To Score or Not to Score

Robot soccer matches in the very early days were quite funny, since most of the time there wasn't any action in the game. Robots only moved to catch a ball that a robot from the other team had shot. The reason for this somewhat strange behavior was the strategy that was used.

The robots made a map of all players from their own team and the opponents. If a player was in possession of the ball, then before shooting he checked whether it was possible to score from the current situation. In the process he checked whether there was a way for the ball to reach the goal via several other players of his team. It was possible to shoot the ball to another player only if no opponent was close enough to the shooting line to catch the ball. An opponent always moved perpendicular to the shooting line, and only if he was sure he could intercept the shot. The ball always traveled exactly three times as fast as a robot could move, so an opponent had to be quite near the shooting line to intercept a shot.

The other part of the game was fouling a player in order to prevent the other team from reaching the goal. The rules stated that only one player could be fouled at a time, so this only happened when fouling that one player prevented the other team from scoring. Also, the initial shooter may never be fouled. Fouling happens almost instantly by knocking the robot out with an electromagnetic pulse, so the distance between the two opponents does not matter and the fouling robot does not move.

For example, suppose there are four players on each team and the player with the ball can only make a limited set of shots, because every other direction is covered by an opponent (for instance, the direct shot to the goal is interceptable). The team might still score by routing the ball through teammates. However, if knocking out a single teammate would cut off every such route, the goal can no longer be scored.

Your university has decided to program a simulator for these ancient robot football matches, and your task is to write the part that checks whether the team in possession of the ball is able to score, based on the current positions of all robots. As a summary of the description above, a team may score if the ball cannot be intercepted by an opponent and if more than one player would have to be fouled to stop it (that is, some scoring route survives the removal of any single teammate).

The first line contains the number of test cases $k$ ($1 \le k \le 10$).

The first line of each test case holds the number $n$ of players per team ($1 \le n \le 20$). The next $2n$ lines contain the coordinates of all players: the first $n$ lines are the first team and the next $n$ lines are the second team. A coordinate is given as two non-negative floating point numbers separated by spaces. The first player of the first team is in possession of the ball. The coordinates of the goal follow below the two teams.

You may assume the inputs are chosen so that small floating point errors do not lead to wrong results.

For each test case, print Goal if the first team is able to score, or No goal if the ball can be intercepted or if fouling a single player is enough to prevent the team from scoring.