Question 9
How many ordered triples of integers $(x, y, z)$ satisfy the following system of inequalities?
$$
-x - y - z \le -2
$$ $$
-x + y + z \le 2
$$ $$
x - y + z \le 2
$$ $$
x + y - z \le 2
$$
$$
-x - y - z \le -2
$$ $$
-x + y + z \le 2
$$ $$
x - y + z \le 2
$$ $$
x + y - z \le 2
$$