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>
typedef long long llong;
using namespace std;

int main(){
	llong N;
	cin>>N;
	
	llong h,n,w;
	for(h=1;h<=3500;++h){
		for(n=1;n<=3500;++n){
			if((4*h*n-N*n-N*h)>0){
				if((N*h*n)%(4*h*n-N*n-N*h)==0){
					w=(N*h*n)/(4*h*n-N*n-N*h);
					cout<<h<<" "<<n<<" "<<w<<endl;
					return 0;
				}
			}
		}
	}
}//解答解説参考.