406792: GYM102556 H Riana and Humongous Numbers

Riana got really bored one day and decided to play with some integers. She started with the positive integer $$$N$$$. She then noticed that $$$N$$$ was too small and boring. Suddenly, she got the idea to create a really big integer. To do so, she multiplied all of the positive divisors of $$$N$$$ and got the integer $$$M$$$. After getting the value of $$$M$$$, she challenged her friend Cisco to determine the value of the original integer $$$N$$$ given $$$M$$$. Help Cisco find the value of $$$N$$$.

The input contains one line containing the integer $$$M$$$. It is guaranteed that $$$M$$$ is a positive integer less than $$$10^{15}$$$.

Output the original integer $$$N$$$ if possible. Otherwise, output $$$-1$$$.

8

4

4

-1

In the first test case, the positive divisors of 4 are 1, 2, and 4. The product is 8.

In the second test case, there is no integer whose product of its positive divisors is 4.