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;

int main()
{
  long long N;
  scanf("%lld",&N);
  bool F=0;
  for(int i=1;i<=3500&&!F;i++){
    for(int j=1;j<=3500&&!F;j++){
      long long a=4*i*j-N*i-N*j,b=N*i*j;
      if(a>0&&b%a==0){
	printf("%d %d %lld\n",i,j,b/a);
	F=1;
      }
    }
  }
  return 0;
}