<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>

from enum import Enum

class Solution:
    def countPairs(self, n: int, edges: List[List[int]]) -> int:
        visited = {i:False for i in range(n)}
        node_graph = {}
        for e in edges:
            if e[0] not in node_graph:
                node_graph[e[0]] = []
            node_graph[e[0]].append(e[1])
            if e[1] not in node_graph:
                node_graph[e[1]] = []
            node_graph[e[1]].append(e[0])
        
        results_cnt = []
        for i in range(n):
            if visited[i]:
                continue

            nodes = deque()
            self.traverse(nodes, i, node_graph, visited)
            results_cnt.append(len(nodes))

        if len(results_cnt) == 1:
            return 0
        
        total = 0
        pre_sum = [0] * len(results_cnt)
        for i in range(len(results_cnt) - 1, -1, -1):
            if i == len(results_cnt) - 1:
                pre_sum[i] = results_cnt[i]
            else:
                pre_sum[i] = pre_sum[i+1] + results_cnt[i]
        for i in range(len(results_cnt) - 1):
            total += results_cnt[i] * pre_sum[i+1]
        return total

    def traverse(self, nodes, val, node_graph, visited):
        if visited[val]:
            return
        visited[val] = True
        for n in node_graph.get(val, []):
            self.traverse(nodes, n, node_graph, visited)
        nodes.appendleft(val)
        
80100