You are given an undirected graph with $n$ nodes, numbered from $0$ to $n - 1$. You are provided with a $0$ indexed integer array scores of length $n$, where scores[i] represents the score of node $i$, and a $2 {D}$ integer array edges, where edges[i] $= [u_i, v_i]$ denotes an undirected edge between nodes $u_i$ and $v_i$.

A valid node sequence is defined as a sequence of $4$ distinct nodes $[a, b, c, d]$ such that an edge exists between every consecutive pair of nodes in the sequence: $(a, b)$, $(b, c)$, and $(c, d)$.

The score of a node sequence is the sum of the scores of the $4$ nodes in that sequence.

Return the maximum possible score of a valid node sequence. If no valid node sequence of length $4$ exists, return $-1$.

Constraints:

• n $==$ scores.length

• $4 \leq n \leq 5 \times 10^4$

• $1 \leq$ scores[i] $\leq 10^8$

• $0 \leq$ edges.length $\leq 5 \times 10^4$

• edges[i].length $== 2$

• $0 \leq a_i, b_i \leq n - 1$

• $a_i \neq b_i$

• There are no duplicate 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.