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;
long long n,k,l;//bilibili
int main()
{
  cin>>n;
  for(long long i=1;i<=3500;i++)
  {
    for(long long j=1;j<=3500;j++)
    {
      k=4*i*j-n*j-n*i;
      l=i*j*n;
      if(k>0&&l%k==0)
      {
        cout<<i<<" "<<j<<" "<<l/k<<endl;
        return 0;
      }
    }
  }
}