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>
using namespace std;
typedef long long ll;
#define MAX (ll)3501
ll N;

int main(){
	cin >> N;
	// cout << "hello";
	for(ll h=1; h<MAX; h++) for(ll w=1; w<MAX; w++){
		ll x = N*h*w;
		ll y = 4*h*w - N*w - N*h;
		if(y!=0 && x%y == 0 && (ll)x/y < MAX && x/y>0){
			cout << h << " " << w << " " << (ll)x/y << endl;
			return 0;
		}
	}
}