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;
using lint = long long int;

int main() {
    lint n;
    cin >> n;

    for(lint a=1; a<=3500; a++)
    for(lint b=1; b<=3500; b++) {
        lint deno = 4 * a * b - n * b - n * a;
        if(deno <= 0)  continue;
        if(n * a * b % deno)  continue;
        cout << a  << " " << b <<  " " << n * a * b / deno << endl;
        return 0;
    }
}