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 Int = long long;
signed main(){
  Int N;
  cin>>N;
  const Int MAX=3500;
  for(Int h=1;h<=MAX;h++){
    for(Int n=1;n<=MAX;n++){
      Int a=N*h*n;
      Int b=4*h*n-N*n-N*h;
      if(b<=0) continue;
      if(a%b) continue;
      Int w=a/b;
      cout<<h<<" "<<n<<" "<<w<<endl;
      return 0;
    }
  }
  return 0;
}