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

You must assign each node a distinct integer from $1$ to n. The value of an edge is the product of the values assigned to its endpoints.

Return the maximum possible sum of all edge values across the entire graph.

Constraints:

• $1 \leq$ n $\leq 5 imes 10^4$

• m $==$ edges.length

• $1 \leq$ m $\leq$ n

• edges[i].length $== 2$

• $0 \leq a_i, b_i <$ n

• $a_i \neq b_i$

• There are no repeated edges.

• The graph is connected.

• Each node is connected to at most $2$ other nodes.

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.