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 $b_{x1}+b_{x2}+\cdots +b_{x6}>b_{y1}+b_{y2}+\cdots +b_{y6}$, 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.