Identifier
Images
=>
=>
0=>0
1=>1
00=>01
01=>10
10=>00
11=>11
000=>011
001=>101
010=>000
011=>110
100=>010
101=>100
110=>001
111=>111
0000=>0111
0001=>1011
0010=>0001
0011=>1101
0100=>0100
0101=>1000
0110=>0010
0111=>1110
1000=>0110
1001=>1010
1010=>0000
1011=>1100
1100=>0101
1101=>1001
1110=>0011
1111=>1111
00000=>01111
00001=>10111
00010=>00011
00011=>11011
00100=>01001
00101=>10001
00110=>00101
00111=>11101
01000=>01100
01001=>10100
01010=>00000
01011=>11000
01100=>01010
01101=>10010
01110=>00110
01111=>11110
10000=>01110
10001=>10110
10010=>00010
10011=>11010
10100=>01000
10101=>10000
10110=>00100
10111=>11100
11000=>01101
11001=>10101
11010=>00001
11011=>11001
11100=>01011
11101=>10011
11110=>00111
11111=>11111
000000=>011111
000001=>101111
000010=>000111
000011=>110111
000100=>010011
000101=>100011
000110=>001011
000111=>111011
001000=>011001
001001=>101001
001010=>000001
001011=>110001
001100=>010101
001101=>100101
001110=>001101
001111=>111101
010000=>011100
010001=>101100
010010=>000100
010011=>110100
010100=>010000
010101=>100000
010110=>001000
010111=>111000
011000=>011010
011001=>101010
011010=>000010
011011=>110010
011100=>010110
011101=>100110
011110=>001110
011111=>111110
100000=>011110
100001=>101110
100010=>000110
100011=>110110
100100=>010010
100101=>100010
100110=>001010
100111=>111010
101000=>011000
101001=>101000
101010=>000000
101011=>110000
101100=>010100
101101=>100100
101110=>001100
101111=>111100
110000=>011101
110001=>101101
110010=>000101
110011=>110101
110100=>010001
110101=>100001
110110=>001001
110111=>111001
111000=>011011
111001=>101011
111010=>000011
111011=>110011
111100=>010111
111101=>100111
111110=>001111
111111=>111111
0000000=>0111111
0000001=>1011111
0000010=>0001111
0000011=>1101111
0000100=>0100111
0000101=>1000111
0000110=>0010111
0000111=>1110111
0001000=>0110011
0001001=>1010011
0001010=>0000011
0001011=>1100011
0001100=>0101011
0001101=>1001011
0001110=>0011011
0001111=>1111011
0010000=>0111001
0010001=>1011001
0010010=>0001001
0010011=>1101001
0010100=>0100001
0010101=>1000001
0010110=>0010001
0010111=>1110001
0011000=>0110101
0011001=>1010101
0011010=>0000101
0011011=>1100101
0011100=>0101101
0011101=>1001101
0011110=>0011101
0011111=>1111101
0100000=>0111100
0100001=>1011100
0100010=>0001100
0100011=>1101100
0100100=>0100100
0100101=>1000100
0100110=>0010100
0100111=>1110100
0101000=>0110000
0101001=>1010000
0101010=>0000000
0101011=>1100000
0101100=>0101000
0101101=>1001000
0101110=>0011000
0101111=>1111000
0110000=>0111010
0110001=>1011010
0110010=>0001010
0110011=>1101010
0110100=>0100010
0110101=>1000010
0110110=>0010010
0110111=>1110010
0111000=>0110110
0111001=>1010110
0111010=>0000110
0111011=>1100110
0111100=>0101110
0111101=>1001110
0111110=>0011110
0111111=>1111110
1000000=>0111110
1000001=>1011110
1000010=>0001110
1000011=>1101110
1000100=>0100110
1000101=>1000110
1000110=>0010110
1000111=>1110110
1001000=>0110010
1001001=>1010010
1001010=>0000010
1001011=>1100010
1001100=>0101010
1001101=>1001010
1001110=>0011010
1001111=>1111010
1010000=>0111000
1010001=>1011000
1010010=>0001000
1010011=>1101000
1010100=>0100000
1010101=>1000000
1010110=>0010000
1010111=>1110000
1011000=>0110100
1011001=>1010100
1011010=>0000100
1011011=>1100100
1011100=>0101100
1011101=>1001100
1011110=>0011100
1011111=>1111100
1100000=>0111101
1100001=>1011101
1100010=>0001101
1100011=>1101101
1100100=>0100101
1100101=>1000101
1100110=>0010101
1100111=>1110101
1101000=>0110001
1101001=>1010001
1101010=>0000001
1101011=>1100001
1101100=>0101001
1101101=>1001001
1101110=>0011001
1101111=>1111001
1110000=>0111011
1110001=>1011011
1110010=>0001011
1110011=>1101011
1110100=>0100011
1110101=>1000011
1110110=>0010011
1110111=>1110011
1111000=>0110111
1111001=>1010111
1111010=>0000111
1111011=>1100111
1111100=>0101111
1111101=>1001111
1111110=>0011111
1111111=>1111111
00000000=>01111111
00000001=>10111111
00000010=>00011111
00000011=>11011111
00000100=>01001111
00000101=>10001111
00000110=>00101111
00000111=>11101111
00001000=>01100111
00001001=>10100111
00001010=>00000111
00001011=>11000111
00001100=>01010111
00001101=>10010111
00001110=>00110111
00001111=>11110111
00010000=>01110011
00010001=>10110011
00010010=>00010011
00010011=>11010011
00010100=>01000011
00010101=>10000011
00010110=>00100011
00010111=>11100011
00011000=>01101011
00011001=>10101011
00011010=>00001011
00011011=>11001011
00011100=>01011011
00011101=>10011011
00011110=>00111011
00011111=>11111011
00100000=>01111001
00100001=>10111001
00100010=>00011001
00100011=>11011001
00100100=>01001001
00100101=>10001001
00100110=>00101001
00100111=>11101001
00101000=>01100001
00101001=>10100001
00101010=>00000001
00101011=>11000001
00101100=>01010001
00101101=>10010001
00101110=>00110001
00101111=>11110001
00110000=>01110101
00110001=>10110101
00110010=>00010101
00110011=>11010101
00110100=>01000101
00110101=>10000101
00110110=>00100101
00110111=>11100101
00111000=>01101101
00111001=>10101101
00111010=>00001101
00111011=>11001101
00111100=>01011101
00111101=>10011101
00111110=>00111101
00111111=>11111101
01000000=>01111100
01000001=>10111100
01000010=>00011100
01000011=>11011100
01000100=>01001100
01000101=>10001100
01000110=>00101100
01000111=>11101100
01001000=>01100100
01001001=>10100100
01001010=>00000100
01001011=>11000100
01001100=>01010100
01001101=>10010100
01001110=>00110100
01001111=>11110100
01010000=>01110000
01010001=>10110000
01010010=>00010000
01010011=>11010000
01010100=>01000000
01010101=>10000000
01010110=>00100000
01010111=>11100000
01011000=>01101000
01011001=>10101000
01011010=>00001000
01011011=>11001000
01011100=>01011000
01011101=>10011000
01011110=>00111000
01011111=>11111000
01100000=>01111010
01100001=>10111010
01100010=>00011010
01100011=>11011010
01100100=>01001010
01100101=>10001010
01100110=>00101010
01100111=>11101010
01101000=>01100010
01101001=>10100010
01101010=>00000010
01101011=>11000010
01101100=>01010010
01101101=>10010010
01101110=>00110010
01101111=>11110010
01110000=>01110110
01110001=>10110110
01110010=>00010110
01110011=>11010110
01110100=>01000110
01110101=>10000110
01110110=>00100110
01110111=>11100110
01111000=>01101110
01111001=>10101110
01111010=>00001110
01111011=>11001110
01111100=>01011110
01111101=>10011110
01111110=>00111110
01111111=>11111110
10000000=>01111110
10000001=>10111110
10000010=>00011110
10000011=>11011110
10000100=>01001110
10000101=>10001110
10000110=>00101110
10000111=>11101110
10001000=>01100110
10001001=>10100110
10001010=>00000110
10001011=>11000110
10001100=>01010110
10001101=>10010110
10001110=>00110110
10001111=>11110110
10010000=>01110010
10010001=>10110010
10010010=>00010010
10010011=>11010010
10010100=>01000010
10010101=>10000010
10010110=>00100010
10010111=>11100010
10011000=>01101010
10011001=>10101010
10011010=>00001010
10011011=>11001010
10011100=>01011010
10011101=>10011010
10011110=>00111010
10011111=>11111010
10100000=>01111000
10100001=>10111000
10100010=>00011000
10100011=>11011000
10100100=>01001000
10100101=>10001000
10100110=>00101000
10100111=>11101000
10101000=>01100000
10101001=>10100000
10101010=>00000000
10101011=>11000000
10101100=>01010000
10101101=>10010000
10101110=>00110000
10101111=>11110000
10110000=>01110100
10110001=>10110100
10110010=>00010100
10110011=>11010100
10110100=>01000100
10110101=>10000100
10110110=>00100100
10110111=>11100100
10111000=>01101100
10111001=>10101100
10111010=>00001100
10111011=>11001100
10111100=>01011100
10111101=>10011100
10111110=>00111100
10111111=>11111100
11000000=>01111101
11000001=>10111101
11000010=>00011101
11000011=>11011101
11000100=>01001101
11000101=>10001101
11000110=>00101101
11000111=>11101101
11001000=>01100101
11001001=>10100101
11001010=>00000101
11001011=>11000101
11001100=>01010101
11001101=>10010101
11001110=>00110101
11001111=>11110101
11010000=>01110001
11010001=>10110001
11010010=>00010001
11010011=>11010001
11010100=>01000001
11010101=>10000001
11010110=>00100001
11010111=>11100001
11011000=>01101001
11011001=>10101001
11011010=>00001001
11011011=>11001001
11011100=>01011001
11011101=>10011001
11011110=>00111001
11011111=>11111001
11100000=>01111011
11100001=>10111011
11100010=>00011011
11100011=>11011011
11100100=>01001011
11100101=>10001011
11100110=>00101011
11100111=>11101011
11101000=>01100011
11101001=>10100011
11101010=>00000011
11101011=>11000011
11101100=>01010011
11101101=>10010011
11101110=>00110011
11101111=>11110011
11110000=>01110111
11110001=>10110111
11110010=>00010111
11110011=>11010111
11110100=>01000111
11110101=>10000111
11110110=>00100111
11110111=>11100111
11111000=>01101111
11111001=>10101111
11111010=>00001111
11111011=>11001111
11111100=>01011111
11111101=>10011111
11111110=>00111111
11111111=>11111111
000000000=>011111111
000000001=>101111111
000000010=>000111111
000000011=>110111111
000000100=>010011111
000000101=>100011111
000000110=>001011111
000000111=>111011111
000001000=>011001111
000001001=>101001111
000001010=>000001111
000001011=>110001111
000001100=>010101111
000001101=>100101111
000001110=>001101111
000001111=>111101111
000010000=>011100111
000010001=>101100111
000010010=>000100111
000010011=>110100111
000010100=>010000111
000010101=>100000111
000010110=>001000111
000010111=>111000111
000011000=>011010111
000011001=>101010111
000011010=>000010111
000011011=>110010111
000011100=>010110111
000011101=>100110111
000011110=>001110111
000011111=>111110111
000100000=>011110011
000100001=>101110011
000100010=>000110011
000100011=>110110011
000100100=>010010011
000100101=>100010011
000100110=>001010011
000100111=>111010011
000101000=>011000011
000101001=>101000011
000101010=>000000011
000101011=>110000011
000101100=>010100011
000101101=>100100011
000101110=>001100011
000101111=>111100011
000110000=>011101011
000110001=>101101011
000110010=>000101011
000110011=>110101011
000110100=>010001011
000110101=>100001011
000110110=>001001011
000110111=>111001011
000111000=>011011011
000111001=>101011011
000111010=>000011011
000111011=>110011011
000111100=>010111011
000111101=>100111011
000111110=>001111011
000111111=>111111011
001000000=>011111001
001000001=>101111001
001000010=>000111001
001000011=>110111001
001000100=>010011001
001000101=>100011001
001000110=>001011001
001000111=>111011001
001001000=>011001001
001001001=>101001001
001001010=>000001001
001001011=>110001001
001001100=>010101001
001001101=>100101001
001001110=>001101001
001001111=>111101001
001010000=>011100001
001010001=>101100001
001010010=>000100001
001010011=>110100001
001010100=>010000001
001010101=>100000001
001010110=>001000001
001010111=>111000001
001011000=>011010001
001011001=>101010001
001011010=>000010001
001011011=>110010001
001011100=>010110001
001011101=>100110001
001011110=>001110001
001011111=>111110001
001100000=>011110101
001100001=>101110101
001100010=>000110101
001100011=>110110101
001100100=>010010101
001100101=>100010101
001100110=>001010101
001100111=>111010101
001101000=>011000101
001101001=>101000101
001101010=>000000101
001101011=>110000101
001101100=>010100101
001101101=>100100101
001101110=>001100101
001101111=>111100101
001110000=>011101101
001110001=>101101101
001110010=>000101101
001110011=>110101101
001110100=>010001101
001110101=>100001101
001110110=>001001101
001110111=>111001101
001111000=>011011101
001111001=>101011101
001111010=>000011101
001111011=>110011101
001111100=>010111101
001111101=>100111101
001111110=>001111101
001111111=>111111101
010000000=>011111100
010000001=>101111100
010000010=>000111100
010000011=>110111100
010000100=>010011100
010000101=>100011100
010000110=>001011100
010000111=>111011100
010001000=>011001100
010001001=>101001100
010001010=>000001100
010001011=>110001100
010001100=>010101100
010001101=>100101100
010001110=>001101100
010001111=>111101100
010010000=>011100100
010010001=>101100100
010010010=>000100100
010010011=>110100100
010010100=>010000100
010010101=>100000100
010010110=>001000100
010010111=>111000100
010011000=>011010100
010011001=>101010100
010011010=>000010100
010011011=>110010100
010011100=>010110100
010011101=>100110100
010011110=>001110100
010011111=>111110100
010100000=>011110000
010100001=>101110000
010100010=>000110000
010100011=>110110000
010100100=>010010000
010100101=>100010000
010100110=>001010000
010100111=>111010000
010101000=>011000000
010101001=>101000000
010101010=>000000000
010101011=>110000000
010101100=>010100000
010101101=>100100000
010101110=>001100000
010101111=>111100000
010110000=>011101000
010110001=>101101000
010110010=>000101000
010110011=>110101000
010110100=>010001000
010110101=>100001000
010110110=>001001000
010110111=>111001000
010111000=>011011000
010111001=>101011000
010111010=>000011000
010111011=>110011000
010111100=>010111000
010111101=>100111000
010111110=>001111000
010111111=>111111000
011000000=>011111010
011000001=>101111010
011000010=>000111010
011000011=>110111010
011000100=>010011010
011000101=>100011010
011000110=>001011010
011000111=>111011010
011001000=>011001010
011001001=>101001010
011001010=>000001010
011001011=>110001010
011001100=>010101010
011001101=>100101010
011001110=>001101010
011001111=>111101010
011010000=>011100010
011010001=>101100010
011010010=>000100010
011010011=>110100010
011010100=>010000010
011010101=>100000010
011010110=>001000010
011010111=>111000010
011011000=>011010010
011011001=>101010010
011011010=>000010010
011011011=>110010010
011011100=>010110010
011011101=>100110010
011011110=>001110010
011011111=>111110010
011100000=>011110110
011100001=>101110110
011100010=>000110110
011100011=>110110110
011100100=>010010110
011100101=>100010110
011100110=>001010110
011100111=>111010110
011101000=>011000110
011101001=>101000110
011101010=>000000110
011101011=>110000110
011101100=>010100110
011101101=>100100110
011101110=>001100110
011101111=>111100110
011110000=>011101110
011110001=>101101110
011110010=>000101110
011110011=>110101110
011110100=>010001110
011110101=>100001110
011110110=>001001110
011110111=>111001110
011111000=>011011110
011111001=>101011110
011111010=>000011110
011111011=>110011110
011111100=>010111110
011111101=>100111110
011111110=>001111110
011111111=>111111110
100000000=>011111110
100000001=>101111110
100000010=>000111110
100000011=>110111110
100000100=>010011110
100000101=>100011110
100000110=>001011110
100000111=>111011110
100001000=>011001110
100001001=>101001110
100001010=>000001110
100001011=>110001110
100001100=>010101110
100001101=>100101110
100001110=>001101110
100001111=>111101110
100010000=>011100110
100010001=>101100110
100010010=>000100110
100010011=>110100110
100010100=>010000110
100010101=>100000110
100010110=>001000110
100010111=>111000110
100011000=>011010110
100011001=>101010110
100011010=>000010110
100011011=>110010110
100011100=>010110110
100011101=>100110110
100011110=>001110110
100011111=>111110110
100100000=>011110010
100100001=>101110010
100100010=>000110010
100100011=>110110010
100100100=>010010010
100100101=>100010010
100100110=>001010010
100100111=>111010010
100101000=>011000010
100101001=>101000010
100101010=>000000010
100101011=>110000010
100101100=>010100010
100101101=>100100010
100101110=>001100010
100101111=>111100010
100110000=>011101010
100110001=>101101010
100110010=>000101010
100110011=>110101010
100110100=>010001010
100110101=>100001010
100110110=>001001010
100110111=>111001010
100111000=>011011010
100111001=>101011010
100111010=>000011010
100111011=>110011010
100111100=>010111010
100111101=>100111010
100111110=>001111010
100111111=>111111010
101000000=>011111000
101000001=>101111000
101000010=>000111000
101000011=>110111000
101000100=>010011000
101000101=>100011000
101000110=>001011000
101000111=>111011000
101001000=>011001000
101001001=>101001000
101001010=>000001000
101001011=>110001000
101001100=>010101000
101001101=>100101000
101001110=>001101000
101001111=>111101000
101010000=>011100000
101010001=>101100000
101010010=>000100000
101010011=>110100000
101010100=>010000000
101010101=>100000000
101010110=>001000000
101010111=>111000000
101011000=>011010000
101011001=>101010000
101011010=>000010000
101011011=>110010000
101011100=>010110000
101011101=>100110000
101011110=>001110000
101011111=>111110000
101100000=>011110100
101100001=>101110100
101100010=>000110100
101100011=>110110100
101100100=>010010100
101100101=>100010100
101100110=>001010100
101100111=>111010100
101101000=>011000100
101101001=>101000100
101101010=>000000100
101101011=>110000100
101101100=>010100100
101101101=>100100100
101101110=>001100100
101101111=>111100100
101110000=>011101100
101110001=>101101100
101110010=>000101100
101110011=>110101100
101110100=>010001100
101110101=>100001100
101110110=>001001100
101110111=>111001100
101111000=>011011100
101111001=>101011100
101111010=>000011100
101111011=>110011100
101111100=>010111100
101111101=>100111100
101111110=>001111100
101111111=>111111100
110000000=>011111101
110000001=>101111101
110000010=>000111101
110000011=>110111101
110000100=>010011101
110000101=>100011101
110000110=>001011101
110000111=>111011101
110001000=>011001101
110001001=>101001101
110001010=>000001101
110001011=>110001101
110001100=>010101101
110001101=>100101101
110001110=>001101101
110001111=>111101101
110010000=>011100101
110010001=>101100101
110010010=>000100101
110010011=>110100101
110010100=>010000101
110010101=>100000101
110010110=>001000101
110010111=>111000101
110011000=>011010101
110011001=>101010101
110011010=>000010101
110011011=>110010101
110011100=>010110101
110011101=>100110101
110011110=>001110101
110011111=>111110101
110100000=>011110001
110100001=>101110001
110100010=>000110001
110100011=>110110001
110100100=>010010001
110100101=>100010001
110100110=>001010001
110100111=>111010001
110101000=>011000001
110101001=>101000001
110101010=>000000001
110101011=>110000001
110101100=>010100001
110101101=>100100001
110101110=>001100001
110101111=>111100001
110110000=>011101001
110110001=>101101001
110110010=>000101001
110110011=>110101001
110110100=>010001001
110110101=>100001001
110110110=>001001001
110110111=>111001001
110111000=>011011001
110111001=>101011001
110111010=>000011001
110111011=>110011001
110111100=>010111001
110111101=>100111001
110111110=>001111001
110111111=>111111001
111000000=>011111011
111000001=>101111011
111000010=>000111011
111000011=>110111011
111000100=>010011011
111000101=>100011011
111000110=>001011011
111000111=>111011011
111001000=>011001011
111001001=>101001011
111001010=>000001011
111001011=>110001011
111001100=>010101011
111001101=>100101011
111001110=>001101011
111001111=>111101011
111010000=>011100011
111010001=>101100011
111010010=>000100011
111010011=>110100011
111010100=>010000011
111010101=>100000011
111010110=>001000011
111010111=>111000011
111011000=>011010011
111011001=>101010011
111011010=>000010011
111011011=>110010011
111011100=>010110011
111011101=>100110011
111011110=>001110011
111011111=>111110011
111100000=>011110111
111100001=>101110111
111100010=>000110111
111100011=>110110111
111100100=>010010111
111100101=>100010111
111100110=>001010111
111100111=>111010111
111101000=>011000111
111101001=>101000111
111101010=>000000111
111101011=>110000111
111101100=>010100111
111101101=>100100111
111101110=>001100111
111101111=>111100111
111110000=>011101111
111110001=>101101111
111110010=>000101111
111110011=>110101111
111110100=>010001111
111110101=>100001111
111110110=>001001111
111110111=>111001111
111111000=>011011111
111111001=>101011111
111111010=>000011111
111111011=>110011111
111111100=>010111111
111111101=>100111111
111111110=>001111111
111111111=>111111111
1010101010=>0000000000
1010101100=>0101000000
1010110010=>0001010000
1010110100=>0100010000
1010111000=>0110110000
1011001010=>0000010100
1011001100=>0101010100
1011010010=>0001000100
1011010100=>0100000100
1011011000=>0110100100
1011100010=>0001101100
1011100100=>0100101100
1011101000=>0110001100
1011110000=>0111011100
1100101010=>0000000101
1100101100=>0101000101
1100110010=>0001010101
1100110100=>0100010101
1100111000=>0110110101
1101001010=>0000010001
1101001100=>0101010001
1101010010=>0001000001
1101010100=>0100000001
1101011000=>0110100001
1101100010=>0001101001
1101100100=>0100101001
1101101000=>0110001001
1101110000=>0111011001
1110001010=>0000011011
1110001100=>0101011011
1110010010=>0001001011
1110010100=>0100001011
1110011000=>0110101011
1110100010=>0001100011
1110100100=>0100100011
1110101000=>0110000011
1110110000=>0111010011
1111000010=>0001110111
1111000100=>0100110111
1111001000=>0110010111
1111010000=>0111000111
1111100000=>0111101111
1111111111=>1111111111
1111111110=>0011111111
1111111101=>1001111111
1111111001=>1010111111
1111101101=>1001001111
1111101011=>1100001111
1111100111=>1110101111
1111100001=>1011101111
1111000001=>1011110111
1110111110=>0011110011
1110111101=>1001110011
1110110111=>1110010011
1110110001=>1011010011
1110101011=>1100000011
1110100101=>1000100011
1110100001=>1011100011
1110011111=>1111101011
1110011110=>0011101011
1110011001=>1010101011
1110010001=>1011001011
1110001101=>1001011011
1110001001=>1010011011
1110000111=>1110111011
1110000101=>1000111011
1110000001=>1011111011
1101111110=>0011111001
1101111011=>1100111001
1101101011=>1100001001
1101100001=>1011101001
1101011111=>1111100001
1101011011=>1100100001
1101010111=>1110000001
1101010101=>1000000001
1101010011=>1101000001
1101010001=>1011000001
1101001110=>0011010001
1101001011=>1100010001
1101001001=>1010010001
1101000101=>1000110001
1101000011=>1101110001
1100110001=>1011010101
1100101011=>1100000101
1100101001=>1010000101
1100100110=>0010100101
1100100101=>1000100101
1100011001=>1010101101
1100010101=>1000001101
1100010010=>0001001101
1100001011=>1100011101
1100001000=>0110011101
1011111110=>0011111100
1011111101=>1001111100
1011110111=>1110011100
1011110001=>1011011100
1011100101=>1000101100
1011100001=>1011101100
1011011111=>1111100100
1011011001=>1010100100
1011010001=>1011000100
1011001101=>1001010100
1011001001=>1010010100
1011000111=>1110110100
1011000101=>1000110100
1011000001=>1011110100
1010111110=>0011110000
1010110101=>1000010000
1010110001=>1011010000
1010101011=>1100000000
1010101001=>1010000000
1010100110=>0010100000
1010100101=>1000100000
1010011101=>1001101000
1010011010=>0000101000
1010011001=>1010101000
1010010111=>1110001000
1010010110=>0010001000
1010010101=>1000001000
1010010001=>1011001000
1010001110=>0011011000
1010000101=>1000111000
1001111111=>1111111010
1001111110=>0011111010
1001111001=>1010111010
1001111000=>0110111010
1001110100=>0100011010
1001110001=>1011011010
1001101101=>1001001010
1001101100=>0101001010
1001101010=>0000001010
1001101001=>1010001010
1001100111=>1110101010
1001100110=>0010101010
1001100101=>1000101010
1001100001=>1011101010
1001011110=>0011100010
1001011010=>0000100010
1001011001=>1010100010
1001010110=>0010000010
1001010101=>1000000010
1001001110=>0011010010
1000111110=>0011110110
1000111101=>1001110110
1000111100=>0101110110
1000111010=>0000110110
1000110111=>1110010110
1000110110=>0010010110
1000110001=>1011010110
1000101110=>0011000110
1000101011=>1100000110
1000100101=>1000100110
1000011111=>1111101110
1000011110=>0011101110
1000011001=>1010101110
1000010110=>0010001110
1000001110=>0011011110
1000001101=>1001011110
1000001010=>0000011110
1000000111=>1110111110
1000000110=>0010111110
1000000100=>0100111110
1000000010=>0001111110
1000000001=>1011111110
1000000000=>0111111110
0111111111=>1111111110
0111111101=>1001111110
0111111001=>1010111110
0111110001=>1011011110
0111100001=>1011101110
0111000001=>1011110110
0110000001=>1011111010
0100000001=>1011111100
0000000001=>1011111111
0111111011=>1100111110
0111110101=>1000011110
0111101001=>1010001110
0111010001=>1011000110
0110100001=>1011100010
0101000001=>1011110000
0010000001=>1011111001
0101010101=>1000000000
0101010011=>1101000000
0101001101=>1001010000
0101001011=>1100010000
0101000111=>1110110000
0100110101=>1000010100
0100110011=>1101010100
0100101101=>1001000100
0100101011=>1100000100
0100100111=>1110100100
0100011101=>1001101100
0100011011=>1100101100
0100010111=>1110001100
0100001111=>1111011100
0011010101=>1000000101
0011010011=>1101000101
0011001101=>1001010101
0011001011=>1100010101
0011000111=>1110110101
0010110101=>1000010001
0010110011=>1101010001
0010101101=>1001000001
0010101011=>1100000001
0010100111=>1110100001
0010011101=>1001101001
0010011011=>1100101001
0010010111=>1110001001
0010001111=>1111011001
0001110101=>1000011011
0001110011=>1101011011
0001101101=>1001001011
0001101011=>1100001011
0001100111=>1110101011
0001011101=>1001100011
0001011011=>1100100011
0001010111=>1110000011
0001001111=>1111010011
0000111101=>1001110111
0000111011=>1100110111
0000110111=>1110010111
0000101111=>1111000111
0000011111=>1111101111
0000000000=>0111111111
0000000110=>0010111111
0000011000=>0110101111
0000011110=>0011101111
0000010010=>0001001111
0001100000=>0111101011
0001100110=>0010101011
0001111000=>0110111011
0001111110=>0011111011
0001110010=>0001011011
0001001000=>0110010011
0001001110=>0011010011
0001000010=>0001110011
0001011010=>0000100011
0110000000=>0111111010
0110000110=>0010111010
0110011000=>0110101010
0110011110=>0011101010
0110010010=>0001001010
0111100000=>0111101110
0111100110=>0010101110
0111111000=>0110111110
0111111110=>0011111110
0111110010=>0001011110
0111001000=>0110010110
0111001110=>0011010110
0111000010=>0001110110
0111011010=>0000100110
0100100000=>0111100100
0100100110=>0010100100
0100111000=>0110110100
0100111110=>0011110100
0100110010=>0001010100
0100001000=>0110011100
0100001110=>0011011100
0100000010=>0001111100
0100011010=>0000101100
0101101000=>0110001000
0101101110=>0011001000
0101100010=>0001101000
0101111010=>0000111000
0101001010=>0000010000
0010101010=>0000000001
0010101000=>0110000001
0010101100=>0101000001
0010100100=>0100100001
0010110100=>0100010001
0010010100=>0100001001
0011010100=>0100000101
0001010100=>0100000011
0101010100=>0100000000
0010101110=>0011000001
0010100000=>0111100001
0010111100=>0101110001
0010000100=>0100111001
0011110100=>0100011101
0000010100=>0100001111
0111010100=>0100000110
0000000010=>0001111111
0000001110=>0011011111
0000111110=>0011110111
0011111110=>0011111101
0000000100=>0100111111
0000001010=>0000011111
0000010110=>0010001111
0000101110=>0011000111
0001011110=>0011100011
0010111110=>0011110001
0101111110=>0011111000
0010110010=>0001010001
0010111000=>0110110001
0011001010=>0000010101
0011001100=>0101010101
0011010010=>0001000101
0011011000=>0110100101
0011100010=>0001101101
0011100100=>0100101101
0011101000=>0110001101
0011110000=>0111011101
0100101010=>0000000100
0100101100=>0101000100
0100110100=>0100010100
0101001100=>0101010000
0101010010=>0001000000
0101011000=>0110100000
0101100100=>0100101000
0101110000=>0111011000
0110001010=>0000011010
0110001100=>0101011010
0110010100=>0100001010
0110100010=>0001100010
0110100100=>0100100010
0110101000=>0110000010
0110110000=>0111010010
0111000100=>0100110110
0111010000=>0111000110
0100000000=>0111111100
0100000011=>1101111100
0100000111=>1110111100
0100011111=>1111101100
0100111111=>1111110100
0101111111=>1111111000
0100000101=>1000111100
0100001011=>1100011100
0100101111=>1111000100
0101011111=>1111100000
0110111111=>1111110010
0101010110=>0010000000
0101011001=>1010100000
0101011010=>0000100000
0101011100=>0101100000
0101100101=>1000101000
0101100110=>0010101000
0101101001=>1010001000
0101101010=>0000001000
0101101100=>0101001000
0101110001=>1011011000
0101110010=>0001011000
0101110100=>0100011000
0101111000=>0110111000
0110010101=>1000001010
0110010110=>0010001010
0110011001=>1010101010
0110011010=>0000101010
0110011100=>0101101010
0110100101=>1000100010
0110100110=>0010100010
0110101001=>1010000010
0110101010=>0000000010
0110101100=>0101000010
0110110001=>1011010010
0110110010=>0001010010
0110110100=>0100010010
0110111000=>0110110010
0111000101=>1000110110
0111000110=>0010110110
0111001001=>1010010110
0111001010=>0000010110
0111001100=>0101010110
0111010010=>0001000110
0111011000=>0110100110
0111100010=>0001101110
0111100100=>0100101110
0111101000=>0110001110
0111110000=>0111011110
0100000100=>0100111100
0011100110=>0010101101
0011101010=>0000001101
0011101100=>0101001101
0001101110=>0011001011
0010110110=>0010010001
0011110010=>0001011101
0001110110=>0010011011
0100111010=>0000110100
0010111010=>0000110001
0011111000=>0110111101
0001111010=>0000111011
0100111100=>0101110100
0001111100=>0101111011
0000000101=>1000111111
0000001101=>1001011111
0000011101=>1001101111
0001111101=>1001111011
0011111101=>1001111101
0000001001=>1010011111
0000010101=>1000001111
0000101101=>1001000111
0010111101=>1001110001
0101111101=>1001111000
10000000000=>01111111110
10000000010=>00011111110
10000000110=>00101111110
10000001110=>00110111110
10000011110=>00111011110
10000111110=>00111101110
10001111110=>00111110110
10011111110=>00111111010
10111111110=>00111111100
11111111110=>00111111111
10000000100=>01001111110
10000001010=>00000111110
10000010110=>00100011110
10000101110=>00110001110
10001011110=>00111000110
10010111110=>00111100010
10101111110=>00111110000
11011111110=>00111111001
10000010000=>01110011110
10000100010=>00011001110
10001000010=>00011100110
10000100100=>01001001110
10001001010=>00000100110
10001000100=>01001100110
10000101000=>01100001110
10010001010=>00000110010
10001010010=>00010000110
10010000100=>01001110010
10001001000=>01100100110
10010010010=>00010010010
10001010100=>01000000110
10010101010=>00000000010
10010001000=>01100110010
10100010010=>00010011000
10010100010=>00011000010
10010010100=>01000010010
10100101010=>00000001000
01111111111=>11111111110
01111111101=>10011111110
01111111001=>10101111110
01111110001=>10110111110
01111100001=>10111011110
01111000001=>10111101110
01110000001=>10111110110
01100000001=>10111111010
01000000001=>10111111100
00000000001=>10111111111
11010101010=>00000000001
11010101000=>01100000001
11010101100=>01010000001
11010100100=>01001000001
11010110100=>01000100001
11010010100=>01000010001
11011010100=>01000001001
11001010100=>01000000101
11101010100=>01000000011
10101010100=>01000000000
00101010101=>10000000001
00101010111=>11100000001
00101010011=>11010000001
00101011011=>11001000001
00101001011=>11000100001
00101101011=>11000010001
00100101011=>11000001001
00110101011=>11000000101
00010101011=>11000000011
01010101011=>11000000000
00000000000=>01111111111
00000000010=>00011111111
00000000110=>00101111111
00000001110=>00110111111
00000011110=>00111011111
00000111110=>00111101111
00001111110=>00111110111
00011111110=>00111111011
00111111110=>00111111101
01111111110=>00111111110
10101010101=>10000000000
10101010010=>00010000000
10101001001=>10100100000
10101001010=>00000100000
10101000100=>01001100000
10100100101=>10001001000
10100100010=>00011001000
10100101001=>10100001000
10100100100=>01001001000
10100010001=>10110011000
10100010100=>01000011000
10100001000=>01100111000
10010010101=>10000010010
10010001001=>10100110010
10010100101=>10001000010
10010101001=>10100000010
10010100100=>01001000010
10010010001=>10110010010
10001000101=>10001100110
10001001001=>10100100110
10001010001=>10110000110
10000100001=>10111001110
01001010101=>10000000100
01001010010=>00010000100
01001001001=>10100100100
01001001010=>00000100100
01001000100=>01001100100
01000100101=>10001001100
01000100010=>00011001100
01000101001=>10100001100
01000101010=>00000001100
01000100100=>01001001100
01000010001=>10110011100
01000010010=>00010011100
01000010100=>01000011100
01000001000=>01100111100
01010010101=>10000010000
01010010010=>00010010000
01010001001=>10100110000
01010001010=>00000110000
01010000100=>01001110000
01010100101=>10001000000
01010100010=>00011000000
01010101001=>10100000000
01010101010=>00000000000
01010100100=>01001000000
01010010001=>10110010000
01010010100=>01000010000
01010001000=>01100110000
01001000101=>10001100100
01001000010=>00011100100
01001010001=>10110000100
01001010100=>01000000100
01001001000=>01100100100
01000100001=>10111001100
01000101000=>01100001100
01000010000=>01110011100
00100010101=>10000011001
00100010010=>00010011001
00100001001=>10100111001
00100001010=>00000111001
00100000100=>01001111001
00100100101=>10001001001
00100100010=>00011001001
00100101001=>10100001001
00100101010=>00000001001
00100100100=>01001001001
00100010001=>10110011001
00100010100=>01000011001
00100001000=>01100111001
00101000101=>10001100001
00101000010=>00011100001
00101001001=>10100100001
00101001010=>00000100001
00101000100=>01001100001
00101010001=>10110000001
00101010010=>00010000001
00101010100=>01000000001
00101001000=>01100100001
00100100001=>10111001001
00100101000=>01100001001
00100010000=>01110011001
00010000101=>10001110011
00010000010=>00011110011
00010001001=>10100110011
00010001010=>00000110011
00010000100=>01001110011
00010010001=>10110010011
00010010010=>00010010011
00010010100=>01000010011
00010001000=>01100110011
00010100001=>10111000011
00010100010=>00011000011
00010100100=>01001000011
00010101000=>01100000011
00010010000=>01110010011
00001000001=>10111100111
00001000010=>00011100111
00001000100=>01001100111
00001001000=>01100100111
00001010000=>01110000111
00000100000=>01111001111
01000000000=>01111111100
01000000011=>11011111100
01000000111=>11101111100
01000001111=>11110111100
01000011111=>11111011100
01000111111=>11111101100
01001111111=>11111110100
01011111111=>11111111000
00000000101=>10001111111
00000001101=>10010111111
00000011101=>10011011111
00000111101=>10011101111
00001111101=>10011110111
00011111101=>10011111011
00111111101=>10011111101
11111111101=>10011111111
101010101010=>000000000000
101010101100=>010100000000
101010110010=>000101000000
101010110100=>010001000000
101010111000=>011011000000
101011001010=>000001010000
101011001100=>010101010000
101011010010=>000100010000
101011010100=>010000010000
101011011000=>011010010000
101011100010=>000110110000
101011100100=>010010110000
101011101000=>011000110000
101011110000=>011101110000
101100101010=>000000010100
101100101100=>010100010100
101100110010=>000101010100
101100110100=>010001010100
101100111000=>011011010100
101101001010=>000001000100
101101001100=>010101000100
101101010010=>000100000100
101101010100=>010000000100
101101011000=>011010000100
101101100010=>000110100100
101101100100=>010010100100
101101101000=>011000100100
101101110000=>011101100100
101110001010=>000001101100
101110001100=>010101101100
101110010010=>000100101100
101110010100=>010000101100
101110011000=>011010101100
101110100010=>000110001100
101110100100=>010010001100
101110101000=>011000001100
101110110000=>011101001100
101111000010=>000111011100
101111000100=>010011011100
101111001000=>011001011100
101111010000=>011100011100
101111100000=>011110111100
110010101010=>000000000101
110010101100=>010100000101
110010110010=>000101000101
110010110100=>010001000101
110010111000=>011011000101
110011001010=>000001010101
110011001100=>010101010101
110011010010=>000100010101
110011010100=>010000010101
110011011000=>011010010101
110011100010=>000110110101
110011100100=>010010110101
110011101000=>011000110101
110011110000=>011101110101
110100101010=>000000010001
110100101100=>010100010001
110100110010=>000101010001
110100110100=>010001010001
110100111000=>011011010001
110101001010=>000001000001
110101001100=>010101000001
110101010010=>000100000001
110101010100=>010000000001
110101011000=>011010000001
110101100010=>000110100001
110101100100=>010010100001
110101101000=>011000100001
110101110000=>011101100001
110110001010=>000001101001
110110001100=>010101101001
110110010010=>000100101001
110110010100=>010000101001
110110011000=>011010101001
110110100010=>000110001001
110110100100=>010010001001
110110101000=>011000001001
110110110000=>011101001001
110111000010=>000111011001
110111000100=>010011011001
110111001000=>011001011001
110111010000=>011100011001
110111100000=>011110111001
111000101010=>000000011011
111000101100=>010100011011
111000110010=>000101011011
111000110100=>010001011011
111000111000=>011011011011
111001001010=>000001001011
111001001100=>010101001011
111001010010=>000100001011
111001010100=>010000001011
111001011000=>011010001011
111001100010=>000110101011
111001100100=>010010101011
111001101000=>011000101011
111001110000=>011101101011
111010001010=>000001100011
111010001100=>010101100011
111010010010=>000100100011
111010010100=>010000100011
111010011000=>011010100011
111010100010=>000110000011
111010100100=>010010000011
111010101000=>011000000011
111010110000=>011101000011
111011000010=>000111010011
111011000100=>010011010011
111011001000=>011001010011
111011010000=>011100010011
111011100000=>011110110011
111100001010=>000001110111
111100001100=>010101110111
111100010010=>000100110111
111100010100=>010000110111
111100011000=>011010110111
111100100010=>000110010111
111100100100=>010010010111
111100101000=>011000010111
111100110000=>011101010111
111101000010=>000111000111
111101000100=>010011000111
111101001000=>011001000111
111101010000=>011100000111
111101100000=>011110100111
111110000010=>000111101111
111110000100=>010011101111
111110001000=>011001101111
111110010000=>011100101111
111110100000=>011110001111
111111000000=>011111011111
100001111100=>010111101110
010101010101=>100000000000
010101010011=>110100000000
010101001101=>100101000000
010101001011=>110001000000
010101000111=>111011000000
010100110101=>100001010000
010100110011=>110101010000
010100101101=>100100010000
010100101011=>110000010000
010100100111=>111010010000
010100011101=>100110110000
010100011011=>110010110000
010100010111=>111000110000
010100001111=>111101110000
010011010101=>100000010100
010011010011=>110100010100
010011001101=>100101010100
010011001011=>110001010100
010011000111=>111011010100
010010110101=>100001000100
010010110011=>110101000100
010010101101=>100100000100
010010101011=>110000000100
010010100111=>111010000100
010010011101=>100110100100
010010011011=>110010100100
010010010111=>111000100100
010010001111=>111101100100
010001110101=>100001101100
010001110011=>110101101100
010001101101=>100100101100
010001101011=>110000101100
010001100111=>111010101100
010001011101=>100110001100
010001011011=>110010001100
010001010111=>111000001100
010001001111=>111101001100
010000111101=>100111011100
010000111011=>110011011100
010000110111=>111001011100
010000101111=>111100011100
010000011111=>111110111100
001101010101=>100000000101
001101010011=>110100000101
001101001101=>100101000101
001101001011=>110001000101
001101000111=>111011000101
001100110101=>100001010101
001100110011=>110101010101
001100101101=>100100010101
001100101011=>110000010101
001100100111=>111010010101
001100011101=>100110110101
001100011011=>110010110101
001100010111=>111000110101
001100001111=>111101110101
001011010101=>100000010001
001011010011=>110100010001
001011001101=>100101010001
001011001011=>110001010001
001011000111=>111011010001
001010110101=>100001000001
001010110011=>110101000001
001010101101=>100100000001
001010101011=>110000000001
001010100111=>111010000001
001010011101=>100110100001
001010011011=>110010100001
001010010111=>111000100001
001010001111=>111101100001
001001110101=>100001101001
001001110011=>110101101001
001001101101=>100100101001
001001101011=>110000101001
001001100111=>111010101001
001001011101=>100110001001
001001011011=>110010001001
001001010111=>111000001001
001001001111=>111101001001
001000111101=>100111011001
001000111011=>110011011001
001000110111=>111001011001
001000101111=>111100011001
001000011111=>111110111001
000111010101=>100000011011
000111010011=>110100011011
000111001101=>100101011011
000111001011=>110001011011
000111000111=>111011011011
000110110101=>100001001011
000110110011=>110101001011
000110101101=>100100001011
000110101011=>110000001011
000110100111=>111010001011
000110011101=>100110101011
000110011011=>110010101011
000110010111=>111000101011
000110001111=>111101101011
000101110101=>100001100011
000101110011=>110101100011
000101101101=>100100100011
000101101011=>110000100011
000101100111=>111010100011
000101011101=>100110000011
000101011011=>110010000011
000101010111=>111000000011
000101001111=>111101000011
000100111101=>100111010011
000100111011=>110011010011
000100110111=>111001010011
000100101111=>111100010011
000100011111=>111110110011
000011110101=>100001110111
000011110011=>110101110111
000011101101=>100100110111
000011101011=>110000110111
000011100111=>111010110111
000011011101=>100110010111
000011011011=>110010010111
000011010111=>111000010111
000011001111=>111101010111
000010111101=>100111000111
000010111011=>110011000111
000010110111=>111001000111
000010101111=>111100000111
000010011111=>111110100111
000001111101=>100111101111
000001111011=>110011101111
000001110111=>111001101111
000001101111=>111100101111
000001011111=>111110001111
000000111111=>111111011111
111111111111=>111111111111
111111111001=>101011111111
111111100111=>111010111111
111111100001=>101110111111
111111101101=>100100111111
111110011111=>111110101111
111110011001=>101010101111
111110000111=>111011101111
111110000001=>101111101111
111110001101=>100101101111
111110110111=>111001001111
111110110001=>101101001111
111110111101=>100111001111
111110100101=>100010001111
111001111111=>111111101011
111001111001=>101011101011
111001100111=>111010101011
111001100001=>101110101011
111001101101=>100100101011
111000011111=>111110111011
111000011001=>101010111011
111000000111=>111011111011
111000000001=>101111111011
111000001101=>100101111011
111000110111=>111001011011
111000110001=>101101011011
111000111101=>100111011011
111000100101=>100010011011
111011011111=>111110010011
111011011001=>101010010011
111011000111=>111011010011
111011000001=>101111010011
111011001101=>100101010011
111011110111=>111001110011
111011110001=>101101110011
111011111101=>100111110011
111011100101=>100010110011
111010010111=>111000100011
111010010001=>101100100011
111010011101=>100110100011
111010000101=>100011100011
111010110101=>100001000011
100111111111=>111111111010
100111111001=>101011111010
100111100111=>111010111010
100111100001=>101110111010
100111101101=>100100111010
100110011111=>111110101010
100110011001=>101010101010
100110000111=>111011101010
100110000001=>101111101010
100110001101=>100101101010
100110110111=>111001001010
100110110001=>101101001010
100110111101=>100111001010
100110100101=>100010001010
100001111111=>111111101110
100001111001=>101011101110
100001100111=>111010101110
100001100001=>101110101110
100001101101=>100100101110
100000011111=>111110111110
100000011001=>101010111110
100000000111=>111011111110
100000000001=>101111111110
100000001101=>100101111110
100000110111=>111001011110
100000110001=>101101011110
100000111101=>100111011110
100000100101=>100010011110
100011011111=>111110010110
100011011001=>101010010110
100011000111=>111011010110
100011000001=>101111010110
100011001101=>100101010110
100011110111=>111001110110
100011110001=>101101110110
100011111101=>100111110110
100011100101=>100010110110
100010010111=>111000100110
100010010001=>101100100110
100010011101=>100110100110
100010000101=>100011100110
100010110101=>100001000110
101101111111=>111111100100
101101111001=>101011100100
101101100111=>111010100100
101101100001=>101110100100
101101101101=>100100100100
101100011111=>111110110100
101100011001=>101010110100
101100000111=>111011110100
101100000001=>101111110100
101100001101=>100101110100
101100110111=>111001010100
101100110001=>101101010100
101100111101=>100111010100
101100100101=>100010010100
101111011111=>111110011100
101111011001=>101010011100
101111000111=>111011011100
101111000001=>101111011100
101111001101=>100101011100
101111110111=>111001111100
101111110001=>101101111100
101111111101=>100111111100
101111100101=>100010111100
101110010111=>111000101100
101110010001=>101100101100
101110011101=>100110101100
101110000101=>100011101100
101110110101=>100001001100
101001011111=>111110001000
101001011001=>101010001000
101001000111=>111011001000
101001000001=>101111001000
101001001101=>100101001000
101001110111=>111001101000
101001110001=>101101101000
101001111101=>100111101000
101001100101=>100010101000
101000010111=>111000111000
101000010001=>101100111000
101000011101=>100110111000
101000000101=>100011111000
101000110101=>100001011000
101011010111=>111000010000
101011010001=>101100010000
101011011101=>100110010000
101011000101=>100011010000
101011110101=>100001110000
101010010101=>100000100000
000000000000=>011111111111
000000000110=>001011111111
000000011000=>011010111111
000000011110=>001110111111
000000010010=>000100111111
000001100000=>011110101111
000001100110=>001010101111
000001111000=>011011101111
000001111110=>001111101111
000001110010=>000101101111
000001001000=>011001001111
000001001110=>001101001111
000001000010=>000111001111
000001011010=>000010001111
000110000000=>011111101011
000110000110=>001011101011
000110011000=>011010101011
000110011110=>001110101011
000110010010=>000100101011
000111100000=>011110111011
000111100110=>001010111011
000111111000=>011011111011
000111111110=>001111111011
000111110010=>000101111011
000111001000=>011001011011
000111001110=>001101011011
000111000010=>000111011011
000111011010=>000010011011
000100100000=>011110010011
000100100110=>001010010011
000100111000=>011011010011
000100111110=>001111010011
000100110010=>000101010011
000100001000=>011001110011
000100001110=>001101110011
000100000010=>000111110011
000100011010=>000010110011
000101101000=>011000100011
000101101110=>001100100011
000101100010=>000110100011
000101111010=>000011100011
000101001010=>000001000011
011000000000=>011111111010
011000000110=>001011111010
011000011000=>011010111010
011000011110=>001110111010
011000010010=>000100111010
011001100000=>011110101010
011001100110=>001010101010
011001111000=>011011101010
011001111110=>001111101010
011001110010=>000101101010
011001001000=>011001001010
011001001110=>001101001010
011001000010=>000111001010
011001011010=>000010001010
011110000000=>011111101110
011110000110=>001011101110
011110011000=>011010101110
011110011110=>001110101110
011110010010=>000100101110
011111100000=>011110111110
011111100110=>001010111110
011111111000=>011011111110
011111111110=>001111111110
011111110010=>000101111110
011111001000=>011001011110
011111001110=>001101011110
011111000010=>000111011110
011111011010=>000010011110
011100100000=>011110010110
011100100110=>001010010110
011100111000=>011011010110
011100111110=>001111010110
011100110010=>000101010110
011100001000=>011001110110
011100001110=>001101110110
011100000010=>000111110110
011100011010=>000010110110
011101101000=>011000100110
011101101110=>001100100110
011101100010=>000110100110
011101111010=>000011100110
011101001010=>000001000110
010010000000=>011111100100
010010000110=>001011100100
010010011000=>011010100100
010010011110=>001110100100
010010010010=>000100100100
010011100000=>011110110100
010011100110=>001010110100
010011111000=>011011110100
010011111110=>001111110100
010011110010=>000101110100
010011001000=>011001010100
010011001110=>001101010100
010011000010=>000111010100
010011011010=>000010010100
010000100000=>011110011100
010000100110=>001010011100
010000111000=>011011011100
010000111110=>001111011100
010000110010=>000101011100
010000001000=>011001111100
010000001110=>001101111100
010000000010=>000111111100
010000011010=>000010111100
010001101000=>011000101100
010001101110=>001100101100
010001100010=>000110101100
010001111010=>000011101100
010001001010=>000001001100
010110100000=>011110001000
010110100110=>001010001000
010110111000=>011011001000
010110111110=>001111001000
010110110010=>000101001000
010110001000=>011001101000
010110001110=>001101101000
010110000010=>000111101000
010110011010=>000010101000
010111101000=>011000111000
010111101110=>001100111000
010111100010=>000110111000
010111111010=>000011111000
010111001010=>000001011000
010100101000=>011000010000
010100101110=>001100010000
010100100010=>000110010000
010100111010=>000011010000
010100001010=>000001110000
010101101010=>000000100000
001010101010=>000000000001
001010101100=>010100000001
001010110010=>000101000001
001010110100=>010001000001
001010111000=>011011000001
001011001010=>000001010001
001011001100=>010101010001
001011010010=>000100010001
001011010100=>010000010001
001011011000=>011010010001
001011100010=>000110110001
001011100100=>010010110001
001011101000=>011000110001
001011110000=>011101110001
001100101010=>000000010101
001100101100=>010100010101
001100110010=>000101010101
001100110100=>010001010101
001100111000=>011011010101
001101001010=>000001000101
001101001100=>010101000101
001101010010=>000100000101
001101010100=>010000000101
001101011000=>011010000101
001101100010=>000110100101
001101100100=>010010100101
001101101000=>011000100101
001101110000=>011101100101
001110001010=>000001101101
001110001100=>010101101101
001110010010=>000100101101
001110010100=>010000101101
001110011000=>011010101101
001110100010=>000110001101
001110100100=>010010001101
001110101000=>011000001101
001110110000=>011101001101
001111000010=>000111011101
001111000100=>010011011101
001111001000=>011001011101
001111010000=>011100011101
001111100000=>011110111101
010010101010=>000000000100
010010101100=>010100000100
010010110010=>000101000100
010010110100=>010001000100
010010111000=>011011000100
010011001010=>000001010100
010011001100=>010101010100
010011010010=>000100010100
010011010100=>010000010100
010011011000=>011010010100
010011100010=>000110110100
010011100100=>010010110100
010011101000=>011000110100
010011110000=>011101110100
010100101010=>000000010000
010100101100=>010100010000
010100110010=>000101010000
010100110100=>010001010000
010100111000=>011011010000
010101001010=>000001000000
010101001100=>010101000000
010101010010=>000100000000
010101010100=>010000000000
010101011000=>011010000000
010101100010=>000110100000
010101100100=>010010100000
010101101000=>011000100000
010101110000=>011101100000
010110001010=>000001101000
010110001100=>010101101000
010110010010=>000100101000
010110010100=>010000101000
010110011000=>011010101000
010110100010=>000110001000
010110100100=>010010001000
010110101000=>011000001000
010110110000=>011101001000
010111000010=>000111011000
010111000100=>010011011000
010111001000=>011001011000
010111010000=>011100011000
010111100000=>011110111000
011000101010=>000000011010
011000101100=>010100011010
011000110010=>000101011010
011000110100=>010001011010
011000111000=>011011011010
011001001010=>000001001010
011001001100=>010101001010
011001010010=>000100001010
011001010100=>010000001010
011001011000=>011010001010
011001100010=>000110101010
011001100100=>010010101010
011001101000=>011000101010
011001110000=>011101101010
011010001010=>000001100010
011010001100=>010101100010
011010010010=>000100100010
011010010100=>010000100010
011010011000=>011010100010
011010100010=>000110000010
011010100100=>010010000010
011010101000=>011000000010
011010110000=>011101000010
011011000010=>000111010010
011011000100=>010011010010
011011001000=>011001010010
011011010000=>011100010010
011011100000=>011110110010
011100001010=>000001110110
011100001100=>010101110110
011100010010=>000100110110
011100010100=>010000110110
011100011000=>011010110110
011100100010=>000110010110
011100100100=>010010010110
011100101000=>011000010110
011100110000=>011101010110
011101000010=>000111000110
011101000100=>010011000110
011101001000=>011001000110
011101010000=>011100000110
011101100000=>011110100110
011110000010=>000111101110
011110000100=>010011101110
011110001000=>011001101110
011110010000=>011100101110
011110100000=>011110001110
011111000000=>011111011110
010101010110=>001000000000
010101011001=>101010000000
010101011010=>000010000000
010101011100=>010110000000
010101100101=>100010100000
010101100110=>001010100000
010101101001=>101000100000
010101101100=>010100100000
010101110001=>101101100000
010101110010=>000101100000
010101110100=>010001100000
010101111000=>011011100000
010110010101=>100000101000
010110010110=>001000101000
010110011001=>101010101000
010110011100=>010110101000
010110100101=>100010001000
010110101001=>101000001000
010110101010=>000000001000
010110101100=>010100001000
010110110001=>101101001000
010110110100=>010001001000
010111000101=>100011011000
010111000110=>001011011000
010111001001=>101001011000
010111001100=>010101011000
010111010001=>101100011000
010111010010=>000100011000
010111010100=>010000011000
010111011000=>011010011000
010111100001=>101110111000
010111100100=>010010111000
010111110000=>011101111000
011001010101=>100000001010
011001010110=>001000001010
011001011001=>101010001010
011001011100=>010110001010
011001100101=>100010101010
011001101001=>101000101010
011001101010=>000000101010
011001101100=>010100101010
011001110001=>101101101010
011001110100=>010001101010
011010010101=>100000100010
011010010110=>001000100010
011010011001=>101010100010
011010011010=>000010100010
011010011100=>010110100010
011010100101=>100010000010
011010100110=>001010000010
011010101001=>101000000010
011010101010=>000000000010
011010101100=>010100000010
011010110001=>101101000010
011010110010=>000101000010
011010110100=>010001000010
011010111000=>011011000010
011011000101=>100011010010
011011000110=>001011010010
011011001001=>101001010010
011011001010=>000001010010
011011001100=>010101010010
011011010001=>101100010010
011011010010=>000100010010
011011010100=>010000010010
011011011000=>011010010010
011011100001=>101110110010
011011100010=>000110110010
011011100100=>010010110010
011011101000=>011000110010
011011110000=>011101110010
011100010101=>100000110110
011100010110=>001000110110
011100011001=>101010110110
011100011100=>010110110110
011100100101=>100010010110
011100101001=>101000010110
011100101010=>000000010110
011100101100=>010100010110
011100110001=>101101010110
011100110100=>010001010110
011101000101=>100011000110
011101000110=>001011000110
011101001001=>101001000110
011101001100=>010101000110
011101010001=>101100000110
011101010010=>000100000110
011101010100=>010000000110
011101011000=>011010000110
011101100001=>101110100110
011101100100=>010010100110
011101110000=>011101100110
011110000101=>100011101110
011110001001=>101001101110
011110001010=>000001101110
011110001100=>010101101110
011110010001=>101100101110
011110010100=>010000101110
011110100001=>101110001110
011110100010=>000110001110
011110100100=>010010001110
011110101000=>011000001110
011110110000=>011101001110
011111000001=>101111011110
011111000100=>010011011110
011111010000=>011100011110
001111000110=>001011011101
001111001010=>000001011101
100111001100=>010101011010
001111001100=>010101011101
001011010110=>001000010001
001111010010=>000100011101
100111010100=>010000011010
001111010100=>010000011101
000111010110=>001000011011
001011011010=>000010010001
100111011000=>011010011010
001111011000=>011010011101
100011011100=>010110010110
010011011100=>010110010100
001011011100=>010110010001
000111011100=>010110011011
000011011110=>001110010111
001101100110=>001010100101
001101101010=>000000100101
100101101100=>010100100010
001101101100=>010100100101
001011100110=>001010110001
001111100010=>000110111101
100111100100=>010010111010
001111100100=>010010111101
010011101010=>000000110100
001011101010=>000000110001
100111101000=>011000111010
001111101000=>011000111101
000111101010=>000000111011
100011101100=>010100110110
010011101100=>010100110100
001011101100=>010100110001
000111101100=>010100111011
000011101110=>001100110111
101001110100=>010001101000
001001110110=>001001101001
001101110010=>000101100101
100101110100=>010001100010
001101110100=>010001100101
000101110110=>001001100011
001011110010=>000101110001
100111110000=>011101111010
001111110000=>011101111101
100011110100=>010001110110
010011110100=>010001110100
001011110100=>010001110001
000111110100=>010001111011
000011110110=>001001110111
110001111000=>011011101101
101001111000=>011011101000
001001111010=>000011101001
100101111000=>011011100010
001101111000=>011011100101
100011111000=>011011110110
001011111000=>011011110001
000011111010=>000011110111
010001111100=>010111101100
001001111100=>010111101001
000101111100=>010111100011
000011111100=>010111110111
100101010101=>100000000010
100101011001=>101010000010
100101100101=>100010100010
100101101001=>101000100010
100101110001=>101101100010
100110010101=>100000101010
100110101001=>101000001010
100111000101=>100011011010
100111001001=>101001011010
100111010001=>101100011010
101001010101=>100000001000
101001101001=>101000101000
101010011001=>101010100000
101010100101=>100010000000
101010101001=>101000000000
101010110001=>101101000000
101011001001=>101001010000
101011100001=>101110110000
101100010101=>100000110100
101100101001=>101000010100
101101000101=>100011000100
101101001001=>101001000100
101101010001=>101100000100
101110001001=>101001101100
101110100001=>101110001100
110001010101=>100000001101
110001011001=>101010001101
110001100101=>100010101101
110001101001=>101000101101
110001110001=>101101101101
110010010101=>100000100101
110010011001=>101010100101
110010100101=>100010000101
110010101001=>101000000101
110010110001=>101101000101
110011000101=>100011010101
110011001001=>101001010101
110011010001=>101100010101
110011100001=>101110110101
110100010101=>100000110001
110100011001=>101010110001
110100100101=>100010010001
110100101001=>101000010001
110100110001=>101101010001
110101000101=>100011000001
110101001001=>101001000001
110101010001=>101100000001
110101100001=>101110100001
110110000101=>100011101001
110110001001=>101001101001
110110010001=>101100101001
110110100001=>101110001001
110111000001=>101111011001
111000010101=>100000111011
111000101001=>101000011011
111001000101=>100011001011
111001001001=>101001001011
111001010001=>101100001011
111010001001=>101001100011
111010100001=>101110000011
111100000101=>100011110111
111100001001=>101001110111
111100010001=>101100110111
111100100001=>101110010111
111101000001=>101111000111
10101010101010=>00000000000000
10101010101100=>01010000000000
10101010110100=>01000100000000
10101010111000=>01101100000000
10101011010100=>01000001000000
10101011100100=>01001011000000
10101011101000=>01100011000000
10101011110000=>01110111000000
10101101010100=>01000000010000
10101110010100=>01000010110000
10101110100100=>01001000110000
10101110101000=>01100000110000
10101110110000=>01110100110000
10101111000100=>01001101110000
10101111010000=>01110001110000
10110101010100=>01000000000100
10110111100000=>01111011100100
10111001010100=>01000000101100
10111010010100=>01000010001100
10111010100100=>01001000001100
10111011000100=>01001101001100
10111011010000=>01110001001100
10111011100000=>01111011001100
10111100010100=>01000011011100
10111100110000=>01110101011100
10111101000100=>01001100011100
10111101001000=>01100100011100
10111101010000=>01110000011100
10111101100000=>01111010011100
10111110000100=>01001110111100
10111110001000=>01100110111100
10111110010000=>01110010111100
10111110100000=>01111000111100
10111111000000=>01111101111100
11001111100000=>01111011110101
11010101010100=>01000000000001
11010101011000=>01101000000001
11010101100100=>01001010000001
11010101101000=>01100010000001
11010101110000=>01110110000001
11010110010100=>01000010100001
11010110011000=>01101010100001
11010110100100=>01001000100001
11010110101000=>01100000100001
11010110110000=>01110100100001
11010111000100=>01001101100001
11010111001000=>01100101100001
11010111010000=>01110001100001
11010111100000=>01111011100001
11011001010100=>01000000101001
11011001011000=>01101000101001
11011001100100=>01001010101001
11011001101000=>01100010101001
11011001110000=>01110110101001
11011010010100=>01000010001001
11011010011000=>01101010001001
11011010100100=>01001000001001
11011010101000=>01100000001001
11011010110000=>01110100001001
11011011000100=>01001101001001
11011011001000=>01100101001001
11011011010000=>01110001001001
11011011100000=>01111011001001
11011100010100=>01000011011001
11011100011000=>01101011011001
11011100100100=>01001001011001
11011100101000=>01100001011001
11011100110000=>01110101011001
11011101000100=>01001100011001
11011101001000=>01100100011001
11011101010000=>01110000011001
11011101100000=>01111010011001
11011110000010=>00011110111001
11011110000100=>01001110111001
11011110001000=>01100110111001
11011110010000=>01110010111001
11011110100000=>01111000111001
11011111000000=>01111101111001
11100101010100=>01000000001011
11100101011000=>01101000001011
11100101100100=>01001010001011
11100101101000=>01100010001011
11100101110000=>01110110001011
11100110010100=>01000010101011
11100110011000=>01101010101011
11100110100100=>01001000101011
11100110101000=>01100000101011
11100110110000=>01110100101011
11100111000100=>01001101101011
11100111001000=>01100101101011
11100111010000=>01110001101011
11100111100000=>01111011101011
11101001010100=>01000000100011
11101001011000=>01101000100011
11101001100100=>01001010100011
11101001101000=>01100010100011
11101001110000=>01110110100011
11101010010100=>01000010000011
11101010011000=>01101010000011
11101010100100=>01001000000011
11101010101000=>01100000000011
11101010110000=>01110100000011
11101011000100=>01001101000011
11101011001000=>01100101000011
11101011010000=>01110001000011
11101011100000=>01111011000011
11101100010100=>01000011010011
11101100011000=>01101011010011
11101100100100=>01001001010011
11101100101000=>01100001010011
11101100110000=>01110101010011
11101101000010=>00011100010011
11101101000100=>01001100010011
11101101001000=>01100100010011
11101101010000=>01110000010011
11101101100000=>01111010010011
11101110000010=>00011110110011
11101110000100=>01001110110011
11101110001000=>01100110110011
11101110010000=>01110010110011
11101110100000=>01111000110011
11101111000000=>01111101110011
11110001010100=>01000000110111
11110001011000=>01101000110111
11110001100100=>01001010110111
11110001101000=>01100010110111
11110001110000=>01110110110111
11110010010100=>01000010010111
11110010011000=>01101010010111
11110010100100=>01001000010111
11110010101000=>01100000010111
11110010110000=>01110100010111
11110011000010=>00011101010111
11110011000100=>01001101010111
11110011001000=>01100101010111
11110011010000=>01110001010111
11110011100000=>01111011010111
11110100010100=>01000011000111
11110100011000=>01101011000111
11110100100010=>00011001000111
11110100100100=>01001001000111
11110100101000=>01100001000111
11110100110000=>01110101000111
11110101000010=>00011100000111
11110101000100=>01001100000111
11110101001000=>01100100000111
11110101010000=>01110000000111
11110101100000=>01111010000111
11110110000010=>00011110100111
11110110000100=>01001110100111
11110110001000=>01100110100111
11110110010000=>01110010100111
11110110100000=>01111000100111
11110111000000=>01111101100111
11111000001100=>01010111101111
11111000010010=>00010011101111
11111000010100=>01000011101111
11111000011000=>01101011101111
11111000100010=>00011001101111
11111000100100=>01001001101111
11111000101000=>01100001101111
11111000110000=>01110101101111
11111001000010=>00011100101111
11111001000100=>01001100101111
11111001001000=>01100100101111
11111001010000=>01110000101111
11111001100000=>01111010101111
11111010000010=>00011110001111
11111010000100=>01001110001111
11111010001000=>01100110001111
11111010010000=>01110010001111
11111010100000=>01111000001111
11111011000000=>01111101001111
11111100000010=>00011111011111
11111100000100=>01001111011111
11111100001000=>01100111011111
11111100010000=>01110011011111
11111100100000=>01111001011111
11111101000000=>01111100011111
11111110000000=>01111110111111
1010101010101010=>0000000000000000
1010101010101100=>0101000000000000
1010101010110100=>0100010000000000
1010101010111000=>0110110000000000
1010101011010100=>0100000100000000
1010101011100100=>0100101100000000
1010101011101000=>0110001100000000
1010101011110000=>0111011100000000
1010101101010100=>0100000001000000
1010101110010100=>0100001011000000
1010101110100100=>0100100011000000
1010101111000100=>0100110111000000
1010110101010100=>0100000000010000
1010111001010100=>0100000010110000
1010111010010100=>0100001000110000
1010111100010100=>0100001101110000
1011010101010100=>0100000000000100
1011100101010100=>0100000000101100
1011101001010100=>0100000010001100
1011110001010100=>0100000011011100
1011110111000000=>0111110110011100
1011111010100000=>0111100000111100
1011111011000000=>0111110100111100
1011111100010000=>0111001101111100
1011111100100000=>0111100101111100
1011111101000000=>0111110001111100
1011111110000000=>0111111011111100
1101010101010100=>0100000000000001
1110010101010100=>0100000000001011
1110100101010100=>0100000000100011
1111000101010100=>0100000000110111
1111011100000010=>0001111101100111
1111101010000010=>0001111000001111
1111101100000010=>0001111101001111
1111110001000010=>0001110011011111
1111110010000010=>0001111001011111
1111110100000010=>0001111100011111
1111111000000010=>0001111110111111
101010101010101010=>000000000000000000
101010101010101100=>010100000000000000
101010101010110100=>010001000000000000
101010101011010100=>010000010000000000
101010101101010100=>010000000100000000
101010110101010100=>010000000001000000
101011010101010100=>010000000000010000
101101010101010100=>010000000000000100
110101010101010100=>010000000000000001
101010101010111000=>011011000000000000
101010101011100100=>010010110000000000
101010101110010100=>010000101100000000
101010111001010100=>010000001011000000
101011100101010100=>010000000010110000
101110010101010100=>010000000000101100
111001010101010100=>010000000000001011
111111110000000010=>000111111101111111
101111111100000000=>011111110111111100
111111101000000010=>000111111000111111
101111111010000000=>011111100011111100
111111100100000010=>000111110010111111
111111011000000010=>000111111010011111
101111111001000000=>011111001011111100
101111110110000000=>011111101001111100
10101010101010101010=>00000000000000000000
10101010101010101100=>01010000000000000000
10101010101010110100=>01000100000000000000
10101010101011010100=>01000001000000000000
10101010101101010100=>01000000010000000000
10101010110101010100=>01000000000100000000
10101011010101010100=>01000000000001000000
10101101010101010100=>01000000000000010000
10110101010101010100=>01000000000000000100
11010101010101010100=>01000000000000000001
11111111100000000010=>00011111111011111111
10111111111000000000=>01111111101111111100
11111111010000000010=>00011111110001111111
10111111110100000000=>01111111000111111100
1111111111000000000010=>0001111111110111111111
1011111111110000000000=>0111111111011111111100
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
Return a binary word of the same length, such that the number of zeros equals the number of occurrences of $10$ in the word obtained from the original word by prepending the reverse of the complement.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.
Properties
bijective, graded
Sage code
def mapping(w): zeros = [] letter = 1 z = 0 for e in reversed(w): if e == letter: z += 1 else: zeros.append(z) z = 0 letter = 1 - letter result = [1]*len(w) last = -1 for z in zeros: last = z + last + 1 result[last] = 0 return Words([0,1])(result)
Weight
40
Created
Dec 02, 2022 at 00:03 by Martin Rubey
Updated
Dec 02, 2022 at 00:03 by Martin Rubey
searching the database
Sorry, this map was not found in the database.