In a particular list of three-digit perfect squares, the first perfect square can be turned into each of the others by rearranging its digits. What is the largest number of distinct perfect squares that could be in the list?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In a particular list of three-digit perfect squares, the first perfect square can be turned into each of the others by rearranging its digits. What is the largest number of distinct perfect squares that could be in the list?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
In a particular list of three-digit perfect squares, the first perfect square can be turned into each of the others by rearranging its digits. What is the largest number of distinct perfect squares that could be in the list?
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