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IOI organizers decided to introduce some new things to the practice session.

The practice session will have 6 problems, each worth 100 points. The organizers have developed a software that does the following things:

- Reports when some competitor logs into the system.
- When a competitor submits a problem, it grades it and reports the score.

Now, you have to implement a system that monitors this software and reports in real time how many of each medals would be assigned based on the current results.

Since the competitors do not have to attend the practice session, you should report the medal assignments based on the number of people that have logged into the system at least once.

Also, for each competitor and each problem, you should use the score of the last submission for that problem.

You have to update the assignments every time someone logs in, or submits a problem.

The rules for assigning the medals are the following:
- No more than 1/6 of the competitors will get a gold medal
- No more than 1/4 of the competitors will receive gold or silver medal
- No more than 1/2 of the competitors will receive a gold, solver or bronze medal.
- Two competitors with the same score must both receive the same medal, or no medal.
- The difference between the lowest gold score and highest silver score, the difference between the lowest silver score and the highest bronze score, as well as the difference between the lowest bronze score and the highest non-medal score must be at least 2 points
- The difference between the the lowest gold score and the highest bronze score, as well as the difference between the lowest silver score and the highest non-medal score must be at least 3 points.
- The difference between the lowest gold score and the highest non-medal score must be at least 4 points.