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;
  cin>>N;
  for (long long h=1; h<=3500; h++) {
    for (long long n=1; n<=3500; n++) {
      long long a = 4*h*n - N*h - n*N;
      if (a <= 0) {
        continue;
      }
      long long b = N*h*n;
      if (b % a == 0) {
        printf("%lld %lld %lld\n", h, n, b / a);
        return 0;
      }
    }
  }
}