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;

int n,i,j;

int main(){
	scanf("%d", &n);
	
	for(i = 1; i <= 3500; i++){
		for(j = 1; j <= 3500; j++){
			long long tmp = 1LL * n * i * j;
			long long tmp1 = 4LL * i * j - 1LL * n * i - 1LL * n * j;
			if(tmp1 != 0 && tmp % tmp1 == 0 && (tmp / tmp1) >= 1 && (tmp / tmp1) <= 3500)
			return 0 * printf("%d %d %d\n", i, j, tmp / tmp1);
		}
	}
}