<p>You are given an integer <code>n</code>. There is an <strong>undirected</strong> graph with <code>n</code> nodes, 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 nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>

<p>Return <em>the <strong>number of pairs</strong> of different nodes that are <strong>unreachable</strong> from each other</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-3.png" style="width: 267px; height: 169px;" />
<pre>
<strong>Input:</strong> n = 3, edges = [[0,1],[0,2],[1,2]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no pairs of nodes that are unreachable from each other. Therefore, we return 0.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/05/tc-2.png" style="width: 295px; height: 269px;" />
<pre>
<strong>Input:</strong> n = 7, edges = [[0,2],[0,5],[2,4],[1,6],[5,4]]
<strong>Output:</strong> 14
<strong>Explanation:</strong> There are 14 pairs of nodes that are unreachable from each other:
[[0,1],[0,3],[0,6],[1,2],[1,3],[1,4],[1,5],[2,3],[2,6],[3,4],[3,5],[3,6],[4,6],[5,6]].
Therefore, we return 14.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= edges.length &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>There are no repeated edges.</li>
</ul>

class Solution:
    def countPairs(self, n: int, edges: List[List[int]]) -> int:
        self.graph = {i: set() for i in range(n)}

        for [left, right] in edges:
            self.graph[left].add(right)
            self.graph[right].add(left)
        
        total_sum = 0

        
        visited = set()
        for i in range(n):
            if i in visited:
                continue
            
            group_count = 0
            to_visit = [i]
            while len(to_visit) > 0:
                node = to_visit.pop()
                if node in visited:
                    continue
                group_count += 1
                visited.add(node)

                neighbours = self.graph[node]
                for neighbour in neighbours:
                    if neighbour not in visited:
                        to_visit.append(neighbour)

            total_sum += group_count*(n-group_count)
        
        return total_sum//2


    #     if n == 0 or n == 1:
    #         return 0
        
    #     self.groups = [[i] for i in range(n)]

    #     for edge in edges:
    #         self.merge(edge)
        
    #     value = 0
    #     for group in self.groups:
    #         value += len(group)*(n-len(group))
        
    #     return value//2

    # def merge(self, edge) -> None:
    #     [left, right] = edge
    #     left_i = None
    #     right_i = None

    #     for i, group in enumerate(self.groups):
    #         if left in group:
    #             left_i = i
    #         if right in group:
    #             right_i = i
            
    #         if left_i is not None and right_i is not None:
    #             break
        
    #     if left_i == right_i:
    #         return
        
    #     merged_group = [*self.groups[left_i], *self.groups[right_i]]

    #     for i in sorted([left_i, right_i], reverse=True):
    #         del self.groups[i]
    #     self.groups.append(merged_group)
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