训练2——B

链接：http://acm.hust.edu.cn/vjudge/contest/view.action?cid=117536#problem/B

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                                                                    Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Description

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 thata² 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.

Input

The first and only line of input contains one integer, n (1 ≤ n ≤ 10¹²).

Output

Print the answer in one line.

Sample Input

Input

10

Output

10

Input

12

Output

6

Hint

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 = 2², so 12 is not lovely, while 6 is indeedlovely.

题意：

给你一个数，找出它的所有中尽可能大的数，这个数没有平方数的因子

解析：

n=10的12次方，数比较大，用long long，并且尽可能减少循环，减少时间。

代码：

#include<iostream>
using namespace std;
int main()
{
    long long n;
    cin>>n;
    long long k=1;
    for(long long i=2;i*i<=n;i++)
   {
       if(n==1) break;
       if(n%i==0) k*=i;
       while(n%i==0)
           n/=i;
   }
    cout<<n*k<<endl;
    return 0;
}