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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
long long n;
int main()
{
	cin>>n;
	for(long long i=1;i<=3500;i++)
	{
		for(long long j=1;j<=3500;j++)
		{
			if((4*i*j-i*n-j*n)>0&&(i*j*n)%(4*i*j-i*n-j*n)==0){cout<<i<<" "<<j<<" "<<	(i*j*n)/(4*i*j-i*n-j*n); return 0;}
		}
	}
	return 0;
}