<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>

INF = 10**9

class Solution:
    def minTrioDegree(self, n: int, edges: List[List[int]]) -> int:
        g, deg = [set() for _ in range(n)], [0 for _ in range(n)]
        for x, y in edges:
            x, y = x - 1, y - 1
            deg[x] += 1
            deg[y] += 1
            g[x].add(y)
            g[y].add(x)

        heavy_g = [[] for _ in range(n)]
        for x, y in edges:
            x, y = x - 1, y - 1
            if deg[x] > deg[y]:
                x, y = y, x
            heavy_g[x].append(y)
        
        res = INF
        for x, y in edges:
            x, y = x - 1, y - 1
            val = deg[x] + deg[y] - 6
            for _ in range(2):
                g_x = g[x]
                for z in heavy_g[y]:
                    if z in g_x:
                        res = min(res, val + deg[z])
                x, y = y, x

        return -1 if res == INF else res
44400