Intersection Points

For an axis-aligned rectangle and a line segment, count how many points lie on both the rectangle boundary and the segment. Print 4 when the segment overlaps the boundary and there are infinitely many intersection points.

The first line contains $T$. Each test case gives a rectangle by $(x_{min}, y_{min})$ and $(x_{max}, y_{max})$, then a segment from $(x_1,y_1)$ to $(x_2,y_2)$.

For each test case, print the finite intersection count, or 4 when the intersections are infinite.