Lucky Light

A point light source sits at $(x_L, y_L)$ with $y_L > 0$, and there are finitely many line segments of non-zero length, each given by the coordinates of its two endpoints. All endpoints are distinct. Every segment lies above the $x$-axis, in the region $y > 0$.

The segments cast shadows onto the $x$-axis. The shadows of two segments either do not overlap at all, or overlap in an interval of non-zero width. They never touch at a single point. No segment has a shadow that shrinks to a point either, so no segment is aimed straight at the light source. The height $y_L$ is at least 1 larger than the $y$-coordinate of every endpoint, so every segment leaves a bounded shadow on the $x$-axis.

The shadows split the $x$-axis into dark and lighted areas. Determine how many lighted areas there are. With at least one segment the count is 2 or more, and with no segments it is 1.

In the picture below the three segments A, B and C create three lighted areas.

The first line contains the number of test cases. Each test case has the following format.

• One line with the number of segments $n$. ($0 \le n \le 100$)
• One line with the coordinates $x_L$ and $y_L$ of the light source, separated by a single space. ($-100 \le x_L \le 100$, $1 \le y_L \le 1000$)
• $n$ lines, each with four integers $x_i$, $y_i$, $u_i$ and $v_i$ separated by single spaces, giving the two endpoints $(x_i, y_i)$ and $(u_i, v_i)$ of the $i$th segment. ($-100 \le x_i, u_i \le 100$, $0 < y_i, v_i < y_L$)

For every test case, print the number of lighted areas on its own line.

The first test case of sample input 1 corresponds to the picture in the statement. The second test case has two crossing segments.