<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Petya cut three $2 \times 2$ squares from an $8 \times 8$ checkered square as shown in the figure. Olya wants to cut as many $1 \times 3$ rectangles as possible from the remaining part of the square (following the grid lines). What is the maximum number of such rectangles she can cut? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
16
Petya cut three $2 \times 2$ squares from an $8 \times 8$ checkered square as shown in the figure. Olya wants to cut as many $1 \times 3$ rectangles as possible from the remaining part of the square (following the grid lines). What is the maximum number of such rectangles she can cut?
test