by Edward Spence Sept. 2006
The number of equivalence classes of 4mX4m skew Hadamard matrices is exactly known for m=1-7: it is 1, 1, 1, 2, 2, 16, 54. [Edward Spence: Classification of Hadamard matrices of order 24 and 28, Discrete Math. 140, 1-3 (1995) 185-243]. We now give one representative of each of these equivalence classes.
2:
+- ++
4:
++++ -++- --++ -+-+
8:
++++++++ -+++-+-- --+++-+- ---+++-+ -+--+++- --+--+++ -+-+--++ -++-+--+
12:
+----------- ++-+---+++-+ +++-+---+++- +-++-+---+++ ++-++-+---++ +++-++-+---+ ++++-++-+--- +-+++-++-+-- +--+++-++-+- +---+++-++-+ ++---+++-++- +-+---+++-++
16 (both this and its transpose):
++++++++ ++++++++ -+++-+-- +--+-+++ --+++-+- +-+-+++- ---+++-+ ++-+++-- -+--+++- +-+++--+ --+--+++ ++++--+- -+-+--++ +++--+-+ -++-+--+ ++--+-++ -------- ++++++++ -++-+--- -+++-+-- -+-+---+ --+++-+- --+---++ ---+++-+ -+---++- -+--+++- ----++-+ --+--+++ ---++-+- -+-+--++ --++-+-- -++-+--+
20 (both this and its transpose):
+------------------- ++-++----+-+-++++--+ +++-++----+-+-++++-- +-++-++----+-+-++++- +--++-++----+-+-++++ ++--++-++----+-+-+++ +++--++-++----+-+-++ ++++--++-++----+-+-+ +++++--++-++----+-+- +-++++--++-++----+-+ ++-++++--++-++----+- +-+-++++--++-++----+ ++-+-++++--++-++---- +-+-+-++++--++-++--- +--+-+-++++--++-++-- +---+-+-++++--++-++- +----+-+-++++--++-++ ++----+-+-++++--++-+ +++----+-+-++++--++- +-++----+-+-++++--++
24: To get the skew-Hadamard matrices from the below sixteen 23x23 matrices, change the off-diagonal zeros to -1, the diagonal to +1, and border with a column of 1s and a row containing -1s in off-diagonal locations:
01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000101000011100111 01100010011010010111001 01100101000101011001101 01101000010110101010110 01110001100001100111010 10011001010100011111000 10100101101010001110100 10101001110011010000011 10101010001101000101110 10110010100100110010101 10110100011000101001011 11000111010000110100110 11001011001001101010001 11001100100110100101001 11010010110011001001100 11010100001111010010010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000101000011100111 01100010011010010111001 01100101000101010101110 01101000010110101010110 01110001100001101011001 10011001010100011111000 10100101101010001110100 10101001110011010000011 10101010001101001001101 10110010110000100101110 10110100001100110010011 11000111010000111000101 11001011001001100110010 11001100100110100101001 11010010100111010010100 11010100011011001001010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000101000011100111 01100010011010010111001 01100101000100111010101 01101000010111001001110 01110001100001100111010 10011001010100011111000 10100101110010010100110 10101001101011001010001 10101010001100100110110 10110010100101010001101 10110100011000101001011 11000111001001001101100 11001011010001110000011 11001100100110100101001 11010010110010101010100 11010100001111010010010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000101000011100111 01100010011010010111001 01100101000100110110110 01101000010111001001110 01110001100001101011001 10011001010100011111000 10100101110010011000101 10101001101011000110010 10101010001100101010101 10110010110000100101110 10110100001101010001011 11000111001001001101100 11001011010001110000011 11001100100110100101001 11010010100111010010100 11010100011010101010010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000101000011100111 01100010011010001111100 01100101000101010101110 01101000010110110010011 01110001100001101011001 10011001010100011111000 10100101101010010110001 10101001110011001000110 10101010100100100101101 10110010011001010001011 10110100001100101010110 11000111010000111000101 11001011001001100110010 11001100001111001001001 11010010100111010010100 11010100110010100101010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000101000011100111 01100010011010001111100 01100101000100110110110 01101000010111010001011 01110001100001101011001 10011001010100011111000 10100101110010011000101 10101001101011000110010 10101010100100100101101 10110010011000110010011 10110100001101001001110 11000111001001010101001 11001011010001101000110 11001100001110101010001 11010010100111010010100 11010100110010100101010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000100100011101101 01100010011010010111001 01100101000100110110110 01101001010001101001011 01110000101011001010110 10011001011000011110010 10100101110010011000101 10101001100111000111000 10101010001100101010101 10110010110000100101110 10110100001101010001011 11000111001001001101100 11001010010111010000110 11001100101010100100011 11010011100001110010001 11010100010110101011000 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000100100011101101 01100010011010010111001 01100101000100110110110 01101001010001101001011 01110000101011001010110 10011001011000011110010 10100101110010001101100 10101001100111010010001 10101010001101000101110 10110010110000110000111 10110100001100101011001 11000111001001011000101 11001010010110101010100 11001100101010100100011 11010011100001100111000 11010100010111010001010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000100100011101101 01100010011010001111100 01100101001001011000111 01101001000101100111010 01110000110010110010011 10011001011000011110010 10100101100110010110100 10101001110011001001001 10101010101000100100111 10110010001101010011001 10110100010100101001110 11000111010000110101001 11001010010111010000110 11001100001110101010001 11010011100001101010100 11010100101011000101010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000100100011101101 01100010011010001111100 01100101000100110110110 01101001010001101001011 01110000101011010010011 10011001011000011110010 10100101110010011000101 10101001100111000111000 10101010101000100100111 10110010010100110011001 10110100001101001001110 11000111001001010101001 11001010010111010000110 11001100001110101010001 11010011100001101010100 11010100110010100101010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000011000011101011 01100011001001011010101 01100100100110010101101 01101000010110101010110 01110001100001100111010 10011001100100011110100 10100101011010001111000 10101001110011010000011 10101010001101000101110 10110010010100110011001 10110100101000101000111 11000111010000110100110 11001010101010100110001 11001101000101101001001 11010010110011001001100 11010100001111010010010 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000001100011110110 01100011010001010101110 01100101001000101111001 01101000100111001001101 01110000110010110010011 10011001110000011101001 10100101010110011010100 10101001101011000110010 10101010011000101000111 10110010100100100111100 10110100001101010001011 11000110101010010100101 11001011000101110010001 11001100010110100101010 11010010011011001011000 11010101100001101000110 01111111111100000000000 00111110000011111100000 00011111000010000011111 00001100111001110011100 00000110110101001110011 00000011101110111001010 00010001011111100100101 01011000001100011110110 01100011010000111010101 01100101001001010101011 01101000100110100111001 01110000110011001001110 10011001110000011101001 10100101101010001110100 10101001010111010010010 10101010001101001001101 10110010011000100111010 10110100100100110000111 11000110010110010101100 11001011100001100100110 11001100011010101000011 11010010101011010010001 11010101000101101011000 01111111111100000000000 00111110000011111100000 00011101100011000011110 00001011011010110011001 00000111010101001110101 00010001101100111110010 00100100110101110001011 01000010101111101001100 01011000011001100100111 01100101001010001101011 01101010000100010111110 01110000110010011010101 10001110101000011000111 10010100011110010101100 10101000011111001010010 10101001110000101101100 10110010101001000111001 10110011000110100000111 11000011110011010100010 11001100100110100110001 11010110010000101011010 11011001000101011001001 11100101001001110010100 01111111111100000000000 00111110000011111100000 00011101100011000011110 00001011011010110011001 00000111010100101110110 00010001101101111000101 00100100110110011001011 01000010101111010110010 01011000011010001100111 01100101001001001111001 01101010000101100001111 01110000110000110111100 10001100011101010101100 10011010100100001111001 10100011110011000100101 10101000111001101010010 10110001001110100101010 10110110001000010010111 11000110101010101001100 11001101100000110100011 11010011010001011001010 11010100010111100010001 11101001000110011010100 01111111111100000000000 00111110000011111100000 00011101100011000011110 00001011011010110011001 00000100111111101000101 00010010011101010110110 00101000110100101111010 01001110001000001101111 01010101000100111010011 01100001101010011110100 01100010100111010001011 01110001010001100101101 10000111100100110101100 10010011110010001100011 10100101011001011001010 10101011000101001010101 10110100001110000111001 10111000101000110000111 11001001001111100100010 11001100110001010110001 11010010101001101011000 11011000010110011001100 11100110010010100010110
28: To get the skew-Hadamard matrices from the below fifty-four 27x27 matrices, change the off-diagonal zeros to -1, the diagonal to +1, and border with a column of 1s and a row containing -1s in off-diagonal locations:
011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001101001110001011 011001010100010101001011110 011010001010011011001100101 011100100011000010011111010 011110000100100100110110101 100111000010110001011011001 101001010101101010001110001 101001100110011000110101100 101010011000110110010101010 101010100011101101000010110 101100011011000100101001101 101100101100010011100010011 110010011110001000111010010 110010110101000011010001101 110011100001010100101100011 110100101100101101001101000 110101001001011110010010100 110101010010100011100100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001101001110001011 011001010100010101001011110 011010001010011010011110010 011100100011000011001101101 011110000100100100110110101 100111000010110001011011001 101001010101101010001110001 101001100110011000110101100 101010011001010110010001101 101010100011101101000010110 101100011010100100101101010 101100101100010011100010011 110010011110001001101000101 110010110100100011010101010 110011100001010100101100011 110100101101001100011011000 110101001000111111000100100 110101010011000010110010110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001101001110001011 011001010100010011001101101 011010001010011101001010110 011100100011000010011111010 011110000100100100110110101 100111000010110001011011001 101001010110101000101110010 101001100101011100010011100 101010011000110110010101010 101010100011101011000100101 101100011011000100101001101 101100101100010011100010011 110010011101001010011010001 110010110110000001110001110 110011100001010100101100011 110100101100101101001101000 110101001010011010110100100 110101010001100111000010110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001101001110001011 011001010100010010011111010 011010001010011011001100101 011100100011000101001011110 011110000100100100110110101 100111000010110001011011001 101001010111001000101010101 101001100100111101000101100 101010011010010100110001110 101010100011101010010110010 101100011001100110001101001 101100101100010011100010011 110010011100101101001010010 110010110101000011010001101 110011100001010100101100011 110100101110001000111101000 110101001001011110010010100 110101010010100011100100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001011100011011010 011001010100100001101101011 011010001010011011001100101 011100100101000011010011101 011110000010100100110110110 100111000010110001011011001 101001010011101011000010110 101001100110011000110101100 101010011100010010110010011 101010100101101100001110001 101100011011000100101001101 101100101000110111000101010 110010011100101101010001100 110010110011000010011101010 110011100001010101100000111 110100101110001001101010010 110101001001101010110100001 110101010100010110001110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001011100011011010 011001010100100001101101011 011010001010011011001100101 011100100101000011010011101 011110000010100100110110110 100111000010110001011011001 101001010011101010010101100 101001100110011001100010110 101010011100010100110001101 101010100101101100001110001 101100011011000010101010011 101100101000110111000101010 110010011100101011010010010 110010110011000101001001110 110011100001010010110100011 110100101110001000111101000 110101001001101101100000101 110101010100010110001110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011101010100011 000110000101111010101001110 010000110010111110100011001 011001001001011100011011010 011001010100010011001101101 011010001010101001101100011 011100100110000001110011110 011110000001100110010110101 100111000010110001011011001 101001010011101011000010110 101001100101101000110101001 101010011100010010110010011 101010100110011100001110100 101100011011000100101001101 101100101000110111000101010 110010011100101101010001100 110010110011000010011101010 110011100001010101100000111 110100101101001011001010001 110101001010011010110100100 110101010100100100101110010 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010111011100011101010 000110000101111011100000111 010000110010111111000011001 011001001010011001110001110 011001010001100010101101011 011010001100011010011110001 011100100101000100110011101 011110000010100101001110110 100111000010110000111011001 101001010111001001001010101 101001100100111100100110010 101010100011101010010101100 101010101001010101001001011 101100011010010110100100101 101100011100100011010011010 110010011100101100101001100 110010110110000001110100011 110011010001010110010010110 110100101011001010101010010 110101001001101101010100001 110101100100010011001101100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010110111101010101010 000110000101111010101010011 010000110011011110100001101 011001001010011001101100011 011001010001100011010011011 011010100100010101001011110 011100001101001010011101100 011110000010100100110110101 100111000011010001011001101 101001010110101000101011100 101001100101011100010110001 101010011000110110001101001 101010100011101011000100110 101100011101000101100000111 101100101010010010110011010 110010011011001100011010010 110010101100101001110001001 110011010100010010110100110 110100110110000011001110001 110101001000111111000010100 110101100001100100101101010 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010110111101010101010 000110000101111010101001101 010000110011011110100010011 011001001010011001110001101 011001010001100011001101011 011010100100010101001011110 011100001101001100011110001 011110000010100010110110110 100111000011010001011010011 101001010110011010001110100 101001100101101000110011010 101010011000110110010011001 101010100011101101000100101 101100011011000100101001110 101100101100010011100100011 110010011101001011010000110 110010110110000000111101001 110011001000111100101100010 110100101010101011001011000 110101010100100101100010101 110101100001010110010101100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010110111101010101010 000110000101111010101001101 010000110011011110100010011 011001001001011101001001110 011001010100010010011111001 011010100010100001101101011 011100001110001001110010101 011110000001100110010110110 100111000011010001011010011 101001010011101011000100101 101001100101101000110011010 101010011010010010110001110 101010100110011100001110100 101100011101000100101100011 101100101000110111000011001 110010011100101011001010010 110010110101000101010001101 110011001000111100110100001 110100101011001010011101000 110101010010100100101011100 110101100100010011100100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010110111101010101010 000110000101111010101001101 010000110011011110100010011 011001001001011100011101001 011001010100010011001011110 011010100010100001101101011 011100001110001001110010101 011110000001100110010110110 100111000011010001011010011 101001010011101011000100101 101001100101101000110011010 101010011100010010110100011 101010100110011100001110100 101100011011000100101001110 101100101000110111000011001 110010011010101010011011000 110010110101000101010001101 110011001000111101100000110 110100101101001011001100010 110101010100100100101110001 110101100010010010110101100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010110111101010101010 000110000101111010101001101 010000110011011110100010011 011001001000111101001011001 011001010101000000111101011 011010100100010011010011110 011100001011001011001100110 011110000010100100110110101 100111000011010001011010011 101001010011101010010011100 101001100110011001100100101 101010011010010100101001110 101010100101101100001110010 101100011100100011100010011 101100101001010110010101001 110010011101001101010000101 110010110010100011001101001 110011001000111010110100010 110100101110001000111011000 110101010100010110001110100 110101100001100101100001110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000111001110001111110100 000100010110111101010101010 000110000101111010101001101 010000110011011110100010011 011001001000111011001011010 011001010101000000111101011 011010100100010101010011101 011100001011001011010100101 011110000010100100101110110 100111000011010001011010011 101001010110101001100010101 101001100011011100001101100 101010011010010010110001110 101010100101101010010110010 101100011100010110001110001 101100101001100101100001011 110010011101001101001000110 110010110010100011001101001 110011001000111100110100001 110100101110001000111011000 110101010001100110010011100 110101100100010011100100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110111011001110100110 000100011001110101101010101 000110000101111010011011010 010001010010111011001101001 011000101010011100101011010 011000110001100110010111100 011010001100101001110001101 011101000100010101010110011 011110000011000010101100111 100110100010110100110101001 101001011001010010110001011 101001100101101000101110001 101010010110011110000010101 101010011010100001011110010 101100101100010011001101100 101101000011101101000001110 110010110101000101001001011 110011001001011100011100100 110011100000110011100010110 110100011100101110100100010 110100101011001011010010001 110101010110000000111011100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110111011001110100110 000100011001110101011110001 000110000101111010101001101 010001010010111100101011010 011000101001011111000001011 011000110100100011001111100 011010001010101001110010101 011101000100010010110110011 011110000011000100011101110 100110100010110011010011010 101001010011101010010101001 101001101001010000111011100 101010011000110110100100110 101010100110011100001110001 101100011110000001101001011 101101000101101101000010110 110010011101001010011010010 110011010100010101010001101 110011100001100001101100011 110100101100101100110101000 110100110011000110100010101 110101001010011011001100100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110111011001011110100 000100011001110101110001110 000110000101111010101100011 010001010010111100101011001 011000101001101011100010101 011000110100010111000101011 011010001010101001011101010 011101000010010010110110110 011110000101000100011011101 100110100010110011010011001 101001010101101010010011010 101001101001010000111101001 101010011000110110001110100 101011000011011101000000111 101100011110000001101010011 101100100110101100100101100 110010101100011100110010010 110010110011000010101001110 110011010100100001110100101 110100011011001110010100001 110101001100011011001001100 110101100001100101001110010 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110111011001011110100 000100011001110100111101010 000110000101111011100000111 010001010010111010110011001 011000101001101011001011010 011000110100100101100101101 011010001010011101010100011 011101000001010110001110101 011110000110000000111011110 100110100010110101001011001 101001011100010001101010011 101001100011011100100001110 101010101000110010110110100 101011000101101000011101001 101100010110101110000110010 101100011011000011010001101 110010011100011110001001100 110010110011000010101100011 110011010001100101010010110 110100101101001100110010001 110101001010101001101100100 110101100100010011010101010 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110110111001110110100 000100011001110101011101010 000110000101111010101010011 010001010011011100101001101 011000101001011111000010110 011000110101000010011111001 011011000000110010110101110 011100001110001001110001011 011110000010100101001110101 100110100011010011010001101 101001010011101011000100011 101001101000110001101011001 101010011011000000111010110 101010100110011100001101010 101100011100010110100100101 101101000101101100010011100 110010011100101011001001100 110010101001101100110100001 110011010100010101010010011 110100110010100110100011010 110101001010011010011110000 110101100101000001101100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101100100110 000100011100110001111011001 000110000011111010011110100 010001010011011011010001011 011000011011001100101010101 011001100001100000111111010 011010100000110111000011101 011100001100011110001101010 011110000110000001110100111 100110100011010100101001011 101000111010010010110101100 101001100110011001001110001 101010010110101100010011010 101010011001100011001100011 101101000101101010100001101 101101001001010101010010110 110010101101001001011001100 110011001000111100110100001 110011010100010010101010110 110100101010101011100010010 110100110101000110010110001 110101010010100101001101100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101100100110 000100011011010001111010101 000110000101111010011011010 010001010010111011010101001 011000101010011010101110010 011001010001100100101011011 011010001100011101001001101 011100100101000010110101101 011110000010100101010110110 100110100010110100101101001 101000111100100001011111000 101001100011011100010011100 101010010110101010100010101 101010011001010110010100011 101101000111001001001100011 101101001000110011100001110 110010110011000011001001110 110011001001101000111100100 110011100100010001110010011 110100011110001100110001010 110100101001101111000010001 110101010100010110001110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101100100110 000100011010110001111110001 000110000101111010011011100 010001010011011011010001011 011000101001101010101101001 011001010100010100101011101 011010100010010011001110110 011100001011001100110010110 011110000100100101010101011 100110100011010100101001011 101000111101000001011011010 101001100010111100010111000 101010010110101010100010011 101010011001010110010100101 101101000111001001001100101 101101001000110011100001110 110010011010101101001001100 110011001100011000111100010 110011100001100001110010101 110100101100011111000010001 110100110110000010110101100 110101010001100110001110010 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101100100110 000100011001110011011110001 000110000111011000111001101 010001010010111010110011010 011000101010101001101101001 011001100001010101010011101 011010001100011100011110010 011100010011000110001101110 011110000100100011100010111 100110100010110101001011010 101000111100010010101011100 101001010111001001001010011 101010011001100100110001011 101010100011101010010110100 101101000100111110000101001 101101001010010001110100110 110010011010011111000000101 110011010100100001011101100 110011100001010010101100011 110100101101001011010001010 110100110110000100110110001 110101001001101100101010100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101100100110 000100011001110011011110001 000110000111011000111001101 010001010010111010110011010 011000101010101001101101001 011001100001010101010011101 011010001100011011001010110 011100010011000110001101110 011110000100100100110110011 100110100010110101001011010 101000111101000000111011010 101001010110011100001110001 101010011000110110100001101 101010100011101010010110100 101101000101101011000001011 101101001010010001110100110 110010011011001101010000011 110011010100100001011101100 110011100001010010101100011 110100101100011110010101000 110100110110000011100010101 110101001001101100101010100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100011101010001111001011 000110000011111010101100110 010001010010111100101011001 011000011010101011010101010 011001100001010010110110011 011010001100011011001010101 011100100011000101001011110 011110000100100100110101101 100110100010110011010011001 101000110111001010100001101 101001101000110001101101100 101010011010010100110010110 101011000101101000011011010 101100011001100110001110001 101101000110011101000100011 110010101001101101100000011 110010110100010110001101010 110011010011000001011100101 110100101110001000111110000 110101001001011110010001100 110101010100100011100010110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100011101010001111001011 000110000011111010101100110 010001010010111011001011001 011000011010101100110101010 011001100001010010110011110 011010001100011100101010101 011100100011000101001110011 011110000100100011010101101 100110100010110100110011001 101000111010010011100100101 101001100101101000101101001 101010010111001010010010011 101011001000110001011110010 101100011001100110001011100 101101000110011101000001110 110010101011001001011001100 110010110100010110001101010 110011010001100101100000111 110100101100101011100010010 110101001001011110010100001 110101010110000000111110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100011010110001111101010 000110000011111010101010101 010001010101011100101001011 011000110011000011001101101 011001001000111011010011001 011010100010010100110110011 011100001101001010110100110 011110000100100101001011110 100110100101010011010001011 101000110110101010100011010 101001101001010001101010110 101010011001100100110001101 101011000110011000011101100 101100011100010110001110001 101101000011101101000100011 110010011010011111000000110 110010101100101001101100001 110011010001100010011110010 110100101011001100011011000 110101010110000001110010101 110101100000110110100101100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100011010110001111101010 000110000011111010101010101 010001010101011011001001011 011000110011000100101101101 011001001000111100110011001 011010100010010011010011110 011100001101001010110100110 011110000100100101001110011 100110100101010100110001011 101000111001100011100010011 101001100110011000101110010 101010010110101010010101001 101011001001010001011100101 101100011100010110001011100 101101000011101101000001110 110010011011001100011010010 110010101100101001101001100 110011010000110110100100110 110100101010011111000100001 110101010110000001110010101 110101100001100010011111000 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100011001110011101100011 000110000110111000111011010 010001010011011100101001101 011000101011001001011101010 011001100000110011100011110 011010010010010110010110011 011100001101001010110010101 011110000100100101001101101 100110100011010011010001101 101000110110101010100101001 101001011100010001011011001 101010011001100100110001110 101011000101011010001100110 101100101010010100101110100 101101000011101101000010011 110010011010101011001010100 110010101100011101100000011 110011100001100000111110001 110100110101000110001011010 110101001000111110010101000 110101010110000001110100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100011001110011101001110 000110000110111000111101001 010001010011011100101010011 011000101011001001110001101 011001100000110011001111001 011010010010010110010101110 011100001101001010011110010 011110000100100101100010111 100110100011010011010010011 101000110110101010100011010 101001011100010001110100011 101010011001100100011011001 101011000011101001001100110 101100101010010100101110100 101101000101011110000001101 110010101100011101001001010 110010110101000010101100101 110011001000111010110010100 110100011010101111000100001 110101010110000001011011100 110101100001100100110101010 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111101010110100 000100010110111010101101010 000110001001110001111001101 010001100011011001101010011 011000011011001100011101001 011001010000110110100011101 011010100010010011010101110 011100001101001010110010110 011110000100100101001110011 100110010011010110010010011 101000111001100011100100011 101001011100010001011011010 101010100110101000110011001 101011000101011010001100101 101100101010010100101110100 101101000011101101000001110 110010011010101011001010100 110010110101000100101001110 110011001000111100110100010 110100101100011111000001001 110101010110000001110100101 110101100001100010011111000 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101110100110011000111 000000110101111100011111000 000100011001110011110100110 000110000110111001101010101 010001010011011011001001011 011000101010011010110110001 011001100000110101100011110 011010010110000000111101110 011100001101001101010001101 011110000001100110001110011 100110100011010100110001011 101000111101000001101010011 101001010011101100100100101 101011000101011010010010110 101011001000110001011101001 101100011010010110001011100 101100100110101011000101010 110010011010101101010010010 110010101001101010101001100 110010110100010111000100101 110101001100011100101100010 110101010100100010110011001 110101100011000001011110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110111010000111 000000110110111100101110100 000100011011100010111001110 000110000111011001011100011 010001010001111001110011001 011000101001011011001101100 011010001100101010101010011 011011000010010100011011110 011100010101000110010110101 011100100010100101100101011 100110100001110110001011001 101000111110000001011011001 101001011001010100101100011 101001100011101010010110010 101010010101101101000001110 101101000110011010100001101 101110001000110001110110100 110010101011001100110000101 110010110100010010110101010 110011010010100011001100101 110100011010011111000010010 110101001100101100011101000 110101100101000001101010110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000111011100001111010101 000100010111011101010001110 000110000110111010101010011 010000110001111110100101001 011001001010011100011011001 011010001001101011001001110 011010010100100101010110011 011100100100010001101111100 011101000011000010110100111 100111000001110001011101001 101001010010111011000110100 101001100101101000110011010 101010011100010010110001101 101010100111001100001100101 101100011010100100101101010 101100101001010111000010011 110001110110000011001001011 110010101010011001110100010 110011010001010100101010110 110100011101001010011110000 110101001100101101100000101 110110100010100110010011100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000111011100001111010101 000100010111011101010001110 000110000110111010101010011 010000110001111110100101001 011001001010011100011011001 011010001001011001101100110 011010010100100101010110011 011100100110000011001101101 011101000001100010110011110 100111000001110001011101001 101001010010111011000110100 101001100111001000110100011 101010011100010010110001101 101010100101101100001011100 101100011010100100101101010 101100101001010111000010011 110001110100010001101011010 110010101010101011010001010 110011010011000110001000111 110100011101001010011110000 110101001100101101100000101 110110100010010100110110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000111011100001111010101 000100010111011101010001110 000110000110111010101010011 010000110001111110100101001 011001001010011001110100011 011010001001011010011011100 011010010100100001101101110 011100100110000100011111001 011101000001100111000010111 100111000001110001011101001 101001010111001010001100101 101001100101101000110011010 101010011010100110010001011 101010100010111101000110100 101100011001010100101110010 101100101100010011100001101 110001110010010011001011010 110010101101001101001000011 110011010100010100110010101 110100011100101011010110000 110101001010101100101001100 110110100011000010110100110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000111011100001111010101 000100010110111101010101001 000110000011111010101001110 010000110101011110100010011 011001010011000010011101011 011010001000111011001110001 011010100010010101010011110 011100001101001001110100110 011101000100100100101011101 100111000101010001011010011 101001010110101011000010110 101001100001111000110111000 101010011100010010110001101 101010100111001100001100101 101100011010010100101110010 101100101001100111000001011 110001011001011101001001100 110010110100100001101101010 110011001010101100110000011 110100101110001010011011000 110101100010010011100100101 110110010001100110010110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000111011100001111010101 000100010110111101010101001 000110000011111010101001110 010000110101011110100010011 011001010001010011001101101 011010001100101010011011001 011010100010010101010011110 011100001101001001110100110 011101000010100100101110011 100111000101010001011010011 101001010110101011000010110 101001100001111000110111000 101010011010010010110100011 101010100111001100001100101 101100011100010100101011100 101100101001100111000001011 110001011011001100011001010 110010110100100001101101010 110011001000111101100000101 110100101010011011001110000 110101100110000010110001101 110110010001100110010110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000111011100001111010101 000100010110111101010101001 000110000011111010101001110 010000110101011110100010011 011001010001010001110101110 011010001100101001101100011 011010100010010010011111001 011100001101001100011011100 011101000010100111000010111 100111000101010001011010011 101001010111001010001100101 101001100110101000110011010 101010011001100110010001011 101010100001111101000110100 101100011010010100101110010 101100101100010011100001101 110001011000111011001011000 110010110110000101001001110 110011001010011100110000101 110100101011001011010100010 110101100001100100101101001 110110010100100010110110100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000110111101101010010101 000100011110010001111001011 000110000011111010101100101 010001010001111100101011010 011000011001011011010101100 011010001100101011001010011 011010100010010100011111001 011100100101000110100001111 011101000010100001110110110 100110100001110011010011010 101000110110011010100110010 101001101001010001101010101 101010011001100100110100011 101011000111001000011001110 101100011010100110001011100 101101000100111101000101001 110001101010101010110001001 110010110100100001101101100 110011010010010111000000111 110100101011001101001100010 110101010101000010011110001 110110001100011100110010100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000110111101101010010101 000100011110010001111001011 000110000011111010101100101 010001010001111011001011010 011000011001011100110101100 011010001100101010110010011 011010100010010111000001111 011100100101000001101110110 011101000010100100011111001 100110100001110100110011010 101000111010100010101011100 101001100100111001100101001 101010010110011100001110010 101011001001010001011010101 101100011001100111000100011 101101000111001010010001110 110001101011001100101000011 110010110101000010011101001 110011010010100001110100110 110100101010011011010110000 110101010100010110100010101 110110001100101101001001100 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000110111101101010010101 000100011110010001111001011 000110000011111010101100101 010001010001111010110011010 011000011001011101001101100 011010001100101100101010011 011010100010010001110110110 011100100101000010011111001 011101000010100111000001111 100110100001110101001011010 101000111001100011100100011 101001100111001000101001110 101010011010100010011011100 101011000100111001010101001 101100010110011110000110010 101101001001010100110010101 110001101010011011001010001 110010110100010110100001101 110011010011000100011100011 110100101010101100110101000 110101010100100001101110100 110110001101001011010000110 011111111111110000000000000 001111110000001111111000000 000111111000001000000111111 000011001111000111100111000 000001101100110110011100110 000000110011111101010110001 000100011110100001111001101 000110000101111010101010011 010001010011011010110001110 011001001001101101001001011 011010010100010101100100111 011010100010100000111111010 011100001010011011001110100 011100100101000110010011101 100110100011010101001001110 101000111001100011100010110 101001100111001000101100101 101010011001010010011101001 101011000100111001010011100 101100010110101110000101010 101101001010010100110010011 110000111100011100101011000 110010101110001011010000011 110011010010100110001010101 110101010101000001011110010 110101100000110011100101001 110110001001101100110100100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001111010010010011100111 000000110101111101010010101 000000011111101110101001010 001100001011011001110101100 010101000101010011101010110 010110010000111001001101011 011001001100100101110100011 011010000110101010011110100 011010011000010110100011101 011100100011000100011011011 100110001010110111010010010 100110011101000000111110001 101001010110010101001111000 101010100001110100101100110 101011000101011010010001011 101100101100100011001001101 101101010010101000100010111 110001101000111000111011000 110010110110000001110001110 110011001011001101001000101 110100100110011110100100001 110101010001100110010101100 111000111001001011000110010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111110010100111110001 000010011001110110101001110 001100001010111001110101100 010100000111011111001011000 010100110001101000011101011 011000100101100101110010110 011001010000111110000110101 011011001000010001011011011 011110000110000010101100111 100101100010110010011010110 100110010100111001100010011 101001010110100101001101010 101001100101011000101001101 101010001101101010011110000 101100101001010111000100011 101110010011000100010011101 110010101010101101001000101 110010110100010011010101100 110011000011011100110100010 110101001100100110110001001 110101011001000001101110100 111000111010001010100011010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111100110110101100101 000010011010110101011011010 001100000110111010110110010 010100010111001100101011001 010100100001111011001001110 011001000101100101011110100 011001110000010000110011111 011010001001011110010101001 011110001010000001101100111 100101100011010100011100011 100110010101010001110101100 101000101011011101100010100 101001011001101000101101010 101010100110101000011001101 101101001100010011001011001 101110010001100110000010111 110010101101000010111010010 110011000100111101100000011 110011010010011010001110100 110100111000101001010110001 110101001010100110110001100 111000110110000111000101010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010111100101100101 000010011001110110011011010 001100001101010101110110001 010100000110111111100001010 010101100000110001011010111 011000110101001000101011011 011001001100100010111101100 011010010010011001010111100 011110000011000110001100111 100100110101010011001101100 100110000111101000111010100 101001010110100101001110010 101001100011010100110001110 101010100100111010010100011 101101001010011010001011001 101110011000100001100001111 110010101110000101011001001 110011001001011001101100010 110011010100010110100010101 110100111010000010110110010 110101010001101100010101001 111000101001101111000010100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010111100101100101 000010011001110110011011010 001100000101111011001110100 010100010110100101110011100 010101100001010000111010111 011000110101000101001101011 011001001000111001110101010 011010000110011110100010011 011110001010000010011101101 100100101110010011101001010 100110010101011000110101001 101001001111000100111110000 101001100100110110010001101 101010110010010001010110110 101101010010101000001011011 101110001001100101100000111 110010101100101001011010001 110011000011011101001001100 110011010100100010101100110 110100100011101110010100010 110101011000010111000110001 111000111001001010100011100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010111100101100101 000010011001110110011011010 001100000101111010110110100 010100010111000101101110010 010101100001010000111001111 011000110100010111000011101 011001000010111101010101010 011010001110001000111011001 011110001000100011001100111 100100101110010011011101000 100110010100111001100001011 101001001101100101101001100 101001110100100000011110011 101010100011011001001010110 101101001010010110100010011 101110010011000100010101101 110010100110100110110000110 110011000101011110001100001 110011011000010001110110100 110100101001101101010010001 110101010010101010001011100 111000111001001010100101010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010111100101100101 000010010101110110011110010 001100001011010101110101010 010100100110010011101010110 010101010000110101010011101 011000100101101101001001011 011001001100100010111101100 011010011000011010100011011 011110000011001000011110101 100100111101000000111011001 100110001001111011001001100 101001010110011001001111000 101001100001111000110010110 101010100110010110010001101 101101001010100110001010011 101110010100100001100100111 110010001110101101110010000 110011010011000100101001110 110011101000010001011100011 110100110010101010010101010 110101000101011110100100001 111000111001000111000110100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010111100101100101 000010001101110110111010010 001100100101010001011110101 010100010110010111100011100 010101000011011000111101010 011000110001101010001011110 011001001000111101010011001 011010011100000001101101011 011110000010100110010100111 100100111000110011010101010 100110010110101000011011001 101001010101100100110101100 101001100110010110001001011 101010010011011101000110010 101101001010100001101010110 101110001001011010100001101 110010101011000101011001100 110011000100111011001100100 110011110000010000110010111 110100100101101101100000011 110101011001000110001110001 111000101110001010110110000 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010110110101100110 000010011101010100111011001 001100000111101000111110100 010100010100111111000110001 010101000011010101011101010 011000101001101101001001101 011001001000111010110011010 011010100100010001110100111 011110010010000010001011111 100101100100110010011001101 100110010001111001100001110 101000110110100101010011010 101001110001011000001110011 101010001110011011001101000 101101001010010101100010101 101110001001100110010100011 110010100011011110010010100 110011000110101100101000011 110011011000100001011110100 110100101101000011101010010 110100111010001000110101001 111001010101000110100101100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010110110101100110 000010011100110101011011001 001100000011111101010110100 010100010101101010101011100 010101010001010100110101011 011000101101000001111110010 011001100000111001001001111 011010000110011110100010011 011110001010000010011101101 100101100110010000111010101 100110001011011001101001010 101000110111001100001101001 101001001100111010110101000 101010110001010010010011110 101101001001100110001010011 101110010100100001100100111 110010101001101100110000101 110011000101010111001100100 110011010010101000011110010 110100100110100111010001010 110100111000011011000110001 111001011010000101100011100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010110110101100110 000010011001111100011011001 001100000110111101100010101 010100010101100101110101010 010101100001010000111010111 011000101100011010110101001 011001010010011001001111010 011010000111000110011110100 011110001000100011001001111 100101001100110011011110000 100110000111011010101001010 101000111101000001101011100 101001100110100100011001011 101010100001111001010100110 101101010001010110000101101 101110011010000000110110011 110010110100010111000010011 110011001010010101110001100 110011010100101000101100101 110100101011001101001100001 110100110010101010010011100 111001001001101110100010010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010110110101100110 000010010101110101011011100 001100001101010110110110001 010100100100111011001010011 010101000010111100110001101 011000111001001000101011101 011001001100100001111101010 011010010010011010010111010 011110000011000101001100111 100101110001010000011101011 100110001011101000111010010 101000100111011101100001010 101001010110101100001110001 101010101000111001010100101 101101001010010011001011100 101110010100100010100001111 110010101110000110011001001 110011000101011010101100100 110011011000010101100010011 110100011001101111000101000 110100110110000001110110100 111001100001100110010010110 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010110110101100110 000010010101110101011011100 001100001001111110010110001 010100100101011010101001101 010101010010010100110011011 011000111000101001001011011 011001000110101000111110100 011010001100010011110101010 011110000011000101001100111 100101100100110001011100011 100110001011101000111001010 101000100111011101100010010 101001011101000100101101001 101010110010011000010101101 101101001010010011001011100 101110010100100010100010111 110010101110000110011010001 110011001000111101100000101 110011010001011010001110010 110100010110101111000101000 110100111001000001110110100 111001100001100110010001110 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001011010000111 000000111010110110101100110 000010010101110101011011100 001100001001111110010110001 010100100100111011001001011 010101010010010100110011011 011000111001001000101011101 011001001100100001111110010 011010000110011010110101100 011110000011000101001100111 100101100101010000111100101 100110001011101000111001010 101000100111011101100010010 101001010110101100001101001 101010111000010001010101011 101101001010010011001011100 101110010100100010100010111 110010101110000110011010001 110011001000111101100000101 110011010001011010001110010 110100011101000111100101000 110100110010101001010110100 111001100001100110010001110 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001010011100101 000000111100110011110010110 000010011010111101001001011 001100001011010110101110010 010100000101111111010101000 010100110001011000101011101 011001001100100100111011001 011001100010010001011101110 011010010101000101100100111 011110000010101010010010111 100101010011100100110001110 100111000101010001011010011 101000100111101101001010100 101010010110011000110111000 101010101001010110010001101 101100110100100010001101011 101101001000111001100100101 110001100110011110100000011 110010101001101000111100010 110011010000110110001110100 110100111010000101010110001 110110001110000011101001100 111001011001001011000011010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001010011100101 000000111011010101110010110 000010011100111001101001011 001100000110111111000010101 010100010101100111010101010 010101000001111000111011100 011000101100100100111110001 011000110010011010001111010 011011000001010101001100111 011110001010000010110001111 100101001010110110101100010 100110100101010010011010011 101001100110100001011001110 101010000111011100110101000 101010011001100110001011100 101100110001101000100100111 101101011000010001010111001 110001110100010110100001101 110010101000111011010100100 110011010010101100010010011 110100101011001101001001001 110110010110000001101110100 111001001101001011100010010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001010011100101 000000111010111101010010011 000010010110110110101001110 001100000111010101110110100 010100110001011000101011101 010101001000110010111110010 011000001101101111001011000 011001100100010011010001111 011010011001000100110101011 011110000010101001001100111 100100110101100001011101010 100110001101011011100000011 101001011000111001100101100 101010101100100000111010101 101011000011011000011011010 101100101010010110001101001 101101010001100110000010111 110001101011000101101000110 110010100001111110010100100 110011010100010101001110001 110101000110101100110001001 110110011010000011010011100 111000110110001010100110010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001010011100101 000000111010111101010010011 000010010101110110101010110 001100001011011011100001110 010100100110010001111110100 010101010000111000101101011 011000100101101101001001101 011001001100010110110011001 011010011001000001011111010 011110000010100110010100111 100100101001110110011101000 100110011100100001110001101 101001001110100101101100010 101010100101011000110100011 101011000010111000011011100 101100110110000010001011011 101101010001010101000110101 110001110011000100110001110 110010010110011111000101000 110011101000010011001000111 110101000101101011010010010 110110001011001100101010001 111000111000101010100110100 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011100011100011100111001 000001011111001010011100101 000000111010111001011011010 000010010101110110110010110 001100001100110011101101100 010100100001111101010100101 010101001010010110110001011 011000111001000100101011101 011001010100011001100110011 011010000111000101011101010 011110000010101010001010111 100100110110100100101100011 100111010001010001001001111 101001001011101101100000110 101010100110011000110001101 101011001000110100011110001 101100010011011110000111000 101100101101000011010010011 110001100110010111001010100 110010011100101111000001001 110010101001011010101100010 110101000101101000111011000 110110011010000001110110100 111001110000100010010101110 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011011011000011100111001 000001100110111011010100101 000000111010110110101010110 000100010101111101100001011 001010000111100110011101010 010010110001011000011110011 010101001001100001111100110 011000101101001010101001101 011011000000110100110011101 011100001010011011010011010 011100010110000101001110101 100101010101010010011011100 100110001110101000111010001 101000101101010101110110000 101001011011001100010000111 101010011000111001001101100 101101100010010000101101011 101110100001100011000010111 110001100011101101001011000 110010110110000001110001110 110011001100010111001000011 110100111000100110010101001 110110000011011110100100100 111001010100101010100110010 011111111111110000000000000 001111110000001111111000000 000111101100001100000111110 000011010011101011000111001 000001101011010110110100101 000000110111011001101010110 000100011100110111100001011 001010001010110101011110010 010101000110101000111100011 010110010001010010011101110 011000100101100110101111000 011000111000101010010010111 011011000100010001110011101 011100001011001101001001101 100010110110100100011001101 100101001101100011011010100 101001011000111000101101100 101010001111001010110001010 101100010101011100010110001 101101100010010010001011011 101110100001100001100100111 110001100001111101010001010 110010101100011011001100001 110011011001000100101010011 110100111010000001110111000 110110000010111110100010100 111001010110000111000100110 011111111111110000000000000 001111110000001111111000000 000111001110001110000111100 000010111001101001100111010 000001100101111101010100101 000100011101011010011010011 001001010010110011001111001 001010000111010011110001110 010010110110000101001010111 010100100011100010111110100 010111000000111000101001111 011000101010011100011101010 011001011001000110100100111 011100001100100101110011001 100000111100110110101001100 100101110110000000110101011 100110001011010101101100001 101001000111101100101010010 101011101001000000011011101 101100101010101011000000111 101110010000110100010110110 110001011010011001110010100 110010010011101110010001001 110011001100100011011100010 110101100001010111000011010 111010100100011010100110001 111100010101001001001101100