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<bits/stdc++.h>
#define ll long long
using namespace std;
const int N=3500;
int n;
int a,b,c;
int main(){
	scanf("%d",&n);
	ll x,y;
	for(int i=1;i<=N;i++)
		for(int j=i;j<=N;j++){
			x=1LL*n*i*j,y=1LL*4*i*j-1LL*n*j-1LL*n*i;
			if(y<=0) continue;
			if((x%y)==0){
				cout<<i<<" "<<j<<" "<<x/y<<endl;
				return 0;
			}
		}
}