<p>You are given an integer <code>n</code>. There is an <strong>undirected</strong> graph with <code>n</code> vertices, numbered from <code>0</code> to <code>n - 1</code>. You are given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting vertices <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>

<p>Return <em>the number of <strong>complete connected components</strong> of the graph</em>.</p>

<p>A <strong>connected component</strong> is a subgraph of a graph in which there exists a path between any two vertices, and no vertex of the subgraph shares an edge with a vertex outside of the subgraph.</p>

<p>A connected component is said to be <b>complete</b> if there exists an edge between every pair of its vertices.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/11/screenshot-from-2023-04-11-23-31-23.png" style="width: 671px; height: 270px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 6, edges = [[0,1],[0,2],[1,2],[3,4]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> From the picture above, one can see that all of the components of this graph are complete.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/11/screenshot-from-2023-04-11-23-32-00.png" style="width: 671px; height: 270px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 6, edges = [[0,1],[0,2],[1,2],[3,4],[3,5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The component containing vertices 0, 1, and 2 is complete since there is an edge between every pair of two vertices. On the other hand, the component containing vertices 3, 4, and 5 is not complete since there is no edge between vertices 4 and 5. Thus, the number of complete components in this graph is 1.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>0 &lt;= edges.length &lt;= n * (n - 1) / 2</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>There are no repeated edges.</li>
</ul>

class UnionFind:
    
    def __init__(self, n: int):
        self.root = list(range(n))
        self.rank = [1 for _ in range(n)]
        self.edges = [0 for _ in range(n)]
        self.group = [1 for _ in range(n)]
        
    def find(self, x: int) -> int:
        if x != self.root[x]: self.root[x] = self.find(self.root[x])
        return self.root[x]
    
    def union(self, x: int, y: int) -> None:
        root_x, root_y = self.find(x), self.find(y)
        if root_x == root_y:
            self.edges[root_x] += 1
            return
        if self.rank[root_x] > self.rank[root_y]:
            self.root[root_y] = root_x
            self.edges[root_x] += self.edges[root_y] + 1
            self.group[root_x] += self.group[root_y]
        elif self.rank[root_x] < self.rank[root_y]:
            self.root[root_x] = root_y
            self.edges[root_y] += self.edges[root_x] + 1
            self.group[root_y] += self.group[root_x]
        else:
            self.root[root_y] = root_x
            self.rank[root_x] += 1
            self.edges[root_x] += self.edges[root_y] + 1
            self.group[root_x] += self.group[root_y]
    
    def are_connected(self, x: int, y: int) -> bool:
        return self.find(x) == self.find(y)
            

class Solution:
    def countCompleteComponents(self, n: int, edges: List[List[int]]) -> int:
        uf = UnionFind(n)
        g = collections.defaultdict(set)
        for u, v in edges:
            g[u].add(v)
            g[v].add(u)
            uf.union(u, v)
        for i in range(n):
            uf.find(i)
        
        s = set(uf.root)
        res = 0
        for x in s:
            v = uf.group[x]
            if uf.edges[x] == (v - 1) * v // 2: res += 1
        return res
            
595