ioXDR is a master in logic circuits. One day he comes up with a special logic gate.
It requires 3 input bits a,b,c. It would then make c=c xor (a and b) and remain a and b unchanged, where and means bitwise and and xor means bitwise exclusive or.
ioXDR has a boolean function f(x1,x2,…,xm), where xi∈{0,1} and f(x1,x2,…xm)∈{0,1}.
He wants to design a circuit and could simulate the boolean function.
He has m input bits, and 1 output bit, and some extra bits. The number of extra bits and the initial value of extra bits could be determined freely. The initial value of output bit could also be set freely.
**This problem is judged by SPJ, so any valid answer could be accepted**
m≤8