Class 1: p00000, p11111
Class 2: p00001, p00010, p00100, p11011, p11101, p11110
Class 3: p00011, p00101, p00110, p01001, p01010, p01011, p01100, p01101, p01110, p10001, p10010, p10011, p10100, p10101, p10110, p11001, p11010, p11100
Class 4: p00111, p11000
Class 5: p01000, p01111, p10000, p10111