<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>

class Solution:
    def countGoodNodes(self, edges: List[List[int]]) -> int:
        n = len(edges) + 1
        neighbors = {key: [] for key in range(n)}
        depths = {}
        for (a, b) in edges:
            if a == 0:
                depths[a] = 0
                depths[b] = 1
            elif b == 0:
                depths[b] = 0
                depths[a] = 1
            else:
                if a in depths:
                    depths[b] = depths[a] + 1
                elif b in depths:
                    depths[a] = depths[b] + 1
        # print('depths: ', depths)
        sons = {key: [] for key in range(n)}
        for (a, b) in edges:
            if depths[a] < depths[b]:
                sons[a].append(b)
            else:
                sons[b].append(a)
        # print('sons: ', sons)
        
        number_of_childern = {}
        def count_childern(node):
            if node not in number_of_childern:
                if len(sons[node]) == 0:
                    number_of_childern[node] = 0
                else:
                    ans = 0
                    for son in sons[node]:
                        ans += 1 + count_childern(son)
                    number_of_childern[node] = ans
            # print('number_of_childern[{}]={}'.format(node, number_of_childern[node]))
            return number_of_childern[node]

        def check_good(node):
            if len(sons[node]) in [0, 1]:
                return True
            else:
                good_flag = True
                i = 0
                cur_childern = count_childern(sons[node][0])
                for son in sons[node][1:]:
                    i += 1
                    if count_childern(son) != cur_childern:
                        good_flag = False
                return good_flag

        ans = 0
        for node in range(n):
            if check_good(node):
                # print('*** good node: ', node)
                ans += 1
        return ans

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