Cows and Primitive Roots

2000ms

262144K

Description:

The cows have just learned what a primitive root is! Given a prime p, a primitive root $\text{[math]}$ is an integer x (1 ≤ x < p) such that none of integers x - 1, x² - 1, ..., x^p - 2 - 1 are divisible by p, but x^p - 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 $\text{[math]}$ .

Input:

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

Output:

Output on a single line the number of primitive roots $\text{[math]}$ .

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Note:

The only primitive root $\text{[math]}$ is 2.

The primitive roots $\text{[math]}$ are 2 and 3.

Informação

Provedor Codeforces

Código CF284A