284A · Cows and Primitive Roots

Problem: The cows have just learned what a primitive root is! Given a prime p, a primitive root $\bmod p$ is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.

Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime p, help the cows find the number of primitive roots $\bmod p$.

Input Format: The input contains a single line containing an integer p (2 ≤ p < 2000). It is guaranteed that p is a prime.

Output Format: Output on a single line the number of primitive roots $\bmod p$.

Note: The only primitive root $\bmod 3$ is 2.

The primitive roots $\bmod 5$ are 2 and 3.