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