In order to check how her students can count, every year Maria Ivanovna gives them the same problem at home — 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 divisible by A. Only the number A changes from year to year and from student to student.
You have decided to help future generations. To do this, you need to write a program that solves this problem.
Input data format
The input file contains a single number A (1 & le; A & le; 1000000000 — just in case; suddenly Maria Ivanovna will set a large number to "fill up" someone).
Output data format
Print the single number N in the output file.
Examples
| # |
Input |
Output |
| 1 |
8 |
4 |
| 2 |
13 |
13 |