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 1

3

Output 1

-1

Input 2

6

Output 2

1 1 1