Closest Power

An integer $x$ is said to be a **Perfect Power** if there exists **positive** integers $a$ and $b$ (i.e $a$, and $b$ should be $\geq 1$) such that $x = a^{b+1}$. Given an integer $n$, find the closest Perfect Power to $n$. If there are multiple *Perfect Powers* equidistant from $n$ and as close as possible to $n$, find the smallest one. More formally, find the smallest integer $x$ such that $x$