Problem B
Boule Judge

By Arne Nordmann, CC BY-SA 3.0.
Jonna recently retired, and nowadays does nothing but drink coffee and play a game Swedes call boule – and she’s all out of coffee. Boule1 is played by two teams throwing $6$ heavy metal balls called boules as close to a small wooden ball, the jack, as possible. Scoring a round of boule is quite simple. The team with the closest boule to the jack wins round, and receives one point for each boule of theirs that is closer to the jack than the closest boule of the opposing team. If neither team was closest, the round is tied.
For example, consider the boule field in Figure 1, illustrating the first sample case. Jonna’s closest boule at coordinates $(22, 80)$ is $\sqrt{29}$ length units away from the jack. The opponents’ closest boule at $(27, 70)$, is $\sqrt{74}$ length units away, so Jonna’s team won the round. Jonna has an additional boule closer to the jack: her fifth boule at $(12, 75)$ is $\sqrt{64}$ length units away. Since Jonna’s team has two boules closer to the jack than the opponents’ closest boule, her team scores two points.
![\includegraphics[width=1\textwidth ]{sample1}](/problems/accenture22.boulejudge/file/statement/en/img-0002.png)
After losing badly in the last weekend tournament Jonna participated in, she’s become convinced that the judge of the tournament isn’t as impartial as he claims. Many times he ruled that the opposing team had a boule closer to the jack than Jonna’s team, even though this was clearly not the case. Jonna therefore wants a mobile app she can pull up whenever she doubts the judge’s decision to determine the score of a round.
Being a computer vision expert, it was trivial for Jonna to write a program that identifies the positions of the jack and all the boules on the playing field. However, actually computing the score of the round was a way too algorithmic task for her. Can you help her?
Input
The first line contains two integers – the coordinates of the jack on the playing field.
The next $6$ lines each contains two integers – the coordinates of a boule that Jonna’s team threw.
The next and final $6$ lines each contains two integers – the coordinates of a boule that the opposing team threw.
The coordinates $(x, y)$ of the jack and the boules satisfy $0 \le x \le 40$ and $0 \le y \le 150$. No boule occupies the same coordinates as another boule or the jack.
Output
If Jonna’s team won the round, first output a line with JONNA. If the opponent’s team won the round, instead output OPPONENTS. If the team tied, output TIE.
If the round was not tied, then output a line with the score of the team that won the round.
Sample Input 1 | Sample Output 1 |
---|---|
20 75 22 80 30 73 39 149 32 10 12 75 22 91 27 70 25 91 35 100 15 30 30 80 17 87 |
JONNA 2 |
Sample Input 2 | Sample Output 2 |
---|---|
2 128 14 92 4 114 22 36 14 83 5 132 2 12 20 105 29 42 30 106 18 21 18 91 2 125 |
OPPONENTS 1 |
Sample Input 3 | Sample Output 3 |
---|---|
16 74 39 7 27 145 5 2 34 143 18 149 34 5 39 141 16 149 33 147 24 2 24 3 12 0 |
TIE |
Footnotes
- Really called pétanque in French – boule is just the French name of the ball.