<p>There is an <strong>undirected</strong> tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given a 2D integer array <code>edges</code> of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>

<p>A node is <strong>good</strong> if all the <span data-keyword="subtree">subtrees</span> rooted at its children have the same size.</p>

<p>Return the number of <strong>good</strong> nodes in the given tree.</p>

<p>A <strong>subtree</strong> of <code>treeName</code> is a tree consisting of a node in <code>treeName</code> and all of its descendants.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]</span></p>

<p><strong>Output:</strong> <span class="example-io">7</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/05/26/tree1.png" style="width: 360px; height: 158px;" />
<p>All of the nodes of the given tree are good.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges = [[0,1],[1,2],[2,3],[3,4],[0,5],[1,6],[2,7],[3,8]]</span></p>

<p><strong>Output:</strong> <span class="example-io">6</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/06/03/screenshot-2024-06-03-193552.png" style="width: 360px; height: 303px;" />
<p>There are 6 good nodes in the given tree. They are colored in the image above.</p>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges = [[0,1],[1,2],[1,3],[1,4],[0,5],[5,6],[6,7],[7,8],[0,9],[9,10],[9,12],[10,11]]</span></p>

<p><strong>Output:</strong> <span class="example-io">12</span></p>

<p><strong>Explanation:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/08/08/rob.jpg" style="width: 450px; height: 277px;" />
<p>All nodes except node 9 are good.</p>
</div>
</div>

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

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>edges.length == n - 1</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>The input is generated such that <code>edges</code> represents a valid tree.</li>
</ul>

from collections import defaultdict
from typing import List

class Solution:
    def countGoodNodes(self, edges: List[List[int]]) -> int:
        graph = defaultdict(list)
        sizes = defaultdict(int)

        # Build the graph
        for x, y in edges:
            graph[x].append(y)
            graph[y].append(x)

        ans = 0 

        # Depth-First Search to calculate subtree sizes
        def dfs(node, parent):
            size = 1
            prev_count = None
            good_node = True
            for neighbor in graph[node]:
                if neighbor != parent:
                    child_size = dfs(neighbor, node)
                    if prev_count is None:
                        prev_count = child_size
                    if good_node and child_size != prev_count:
                        good_node = False
                    size += child_size

            sizes[node] = size

            nonlocal ans
            if good_node:
                ans += 1
            return size

        dfs(0, -1)

        return ans
80731