<|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
 A $10 \times 10$ square has been cut into rectangles whose areas are distinct and expressed as natural numbers. What is the maximum number of rectangles that can be obtained? 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
14
A $10 \times 10$ square has been cut into rectangles whose areas are distinct and expressed as natural numbers. What is the maximum number of rectangles that can be obtained?
test