Problem Description

An integer $a$ is a perfect square number, meaning it is the square of some integer. That is, there exists an integer $b$ such that $a=b^{2}$.

Given a positive integer $n$, find the smallest positive integer $x$ such that their product is a perfect square number.

Input Format

The input contains one line with a positive integer $n$.

Output Format

Output the smallest positive integer $x$ found.

12

3

15

15 

Hint

For $30\%$ of the testdata, $1 \leq n \leq 1000$, and the answer does not exceed $1000$.

For $60\%$ of the testdata, $1 \leq n \leq 10^{8}$, and the answer does not exceed $10^{8}$.

For all testdata, $1 \leq n \leq 10^{12}$, and the answer does not exceed $10^{12}$.

Lanqiao Cup 2021, Second Round Provincial Contest, Group A Problem G (Group B Problem H).

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