Distinct Rows in Submatrices

Let's define the *strength* of a matrix as the number of distinct rows in it. Two rows $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_n$ are distinct if there is an index $i$ such that $a_i \neq b_i$. You are given an integer matrix $A$ with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). A submatrix of $A$ is formed as the intersection of rows $r_1$ through $r_2$