You are given an integer n, indicating that there are n courses labeled from $1$ to n. You are also given an array relations where relations[i] = [prevCourse_i, nextCourse_i], representing that course prevCourse_i must be completed before course nextCourse_i can be taken, and an integer k.

In one semester, you can complete at most k courses as long as all prerequisite courses for them have been completed in previous semesters.

Return the minimum number of semesters required to take all n courses.

Constraints:

• $1 \leq$ n $\leq 15$

• $1 \leq$ k $\leq$ n

• $0 \leq$ relations.length $\leq$ n $ imes ($n $- 1) / 2$

• relations[i].length $= 2$

• $1 \leq$ prevCourse_i, nextCourse_i $\leq$ n

• prevCourse_i $\neq$ nextCourse_i

• All the pairs [prevCourse_i, nextCourse_i] are unique.

• The given graph is a directed acyclic graph.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.