AMC 10 2017a Problem 23

How many triangles with positive area have all their vertices at points $(i,j)$ in the coordinate plane, where $i$ and $j$ are integers between $1$ and $5$, inclusive? $\textbf{(A)}\ 2128 \textbf{(B)}\ 2148 \textbf{(C)}\ 2160 \textbf{(D)}\ 2200 \textbf{(E)}\ 2300$