Wi-Fi Network

Hektor came up with an idea to make himself rich. He decided to write a program that solves the well-known problem of placing a Wi-Fi router so that every computer in an apartment can reach it, meaning the shortest route connecting the router to a computer does not pass through any wall.

The first version of the program is heavily simplified: it handles only apartments with at most three computers, and the router has unlimited range. Because the range is unlimited, the shortest route from the router to a computer is simply the straight segment between them, so a computer is reachable exactly when that straight segment does not cross any wall.

Can you write such a program? For each test set decide whether at least one spot for the router exists from which every computer is reachable.

The first line contains the number of test sets $Z$ ($1 \le Z \le 10$). The test sets follow.

The first line of each set contains three integers $R$, $N$, $M$ ($2 \le R \le 10000$, $2 \le N \le 3$, $1 \le M \le 100$). The area searched for the router is limited to points $(X, Y)$ with $-R < X < R$ and $-R < Y < R$. Here $N$ is the number of computers and $M$ is the number of walls in the area.

The next $N$ lines each contain two integers $X$, $Y$ ($-R < X < R$, $-R < Y < R$), the position of a computer.

The next $M$ lines each contain four integers $x_0$, $y_0$, $x_1$, $y_1$ (each strictly between $-R$ and $R$), describing the segment from $(x_0, y_0)$ to $(x_1, y_1)$ that represents one wall.

You may assume that no two walls cross, although they may share endpoints. No computer lies on a wall.

For each test set print TAK if the router can be placed so that its signal reaches every computer without passing through a wall, and NIE otherwise. Print each answer on its own line.