Write a predicate factorial/2 that calculates the factorial of the Peano numbers. In this system, \(0\) is presented by 0, \(1\) by s(1), \(2\) by s(s(0)), and so on. To be precise, \(n\) is represented by taking 0 and wrapping it \(n\) times with s/1.

The value of \(0! = 1\), according to the convention for an empty product. The following predicates are assumed to be defined.

• p_add(A,B,C) iff \(A + B = C\)
• p_sub(A,B,C) iff \(A - B = C\)
• p_mul(A,B,C) iff \(A \cdot B = C\)
• p_exp(A,B,C) iff \(A^B = C\)