<p>You are given an undirected graph. You are given an integer <code>n</code> which is the number of nodes in the graph and an array <code>edges</code>, where each <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an undirected edge between <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>.</p>

<p>A <strong>connected trio</strong> is a set of <strong>three</strong> nodes where there is an edge between <b>every</b> pair of them.</p>

<p>The <strong>degree of a connected trio</strong> is the number of edges where one endpoint is in the trio, and the other is not.</p>

<p>Return <em>the <strong>minimum</strong> degree of a connected trio in the graph, or</em> <code>-1</code> <em>if the graph has no connected trios.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/26/trios1.png" style="width: 388px; height: 164px;" />
<pre>
<strong>Input:</strong> n = 6, edges = [[1,2],[1,3],[3,2],[4,1],[5,2],[3,6]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> There is exactly one trio, which is [1,2,3]. The edges that form its degree are bolded in the figure above.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/26/trios2.png" style="width: 388px; height: 164px;" />
<pre>
<strong>Input:</strong> n = 7, edges = [[1,3],[4,1],[4,3],[2,5],[5,6],[6,7],[7,5],[2,6]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are exactly three trios:
1) [1,4,3] with degree 0.
2) [2,5,6] with degree 2.
3) [5,6,7] with degree 2.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 400</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>1 &lt;= edges.length &lt;= n * (n-1) / 2</code></li>
	<li><code>1 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n</code></li>
	<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>
	<li>There are no repeated edges.</li>
</ul>

from typing import List
from collections import defaultdict

class Solution:
    def minTrioDegree(self, n: int, edges: List[List[int]]) -> int:
        graph = defaultdict(set)
        degree = [0] * (n + 1)
        
        for u, v in edges:
            graph[u].add(v)
            graph[v].add(u)
            degree[u] += 1
            degree[v] += 1
        
        min_degree_sum = float('inf')

        for u in range(1, n + 1):
            for v in graph[u]:
                if v > u:  # To avoid checking pairs twice
                    for w in graph[v]:
                        if w > v and w in graph[u]:  # Ensure u, v, w form a triangle
                            trio_degree_sum = degree[u] + degree[v] + degree[w] - 6  # Subtract 6 for the edges in the triangle
                            min_degree_sum = min(min_degree_sum, trio_degree_sum)

        return min_degree_sum if min_degree_sum != float('inf') else -1

# Example usage
solution = Solution()
print(solution.minTrioDegree(5, [[1, 2], [1, 3], [2, 3], [3, 4], [4, 5], [2, 4]]))  # Example input

43800