Using a 2-D prefix sum array, we can calculate the total number of scales in any rectangle in $\mathcal{O}(1)$. For a rectangle with its top left corner at $(a,b)$ and its bottom right corner at $(c,d)$, we can use inclusion-exclusion to see that the total number of scales = $prefix[c][d]-prefix[a][d]-prefix[c][b]+prefix[a][b]$.

Brute forcing all possible rectangles gives us an $\mathcal{O}(W^2\times H^2)$ solution, which will give us $50\mathrm{\%}$ of the points. To get $100\mathrm{\%}$, we need to make the insight that since all cells have a non-negative number of scales, we only need to consider the number of scales in the rectangle with maximum length with each possible width.

Time Complexity: $\mathcal{O}(W\times H\times min(W,H))$