There are $n$ languages numbered from $1$ to $n$, and $m$ users numbered from $1$ to $m$.

You are given an integer $n$, a $2$D integer array languages where languages[i] is the list of languages known by the $(i + 1)^{ ext{th}}$ user, and a $2$D integer array friendships where friendships[j] = [$u_j$, $v_j$] denotes a friendship between user $u_j$ and user $v_j$.

Two friends can communicate if there is at least one language that both of them know. You can choose exactly one language and teach it to some users.

Return the minimum number of users you need to teach that chosen language to ensure that every pair of friends can communicate.

Constraints:

• $2 \leq n \leq 500$

• languages.length $== m$

• $1 \leq m \leq 500$

• $1 \leq$ languages[i].length $\leq n$

• $1 \leq$ languages[i][j] $\leq n$

• $1 \leq u_i < v_i \leq$ languages.length

• $1 \leq$ friendships.length $\leq 500$

• All pairs $(u_i, v_i)$ are unique

• languages[i] contains only unique values

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.