How many ordered pairs $(x, y)$ satisfy BOTH conditions below?

$\bullet$  Condition I: $x = 1$ or $y = 0$ or $y = 2$

$\bullet$  Condition II: $x = 0$ or $x = 2$ or $y = 1$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many ordered pairs $(x, y)$ satisfy BOTH conditions below?

$\bullet$  Condition I: $x = 1$ or $y = 0$ or $y = 2$

$\bullet$  Condition II: $x = 0$ or $x = 2$ or $y = 1$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5
How many ordered pairs $(x, y)$ satisfy BOTH conditions below?

$\bullet$  Condition I: $x = 1$ or $y = 0$ or $y = 2$

$\bullet$  Condition II: $x = 0$ or $x = 2$ or $y = 1$
train