z-ioi

You deserve an easy problem before the IOI.

You know the number of competitors that will compete at IOI, and you know that each competitor can score from 0 to 600 points.

You also know the rules about assigning medals:
- 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.

For given number of competitors N, you have to find out how many different distributions of medals there can be.