# Finding a Perfect Square

$N$ is a 3-digit number that is a perfect square. When the first digit is increased by 1, the second digit is increased by 2, the third digit is increased by 3, the result is still a perfect square. Determine $N$.

Details and assumptions:

Since digits do not exceed 9, the challenge assumes that the units digit of $N$ to be at most 6, the tens digit of $N$ to be at most 7 and the hundreds digit of $N$ to be at most 8.

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