A positive integer n is a perfect power if it can be expressed as the power b^e for some two integers b and e that are both greater than one. (Any positive integer n can always be expressed as the trivial power n¹, so we don’t care about those.) For example, the integers 32, 125 and 441 are perfect powers since they equal 2⁵, 5³ and 21², respectively.

This function should determine whether the positive integer n is a perfect power. Your function needs to somehow iterate through a sufficient number of possible combinations of b and e that could work, returning True right away when you find some b and e that satisfy b^e == n, and returning False when all relevant possibilities for b and e have been tried and found wanting.

Since n can get pretty large, your function should not examine too many combinations above and beyond those that are both necessary and sufficient to reliably determine the answer. Achieving this efficiency is the central educational point of this problem.

Input: Integer (int).

Output: Logic value (bool).

Examples:

assert perfect_power(8) == True
assert perfect_power(42) == False
assert perfect_power(441) == True
assert perfect_power(469097433)...