Fadi and LCM

Today, Osama gave Fadi an integer $X$, and Fadi was wondering about the minimum possible value of $max(a,b)$ such that $LCM(a,b)$ equals $X$. Both a and b should be positive integers.

$LCM(a,b)$ is the smallest positive integer that is divisible by both $a$ and $b$. For example, $LCM(6,8)=24,LCM(4,12)=12,LCM(2,3)=6$.

Of course, Fadi immediately knew the answer. Can you be just like Fadi and find any such pair?

Input

The first and only line contains an integer $X(1\le X\le 10^{12})$.

Output

Print two positive integers, $a$ and $b$, such that the value of $max(a,b)$ is minimum possible and $LCM(a,b)$ equals $X$. If there are several possible such pairs, you can print any.

Examples
input

2

output

1 2

input

6

output

2 3

input

4

output

1 4

input

1

output

1 1

思路

$lcm(a,b)=a\ast b/gcd(a,b)=x$
要让$max(a,b)$最小
$a\ast b=x$ && $gcd(a,b)=1$

#include<bits/stdc++.h>
 
using namespace std;
typedef long long ll;
ll X,ans=1e12+10,ansa,ansb;
int main() {
    
    
    scanf("%lld", &X);
    for (ll i = 1; i * i <= X; i++) {
    
    
        if (X % i == 0) {
    
    
            ll a = i, b = X / i;
            if (__gcd(a, b) == 1 && max(a, b) < ans) {
    
    
                ansa = a;
                ansb = b;
                ans = max(a, b);
            }
        }
    }
    printf("%lld %lld\n", ansa, ansb);
    return 0;
}