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