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 main(){
  ll n;
  cin >> n;
  ll a,b,c;
  for(ll i=1;i<=3500;i++){
    for(ll j=1;j<=3500;j++){
      if(4*i*j-i*n-j*n>0){
        if((i*j*n)%(4*i*j-i*n-j*n)==0){
          a=i,b=j,c=(i*j*n)/(4*i*j-i*n-j*n);
        }
      }
    }
  }
  cout << a << " " << b << " " << c << endl;
}