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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