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 rep(i,n) for(int i=0;i<(n);i++)

using namespace std;
using lint=long long;

int main(){
	lint n; cin>>n;
	for(lint a=1;a<=3500;a++) for(lint b=1;b<=3500;b++) {
		lint d=4*a*b-n*a-n*b;
		if(d>0 && n*a*b%d==0){
			cout<<a<<' '<<b<<' '<<n*a*b/d<<'\n';
			return 0;
		}
	}
	return 0;
}