Rectangle Coloring

You are given $n$ axis-parallel rectangles on the plane. An axis-parallel rectangle is a rectangle whose edges are parallel to the $x$-axis or the $y$-axis. Determine the number of colors needed to paint the $n$ rectangles according to the following rules.

1. Each rectangle is painted with exactly one color.
2. Two intersecting rectangles must be painted the same color. Regarding a rectangle as the set of points including its boundary, two rectangles intersect if their intersection is non-empty.
3. For rectangles $R_a$ and $R_b$, if there exists a sequence $R_a = R_{i_1}, R_{i_2}, \dots, R_{i_k} = R_b$ such that $R_{i_j}$ and $R_{i_{j+1}}$ intersect for every $1 \le j < k$, then $R_a$ and $R_b$ must have the same color; otherwise they must have different colors. For example, in the figure below rectangle $R_9$ must have the same color as $R_4$, $R_5$, $R_8$, and a different color from $R_1$, $R_2$, $R_3$, $R_6$, $R_7$.

In other words, rectangles connected through the intersection relation form one group, and each group is painted a single distinct color. Hence the number of colors needed equals the number of such groups (connected components).

The input consists of $T$ test cases. The first line contains the number of test cases $T$. The first line of each test case contains the number of rectangles $N$ ($1 \le N \le 200$). Each of the next $N$ lines contains four positive integers $x_1$, $y_1$, $x_2$, $y_2$ ($1 \le x_1, y_1, x_2, y_2 \le 10000$) describing one rectangle, where $(x_1, y_1)$ is the lower-left corner and $(x_2, y_2)$ is the upper-right corner. The four integers are separated by one or more spaces.

For each test case, print the number of colors needed, one per line.