A perfect power is a classification of positive integers:

In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer. More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that mk = n.

Your task is to check whether a given integer is a perfect power. If it is a perfect power, return a pair m and k with mk = n as a proof. Otherwise return Nothing, Nil, null, NULL, None or your language's equivalent.

Note: For a perfect power, there might be several pairs. For example 81 = 3^4 = 9^2, so (3,4) and (9,2) are valid solutions. If a number is a perfect power, return any pair that proves it.

Examples

isPP(4) => [2,2]
isPP(9) => [3,2]
isPP(5) => None

Tests

isPP(4)
isPP(8)
isPP(14)

Good luck!

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