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Problem I
Power of Divisors
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 $n^{f(n)}=x$?
Input
The single line of input contains a single integer $x$ ($1 \le x \le 10^{18}$). This is the $x$ of the statement above.
Output
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.
| Sample Input 1 | Sample Output 1 |
|---|---|
15625 |
25 |
| Sample Input 2 | Sample Output 2 |
|---|---|
64000000 |
20 |
| Sample Input 3 | Sample Output 3 |
|---|---|
65536 |
-1 |
