 0000010 => 0 0000011 => 0 0000100 => 1 0000101 => 0 0000110 => 1 0000111 => 0 0001000 => 2 0001001 => 1 0001010 => 2 0001011 => 0 0001100 => 0 0001101 => 1 0001110 => 2 0001111 => 0 0010000 => 3 0010001 => 2 0010010 => 3 0010011 => 1 0010100 => 1 0010101 => 2 0010110 => 3 0010111 => 0 0011000 => 2 0011001 => 0 0011010 => 1 0011011 => 1 0011100 => 2 0011101 => 2 0011110 => 3 0011111 => 0 0100000 => 4 0100001 => 3 0100010 => 4 0100011 => 2 0100100 => 2 0100101 => 3 0100110 => 4 0100111 => 1 0101000 => 3 0101001 => 1 0101010 => 2 0101011 => 2 0101100 => 3 0101101 => 3 0101110 => 4 0101111 => 0 0110000 => 4 0110001 => 2 0110010 => 3 0110011 => 0 0110100 => 4 0110101 => 1 0110110 => 2 0110111 => 1 0111000 => 0 0111001 => 2 0111010 => 3 0111011 => 2 0111100 => 4 0111101 => 3 0111110 => 4 0111111 => 0 1000000 => 5 1000001 => 4 1000010 => 5 1000011 => 3 1000100 => 3 1000101 => 4 1000110 => 5 1000111 => 2 1001000 => 4 1001001 => 2 1001010 => 3 1001011 => 3 1001100 => 4 1001101 => 4 1001110 => 5 1001111 => 1 1010000 => 5 1010001 => 3 1010010 => 4 1010011 => 1 1010100 => 5 1010101 => 2 1010110 => 3 1010111 => 2 1011000 => 1 1011001 => 3 1011010 => 4 1011011 => 3 1011100 => 5 1011101 => 4 1011110 => 5 1011111 => 0 1100000 => 6 1100001 => 4 1100010 => 5 1100011 => 2 1100100 => 6 1100101 => 3 1100110 => 4 1100111 => 0 1101000 => 2 1101001 => 4 1101010 => 5 1101011 => 1 1101100 => 6 1101101 => 2 1101110 => 3 1101111 => 1 1110000 => 3 1110001 => 0 1110010 => 1 1110011 => 2 1110100 => 2 1110101 => 3 1110110 => 4 1110111 => 2 1111000 => 3 1111001 => 4 1111010 => 5 1111011 => 3 1111100 => 6 1111101 => 4 1111110 => 5 1111111 => 0 00000000 => 0 00000001 => 0 00000010 => 0 00000011 => 0 00000100 => 1 00000101 => 0 00000110 => 1 00000111 => 0 00001000 => 2 00001001 => 1 00001010 => 2 00001011 => 0 00001100 => 0 00001101 => 1 00001110 => 2 00001111 => 0 00010000 => 3 00010001 => 2 00010010 => 3 00010011 => 1 00010100 => 1 00010101 => 2 00010110 => 3 00010111 => 0 00011000 => 2 00011001 => 0 00011010 => 1 00011011 => 1 00011100 => 2 00011101 => 2 00011110 => 3 00011111 => 0 00100000 => 4 00100001 => 3 00100010 => 4 00100011 => 2 00100100 => 2 00100101 => 3 00100110 => 4 00100111 => 1 00101000 => 3 00101001 => 1 00101010 => 2 00101011 => 2 00101100 => 3 00101101 => 3 00101110 => 4 00101111 => 0 00110000 => 4 00110001 => 2 00110010 => 3 00110011 => 0 00110100 => 4 00110101 => 1 00110110 => 2 00110111 => 1 00111000 => 0 00111001 => 2 00111010 => 3 00111011 => 2 00111100 => 4 00111101 => 3 00111110 => 4 00111111 => 0 01000000 => 5 01000001 => 4 01000010 => 5 01000011 => 3 01000100 => 3 01000101 => 4 01000110 => 5 01000111 => 2 01001000 => 4 01001001 => 2 01001010 => 3 01001011 => 3 01001100 => 4 01001101 => 4 01001110 => 5 01001111 => 1 01010000 => 5 01010001 => 3 01010010 => 4 01010011 => 1 01010100 => 5 01010101 => 2 01010110 => 3 01010111 => 2 01011000 => 1 01011001 => 3 01011010 => 4 01011011 => 3 01011100 => 5 01011101 => 4 01011110 => 5 01011111 => 0 01100000 => 6 01100001 => 4 01100010 => 5 01100011 => 2 01100100 => 6 01100101 => 3 01100110 => 4 01100111 => 0 01101000 => 2 01101001 => 4 01101010 => 5 01101011 => 1 01101100 => 6 01101101 => 2 01101110 => 3 01101111 => 1 01110000 => 3 01110001 => 0 01110010 => 1 01110011 => 2 01110100 => 2 01110101 => 3 01110110 => 4 01110111 => 2 01111000 => 3 01111001 => 4 01111010 => 5 01111011 => 3 01111100 => 6 01111101 => 4 01111110 => 5 01111111 => 0 10000000 => 6 10000001 => 5 10000010 => 6 10000011 => 4 10000100 => 4 10000101 => 5 10000110 => 6 10000111 => 3 10001000 => 5 10001001 => 3 10001010 => 4 10001011 => 4 10001100 => 5 10001101 => 5 10001110 => 6 10001111 => 2 10010000 => 6 10010001 => 4 10010010 => 5 10010011 => 2 10010100 => 6 10010101 => 3 10010110 => 4 10010111 => 3 10011000 => 2 10011001 => 4 10011010 => 5 10011011 => 4 10011100 => 6 10011101 => 5 10011110 => 6 10011111 => 1 10100000 => 7 10100001 => 5 10100010 => 6 10100011 => 3 10100100 => 7 10100101 => 4 10100110 => 5 10100111 => 1 10101000 => 3 10101001 => 5 10101010 => 6 10101011 => 2 10101100 => 7 10101101 => 3 10101110 => 4 10101111 => 2 10110000 => 4 10110001 => 1 10110010 => 2 10110011 => 3 10110100 => 3 10110101 => 4 10110110 => 5 10110111 => 3 10111000 => 4 10111001 => 5 10111010 => 6 10111011 => 4 10111100 => 7 10111101 => 5 10111110 => 6 10111111 => 0 11000000 => 8 11000001 => 6 11000010 => 7 11000011 => 4 11000100 => 8 11000101 => 5 11000110 => 6 11000111 => 2 11001000 => 4 11001001 => 6 11001010 => 7 11001011 => 3 11001100 => 8 11001101 => 4 11001110 => 5 11001111 => 0 11010000 => 5 11010001 => 2 11010010 => 3 11010011 => 4 11010100 => 4 11010101 => 5 11010110 => 6 11010111 => 1 11011000 => 5 11011001 => 6 11011010 => 7 11011011 => 2 11011100 => 8 11011101 => 3 11011110 => 4 11011111 => 1 11100000 => 6 11100001 => 3 11100010 => 4 11100011 => 0 11100100 => 5 11100101 => 1 11100110 => 2 11100111 => 2 11101000 => 6 11101001 => 2 11101010 => 3 11101011 => 3 11101100 => 4 11101101 => 4 11101110 => 5 11101111 => 2 11110000 => 0 11110001 => 3 11110010 => 4 11110011 => 4 11110100 => 5 11110101 => 5 11110110 => 6 11110111 => 3 11111000 => 6 11111001 => 6 11111010 => 7 11111011 => 4 11111100 => 8 11111101 => 5 11111110 => 6 11111111 => 0 000000000 => 0 000000001 => 0 000000010 => 0 000000011 => 0 000000100 => 1 000000101 => 0 000000110 => 1 000000111 => 0 000001000 => 2 000001001 => 1 000001010 => 2 000001011 => 0 000001100 => 0 000001101 => 1 000001110 => 2 000001111 => 0 000010000 => 3 000010001 => 2 000010010 => 3 000010011 => 1 000010100 => 1 000010101 => 2 000010110 => 3 000010111 => 0 000011000 => 2 000011001 => 0 000011010 => 1 000011011 => 1 000011100 => 2 000011101 => 2 000011110 => 3 000011111 => 0 000100000 => 4 000100001 => 3 000100010 => 4 000100011 => 2 000100100 => 2 000100101 => 3 000100110 => 4 000100111 => 1 000101000 => 3 000101001 => 1 000101010 => 2 000101011 => 2 000101100 => 3 000101101 => 3 000101110 => 4 000101111 => 0 000110000 => 4 000110001 => 2 000110010 => 3 000110011 => 0 000110100 => 4 000110101 => 1 000110110 => 2 000110111 => 1 000111000 => 0 000111001 => 2 000111010 => 3 000111011 => 2 000111100 => 4 000111101 => 3 000111110 => 4 000111111 => 0 001000000 => 5 001000001 => 4 001000010 => 5 001000011 => 3 001000100 => 3 001000101 => 4 001000110 => 5 001000111 => 2 001001000 => 4 001001001 => 2 001001010 => 3 001001011 => 3 001001100 => 4 001001101 => 4 001001110 => 5 001001111 => 1 001010000 => 5 001010001 => 3 001010010 => 4 001010011 => 1 001010100 => 5 001010101 => 2 001010110 => 3 001010111 => 2 001011000 => 1 001011001 => 3 001011010 => 4 001011011 => 3 001011100 => 5 001011101 => 4 001011110 => 5 001011111 => 0 001100000 => 6 001100001 => 4 001100010 => 5 001100011 => 2 001100100 => 6 001100101 => 3 001100110 => 4 001100111 => 0 001101000 => 2 001101001 => 4 001101010 => 5 001101011 => 1 001101100 => 6 001101101 => 2 001101110 => 3 001101111 => 1 001110000 => 3 001110001 => 0 001110010 => 1 001110011 => 2 001110100 => 2 001110101 => 3 001110110 => 4 001110111 => 2 001111000 => 3 001111001 => 4 001111010 => 5 001111011 => 3 001111100 => 6 001111101 => 4 001111110 => 5 001111111 => 0 010000000 => 6 010000001 => 5 010000010 => 6 010000011 => 4 010000100 => 4 010000101 => 5 010000110 => 6 010000111 => 3 010001000 => 5 010001001 => 3 010001010 => 4 010001011 => 4 010001100 => 5 010001101 => 5 010001110 => 6 010001111 => 2 010010000 => 6 010010001 => 4 010010010 => 5 010010011 => 2 010010100 => 6 010010101 => 3 010010110 => 4 010010111 => 3 010011000 => 2 010011001 => 4 010011010 => 5 010011011 => 4 010011100 => 6 010011101 => 5 010011110 => 6 010011111 => 1 010100000 => 7 010100001 => 5 010100010 => 6 010100011 => 3 010100100 => 7 010100101 => 4 010100110 => 5 010100111 => 1 010101000 => 3 010101001 => 5 010101010 => 6 010101011 => 2 010101100 => 7 010101101 => 3 010101110 => 4 010101111 => 2 010110000 => 4 010110001 => 1 010110010 => 2 010110011 => 3 010110100 => 3 010110101 => 4 010110110 => 5 010110111 => 3 010111000 => 4 010111001 => 5 010111010 => 6 010111011 => 4 010111100 => 7 010111101 => 5 010111110 => 6 010111111 => 0 011000000 => 8 011000001 => 6 011000010 => 7 011000011 => 4 011000100 => 8 011000101 => 5 011000110 => 6 011000111 => 2 011001000 => 4 011001001 => 6 011001010 => 7 011001011 => 3 011001100 => 8 011001101 => 4 011001110 => 5 011001111 => 0 011010000 => 5 011010001 => 2 011010010 => 3 011010011 => 4 011010100 => 4 011010101 => 5 011010110 => 6 011010111 => 1 011011000 => 5 011011001 => 6 011011010 => 7 011011011 => 2 011011100 => 8 011011101 => 3 011011110 => 4 011011111 => 1 011100000 => 6 011100001 => 3 011100010 => 4 011100011 => 0 011100100 => 5 011100101 => 1 011100110 => 2 011100111 => 2 011101000 => 6 011101001 => 2 011101010 => 3 011101011 => 3 011101100 => 4 011101101 => 4 011101110 => 5 011101111 => 2 011110000 => 0 011110001 => 3 011110010 => 4 011110011 => 4 011110100 => 5 011110101 => 5 011110110 => 6 011110111 => 3 011111000 => 6 011111001 => 6 011111010 => 7 011111011 => 4 011111100 => 8 011111101 => 5 011111110 => 6 011111111 => 0 100000000 => 7 100000001 => 6 100000010 => 7 100000011 => 5 100000100 => 5 100000101 => 6 100000110 => 7 100000111 => 4 100001000 => 6 100001001 => 4 100001010 => 5 100001011 => 5 100001100 => 6 100001101 => 6 100001110 => 7 100001111 => 3 100010000 => 7 100010001 => 5 100010010 => 6 100010011 => 3 100010100 => 7 100010101 => 4 100010110 => 5 100010111 => 4 100011000 => 3 100011001 => 5 100011010 => 6 100011011 => 5 100011100 => 7 100011101 => 6 100011110 => 7 100011111 => 2 100100000 => 8 100100001 => 6 100100010 => 7 100100011 => 4 100100100 => 8 100100101 => 5 100100110 => 6 100100111 => 2 100101000 => 4 100101001 => 6 100101010 => 7 100101011 => 3 100101100 => 8 100101101 => 4 100101110 => 5 100101111 => 3 100110000 => 5 100110001 => 2 100110010 => 3 100110011 => 4 100110100 => 4 100110101 => 5 100110110 => 6 100110111 => 4 100111000 => 5 100111001 => 6 100111010 => 7 100111011 => 5 100111100 => 8 100111101 => 6 100111110 => 7 100111111 => 1 101000000 => 9 101000001 => 7 101000010 => 8 101000011 => 5 101000100 => 9 101000101 => 6 101000110 => 7 101000111 => 3 101001000 => 5 101001001 => 7 101001010 => 8 101001011 => 4 101001100 => 9 101001101 => 5 101001110 => 6 101001111 => 1 101010000 => 6 101010001 => 3 101010010 => 4 101010011 => 5 101010100 => 5 101010101 => 6 101010110 => 7 101010111 => 2 101011000 => 6 101011001 => 7 101011010 => 8 101011011 => 3 101011100 => 9 101011101 => 4 101011110 => 5 101011111 => 2 101100000 => 7 101100001 => 4 101100010 => 5 101100011 => 1 101100100 => 6 101100101 => 2 101100110 => 3 101100111 => 3 101101000 => 7 101101001 => 3 101101010 => 4 101101011 => 4 101101100 => 5 101101101 => 5 101101110 => 6 101101111 => 3 101110000 => 1 101110001 => 4 101110010 => 5 101110011 => 5 101110100 => 6 101110101 => 6 101110110 => 7 101110111 => 4 101111000 => 7 101111001 => 7 101111010 => 8 101111011 => 5 101111100 => 9 101111101 => 6 101111110 => 7 101111111 => 0 110000000 => 10 110000001 => 8 110000010 => 9 110000011 => 6 110000100 => 10 110000101 => 7 110000110 => 8 110000111 => 4 110001000 => 6 110001001 => 8 110001010 => 9 110001011 => 5 110001100 => 10 110001101 => 6 110001110 => 7 110001111 => 2 110010000 => 7 110010001 => 4 110010010 => 5 110010011 => 6 110010100 => 6 110010101 => 7 110010110 => 8 110010111 => 3 110011000 => 7 110011001 => 8 110011010 => 9 110011011 => 4 110011100 => 10 110011101 => 5 110011110 => 6 110011111 => 0 110100000 => 8 110100001 => 5 110100010 => 6 110100011 => 2 110100100 => 7 110100101 => 3 110100110 => 4 110100111 => 4 110101000 => 8 110101001 => 4 110101010 => 5 110101011 => 5 110101100 => 6 110101101 => 6 110101110 => 7 110101111 => 1 110110000 => 2 110110001 => 5 110110010 => 6 110110011 => 6 110110100 => 7 110110101 => 7 110110110 => 8 110110111 => 2 110111000 => 8 110111001 => 8 110111010 => 9 110111011 => 3 110111100 => 10 110111101 => 4 110111110 => 5 110111111 => 1 111000000 => 9 111000001 => 6 111000010 => 7 111000011 => 3 111000100 => 8 111000101 => 4 111000110 => 5 111000111 => 0 111001000 => 9 111001001 => 5 111001010 => 6 111001011 => 1 111001100 => 7 111001101 => 2 111001110 => 3 111001111 => 2 111010000 => 3 111010001 => 6 111010010 => 7 111010011 => 2 111010100 => 8 111010101 => 3 111010110 => 4 111010111 => 3 111011000 => 9 111011001 => 4 111011010 => 5 111011011 => 4 111011100 => 6 111011101 => 5 111011110 => 6 111011111 => 2 111100000 => 4 111100001 => 0 111100010 => 1 111100011 => 3 111100100 => 2 111100101 => 4 111100110 => 5 111100111 => 4 111101000 => 3 111101001 => 5 111101010 => 6 111101011 => 5 111101100 => 7 111101101 => 6 111101110 => 7 111101111 => 3 111110000 => 4 111110001 => 6 111110010 => 7 111110011 => 6 111110100 => 8 111110101 => 7 111110110 => 8 111110111 => 4 111111000 => 9 111111001 => 8 111111010 => 9 111111011 => 5 111111100 => 10 111111101 => 6 111111110 => 7 111111111 => 0 1010101010 => 6 1010101100 => 7 1010110010 => 7 1010110100 => 8 1010111000 => 9 1011001010 => 7 1011001100 => 8 1011010010 => 8 1011010100 => 9 1011011000 => 10 1011100010 => 2 1011100100 => 3 1011101000 => 4 1011110000 => 5 1100101010 => 7 1100101100 => 8 1100110010 => 8 1100110100 => 9 1100111000 => 10 1101001010 => 8 1101001100 => 9 1101010010 => 9 1101010100 => 10 1101011000 => 11 1101100010 => 3 1101100100 => 4 1101101000 => 5 1101110000 => 6 1110001010 => 9 1110001100 => 10 1110010010 => 10 1110010100 => 11 1110011000 => 12 1110100010 => 4 1110100100 => 5 1110101000 => 6 1110110000 => 7 1111000010 => 5 1111000100 => 6 1111001000 => 7 1111010000 => 8 1111100000 => 0 1111111110 => 8 1111111101 => 7 1111000001 => 4 1110111110 => 7 1110100001 => 3 1110011110 => 4 1110010001 => 9 1110001001 => 8 1110000101 => 7 1101111110 => 6 1101100001 => 2 1101010001 => 8 1101001110 => 5 1101001001 => 7 1101000101 => 6 1100110001 => 7 1100101001 => 6 1100100110 => 6 1100100101 => 5 1100011001 => 10 1100010101 => 9 1100010010 => 7 1100001000 => 8 1011111110 => 8 1011111101 => 7 1011100001 => 1 1011010001 => 7 1011001001 => 6 1011000101 => 5 1010111110 => 6 1010110001 => 6 1010101001 => 5 1010100110 => 5 1010100101 => 4 1010011010 => 10 1010011001 => 9 1010010110 => 9 1010010101 => 8 1010001110 => 8 1001111110 => 8 1001111000 => 8 1001110100 => 7 1001110001 => 5 1001101100 => 6 1001101010 => 5 1001101001 => 4 1001100110 => 4 1001100101 => 3 1001011110 => 6 1001011010 => 9 1001011001 => 8 1001010110 => 8 1001010101 => 7 1001001110 => 7 1000111110 => 8 1000111100 => 9 1000111010 => 8 1000110110 => 7 1000101110 => 6 1000011110 => 8 1000010110 => 6 1000001110 => 8 1000001010 => 6 1000000110 => 8 1000000100 => 6 1000000010 => 8 1000000000 => 8 0111111111 => 0 0111111101 => 6 0111111001 => 8 0111110001 => 6 0111100001 => 0 0111000001 => 6 0110000001 => 8 0100000001 => 6 0000000001 => 0 0111111011 => 5 0111110101 => 7 0111101001 => 5 0111010001 => 6 0110100001 => 5 0101000001 => 7 0010000001 => 5 0101010101 => 6 0101010011 => 5 0101001101 => 5 0101001011 => 4 0101000111 => 3 0100110101 => 5 0100110011 => 4 0100101101 => 4 0100101011 => 3 0100100111 => 2 0100011101 => 6 0100011011 => 5 0100010111 => 4 0100001111 => 3 0011010101 => 5 0011010011 => 4 0011001101 => 4 0011001011 => 3 0011000111 => 2 0010110101 => 4 0010110011 => 3 0010101101 => 3 0010101011 => 2 0010100111 => 1 0010011101 => 5 0010011011 => 4 0010010111 => 3 0010001111 => 2 0001110101 => 3 0001110011 => 2 0001101101 => 2 0001101011 => 1 0001100111 => 0 0001011101 => 4 0001011011 => 3 0001010111 => 2 0001001111 => 1 0000111101 => 3 0000111011 => 2 0000110111 => 1 0000101111 => 0 0000011111 => 0 0000000000 => 0 0000000110 => 1 0000011000 => 2 0000011110 => 3 0000010010 => 3 0001100000 => 6 0001100110 => 4 0001111000 => 3 0001111110 => 5 0001110010 => 1 0001001000 => 4 0001001110 => 5 0001000010 => 5 0001011010 => 4 0100000010 => 7 0010101010 => 6 0010101000 => 3 0010101100 => 7 0010100100 => 7 0010010100 => 6 0001010100 => 5 0010101110 => 4 0010100000 => 7 0010111100 => 7 0010000100 => 4 0011110100 => 5 0000010100 => 1 0111010100 => 8 0000000010 => 0 0000001110 => 2 0000111110 => 4 0000000100 => 1 0000001010 => 2 0000010110 => 3 0000101110 => 4 0001011110 => 5 0100000000 => 7 0100000011 => 5 0100000111 => 4 0100011111 => 2 0100111111 => 1 0101111111 => 0 0100000101 => 6 0100001011 => 5 0100101111 => 3 0101011111 => 2 0110111111 => 1 0101010110 => 7 0101011001 => 7 0101011010 => 8 0101011100 => 9 0101100101 => 2 0101100110 => 3 0101101001 => 3 0101101010 => 4 0101101100 => 5 0101110001 => 4 0101110010 => 5 0101110100 => 6 0101111000 => 7 0110010101 => 7 0110010110 => 8 0110011001 => 8 0110011010 => 9 0110011100 => 10 0110100101 => 3 0110100110 => 4 0110101001 => 4 0110101010 => 5 0110101100 => 6 0110110001 => 5 0110110010 => 6 0110110100 => 7 0110111000 => 8 0111000101 => 4 0111000110 => 5 0111001001 => 5 0111001010 => 6 0111001100 => 7 0111010010 => 7 0111011000 => 9 0111100010 => 1 0111100100 => 2 0111101000 => 3 0111110000 => 4 0100000100 => 5 0011100110 => 2 0011101010 => 3 0011101100 => 4 0001101110 => 3 0010110110 => 5 0011110010 => 4 0001110110 => 4 0100111010 => 7 0010111010 => 6 0011111000 => 6 0001111010 => 5 0100111100 => 8 0001111100 => 6 0000000101 => 0 0000001101 => 1 0000011101 => 2 0001111101 => 4 0011111101 => 5 0000001001 => 1 0000010101 => 2 0000101101 => 3 0010111101 => 5 0101111101 => 6 0010110001 => 1 0001100001 => 4 0001000001 => 4 0000111111 => 0 0001110100 => 2 0001101100 => 6 0010011100 => 6 0001011100 => 5 0000111100 => 4 0001101010 => 5 0010011010 => 5 0000111010 => 3 0010100110 => 5 0010010110 => 4 0001010110 => 3 0000110110 => 2 0010001110 => 6 0001101001 => 4 0000110001 => 2 0000010001 => 2 0000001100 => 0 0000011001 => 0 0000110011 => 0 0000110100 => 4 0000000011 => 0 0000011011 => 1 0001101111 => 1 0000110101 => 1 0010000010 => 6 0001000011 => 3 0010011110 => 6 0001010000 => 5 0001000100 => 3 0001010101 => 2 0001001011 => 3 0001100011 => 2 0001110111 => 2 0010000000 => 6 0000000111 => 0 0000001111 => 0 0001111111 => 0 0000001011 => 0 0000010111 => 0 0001011111 => 0 0001111001 => 4 0000011010 => 1 0000101010 => 2 0000100101 => 3 0010010001 => 4 0010000101 => 5 0010010101 => 3 0010010011 => 2 0000101011 => 2 0001000111 => 2 0000100111 => 1 0010010010 => 5 0001001010 => 3 0001001001 => 2 0001000101 => 4 0000100011 => 2 0000100100 => 2 0000100010 => 4 0010110000 => 4 0000011100 => 2 0000001000 => 2 0000101100 => 3 0010101111 => 2 0000101000 => 3 0010001000 => 5 0001001100 => 4 0001000110 => 5 0001100100 => 6 0001100010 => 5 0000100110 => 4 0000110010 => 3 0010010000 => 6 0001010010 => 4 0001000000 => 5 0001011001 => 3 0001100101 => 3 0001110001 => 0 0010011001 => 4 0010100101 => 4 0010101001 => 5 0010011111 => 1 0000111001 => 2 0010001101 => 5 0001001101 => 4 0001010001 => 3 0001010011 => 1 0001111011 => 3 0010011000 => 2 0001011000 => 1 0000100000 => 4 0010001011 => 4 0010000111 => 3 0000010011 => 1 0010001100 => 5 0010000110 => 6 0000110000 => 4 0000100001 => 3 0010100011 => 3 0010100001 => 5 0000111000 => 0 0001101000 => 2 0000010000 => 3 0000101001 => 1 0010100010 => 6 0010001001 => 3 0010000011 => 4 0010001010 => 4 0001110000 => 3 10000000000 => 9 10000000010 => 9 10000000110 => 9 10000001110 => 9 10000011110 => 9 10000111110 => 9 10001111110 => 9 10011111110 => 9 10111111110 => 9 11111111110 => 9 10000000100 => 7 10000001010 => 7 10000010110 => 7 10000101110 => 7 10001011110 => 7 10010111110 => 7 10101111110 => 7 11011111110 => 7 10000010000 => 9 10000100010 => 9 10001000010 => 10 10000100100 => 10 10001001010 => 10 10001000100 => 11 10000101000 => 6 10010001010 => 11 10001010010 => 6 10010000100 => 12 10001001000 => 7 10010010010 => 7 10001010100 => 7 10010101010 => 7 10010001000 => 8 10100010010 => 8 10010100010 => 8 10010010100 => 8 10100101010 => 8 01111111111 => 0 01111111101 => 7 01111111001 => 10 01111110001 => 9 01111100001 => 4 01111000001 => 4 01110000001 => 9 01100000001 => 10 01000000001 => 7 00000000001 => 0 00000000010 => 0 10101010101 => 6 10101010010 => 10 10101001001 => 8 10101001010 => 9 10101000100 => 11 10100100101 => 6 10100100010 => 9 10100101001 => 7 10100100100 => 10 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111001010001 => 9 111010001001 => 9 111010100001 => 11 111100000101 => 9 111100001001 => 10 111100010001 => 11 111100100001 => 12 111101000001 => 4 10110111100000 => 14 10111011010000 => 14 10111011100000 => 15 10111100110000 => 14 10111101001000 => 14 10111101010000 => 15 10111101100000 => 16 10111110000100 => 3 10111110001000 => 4 10111110010000 => 5 10111110100000 => 6 10111111000000 => 7 11001111100000 => 14 11011110000010 => 3 11101101000010 => 14 11101110000010 => 4 11110011000010 => 14 11110100100010 => 14 11110101000010 => 15 11110110000010 => 5 11111000001100 => 14 11111000010010 => 14 11111000100010 => 15 11111001000010 => 16 11111010000010 => 6 11111100000010 => 7 1011110111000000 => 18 1011111010100000 => 18 1011111011000000 => 19 1011111100010000 => 5 1011111100100000 => 6 1011111101000000 => 7 1011111110000000 => 8 1111011100000010 => 5 1111101010000010 => 18 1111101100000010 => 6 1111110001000010 => 18 1111110010000010 => 19 1111110100000010 => 7 1111111000000010 => 8 111111110000000010 => 9 101111111100000000 => 9 111111101000000010 => 8 101111111010000000 => 8 111111100100000010 => 22 111111011000000010 => 7 101111111001000000 => 7 101111110110000000 => 22 11111111100000000010 => 10 10111111111000000000 => 10 11111111010000000010 => 9 10111111110100000000 => 9 1111111111000000000010 => 11 1011111111110000000000 => 11 ----------------------------------------------------------------------------- Created: Aug 01, 2017 at 08:16 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 19, 2019 at 22:18 by Martin Rubey