You are given an undirected graph with $n$ vertices labeled from $1$ to $n$, represented by a $2$D integer array edges where each edges[i] $=$ $[u_i, v_i]$ denotes an edge connecting vertex $u_i$ and vertex $v_i$.

A connected trio is defined as a subset of three distinct vertices where an edge exists between every pair among the three.

The degree of a connected trio is the total number of edges incident to at least one of the three vertices that are not part of the trio itself.

Return the minimum degree among all connected trios in the graph. If no connected trio exists, return $-1$.

Constraints:

• $2 \leq$ n $\leq 400$

• $1 \leq$ edges.length $\leq \frac{n \times (n - 1)}{2}$

• edges[i].length $= 2$

• $1 \leq u_i, v_i \leq$ n

• $u_i \neq v_i$

• 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.