A Strict Table

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 .