You are given n people labeled from $0$ to $n - 1$. There is a relationship knows(a, b) indicating whether person a knows person b. The relationships are also represented by a matrix graph where graph[i][j] == 1 means person i knows person j, and graph[i][j] == 0 means they do not.

A person c is a celebrity if both conditions hold:

1. For every person i != c, graph[i][c] == 1 (everyone knows c).

2. For every person i != c, graph[c][i] == 0 (c knows nobody else).

Return the label of the celebrity if one exists, otherwise return $-1$.

Note: You should solve the problem using the knows API, and aim to keep the number of knows calls within $3 \cdot n$.

Constraints:

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

• $2 \leq$ n $\leq 100$

• graph[i][j] is $0$ or $1$

• graph[i][i] == 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.