Problem Numbers Aren't Sorted by Difficulty

Map the tier names, from easiest to hardest, to $0,1,\ldots,5$. If the mapped tier value is $g$, assign difficulty $(g,d)$ the rank

$$r=5g+(5-d).$$

A smaller rank means an easier difficulty. This also correctly handles the reversed numeric direction within one tier name: level $5$ is easier than level $1$.

Let $R$ be the rank of the threshold difficulty. Keep exactly the problems whose rank is at most $R$, then sort them by rank in increasing order. The relative order of problems with the same rank is irrelevant.

The reference implementation additionally sorts equal-difficulty problems by problem number, only to make its own output deterministic.

The time complexity is $O(N\log N)$ per test case and the memory complexity is $O(N)$.

Solution written by GPT5.6