You are designing a course schedule for a university with n courses, labeled from 1 to n. The prerequisite requirements are given in an array, relations, where each $\text{relations}[i] = [\text{prevCourse}_i, \text{nextCourse}_i]$ means that $\text{prevCourse}_i$ must be completed before you can enroll in $\text{nextCourse}_i$.

You can take any number of courses during a single semester, as long as the prerequisite for each course has been met in a previous semester.

Your task is to determine the minimum number of semesters required to complete all n courses. If the prerequisites contain a circular dependency (e.g., course A requires B, and course B requires A), it’s impossible to complete them all, so you should return -1.

Constraints:

• $1 \leq$ n $\leq 5 \times10^3$

• $1 \leq$ relations.length $\leq 5 \times 10^3$

• relations[i].length $== 2$

• $1 \leq \text{prevCourse}_i$, $\text{nextCourse}_i \leq$ n

• $\text{prevCourse}_i \neq \text{nextCourse}_i$

• All the pairs $[\text{prevCourse}_i, \text{nextCourse}_i]$ are unique.

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.