A Strict Table

Level pending

Each entry of a \(4 \times 4\) square table of numbers is either \(1\) or \(2\). Suppose that the sum of \(9\) entries in each of the four \( 3 \times 3 \) sub-square tables is divisible by \(4\), while the sum of all the \(16\) entries in the table is not divisible by \(4\). Let the least and the greatest possible values of the sum of all the entries be \(m\) and \(n\), respectively. Find \( m + n \).

This problem is part of the set AMSP.
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