A six-digit number (base 10) is considered "squarish" if it satisfies the following conditions:

1. None of its digits are zero.
2. It is a perfect square.
3. The first two digits, the middle two digits, and the last two digits of the number are all perfect squares when considered as two-digit numbers.

How many squarish numbers are there? Provide your answer as an integer.

Let's think step by step and output the final answer within \boxed{}.
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