分解质因数之codeforces_588B

最新推荐文章于 2023-11-27 17:56:46 发布

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本文介绍了一个算法问题，即从给定正整数n的所有正除数中找出最大的可爱数。可爱数是指不能被任何大于1的完全平方数整除的正整数。文章通过分解质因数的方法给出了求解该问题的AC代码。

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 that a² is a divisor of x.

$\text{[math]}$

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

Output

Input

Output

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 indeed lovely.

分析：分解质因数

AC代码如下：

#include"stdio.h"

int main()  
{  
    _int64 n;  
    while(scanf("%I64d",&n)!=EOF)  
    {  
        _int64 ans=1;  
        for(_int64 i=2;i*i<=n;i++)  
        {  
            if(n%i==0)  
            {  
                ans*=i;
                while(n%i==0)
				{
					n/=i;  
				}
            }  
            if(n==1) break;  
        }  
        if(n>1)  
		{
			ans*=n;	
		}
        printf("%I64d\n",ans);  
    }  
    return 0;  
}