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  1. Practice
  2. Mathematics
  3. Number Theory
  4. Primitive Problem

Primitive Problem

We define a primitive root of prime number to be some integer satisfying the property that all values of where are different.

For example: if , we want to look at all values of in the inclusive range from to . For , the powers of (where is in the inclusive range from to ) are as follows:

Note that each of these evaluates to one of the six distinct integers in the range .

Given prime , find and print the following values as two space-separated integers on a new line:

  1. The smallest primitive root of prime .
  2. The total number of primitive roots of prime .

Need Help? Check out a breakdown of this process at Math Stack Exchange.

Input Format

A single prime integer denoting .

Constraints

Output Format

Print two space-separated integers on a new line, where the first value is the smallest primitive root of and the second value is the total number of primitive roots of .

Sample Input 0

7

Sample Output 0

3 2

Explanation 0

The primitive roots of are and , and no other numbers in satisfy our definition of a primitive root. We then print the smallest primitive root () followed by the total number of primitive roots ().