There are n people, each of whom is either good or bad:

• A good person always tells the truth.

• A bad person may tell the truth or lie.

You are given a $0$ indexed two dimensional integer array statements of size n $ imes$ n, where statements[i][j] represents the statement made by person i about person j:

• statements[i][j] == $0$ indicates person i states that person j is bad.

• statements[i][j] == $1$ indicates person i states that person j is good.

• statements[i][j] == $2$ indicates person i makes no statement about person j.

Additionally, no person makes a statement about themselves, meaning statements[i][i] == $2$ for all i.

Return the maximum number of people who can be good based on the given statements.

Constraints:

• n == statements.length == statements[i].length

• $2 \leq$ n $\leq 15$

• statements[i][j] is either $0$, $1$, or $2$.

• statements[i][i] == $2$

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.