You are given an integer n representing the number of cities, labeled from $0$ to n $- 1$, and an array roads where each roads[i] $= [$ a_i, b_i $]$ indicates a bidirectional road between city a_i and city b_i.

The network rank of two distinct cities is the total number of directly connected roads to either city. If a road directly connects both cities, it is counted only once.

The maximal network rank is the maximum network rank across all pairs of distinct cities.

Return the maximal network rank of the infrastructure.

Constraints:

• $2 \leq$ n $\leq 100$

• $0 \leq$ roads.length $\leq \frac{ ext{`n`} \cdot ( ext{`n`} - 1)}{2}$

• roads[i].length $= 2$

• $0 \leq$ a_i, b_i $\leq$ n $- 1$

• a_i $\neq$ b_i

• Each pair of cities has at most one road connecting them.

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.