<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 Tree:
    def __init__(self, value, parent):
        self.value = value
        self.parent = parent
        self.children = []
        self.node_num_total = -1
        self.tem_total = 1
        self.good = -1
    
    def add_child(self, value):
        self.children.append(Tree(value, self))

    def node_num(self):
        if self.node_num_total != -1:
            return self.node_num_total
        self.node_num_total = 1
        for i in range(len(self.children)):
            self.node_num_total += self.children[i].node_num()
        return self.node_num_total

    def is_good(self):
        if self.good == 1:
            return True
        elif self.good == 0:
            return False
        if len(self.children) <=1:
            self.good = 1
            return True
        base_num = self.children[0].node_num()
        # base_num = self.children[0].tem_total
        for i in range(1, len(self.children)):
            if base_num != self.children[i].node_num():
            # if base_num != self.children[i].tem_total:
                self.good = 0
                return False
        self.good = 1
        return True

class Solution:
    def countGoodNodes(self, edges: List[List[int]]) -> int:
        root = Tree(0, None)
        tree_list = [None for i in range(len(edges)+1)]
        tree_list[0] = root

        for item in edges:
            source, target = item[0], item[1]
            if tree_list[source] == None:
                source, target = target, source
            tree_list[source].add_child(target)
            tree_list[target] = tree_list[source].children[-1]
        # if len(edges)> 1000:
        #     exit()
        good_num = 0

        for i in range(len(tree_list)):
            if tree_list[i].is_good():
                good_num += 1

        return good_num

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