I. Integer Triple
time limit per test
1 second
memory limit per test
512 megabytes
input
standard input
output
standard output

Given an integer $$$n$$$, find three integers $$$a, b, c$$$ satisfying

  • $$$|a|,|b|,|c|\le 10^{18};$$$
  • $$$n=ab(a+b)+bc(b+c)+ac(a+c).$$$

If no such triple of integers exists, report that there is no solution.

Input

The input contains one integer $$$n$$$ ($$$0\le n\le 10^{18}$$$).

Output

If there is no solution, output $$$-1$$$. Otherwise, output three integers $$$a, b, c$$$ that satisfy all the requirements.

If there are multiple valid answers, output any one of them.

Examples
Input
3
Output
-1
Input
6
Output
1 1 1