Square entries

Level pending

How many ordered pairs \((m,n)\) are there such that:

(i) \(0<m<30\), \(0<n<30\)

(ii) \(m\) and \(n\) are integers

(iii) there exists an \(m \times n\) table such that all entries are perfect squares, and the sum of entries in each row and each column is a perfect square.

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