Practice Arithmetic and Mathematics with the exercise "Number derivation"

Learning Opportunities

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Arithmetic
Mathematics

Statement

Goal

You have to calculate the derived number of a given positive integer, following these rules:
If a number is prime p, p′=1.
If a number is the product n×m, (n×m)′=n′×m+n×m′.
Yes, it follows almost all the traditional rules of the derivation, including 1′=0 and (p^n)′=n×p^(n−1) if p is prime; but not (p+q)′=p′+q′ for all p and q.

Input

A number n.

Output

the derivation of n

Constraints

1<n⩽10000

Example

Input

Output

Solve it

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