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 <stdio.h>
typedef long long ll;

int main(void) {
  ll n, i, j;
  scanf("%lld", &n);
  for(i = 1; i <= 3500; ++i) for(j = 1; j <= 3500; ++j) if(4 * i * j - i * n - j * n > 0 && !((n * i * j) % (4 * i * j - i * n - j * n))) {
    printf("%lld %lld %lld", i, j, (n * i * j) / (4 * i * j - i * n - j * n));
    return 0;
  }
}