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 <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;

typedef long long LL;

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