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>
typedef long long ll;
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll n;
int main()
{
	scanf("%lld",&n);
	for(int i=1;i<=3500;i++)
		for(int j=1;j<=3500;j++)
		{
			ll a=4ll*i*j-n*j-n*i,b=n*i*j;
			if(a<=0)continue;

			if(b%a==0)
			{
				printf("%d %d %lld\n",i,j,b/a);
				exit(0);
			}
		}
	return 0;
}