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;
#define ll long long
int main()
{
    ll n;scanf("%lld",&n);
    for(ll a=1;a<=3500;a++)for(ll b=a;b<=3500;b++)
    {
        ll p=n*a*b,q=4*a*b-n*a-n*b;
        if(q>0 && p%q==0){printf("%lld %lld %lld",a,b,p/q);return 0;}
    }
    return 0;
}