For a given natural A find the minimum natural N such that N to the power of N ( N multiplied by itself N times) is divided by A.
Input data
The input is a single number A (\(1 <= A <= 10^9\)).
Output
It is necessary to output a single number N.
Examples
| # |
Input |
Output |
| 1 |
8 |
4 |
| 2 |
13 |
13 |