Duff in Love

题意翻译

## 问题描述 如果不存在一个数 $ a (a>1)$ ，使得 $ a^2 $ 是 $ n $ 的约数，我们就称 $ n $ 是一个可爱的数。 给出一个正整数 $ n $ ，在 $ n $ 的所有约数中，寻找最大的可爱的数。 ## 输入格式 输入一个整数 $ n $ 。 ## 输出格式 输出本题的答案。

题目描述

Duff is in love with lovely numbers! A positive integer $ x $ is called lovely if and only if there is no such positive integer $ a>1 $ such that $ a^{2} $ is a divisor of $ x $ . Malek has a number store! In his store, he has only divisors of positive integer $ n $ (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible. Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.

输入输出格式

输入格式

The first and only line of input contains one integer, $ n $ ( $ 1<=n<=10^{12} $ ).

输出格式

Print the answer in one line.

输入输出样例

输入样例 #1

10

输出样例 #1

10

输入样例 #2

12

输出样例 #2

6

说明

In first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely. In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by $ 4=2^{2} $ , so 12 is not lovely, while 6 is indeed lovely.