10363: ABC327 —— B - A^A
[Creator : ]
Description
You are given an integer $B$.
If there exists a positive integer $A$ such that $A^A = B$, print its value; otherwise, output `-1`.
If there exists a positive integer $A$ such that $A^A = B$, print its value; otherwise, output `-1`.
Input
The input is given from Standard Input in the following format:
```
$B$
```
```
$B$
```
Output
If there exists a positive integer $A$ such that $A^A = B$, print its value; otherwise, print `-1`.
If there are multiple positive integers $A$ such that $A^A = B$, any of them will be accepted.
If there are multiple positive integers $A$ such that $A^A = B$, any of them will be accepted.
Constraints
- $1 \leq B \leq 10^{18}$
- $B$ is an integer.
- $B$ is an integer.
Sample 1 Input
27
Sample 1 Output
3
$3^3=27$, so print 3.
Sample 2 Input
100
Sample 2 Output
-1
There is no $A$ such that $A^A=B$.
Sample 3 Input
10000000000
Sample 3 Output
10