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;

int main() {
	ll n, a, b, c;
	scanf("%lld", &n);
	for(a = 1; a <= 3500; a++) {
		for(b = 1; b <= 3500; b++) {
			ll A = a*b*n, B = 4*a*b-a*n-b*n;
			if(B <= 0) continue;
			if(A % B == 0) {
				printf("%lld %lld %lld\n", a, b, A/B);
				return 0;
			}
		}
	}
	return 0;
}