Identifier
Identifier
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
0000111110 => 5
0001111010 => 5
0001111100 => 5
0001110110 => 5
0011110010 => 5
0011110100 => 5
0010111010 => 3
0010111100 => 5
0011111000 => 5
0001101110 => 5
0011101010 => 4
0011101100 => 5
0011100110 => 5
0111100010 => 5
0111100100 => 5
0100111010 => 3
0100111100 => 5
0111101000 => 5
0010110110 => 3
0110110010 => 3
0110110100 => 3
0101101010 => 2
0101101100 => 3
0110111000 => 5
0101110010 => 3
0101110100 => 3
0101111000 => 5
0111110000 => 5
0101010101 => 1
0000011111 => 5
0100001111 => 4
0000110111 => 3
0000101111 => 4
0101000111 => 3
0000111011 => 3
0100011011 => 2
0001101011 => 2
0001011011 => 2
0100010111 => 3
0001100111 => 3
0001001111 => 4
0001010111 => 3
0101010011 => 2
0000111101 => 4
0100011101 => 3
0001101101 => 2
0001011101 => 3
0101001101 => 2
0001110101 => 3
0100110101 => 2
0011010101 => 2
0010110101 => 2
0100101101 => 2
0011000111 => 3
0010001111 => 4
0010101101 => 2
0101001011 => 2
0001110011 => 3
0100110011 => 2
0011010011 => 2
0010110011 => 2
0100100111 => 3
0011001101 => 2
0010011101 => 3
0010100111 => 3
0100101011 => 2
0011001011 => 2
0010011011 => 2
0010010111 => 3
0010101011 => 2
0111100001 => 4
0111000101 => 3
0110110001 => 2
0111010001 => 3
0110010101 => 2
0101110001 => 3
0101100101 => 2
0101011001 => 2
0101101001 => 2
0110100101 => 2
0110101001 => 2
0110011001 => 2
0111001001 => 3
0111011000 => 5
0110101100 => 4
0111001100 => 5
0111010100 => 4
0101011100 => 4
0101010110 => 3
0101011010 => 2
0111000110 => 5
0110011100 => 5
0110010110 => 4
0110011010 => 3
0101100110 => 3
0111001010 => 4
0110100110 => 4
0111010010 => 4
0110101010 => 3
0000000010 => 1
0100000100 => 2
0000000001 => 1
0100000001 => 1
0110000001 => 2
0111000001 => 3
0111110001 => 5
0111111001 => 6
0111111101 => 7
0111111111 => 9
0010000001 => 1
0101000001 => 1
0110100001 => 2
0111101001 => 4
0111110101 => 5
0111111011 => 6
0000000101 => 1
0000001101 => 2
0000011101 => 3
0001111101 => 5
0011111101 => 6
0000001001 => 1
0000010101 => 1
0000101101 => 2
0010111101 => 4
0101111101 => 5
0100000000 => 1
0100000011 => 2
0100000111 => 3
0100011111 => 5
0100111111 => 6
0101111111 => 7
0100000010 => 2
0100000101 => 1
0100001011 => 2
0100101111 => 4
0101011111 => 5
0110111111 => 6
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
00001000001 => 1
00000000010 => 1
00000000001 => 1
01000000001 => 1
01100000001 => 2
01110000001 => 3
01111000001 => 4
01111100001 => 5
01111110001 => 6
01111111001 => 7
01111111101 => 8
01111111111 => 10
00000000101 => 1
00000001101 => 2
00000011101 => 3
00000111101 => 4
00001111101 => 5
00011111101 => 6
00111111101 => 7
11111111101 => 10
01000000000 => 1
01000000011 => 2
01000000111 => 3
01000001111 => 4
01000011111 => 5
01000111111 => 6
01001111111 => 7
01011111111 => 8
00010100001 => 1
00100100001 => 1
00010010001 => 1
01000001000 => 2
01000100001 => 1
00101010001 => 1
00010000010 => 2
00010001001 => 1
10100001000 => 1
10000100001 => 2
01000010100 => 2
01001010001 => 1
00100000100 => 2
00100010001 => 1
00101000010 => 2
00101001001 => 1
00010000101 => 1
10100010100 => 1
10010100100 => 1
10001010001 => 2
01000100100 => 2
01000010010 => 2
01010000100 => 2
01010010001 => 1
01001000010 => 2
01001001001 => 1
00100001010 => 2
00100100010 => 2
00100101001 => 1
00101000101 => 1
10101010010 => 1
10101001010 => 1
01001001010 => 2
01001010010 => 2
01010001010 => 2
01010010010 => 2
00100010010 => 2
10100100010 => 1
10100100100 => 1
00100101010 => 2
01010101010 => 2
01010100010 => 2
01000101010 => 2
01000100010 => 2
10101000100 => 1
00101010010 => 2
00101001010 => 2
01001000100 => 2
00100010101 => 1
01001000101 => 1
10001000101 => 2
01000010001 => 1
10100010001 => 2
00101010100 => 2
00101000100 => 2
00100100100 => 2
01010100100 => 2
10010010001 => 2
00010010100 => 2
00100010100 => 2
00010010010 => 2
00010001010 => 2
00100001001 => 1
10010001001 => 2
01001010101 => 1
01010010100 => 2
01000100101 => 1
01010010101 => 1
01010001000 => 2
01010101001 => 1
01001010100 => 2
01000101001 => 1
01010100101 => 1
01001001000 => 2
01010001001 => 1
01000101000 => 2
00101001000 => 2
10010100101 => 2
10100101001 => 2
10010010101 => 2
10100100101 => 2
10101001001 => 2
10101010101 => 2
00001000010 => 2
00010100010 => 2
00010000100 => 2
00001000100 => 2
00010100100 => 2
00100100101 => 1
10001001001 => 2
00001001000 => 2
00001010000 => 2
00010001000 => 2
00100101000 => 2
00010101000 => 2
00100010000 => 2
00000100000 => 1
00010010000 => 2
01000010000 => 2
00100001000 => 2
10010101001 => 2
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
110110001010 => 2
110110001100 => 2
110110010010 => 2
110110010100 => 2
110110011000 => 2
110110100010 => 2
110110100100 => 2
110110101000 => 2
110110110000 => 2
110111000010 => 3
110111000100 => 3
110111001000 => 3
110111010000 => 3
110111100000 => 4
111000101010 => 3
111000101100 => 3
111000110010 => 3
111000110100 => 3
111000111000 => 3
111001001010 => 3
111001001100 => 3
111001010010 => 3
111001010100 => 3
111001011000 => 3
111001100010 => 3
111001100100 => 3
111001101000 => 3
111001110000 => 3
111010001010 => 3
111010001100 => 3
111010010010 => 3
111010010100 => 3
111010011000 => 3
111010100010 => 3
111010100100 => 3
111010101000 => 3
111010110000 => 3
111011000010 => 3
111011000100 => 3
111011001000 => 3
111011010000 => 3
111011100000 => 3
111100001010 => 4
111100001100 => 4
111100010010 => 4
111100010100 => 4
111100011000 => 4
111100100010 => 4
111100100100 => 4
111100101000 => 4
111100110000 => 4
111101000010 => 4
111101000100 => 4
111101001000 => 4
111101010000 => 4
111101100000 => 4
111110000010 => 5
111110000100 => 5
111110001000 => 5
111110010000 => 5
111110100000 => 5
111111000000 => 6
100001111100 => 5
000011011110 => 6
010000011111 => 5
000001111101 => 5
111100000101 => 5
011111000001 => 5
010111110000 => 6
000111011100 => 6
100011111000 => 5
000111011010 => 4
001011011100 => 4
100011110100 => 4
100101111000 => 4
000111010110 => 5
001111011000 => 6
010011011100 => 4
000101101110 => 4
100011101100 => 3
100111110000 => 5
010001111010 => 4
101001111000 => 4
000111001110 => 6
001111010100 => 5
001011011010 => 2
010111011000 => 3
100011011100 => 3
001101101100 => 4
100111101000 => 4
001001110110 => 3
100101110100 => 3
010011110010 => 4
110001111000 => 4
001111001100 => 6
001111010010 => 5
010111010100 => 3
011011011000 => 4
100111011000 => 3
001101101010 => 3
010101101100 => 3
001011100110 => 3
100111100100 => 4
010011101010 => 3
011001110100 => 3
010101110010 => 3
000010111101 => 4
010000101111 => 4
000011011101 => 3
000100111101 => 4
010000110111 => 3
010001001111 => 4
000011101101 => 3
000101011101 => 3
001000111101 => 4
000011110011 => 4
010000111011 => 3
010001010111 => 3
001100001111 => 4
010010001111 => 4
000011110101 => 4
000101101101 => 2
000110011101 => 3
001001011101 => 3
010000111101 => 4
000101110011 => 3
010001011011 => 2
000111000111 => 3
010001100111 => 3
001100010111 => 3
010010010111 => 3
010100001111 => 4
000101110101 => 3
000110101101 => 2
001001101101 => 2
001010011101 => 3
010001011101 => 3
000110110011 => 2
001001110011 => 3
000111001011 => 3
010001101011 => 2
001100011011 => 2
010010011011 => 2
001011000111 => 3
001100100111 => 3
010010100111 => 3
010100010111 => 3
011110100001 => 4
111010000101 => 4
011101100001 => 3
011110010001 => 4
110110000101 => 3
111001000101 => 4
011011100001 => 3
011101010001 => 3
011110001001 => 4
100111100001 => 4
101110000101 => 3
110101000101 => 3
111000011001 => 4
111000100101 => 4
010111100001 => 4
011011010001 => 2
011100110001 => 3
011101001001 => 3
011110000101 => 4
100111010001 => 3
101101000101 => 2
110001110001 => 3
110011000101 => 3
110100011001 => 3
110100100101 => 3
111000010101 => 4
010111010001 => 3
011010110001 => 2
011011001001 => 2
011100101001 => 3
011101000101 => 3
100110110001 => 2
100111001001 => 3
101001110001 => 3
101011000101 => 2
101100011001 => 2
101100100101 => 2
110001101001 => 3
110010011001 => 3
110010100101 => 3
110100010101 => 3
010111101000 => 4
010111100100 => 4
010110111000 => 4
010111100010 => 4
011001111000 => 6
011110000110 => 6
010101111000 => 5
010110110100 => 2
010111001100 => 3
010111010010 => 3
011100011100 => 6
011101000110 => 5
010101110100 => 3
010110101100 => 3
010110110010 => 2
010111001010 => 3
011001101100 => 4
011001110010 => 3
011010011100 => 5
011011000110 => 4
011100011010 => 4
011100100110 => 5
011111000100 => 6
011111000010 => 6
011101100100 => 4
011101100010 => 4
011011100100 => 3
011011010100 => 3
011011100010 => 3
011011010010 => 3
011111010000 => 6
011111001000 => 6
001111001010 => 5
011101110000 => 6
011111100000 => 6
011101101000 => 4
010101101010 => 2
001111000110 => 6
010011110100 => 4
010011101100 => 3
011011110000 => 6
011011101000 => 3
010011011010 => 2
001101100110 => 4
001011010101 => 2
001101010101 => 2
001011010011 => 2
001101010011 => 2
001011001011 => 2
001011001101 => 2
001101001011 => 2
001101001101 => 2
001001110101 => 3
001010101101 => 2
001100101101 => 2
001101000111 => 3
001010110101 => 2
001100110101 => 2
001001100111 => 3
001001101011 => 2
000110110101 => 2
001010100111 => 3
001010101011 => 2
001100101011 => 2
001010110011 => 2
001100110011 => 2
000111010101 => 3
001000110111 => 3
001000111011 => 3
001001010111 => 3
001001011011 => 2
001010010111 => 3
001010011011 => 2
001100011101 => 3
000111010011 => 3
010101001011 => 2
010101010011 => 2
010011001011 => 2
010011010011 => 2
010100011011 => 2
010010101011 => 2
010010110011 => 2
010100101011 => 2
010100110011 => 2
000110011011 => 2
010100100111 => 3
000110101011 => 2
010101000111 => 3
000100111011 => 3
000101011011 => 2
000101101011 => 2
010001110011 => 3
010101101001 => 2
010101011001 => 2
100101101001 => 2
100101011001 => 2
101001101001 => 2
011001101001 => 2
101001011001 => 2
011001011001 => 2
010111001001 => 3
011010101001 => 2
011010011001 => 2
110001011001 => 3
010110101001 => 2
010110011001 => 2
110011001001 => 3
101011001001 => 2
010110110001 => 2
110010101001 => 3
101010101001 => 2
101010011001 => 2
100110101001 => 2
100110011001 => 2
010101110001 => 3
110110001001 => 3
101110001001 => 3
110101001001 => 3
101101001001 => 2
110100101001 => 3
101100101001 => 2
011100011001 => 3
100101110001 => 3
010101011010 => 2
010101010110 => 3
011001011010 => 3
011001010110 => 4
011010011010 => 3
010110011010 => 2
011010010110 => 4
010110010110 => 3
010110101010 => 2
010110100110 => 3
011100010110 => 5
010101100110 => 3
011100110010 => 4
011010110010 => 3
011100101010 => 4
011010101010 => 3
011010100110 => 4
011001101010 => 3
011001100110 => 4
010101011100 => 4
011101010010 => 4
011101001010 => 4
011011001010 => 3
010111000110 => 3
011001011100 => 5
100101101100 => 2
100111001100 => 3
001111110000 => 6
001011110010 => 4
001101110010 => 3
001111100010 => 6
100111010100 => 3
001101111000 => 6
001101110100 => 3
001011101010 => 3
001011010110 => 3
010100011101 => 3
010001110101 => 3
000101010111 => 3
000110010111 => 3
000110100111 => 3
010001101101 => 2
000101001111 => 4
000101100111 => 3
001001001111 => 4
001010001111 => 4
000111001101 => 3
010010011101 => 3
000011010111 => 3
000011011011 => 2
000011101011 => 3
010011000111 => 3
110001010101 => 3
101100010101 => 2
011100010101 => 3
100111000101 => 3
010111000101 => 3
110101010001 => 3
110100110001 => 3
110010110001 => 3
101010110001 => 2
011011000101 => 2
111001010001 => 4
110011010001 => 3
111001001001 => 4
101100110001 => 2
111000101001 => 4
011001110001 => 3
011101010100 => 4
011101001100 => 5
011100101100 => 5
011010101100 => 4
011110010100 => 5
011100110100 => 4
011110010010 => 5
011011001100 => 4
011110001010 => 5
010110011100 => 4
101001110100 => 3
010011001101 => 2
110001100101 => 3
011001100101 => 2
001111100100 => 6
000111100110 => 6
001111101000 => 6
000111101010 => 5
001011101100 => 3
000111101100 => 6
000111110010 => 6
000010111011 => 3
001000101111 => 4
100101010101 => 2
100101100101 => 2
101011010001 => 2
100110010101 => 2
101001010101 => 2
101011100001 => 3
101010100101 => 2
101101010001 => 2
100110100101 => 2
101010010101 => 2
101101100001 => 2
101001100101 => 2
101110010001 => 3
101110100001 => 3
110101100001 => 3
011001010101 => 2
011010110100 => 3
011010010101 => 2
011010111000 => 5
011010100101 => 2
011101011000 => 5
010100101101 => 2
010010110101 => 2
010101001101 => 2
010100110101 => 2
010011010101 => 2
010101010101 => 1
010110100101 => 2
010110010101 => 2
010101100101 => 2
010001111100 => 6
010011111000 => 6
001001111010 => 4
001001111100 => 6
001011111000 => 6
001000011111 => 5
000110001111 => 4
000100011111 => 5
000100101111 => 4
000001111011 => 4
000011100111 => 3
000001110111 => 3
000010110111 => 3
111100001001 => 5
111010001001 => 4
111000110001 => 4
111100010001 => 5
111010010001 => 4
011110100010 => 5
011110001100 => 6
011110100100 => 5
110010010101 => 3
011100100101 => 3
000101111100 => 6
000011111100 => 6
001011110100 => 4
000101111010 => 4
000111110100 => 6
000111111000 => 6
000010011111 => 5
000001011111 => 5
000100110111 => 3
000011001111 => 4
000010101111 => 4
000001101111 => 4
111100100001 => 5
111101000001 => 5
110110010001 => 3
111001100001 => 4
110110100001 => 3
111010100001 => 4
011110011000 => 6
011110101000 => 5
000011110110 => 6
000001111110 => 6
000011111010 => 6
000000111111 => 6
110111000001 => 3
111110000001 => 6
111011000001 => 4
011110110000 => 6
000011101110 => 6
000101110110 => 3
101111000001 => 4
110011100001 => 3
011100111000 => 6
010010101101 => 2
10110111100000 => 4
10111011010000 => 3
10111011100000 => 3
10111100110000 => 4
10111101001000 => 4
10111101010000 => 4
10111101100000 => 4
10111110000100 => 5
10111110001000 => 5
10111110010000 => 5
10111110100000 => 5
10111111000000 => 6
11001111100000 => 5
11011110000010 => 4
11101101000010 => 3
11101110000010 => 3
11110011000010 => 4
11110100100010 => 4
11110101000010 => 4
11110110000010 => 4
11111000001100 => 5
11111000010010 => 5
11111000100010 => 5
11111001000010 => 5
11111010000010 => 5
11111100000010 => 6
1011110111000000 => 4
1011111010100000 => 5
1011111011000000 => 5
1011111100010000 => 6
1011111100100000 => 6
1011111101000000 => 6
1011111110000000 => 7
1111011100000010 => 4
1111101010000010 => 5
1111101100000010 => 5
1111110001000010 => 6
1111110010000010 => 6
1111110100000010 => 6
1111111000000010 => 7
111111110000000010 => 8
101111111100000000 => 8
111111101000000010 => 7
101111111010000000 => 7
111111100100000010 => 7
111111011000000010 => 6
101111111001000000 => 7
101111110110000000 => 6
11111111100000000010 => 9
10111111111000000000 => 9
11111111010000000010 => 8
10111111110100000000 => 8
1111111111000000000010 => 10
1011111111110000000000 => 10
click to show generating function       
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.
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])

Created
Mar 19, 2019 at 22:50 by Martin Rubey
Updated
Jun 22, 2019 at 13:50 by Martin Rubey