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