You are given $n$ toothpicks. You want to use them to make a $a \times b$ rectangular grid. Determine whether it is possible to do so. If it is possible, also find any grid that you can make.

Input

The first line of the input consists of a line with an integer, $n$, the number of toothpicks.

Output

If it is not possible to make a rectangular grid, output Impossible.

Otherwise, output Possible on the first line, then two integers $a$ and $b$ in the second line.

Constraints

For all testcases: $1 \le n \le 10^9$
Subtask 1 (30%): $n \le 1000$
Subtask 2 (70%): No additional constraints