There are m students and m mentors, each labeled from $0$ to m $- 1$. You are given two $2$D integer arrays students and mentors of dimensions m $ imes$ n, where students[i] and mentors[j] represent the responses of student i and mentor j to n survey questions.

The compatibility score between student i and mentor j is defined as the number of questions for which their answers match (specifically, the count of indices k where students[i][k] == mentors[j][k]).

Every student must be assigned to exactly one mentor, and each mentor must be assigned to exactly one student.

Return the maximum possible compatibility score sum across all assignments.

Constraints:

• m == students.length == mentors.length

• n == students[i].length == mentors[j].length

• $1 \leq$ m, n $\leq 8$

• students[i][k] is either $0$ or $1$.

• mentors[j][k] is either $0$ or $1$.

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.