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()
{
    int n; cin >> n;

    for(int i=1; i<=3500; i++) for(int j=1; j<=3500; j++)
    {
        ll p = 1LL*n*i*j;
        ll q = 4LL*i*j - n*i - n*j;

        if(q > 0 && p % q == 0)
        {
            cout << i << ' ' << j << ' ' << p/q << endl;
            return 0;
        }
    }

    return 0;
}