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>
using namespace std;
typedef long long ll;
int N;

int main(){
    cin >> N;
    for(ll h=1;h<=3500;h++){
        for(ll n=1;n<=3500;n++){
            if(4*h*n-n*N-N*h<=0) continue;
            if((N*h*n)%(4*h*n-n*N-N*h)==0){
                cout << h << " " << n << " " << (N*h*n)/(4*h*n-n*N-N*h) << endl;
                return 0;
            }
        }
    }
}