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;
ll n,t1,t2;
bool f;
int main() {
	scanf("%lld",&n);
	for (ll a=1;a<=3500;a++) {
		for (ll b=1;b<=3500;b++) {
			t1=n*a*b;
			t2=4*a*b-n*b-n*a;
			if (t2==0) continue;
			if (t1%t2==0&&t1/t2>0) {
				printf("%lld %lld %lld\n",a,b,t1/t2);
				f=1; break;
			}
		}
		if (f) break;
	}
	return 0;
}