0011010101101101010000111101110001011110000001111011011101010110011101000101000101110101011011001101001011111000100000000000100110001111000101000101011111100101001001011111110100000000101100100100101101111111110101101011001110110100001101101111101100001010110001111111010000011110111000111011000010011110101010110110011000001000100100000101110000101010110011111000011100010010010000110100101101000000 0001010011100111100110111110001010010101110100010111011010111110101100010011000111110000110100010100111011010100011000011001000101010100011010111101011101001011010010100100001111011100001101001101001110001001011100101100101011100100111011111110110001101111110010001000110100000000001010100011010010101110010010011100011000010110111111010101001111001001101011100011010010000010110000000110111110011010 1100111000001110100101011110001011010011010111101101010000100011111011011011101000111001000110001010001001110111111110010011001101000001010100101011011011001100110111011010000110101101111001111111011110011101001000010000000110000001001101100100100111101001001010010011000011011111101001100110100001010010000101101111011111111110110011111011001011011110011100111010101010000011000101001011100010001001 0001100110111000101111001001100010110010010000110010111101100111111100100010000110001111101000110011100111101100111011111110100001101011010000011001000110101000001101010010111111100111110111001101111000011111010011101101101101110010101111011011010010101100111000011111101111100000010000001001110011001101001110110010011000011001000010000010100111111001011010110101000001100110101111100110000100000101 0000110001101110110001010001101111111011111110111101101001110111100010101000111011100110010110100000010111010110101100101001100001100111100000010011111100100110110010001110011101110111000111110010100110111001110111100001101110000011000110010111011111100101001110001111001101001011000110100000111101100001010111100101110110110101100011100111101111001101100101000011111001010011100100100110100000010100 1101001110100010000110010001000000111011011000100111001110110001011101001001111000000110001000101000101111010011111110101000011000111111100000100100001001101010000011110110110001000111011011000100001010100001001110001100111010111011011111010011110111011111011100000111001100011111000110101001111100011000011001000111010000010010000111111010001010101100101110110111001000010011100110100110010001111000 0100011010010010001001010101011101011111011110100000000011010011001001010011001110101000100011100001110110110110111111100111111001101000100001111010100011010000000110000001001111101100110101100100001011010110110100110110011110101010001101111111010111000100110011110001100111000000100110100011110000100110100000101101010011111100011010000001101110010010010000001001011001100000000011101001001101111010 1100000101001010101111101001110000000101010001000111010010011101010000101111011111010110000101101001000010010000111000011010101001000111101010010000111010111011001100001011001011101001010101100110001001101010110101110010111010001011110110000000100111000100001100100011100100010000101101101110101110100100000100110110100110101111110001100011100010101000011010011110010110111011001011111010110100000101 1010110010011101001110010101111001101000010100011111010111100001000100000011000010111001100001000101110000010010000111001001000101101000001111100011001111001101110001110111110111001001011001010110100110001111000010001010110001101011111011111100110001000110100011100011101110010101100000011100101101101010000000011110111011011111100001010010100000100110000100100101000110011111000111110110001011100001 1011101101001010001111011110111001001110101000101111111110000101000011000001000001000001001110010110110111100011011011011011100110010100000001000110000100111000010101001000011111001110100110101010011010110100100110100110111101001110010001111000001101110100000011010110011110101011100110000000100000001011001000110100011011101010011101101000000111000010000110000001110101010111001001111010011001101001 0101000111110101100000000101000011001010101001110010101000010100110011000101111011000000100000011011001011101101100001000010011010101001100000000101001001100111011110001001001011101111111000110000101010010010011111110100010010000010000010000100101110100100000111010011010110100111101110111000011000100101101110100111110100100011001010001000001010111001011000101101111000100100010111000000011001101111 0110000010100110011000111101100001011111110011000010000111001101110110001100111001101111000111100100010110100111010011100101110001010110011100010011010010001100000110101110111101000101101011011100010010101111101110101001001001010001100100101110000101010011000100000110001010101001010101110011000011011001111101000110010101111101101001110010100111011111001101011000100110110010101011000001001011010001 1011101111100110011000000010101110100011101111001110100100010010100100000001011111100010111100111100111000000101110101000001111101101001001010101010100111000101110001111010011001001001100000010001110010001100100001011101110100101111001011111000011011010110001111010111001101001111110111001110001110000110001001101100101000011010011111010111110101011110010111001110100101000011000011110010000000010100 0010100001000110001110101010100010110101100101010111010110000110010011010101100010010111110100001010000011001010000001110111011000111110110111111010001110001001110101001010110111011010000100010000000000001011001110011011101101111110100111000000000101100001110100001101001011101101011001011100101111100111000011001011110100001101010011111111100001100111011000000011111000100100101101100011110110101010 0000110110011011110100001111010011010000111110100001000100100001001111000001011011000000101010001110010110010111000000100000000000010001010011011110011011111110001010011011010010011011111100010100000010110111010001011001111001011110000010011000010011010111000010000111001100010010000100100001000101000111110111010100000000101001001010011001101011010111010000000001011100100011100011011000111001000011 0110101000110011001100100000000011001100010111001010100001110010000100110011111001001011110000100110001101010101011110111101101100010111001010110110000110111100000110000101101100110011011101000110110000001101101111100110101101111101001110000110000110110100110001100100101000111000000101010101111101100111011111110000110001010101110011000111110111010000110010000000111100001100101011100001110001100100 0011110001000000100101111000100111111111101000011011011110100101011011101011101001101110011010100101101100000010111011101001001001010000011000111110111101011000011111010010110101000111111010011111000000000101001100000001101000110111110111001100100010010111110000001101000111010101001011111010000100010101001111101111011000000010010000100111100011011010101010111010001010111111100100001011010000110010 0100000000000010011001000110100011101001101111110110110011010011010011001011111011111101101100011111111011000100111111100001011110011111001010000111100011001110111010100101100011001010100111011001110111000100011100001000001111100100101100011000000101000100001100110001000111001000011001001011101111100100101011010001010110010110010101101000010101011000001000101010111010001110101101110010100110001110 1100111100100010011010010001111111101101101110000111011001110110111101110111100111110010110001110110000001010110110111011100000100011000100110000011011110100111011010100001111011111010010010111101000000010101110001101110110111111110110111100001010000110101100001111101001001001011011011011010010111011110110010010000000010100000001000100010000110100101110100111001101000110000000111011111110000101011 1010101000001001000010011010111100111011010000001111110101101011100111110111101100111000011111111100010000100100011110011101101111110100101010111000110001100111110101000011001101101011001100001110011101110110101110010000010011110110001111101010010100001100011110111111110110011001001000110100011100001110100000000011000010111110101001010101110100110101001011101011001110110001000001010100111010100101 0001110000100111001110100000111000011000010110110010100111011001100100001001111010111100010101010100010110100110000110110010110010010010001110010000011110000011111111100100111100100110111111010000110011001001011110101101111011101100010001101010101100001000100000101000010001100011010111011111101000010101100101010001001010111101010101010011111011010110011101010100001100010101001110110001100011011111 0111101000001010110101000100010111100010111010100010100001000111101000101101001010110010001011001000111010001111000101010111010011000100000000010100100111111010111111001001000101000001111111001000001110001001110101010000101011101001101100011111111010100011011011110000011101111110011011100100110100111010101000110100101001111011110000111110010000101111000010010000000110110111111010100011100110110111 0011011110110011110011011100011000101100010010101101001110000100101011100101111100011000011000100011001000010000110001001010010101000110100101100011101011101000100110110100101111101000000001000011100011000101011010101010110100110010010010001010110010011101111000100111100110110110011000111011010001100010101011000111111011101100110101111111011111100110110010111101001010111111011111011011111101010010 1011110111100000000010111110011000111011101111110101111101010101011001110100100101101110100000101001000011011011100000111000100101100111101111011110111000110011101011101110011100111011110100100011110001010111110011011101001110110010110001111111110100101110100111011000011101111101111000101011000010010011000101011011111100101000011011110010110010010100000100010000100000100010100010100000101010110101 0001110000100001110101100010101010000100100111000000100101000011110010010011001110010110111100001100101110010101111110011100001010100011100010101000000100000010110101110110011010111100111101110010011101110001011011001101101010010000111001000110001100000001101111110101101110111111000001101101011101001001001001010100101000110010101111100111011111101111010000111011000010111000101000000010101111110001 1100010000110101101011100011110001111100101101011001000011001010110101101010011000101101011011001100001100010001010111011100001001101000000111100000000110011100111111100001010000000000100001101011101111000011011110001110101110000011100100001010110010000101100010111011010111001101010011001000110101101000100110100001010000111111110101011111001101010110010001001101100110010011011100011000100011010100 1111110100100101110101101100101101111001110010001100111010010111011101010110001001011110010000100011001101011010100011111111000011001001011011111111101100011000000000101100100010101111110111010001110101000111001001111111110001001000110100110101011100000001101000110011100000111011011001101000011110111001101011001000011101001000010110010101011110011001111001001101001100100111001001110001100001000001 1000000000010011001010011101010000010000110101000110000010010110111010011011010101010100100000000100100000101010011111010010001110000100001100001010111000101011010111011010011011011101011000110011001001101100001010001110011001101110010111110101110111011111100000101110100111100101100111101001100000010001101100011111100000011111010110110001001001000011010001111011001010000111000110110011011000110001 1110010111011110011100010011010000110110100111100011010101101001001101010111110011101110111100010110011001100111000101101111110000101100001111011101000100010111101100001110001011110001000000110001101000111010010100010101010010001100101001001011100111000101000010001000110010100111000100101100010010001101010011101101101100111000101010101110010111111011011110101101110010011001010110110011011110101110 0011101101111011000101110000000010111110100101011001111011011011100000101111111001000001011100101011010010011110111100101110101110101110000001000001101010010011110000111110110011010110110010000111001010001010010110101000010010100010101011100011101011101001101100010001001001101110010101010001010101000000010000100101110011000010001101000011000010001010011100110101100001011001101100011100001111110100 0000101101100010110110011011100110010110110010100011101101010110010100100111110000101011111111001101101111011101111101110110111101101010101000110101011010111101110000111110100001110000010111000110011000010100111101101001110011100010100000111011011000010110011101010111001010100101100011111110100011101101110000110101110111111100001010101111111100111000111111101001010010110000001101001111010000000100 0100100100110010001000011111010010110111011010111001011011011001101110011010111110111001110100110100000011100000100001110101000011010101111011110100001010010011110011110100111111111001010110001011010011101001111111110000010111011100011110101010101111110000111000101011000111101111110110110110111100101000101101001111011111010111100011110011011101110011100100000011100110100101111000110010101010100011 1110100000000000111101100011100010010111111101100010111110011111010101011000100001100101000110010101001000000111101100000100010011111110000001100100011100011000001101100010111100110110000000100100010101011000110110011010110000111010001011001111001001101011001000101000010111100000101110010010000000000101100010011111101001010110110001011010010100000101111101101000111110100001000111100101110101011111 0001001000010100111000111111001000110011010111111000101001010011010000010111101100000000101011110000000001111010111100110011100100011101010110000011100100101111010000010110110011000000110101001000011101011011001110010100011101011101001101011110110000001011010000100001011011101011111001011110101011000101011101101111111000110000100100011110000011011010100010100101011110001010000101000101111111101011 1011011110101011110010100010110010011111110110001110011111001010001000100110000011101110010110111011110001000100010100000000111101011100100111001010010111111100010011101011100001001111101001000110101101101100110010111001000011101011011000110110000101110101101000110011111110111001110110110101000110110110000101000100111110001110100100010001110100110111101010110110111001011101010111101011000010001101 1000101010000111100001101100010011001100001000011100111011110011001101011011101000100111111011110110100101110010011001111110111011101111000000111000000000101011011110000111000100101100011100000001011010011000011010011000100111110010001001011000011101010010100010010010100111100010010111001111100000111011111111010101110001101111101010000011101100110000001001001100000011001111111010101010100111001001 0100000111010011101011100101110011010011101111001111100000001010001110111111101110111100010010000010110010111001001100010001111110011110111011001111101100111101000010111101001001011100110001000110011010111000111001101101011000010100010110111100100011111001100011110011100100010101100011101011000000100001100011100111011100010101100101100111010110011100101010111011000111111001011111010101111011100110 0000000101111011011100001011000101010000001001011010000101100111110111001101101001111101010110011110001110010110011110100011110100001000111111010000110100000000010010100101011001010000010100000011010101110010101100100111100000111110011011100001100110011011001010101101010101000010000101110010001101001100101100110000111111101110111101100001101010010101111100101110000010110001111010011011010100011001 1010000101000100000000001011101101101000110010110010001100110101111011110110010101011111101010111101011000110101010100111001111001011100111101100110001001111011101011010011011000011101001101000100111111111111100010100011001100100111111011010010010111101001001110101010110001011010111110010001010110110010101111110100111000000001000010001110001010100010110100111001110101111000001001000110011111011111 1000011111100000111001011111011000111000111011101010011111110000001100110100100010101110110011110111001100010010111111101011011010100011100000001101010100110110110010001001111110011101011011110011100100010000001101110110010111100010100111000100100011111010100001001010001100011110011111011001101010000000000100010110101101101001110011100110011011101011010010100111110110001101100111100010010010100110 0110111101000001101111010100101100001100111100101011011010101110001000001011111111100010011110010010000001011110100000010101100001100100111000101000110100000010101001001011001010011100010100110010000001101111110000001000001111001001001101111100110010110111110001110011101000110011001110110101111011110010011000010110110101000111011101000010110010000000001011110001011111101111111000000001011101100010 1001001110011110101000001110011100111100110011110010011110111111111010010101100000001000110110111010110011000110001011010001011101100101101101101011101001100100000011001111001010111000110101010100000001001101100100101000100111111010100100001110111110011000100111011101110100000010101000111011001000110111110101100100001011101000001110001011111000000000011110100001101101100010010100100001111110110010 1011001111101111100010001010010101100000101111001101000011111101010010001010000100101101110110010101011011101000111011001111100000100111000011001001010100111011101100000000100100010100010011111011010001011001000100100110000010011110110001000011101111100000101100011111110111010101101011000111000001100111000111110000010101010111110100110110001001010010000111000001101111100111101101101000001001100001 0100000101101011011001111001100010001011000000010001001111011111110010110110000111101001010111110110111111011101110101111010111110110001010101010110000000010101010010011100101100111101001011110111111010001011101101010010101100101010000100010111100100111000101011011000000011100101000010101011110110111111011001110100010111111011011000011001011011101010011100001011010001001101000011110000111001011111 1011010101001000010111101000110100111010001100101100110110011110110011000101001110001000011111011101111110010110111110101011001110110111000101100101101100101100010000010010100110111000100000000000101011110111011101000110111101000010110110110010010010011110110000101000010000000111010110010101110100000000100010010110011111100111010111101011100000111100001010001001001111111100100000010001100111101001 1101010111000100111010110000011000110011100011110001001011011001101010111100000011010101111101000100110101000000101101010010011111101101001101010110001100101011011110010100110010101101000101101101111111000010010000100001100110110001101011011111001000110101000101101110111101011010000111110100010001001101010011110100010011101110000010110100000110001001000100001001011001011010001100101001000000010001 1000010101000010101010111110110001011101001100011011101011010001001000000011110100111111111010111101111000011010011111010100011100101010100011000011001101010001000001010010000011010101110010110110011001010111101000010011110010000001111111101000010010110000100100100010011001000010111111011101101000001111101000100111000001111101100010100110000010110110010100111100100010011001111010000110111110011110 0001011100011111001101100011101111010000000001010000101101011010100100011001001000101101100111100011101010101001010001011010111011100010010010101110010011111100101001100111011111011110010100101011111000100001011111100010011111100111001011010011011001100010010111001011000000101011011001000000001110001010101111100011010101010001101110110101001011110011010100011010010110011111110001101111000010010010 1010100000001111111110000010010001101000111111101001101111100110001011110100010011010000110010101011001110111011010110000010010101111010001001110001010110110111001000111111010101100111100001010001010001111001111011000100000000101011110001111110011100001010000101100100010010100111000100100110100011111011011011101110100010111010110110000101110011001101010001010001010111001001011111110110111100000011 0000111011111110011010101010010100101110000110110011001000111010010110000111101001000011111110111011100110010100111011011011110000100011111101001001111000000001101010000010100001101101011010001010010100000001011100001000001011110111010110010111101000000011010011001100111010001100101100010010000010001000101110101100001000011010101110011100000101101000011010010001101010001000010011111001101011100001 0011000111110011100001001100011110000011100110000001010111011001010001001101111101110010001001000000000101100000000010110111011101100001110111100011100110111110100100001001010110101101110111001111010101100101001110101001111001110001111011011011001000010001000100011111110110110011010001101010010111100000100110101000010011010000111101001000000101100110010110111110010100111000010010011111110011110000 0100110010101110101011110110000110011110100111100111001011001101111011011110011101000100010001001100111010100000101001110010001010001111000001110101111011001001101010101010001010100011100111010010011110000110110101111101110100111110101100001010000110010111101011101111001110001001000111000100100001110111100010010100010001000010000010000011011111001001000110011011100010100111101111111001011100100010 0111100101110000011011010000001100000100100000101101100100001110101011000001101010010110111010010111000000111000100010000000001100111001000111001100111000111111001001010010110000010101110000110001110000100100100101000110001110100000011000011000001101100010000111011001011011011101010001101110010001110010000011110000011111101010010101110010010111000010001100000110001110011011011001111000010001010101 1001000100111010010111111111100011011001110101101100011100011111010001110100010001010110001010011011100111000000111010100010110010010010001101000110010000000101111110101001101101000111110101110010100000110100110010001110110001100010011011000111101001110001001011111110100101111011010011001011100101100101101010011111001101100001111111110101011010011110011100010010011110100010100111111001000010010111 1111000110011100111011101110010101011011000010101100100001000010011001100101011100101011001100110100011111001111011001101101000011111010110010110111101011111111110110110101101111101010000101000000011011001000010000000110110010010001000110111011011001111000100011110100010100010101111010100000000010101010100100011111000011010100101101111111001000100110000111001100000111100110101001010110100100011001 0001010001011010000001010001110011101100000101011011110000110001110010011100101000010001101011101011100001111110100110001100000100000110010011011001101000001110110100100111111111101111100001001110100110001110010111110000001010110011100111111110111011110110100010110110001100010000110011010010001101001110010101011010100011010100000001000111110010110011100011001000000101001101101001001001100010101010 1000010100111000101111010000101100100001011001110111011110101011011100101000000110000010101110100111100101011110110101001010011100100111011000110000001101010000001001001000110111101000101101001001101010100101110110010111111001110001110011101000100100111000001110000011101000001111110010001001000010010101011101011101001011010110000010010001111001100011100010001011100000101001101010110001100011110110 1000010000111100001001100110101111010001000000000000001110100000011110101101000101110100010011101111111010000010111101101011101101010001111110110011000100011111110101101101011111110011000111000111100000111100111101010001100000100111110011010111010010101110011011110011000000110000100110110000101110101110010100111111011100101100111110110000110000010010010101010000000010101000011111111111001101010011 1110011110000000011011111100101101011011011100110111110101001001001100100101101000100111010010000100001000111010010011000001100111001101010101000111000000010101101001001010100101001111110001000010110110001011110001111000110101100011111101000101110101010100100101101000010010100111101001101000111010001101000010100100110111011001001111010000011011101010110001110011101000010100011111101000001010001111 1101011100100111110001010110011100100000100001001001011001101000001001100111110000000010001111010001010001001001101100011010111010100111101011100111110101001111010010010001001111001101101011010011100011000011101110001111000101100110101100100001001000010110100001100010001000010110011010010100111100111001011001011100010011100000110010110101000100111000110001111100111000101011110001100001010100110101 0110010011111010100100011010000010000110001010101110100101001111011010101000000110010110111010010010001101001011110111000011001110100110101000110011010010110010111001111011001101010111010010000101000100111010100000000110000111010000111110000100100111011000100111010000110111010110101001101000101111000011000100010011111110000100110001000010011100111011000111100101111010000011110001011111111010111000 0010110111111100100111111011001101110010011111001110100110110110110011011001000110001011101110000111101100000000101010101001000001101100101100010000010110011110010010100101011101101010101101010010010001001010100011100001000001101010010110010111010101011110001110110011011001011010101011101011011111001111111101010111101000011100111110100010110001111111011000110101110101011110100111101011001010011001 1100001011011110110011100010110001000010111010011111000001001001101000010111010011101100100011001011110000100100101101011100110100011001000111011101110010110110110000011110011011011011000100000111111001100100010011001100110111111110101000001010001110111010010010110110101001000000110101010111111011011010110011100001000011101000011111011111100110111010000010011010101000100101000011010010010101101111 1100001000111001111010010010100101000101100111000100001111101111011110101000000011001000110110010100011110000010110001110001011100110010001000001001011110110001011100010011010111111100010100000011110110010000110100110011111001110110101111011010001100010000101100101110101000000001100101110110101010100110110101100011111000001100101100011111100011011001010011101100101101000100011000110111101011001110 1011111101101000111011001001000101000010010101000101110110011000011000000100111000100001100100001101100000010100001011111010111010010010010101000101100001011011000000011000000111000011101010001101000101111100010001110111001001011001001110100001000100100101000011011001000111010000100111001111011001001011010110101100000001000100110111010001011011011111001010100110100100000010101100010100110110111110 0000101011101010000011001110000010111110100110010001100100101100101001000101000000001000100100111000110111110110100101110100010100001000011110010000111101001111100001010101000010010110100001110000110000110001011000010001010011110111110110011101000111010100100011111100001000101110101111100101001010001111001001100000000111111111100110111111000001101100000100010010011001101100010111100111110010000101 0111100001100000001001011111011100100111000000110001000101011111001011001010000111010000010101000010001111100000111101111010100010000100000001000111111100101001010010100000101011101010010011110111111000101010101001101110100000110011101010011101111110001000110001110111010001110011011100100011011000111010010100010000000101001010111011001000111110001010000000101010100101100011110011010010000101111000 1010001100111001101101011000110001111110100101000110001110100100001000100001000111010101000110001111010010111101101100110000001011101110111110100100100110110100101000111011000111010111001110110111010011010100000000110110110100101111001000101010011011001100101001100110111110111111011001010111010000011110011111101010011000001100010010101111010110111000001100101100000100110001101001100100000010010100 0010000100000000001101010011101000001000110010010100111100110110110001001101100000100100111001110010001010100110111000101100001000000101011001011010011111111000011011010001001100001011101111010010110101011110010101111111111111011110001010101001011111001100011001001011110000010101011000001011011100001100101100100101110101010010001011110111010100000000100001110110011100100101000100010011001011110100 0100000110110010110011000010000010100101011111100101010000110110101000101011011111000111111111010000010101001100110111100011100011001011101100111010000000000011011011000001000000110110110000011111100110100000000010101000010111110100011110111110111110010101101000111010101001011010110001111000101001110101011000001111010011011100000110110111000001111011101111110010000100101111000000000011111111100010 1110010011000011110100111101100000110001000001001111110110011111000001100110110000000110010010010110101110111011110111111100111010001100111001100101100101111100000110110110000011010000101000100011000001011101110111001100101101110010010100111111000100100000111010111001000110100010110101110101001010010100010100000000011011010000111100011001001100001001000101000111101100101111111010011110011110011010 1101110011101010000000010000011101111111010011111110001110011000001000110110011001011000010011100010111111100110010010001001101110001001011001000001011110110111011100101110010100100010011101001101101010110101001110110100001101101110011111000010000001011011000001101000101001011010000001110111101100000010100111110111001001010011111000011000111001001001011101100011000101011000001001000110100100001011 0011010001100111100010001111010101111001010011101100110100100101100101010010010111110000000001001110011111000010010110000110101011100110010010011111000000110010000110010000101101000001110110111110011001101111111111101001110110011001010011001101000101010001101110000010100001111111100111001011011101110101011110011010101001011111001000111000010001110101101111111110010011010100111011110000100101011101 1111010001110010010110011111111111101010110111110110101101001100010110011010001011100001111011011011110010101011101110110111000110100010111111100001101110010101011110101001111100011101001001101100011010000110000101000101100101101011011100001000001110111011111001100010101110001100111100110010001100111101101010000010000100001110011011111101110111001100010001110001111100100100010110101101100110111010 0010101000110010101101011110010101001000011000010111110000101110101010000010101000000101000110110001111101001111101010101110101110001101001011111100101011100000000010101111011001010111100100111011111001101001000000100000011000010110101011100111101011110000110000110100110110010100101011110011000111000010001110000011110110100010110011111100101000001111110111111010001101110011001101011101011011010101 0100001011111101011100111011011101010011001011000100100110100110100010000000111000100100111011001110100100011010010100101100011001100100110100101001100011101111001111100101011111010100111100000111101101100110010001010010000100001001000000100000010110011001101011100101000101111010101001110100101011001000010000101011000111000110110110001110111110010111000011000111110101010001101001101000000101001010 0001000010000010100000010011001010000100101000111011001111010101110000110001100000101011000011110100111111001110101000111111000011001011110100100001010111010011101101110100000111011111011011010100101110000000110010100011100010010011101011001011110100011000110000011100101101110110111111011111001110001101000101101111110101011110001101101111101101110111010101101111111001010000101000111010110010110001 0111010100000001110010000000110000100001001000011000000000000010110010010100110110110001111100100010010000001010100001110111101000100110001101001000101101000100101101110100111100000010001101101010000010000101100001111010101001111100011100010001010000111101101101111101010001011001011101101000010101100110000110010100010101100011001111001111100011101000111110100001111010000001010000111000001100010100 0101010100101000001111101111101001000101101100101100001000000101101111010001000100111010100101010000110011100010000000010110101111001011110011110110110011100011101001101100000100111010001010101111010011100011111110011011010001001011111100000001101010110011001111110100110111111100011000001101111011101001111011110001011010001011100101010110110001000100111100110010100110110100111100010010001111010001 0100011100011100010111110000110001001110001101110011101110011111011100010010011101110101011110010010011110000100010001100110001100010111110110011110000000011111101111011111001001100100011111000010011110111100010000100001011011010001111100010000000000101111101001110110100000011011011011010000001001010111001100010000001111111111110101111101101010100110110101101011001110000011101001111011000011010000 1010111000011011011000110011010000111101011100100001110011001101010011110110111011001010111000000111110110010010011101110000111110101110111001100111001111100111110001010100010000111101011111100100100110011110010001011100001010100001000111011001010110101101011110111100100011110110110111101011111000011111011101000110010011110000001110110100010110011011101011011111010100011000110101001000010110010001 0011011100101011111010011110111000100010111101111111110101110010100001001101111001011101010011010111000010010011111110100001000011010111011100101000001111101011010010110100000100001011111100101000101010001110011111010110001010001000101110010101100011110101000100011010110101100010111110110110000111011010101010101000001111011111100010100101000111001011010001001100011001101101101101110000011001011100 1000000111010011100010001001111110011111000100010001000100110000110000001101110110011000100010011111001101100101000000100100010111110110101110110100010010100001100011010010011000101010000101101110111010001011001110111110000011001101011011011010100101111101101100111101001000111010101011011110000010100010000111011001100001000111111110011011100110000010111011110010010110000000010101100011001011101011 0011100100100010000101011111101001101110011001110111101011100101100100000000100100010001010110110100010011110100001101011001101111100111000001111001111011000111110000011000010010100111010011111000101110000101000100100001010000001100001100000000100111110101101111110100100110101001110110110101000110100010100110110000011001110001000011011101111101100000111001110101010111101111100001111011000101100101 1100011001011001011011010111111110101001000010011101110011000111001110001110001110100000101001001110111101000110000101110111000001001100011101100111011110001000100011011000100101001011011100111101111000000111011110011000110111010011100000111000111101111111010111010001110100010101000100010010010110110011100110010110111111000000110010000001001111010010101001011010010011000001000100100100010110101111 0100110110001110011111111100110010101110101100100011011111010110100000011100000110100101010010010110011010111101101100111011101011011111011011010101111111110110010110000010110011111110011011110110010100010101001101011110101100111111001011110001011001111000010010011100010000100110101110001000101101111001101010110011000000011001101010011110000001110110110010110000111100110110010000100001010011101001 1001000001001001001111101001111011011110101000101000001011010100100011011000010111000011100000111000001101111011110101101001010101110100000000011101101010010110111110110111110001101101001100100011010101000110101010001111100011011010111111110100111001001011101101000010001010001100111010101011010100001010000100100100001010100101100011111111111010001000011010111101010100000111101001110111001100100101 1101011111000010010101101000011011010000100110110001110000110011110000001011001100000100111010011001100000001111110111010101000000110001111000111100010010010100000101011000101111000001010001110111101010000111100101010110110001110000100001000010010111000100000010000111101011110001110111011010010000111001010010101111100111111000001100001001000100100100001110010000011000000111011110101101111011001101 1110011010011001001011111101110001000000000101100010011000011101010001110001111011100101101000101010011111110010101110100110001100110110011101010110111010101000110110011000001010111110101100000010111101110111100111111000011001000111000101110101101100101100110100101110011110111100010000011011011110010100000111001011100101000100101111010010110000111001001110100100101110011000110100000000011001000011 1110000111101011000011001011011101001101010110010011010000101000100110100000110101101101011010101011010110010010110111011000000011000110101010001101100111110110111110110100011011100001100111001001111001000111101011101101100101000110010111110111101000110011110111011110100111000101001011110001000100110001101010100110000101100101110111110011001101101001011101111110100110000100001100111101111110001111 0000011010101101011101010100101101111010011100011101001010111110001000100100011010000011111100101011100010011111100101101111001000011001001110001101010000000001000010111001010111111100001001011010111101111111010011011100010100001011010100011100111011100110100110000000111100101101000101000110100100001000001111111100011110001101001010110111001000011101111000010101000101100100111101010001001001000111 0110111000100000000010010011111101100100110101111001001110110101000111011011110000000000011110010110010101111010000110010010100110100110110001000001011010100010011100001101000111000110111100110011011001101011001110001101010001011000111100110100011010101111011101110111000110000100101001110111100111001101001010011111110011111001100010111110010100011100001110101101101010001101010111111100110001110111 1001000111111001110101101001111011111100110000001011101010111110001000100001001100011100110010111110010010111010000011111101111011100001010001100100110101110001101001100001010110100111101001101110110000101100001010111100001111011001011110110000101110011000011011110110000001011000010100110101011010001110010110101111101000001101001101011110000100010011100101101001000000000011010001001100111011000101 0011110011111010011111111110100001010100111000101001111001111000010111101111110101000011000010000000001100110010001111011010110110010010111111010001011001100011110100000011001011011011000010100011100010001110111110011100100000000111110000011101111111111011011100001011100010100000000111101000001111111001010001110001011101100000110011101111000111110110011101110101001110011111001000011111111111101010 1010110110001110011110010011000101110000111010011100101101010001001011111111001001110010110101111110010110101011111001001010101001010100010010111111011100100111101101000101011100011110010001101111011111110000110010101101001100101101000010011010011110011110111101111010011111100110110101010100011101101011001101010000101101001110110111110001101101110000110000101111111010100010100000111110010100111011 0010000011101100001001011011001001010100001011010010100101011000000110101111000010101010010000101010000000000010110101000101111111100010110101110100101000010010100111110101110000010111101100001000000011111010010010000001010101001110110110011011111111111110010111001100001000011110010110111111111100101100001010101011101010100100011000000010111001110000101011100011001100011111100001111101010001110000 0111110001010000000111010101000000010000111110110110010010110010101001000111100110100001110101101001010011011010010111011011001000011111000001010010001111011010001111101101010110011001110010110001101001010001010000011001110000000010110100011111001101000001100100001110010101101011110110011010111101010010110010100010010101101110001101111001010010100010001100000101110110000100100111010111001110010101 1001011101000110000011001001001010110101110010101111111101111011101111101011101011010011001001111010011001000000111011101001101100000010111001100100001000000010111010110011001111100101000001000001100110000010011100111101110101110110100100001011111011100010010110011001011010111010011101111111111000001110101101110000111011011000010100001100000110110000111111101010111000001110010011011110101101010101 0011101111001100010101101000000101011000111000100001001011010010001110101111001011110000001100101011001111000000001001001100000110100000001000011001101000100011111010101110011110001110011000010100100010000100001101100100001100111100100010001100000010011101101101111000111110011010111001001001110000011110100110101011100000100111011100000100101111110011000110101110011001000111100010011101011001001001 1111101110000111100111111011000110010000011111010100001100100110100001010111111010111110000101011101001011011001001011011011001101110110000100111011101100000111110101111101010001110000101100111111110110000110011011111101001101011101000101101010100010001001000000101110011001111010000011011000100010000000100010101001010110010001111101101100111100111110101111111000011011110010011110110000010011111010
cTrader Algoシステムトレード

【cAlgo】ナンピンマーチンcBot【Sample】

4/10/2021 12/18/2023

5年以上前の記事です。内容が古くなっている可能性があります。

悪名高いナンピンマーチン

世の中にはいろいろなロジックのEAやcBotがありますが、ナンピンマーチンほどシステムトレード初心者を魅了し、そして地獄の底に蹴落としてきたロジックはないのではないでしょうか。

(EAやcBot・・・cTrader信者のajinoriとしては全部cBotと呼びたいところですが、一般的な呼び名で総称してEAと呼んでおきます。)

 

ナンピンマーチンとは

説明は不要でしょうが一応簡単に。

ポジションが損失を抱えたら、同じ方向で追加エントリーすることで、平均エントリー価格を下げる「ナンピン」と、負けたら倍掛けして負けを取り返すギャンブル手法「マーチンゲール法」を組み合わせたロジックです。

一般的にはポジションに一定以上の損失が出たらより大きなロットでナンピンして損失の相殺を図るロジック全般を総じてナンピンマーチンと呼ぶことが多いでしょう。

 

なんでダメなのか

一番大きな理由は破産リスクの大きさです。「マーチンゲール法」自体、無限に倍掛けできることを前提とした必勝法のため、ロットが資金的ににエントリーできないくらい膨れ上がった時点で口座破綻を起こします。

破産リスクを小さくするためには最初のエントリーをできるだけ小さくする必要がありますが、その結果リターンが少なくなり、その割にはそこそこの口座破綻可能性を秘めるという、どう頑張ってもハイリスクローリターンの設計になってしまうのです。

 

本当の問題

ハイリスクローリターンであると最初からわかっていれば誰も使うことはなく、ただすたれていくだけの手法のはずです。しかしナンピンマーチンロジックはいまだに人気・・・かどうかはわかりませんが、少なくとも有名です。

ナンピンマーチンの怖さは口座破綻のリスクが感覚的にはわかりにくい、という部分にあるのでしょう。人は小さすぎる確率を0として扱ってしまうんですよね。特にマイナスの事象に関しては。

「さすがに〇回も連続で負けるわけないっしょ!」って。この思考が破滅への道を着々と進んでいくのです。

また、EA開発の視点から言うなら、このロジックを使えば比較的簡単にきれいな右肩上がりのバックテスト結果が出せてしまうんで、EA販売をする人からしたら都合がよかったというのもあるかもしれません。

 

作ってみた

どうしてもナンピンマーチン=ヤベーやつというイメージが強かったため、手を出したことがなかったのですが、今回ブログのネタとして、至極単純なナンピンマーチンcBotを作ってみました。

ソースコードも公開してますので、よかったらなんかの参考にしてください。なるかわからないですけど。

 

何も考えないナンピンマーチンcBot

ロジック

最初に適当にエントリーします。プログラムに「適当に」とか言えないので、とりあえず起動時の最後のローソク足が陽線なら買い、陰線なら売りにしておきます。特に意味はないので別に逆でもいいです。以降、ずっと同じ方向でエントリーを繰り返します。

あとは設定値(Pipsパラメータ)以上損失が出たら倍掛けエントリーします。損失が相殺された時点でナンピンポジションは全決済します。

利確も同じ幅にして利確したら再エントリー、にしようかと思ったのですが、決済直後に再エントリーはさすがにあり得ないので、「最初のポジションは一番いいところで決済して再エントリーした」と仮定して、最初のポジションが一番いいところから設定Pips以上落ちたらナンピンさせるという設定にしました。

・・・説明がわかりにくくてすみません。ロジック気になる方はソースコード読み解いてください。

 

ソースコード

using System.Linq;
using cAlgo.API;
using cAlgo.API.Internals;

namespace cAlgo.Robots {
    [Robot(TimeZone = TimeZones.UTC, AccessRights = AccessRights.None)]
    public class NanMar : Robot {
        [Parameter(DefaultValue = 100.0)]
        public double Pips { get; set; }

        const string LABEL = "NanMar";
        const string COMMENT = "namping";
        TradeType _tradeType;
        Position _basePosition;
        Position _lastPosition = null;
        double _maxPips = 0;

        protected override void OnStart() {
            if (Account.IsLive && RunningMode == RunningMode.RealTime) {
                /* 当cBotはブログ記事用に作成されたサンプルcBotです。
                 * 何の工夫もないナンピンマーチンロジックにより売買を繰り返すため、高確率で口座破綻を引き起こします。
                 * 間違い防止のため、初期状態ではリアル口座で稼働ができないようになっています。
                 * リスクを承知の上、動かしたい場合はこのifブロックを削除の上ビルドしてください。 */
                Print("初期状態ではリアル運用できません。ソースコードを確認してください。");
                Stop();
            }
            // --- 適当に売買方向を決めて発注
            _tradeType = (Bars.LastBar.Close > Bars.LastBar.Open ? TradeType.Buy : TradeType.Sell);
            var res = ExecuteMarketOrder(_tradeType, SymbolName, Symbol.VolumeInUnitsMin, LABEL);
            if (res.IsSuccessful) {
                _basePosition = res.Position;
            } else {
                // --- 発注失敗したら一度止める
                Print(res.Error);
                Stop();
            }
        }

        protected override void OnTick() {
            // --- 初期ポジションの最大獲得Pipsを覚えておく。
            if (_basePosition.Pips > _maxPips) {
                _maxPips = _basePosition.Pips;
            }

            // --- ナンピンしてなくて、初期ポジションが最大Pipsより設定値以上落ちてるか、ナンピンポジションの損失が設定値を超えてたとき
            if ((_lastPosition == null && _maxPips - _basePosition.Pips > Pips) || (_lastPosition != null && _lastPosition.Pips < -1 * Pips)) {
                // --- 前のポジションの2倍ロットでナンピン
                var volume = (_lastPosition != null ? _lastPosition.VolumeInUnits : Symbol.VolumeInUnitsMin) * 2;
                var res = ExecuteMarketOrder(_tradeType, SymbolName, volume, LABEL, null, null, COMMENT);
                if (res.IsSuccessful) {
                    _lastPosition = res.Position;
                } else {
                    Print(res.Error);
                }
            }

            // --- ナンピンポジションが前の損失を相殺できてれば初期ポジションだけ残して全決済
            if (_lastPosition != null && _lastPosition.Pips > Pips) {
                var myPositions = Positions.Where(pos => pos.Label == LABEL && pos.SymbolName == SymbolName && pos.Comment == COMMENT);
                foreach (var pos in myPositions) ClosePositionAsync(pos);//本当はクローズされたか成否確認しないと危険。今回は面倒なので省略。
                _lastPosition = null;
                _maxPips = 0;
            }
        }
    }
}

たったこれだけのコードです。ろくに確認してないので説明と違う動きになってたらごめんなさい(笑)

あ、少しくらいはcBot開発の参考になりそうなこと書いておきます。

ポジションのラベルとコメント

cBotからの注文ではポジションにラベルとコメントがつけられます

あくまで私の使い方ですが、基本的にラベルはMT4のマジックナンバーと同じ感覚で使います。どのcBotから注文されたかわかるようにするため、基本的に一つのcBot内では同じものを使います。

コメントは注文に追加情報をつけておきたいときに使います。cAlgoのメソッドPositions.Findではコメントを指定しての検索はできないのですが、LINQを使えば特定のコメントのポジションだけ抜き出すことは可能です。

このサンプルではナンピンポジションであることをコメントに残し、一括決済時にコメントがついたものだけを取り出してすべて決済しています。

 

ダウンロード

いろいろ改造して試してみたいという方はこちらからどうぞ。

(2023/12/18 更新 古いものはバックテストレポートが出ないようなので、.NET6.0版に差し替えました)

 

バックテスト結果

10年バックテストの結果がこんな感じ。さすがにいい結果とは言えませんが、一応右肩上がりです。

ちなみに最適化一切なしの一発バックテストです。これはEURUSDの結果ですが、どの通貨でやってもだいたい同じような結果が出ます。

よく見ると資金が極大なのがわかるとは思いますが、つまりはそういうことです。100万円程度だとたとえ1000通貨から始めても破綻します。

こんな簡単なコードで、価格も一切見ないでトレードさせるだけなのに、資金さえあれば最適化もなしで右肩上がりのグラフが出るわけです。よく見ればおかしいのはわかるんですけどね。このリターンの少なさとか。

 

最適化してみた

最適化というかPips設定一つ変えただけなんですが、こんな荒いカーブフィッティングでもよさげなグラフができるから面白いですね。

トレード回数も増えて、目立ったドローダウンもうまい具合に隠れて、あとは縦軸の金額さえ目に入らなきゃいい感じです。(笑)

 

ちなみにこんな感じの時々下にスパイクが出てる直線右肩上がりグラフこそ、まさに典型的な損切りなしナンピンマーチンEAの特徴ですので見れば一目でわかります。

(確かMT4だと決済順序に気をつければ下方向スパイクは見えなくできた気がします。見えないとナンピンマーチンか損切りなしグリッド系EAか見分けつかないですが、cTraderなら見えてしまうため明白にわかります。)

間違ってもこんなグラフのEAにひっかからないようにお気を付けください。最近はまともな販売サイトであればナンピンマーチン使ってるかくらいは書いてあるので大丈夫だとは思いますが。

 

まとめ

実際に簡単なナンピンマーチンEA(cBot)を試してみることでその破産リスクの大きさとリターンの少なさを実感することができました。

皆さんもぜひ上記のコードをいじったり、プログラムがわからなければバックテストだけでもいろいろやってみてください。

もちろんこのロジック自体がナンピンマーチンの中でも特に酷いせいはあるのですが、こんなものですらなんとなくよさげなグラフに見えてしまうことを忘れてはなりません。

ロジックを改良して、ちょっとよさげなモノが出来上がったときに、正しくリスクとリターンを評価できるのでしょうか。ナンピンマーチンで一番怖いのはここだと思います。

もちろんナンピンマーチンのすべてを否定するつもりはありません。1回1回の勝率が独立事象のギャンブルでマーチンゲール法使うのに比べたら、FXでナンピンマーチン使う方がよっぽど理にかなっているのも確かです。

人によってはこれに、まともなエントリーロジック、ナンピンの仕掛け方、損切りの仕方など工夫に工夫を重ねて実用的なEAを作ることも可能なのだと思います。

でもそれって、第三者から見た時に中身もわからない状態でまともかどうか判断できるんですかね。少なくともグラフだけでは難しそうですよね。

基本的には「危うきには近寄らず」で敬遠しておく方が無難な気がします。


まだコメントはありません

新しいコメント

コメントは承認後に公開されます。承認まで次のコメントは投稿できません。

cTrader's Life

© 2026 ajinori