Problem: You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

* It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:


N


Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:


h n w

Examples

Input

2


Output

1 2 2


Input

3485


Output

872 1012974 1539173474040


Input

4664


Output

3498 3498 3498

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <stdio.h>
using namespace std;
typedef long long LL;
LL n,a,b;
int main(){
	cin>>n;
	for(LL i=1;i<=3500;i++)for(LL j=1;j<=3500;j++){
		a=n*i*j;b=4*i*j-(i+j)*n;
		if(b>0&&a%b==0){printf("%lld %lld %lld\n",i,j,a/b);return 0;}
	}
	return 0;
}