You are given an integer n representing the number of nodes in an undirected graph, with nodes labeled from $0$ to n $- 1$. You are also given a $2$D integer array edges, where edges[i] $= [$ a_i, b_i $]$ indicates that an undirected edge exists between node a_i and node b_i.

Return the total number of pairs of distinct nodes such that there is no path between them.

Constraints:

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ edges.length $\leq 2 imes 10^5$

• edges[i].length $= 2$

• $0 \leq$ a_i, b_i $<$ n

• a_i $\neq$ b_i

• There are no repeated edges.

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.