Practice Number theory and Mathematics with the exercise "Beautiful base : The most beautiful"

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Number theory
Mathematics

Statement

Goal

Let n be a positive integer. A "beautiful base" of n is any integer b > 1 such that log_⁡b(n) is an integer > 1, where log_b(n) denotes the logarithm of n in base b.

Find the beautiful base B of n such that log_⁡B(n) is as large as possible. We shall refer to B as the "most beautiful base" of n.

Input

An integer n.

Output

The most beautiful base of n if it exists otherwise NONE.

Constraints

1 <= n <= 10 ^ 18

Example

Input

Output

NONE

Solve it

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