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>
#include <math.h>

using namespace std;

long long inf=1000000007;

int main(){
	long long und;
	cin>>und;

	for(long long i=1;i<=3500;i++){
		for(long long j=1;j<=3500;j++){
			if((4*i*j-und*j-und*i)>0 && (und*i*j)%(4*i*j-und*j-und*i)==0){
				cout<<i<<" "<<j<<" "<<(und*i*j)/(4*i*j-und*j-und*i)<<endl;
				return 0;
			}
		}
	}

	return 0;
}