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;
signed main(){
  ll n,N,t0,t1;
  cin >> N;
  for(ll w=1;w<=3500;w++){
    for(ll h=1;h<=3500;h++){
      t0 = w*h*N;
      t1 = 4*h*w-N*w-N*h;
      if(t1!=0&&t0%t1==0&&t0/t1>0){
        printf("%lld %lld %lld\n",h,w,t0/t1);
        return 0;
      }
    }
  }
}