题目描述

Consider a positive integer $n$. Let $f(n)$ be the number of positive integer divisors of $n$. For example, if $n = 8$ then $f(n) = 4$, since the divisors of $8$ are $1, 2, 4$ and $8$.

Now, consider a positive integer $x$. What is the smallest value of $n$ such that $n^{f(n)} = x$?

输入格式

The single line of input contains a single integer $x$ ($1 \le x \le 10^{18}$). This is the $x$ of the statement above.

输出格式

Output a single integer, which is the smallest value of $n$ such that $n^{f(n)} = x$, or $-1$ if no such value of $n$ exists.

15625

25

64000000

20

65536

-1