Intersection Matrix

You are given a matrix $A$ with $N$ rows and $M$ columns. We can select some non-empty subset of rows and some non-empty subset of columns of the given matrix and add all the elements which occur at the intersection of selected rows and columns. This value is called the *happiness* of the selected rows and columns. For example, let the matrix be the following: $1$ $2$ $3$ $7$ $5$ $6$