
After a very productive art class, it's time for gym class. The gym teacher is away though, so your English teacher Joey is substituting. However, Joey isn't particularly athletic and doesn't know how to run a gym class properly. So, instead of teaching, he decides to have your class play dodgeball while he sits on a bench and solves problems on DM::OJ.
Your class comes to a mutual agreement to play a variant of the game called basketball dodgeball. The main objective is to shoot the dodgeballs into the enemy's basket.
After an hour of epic basketball dodgeball, the score is completely tied. One more goal and your team will win. Both teams have one ball that they need to score with. To ensure the best results, your team will try to pass the ball to the baller of the team.
The ball on both sides starts off in the hands of the player furthest back from the center line (it is guaranteed that only one player will meet this criterion). This player must get the ball to the baller. Everyone has a certain throwing range though, so this may involve several passes. Your goal as the strategist on your team is to figure the least amount of passes both teams need to take for the ball to get to their baller near the center line.
Since you go to a well-funded private school, both sides of the gym are squares whose areas are
Figure out which team will win or whether it will be a draw, in which case your class will play an actual game of dodgeball as a tie breaker.
Input Specification
The first line will contain two integers,
Each of these lines will be composed of three integers
Output Specification
If your team wins output We are the champions!
. If your team loses output :'(
. In the case of a draw, whether that be when the amount of passes for both teams are equal or when both teams will never be able to get their ball to their ballers, output SUDDEN DEATH
.
Sample Input 1
5 6
5 0 9001
3 3 10
2 3 5
3 10 7
4 11 2
5 0 9001
3 3 10
2 3 5
3 10 7
4 11 2
5 12 2
Sample Output 1
We are the champions!
Explanation for Sample Output 1
The ball starts off in the hands of the player in
Sample Input 2
2 2
2000 2000 1000
1000 0 9001
999 0 9001
4 7 2
Sample Output 2
SUDDEN DEATH
Explanation for Sample Output 2
The player at the back of your team is
Sample Input 3
3 4
2222 4 2220
4 2222 2227
155 0 9001
42 73 9
42 64 64
42 0 9001
42 66 0
Sample Output 3
:'(
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