This problem is intended to check whether participants can write their own comparator function for sorting. Assume that the sixth round was also held. A competitor with name ~x~ and points ~b_{x1}, b_{x2}, \dots, b_{x6}~ will be ahead of a competitor with name ~y~ and points ~b_{y1}, b_{y2}, \dots, b_{y6}~ if and only if ~b_{x1} + b_{x2} + \dots + b_{x6} > b_{y1} + b_{y2} + \dots + b_{y6}~, or if the sums are equal and ~x~ is lexicographically smaller than ~y~.

For each competitor, we can look at the worst and best possible scenario - all competitors except them win ~500~ points and they get ~0~ points, and vice versa. For each scenario, we sort the ranking according to the comparator and find the best and worst possible positions for them.

In C++, this can be done by writing a custom comparator function and then using std::sort, while in Python, this can be done by sorting twice with different key functions for list.sort.