The Two-ball Game

The national soccer team of Lizarb is one of the favourites for the upcoming World Cup. Their greatest strengths are precise dribbling and passing: any player can pass the ball directly to any other player on the field, at any distance. The captain, Oicul, insists that a drill called the two-ball game sharpens these skills.

In the two-ball game, $n \ge 4$ players stand on the field and never move during the game. Four of them are special: two starting players $s_1$ and $s_2$, and two terminal players $t_1$ and $t_2$. At the start, $s_1$ holds a white ball and $s_2$ holds a black ball.

Each ball travels from player to player. A single pass is a straight line segment between two players. The aim is for the white ball to end up with $t_1$ and the black ball to end up with $t_2$.

To avoid collisions the game has two rules:

• No two ball trajectories may cross each other.
• No player may touch a ball more than once. This includes the starting and terminal players.

For some placements of the players the two-ball game can be played, and for others it cannot. Write a program that decides, for a given placement, whether the two-ball game is possible.

The first line contains a single integer: the number of test cases.

Each test case begins with a line containing the number of players $n$ ($4 \le n \le 100000$), followed by $n$ lines giving the players' coordinates, one player per line. All coordinates are pairwise distinct, and no three players are collinear (no three lie on a single straight line).

The coordinates are listed in a fixed role order: the first is $s_1$, the second is $t_1$, the third is $s_2$, the fourth is $t_2$, and each remaining line is another player.

For each test case, print a single line containing POSSIBLE if the two-ball game can be played for that placement, or IMPOSSIBLE otherwise.