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 ll;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
	
using namespace std;
ll N;
int main(){
	cin>>N;
	ll n;
	FOR(h,1,3501){
		FOR(w,1,3501){
			if(4*h*w-N*w-N*h>0 && N*w*h%(4*h*w-N*w-N*h)==0){
				n=N*w*h/(4*h*w-N*w-N*h);
				cout<<h<<" "<<n<<" "<<w<<endl;
				return 0;
			}
		}
	}
}