Everywhere perfect square

Number Theory Level pending

A number $$N$$ is called good if it has the following properties

(1) It is consists of even number of digits (say $$2n$$).

(2) The number consists of first $$n$$ digits is a perfect square.The number consists of last $$n$$ digits is also a perfect square.

(3) The number itself a perfect square.

Find the sum of all such good numbers where $$N < 10^4$$

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