We are attaching a breakdown of the Final Results for each submission.

1. Final Results:

Initially, for preliminary testing published on contest.com, we ran each test in a separate process. This allowed us to fully evaluate even solutions that crashed or hung on specific tests. However, this method disrupted many participants' performance optimizations and introduced substantial noise into the results.

Therefore, for the final evaluation, we executed all tests in a single process using a grader closely resembling the provided contest-grader.cpp. Consequently, solutions that crashed or hung on any test received a final score of 0.

2. Post-Contest Corrections:

After announcing preliminary results, several participants submitted bug fixes via comments on contest.com. Although we typically do not accept post-contest corrections, one corrected solution turned out to be significantly faster than any solution submitted during the contest. As an exception, we decided to evaluate all corrected submissions and include them in the final standings. To maintain fairness, these late submissions incurred a 20% penalty on the prize amounts awarded.