<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 helper(self, root: int) -> int:
        if len(self.relation[root]['children']) == 0:
            self.relation[root]['size'] = 1
        else:
            self.relation[root]['size'] = 1
            for i in self.relation[root]['children']:
                self.relation[root]['size'] += self.helper(i) 
        return self.relation[root]['size']


    def countGoodNodes(self, edges: List[List[int]]) -> int:
        #create a tree dict for the relationship of parent <-> children
        n = len(edges) + 1 # n is the number of nodes 
        self.relation = {i: {
                             'children': [],
                             'size': None # size of the tree with this node being the root
                           }           
                        for i in range(n)
        }
        nodes = set(range(1, n))
        nodes_dict = {i :[] for i in range(n)}
        for i, j in edges:
            nodes_dict[i].append(j)
            nodes_dict[j].append(i)
        print(nodes_dict)
        layer = [0]
        while len(layer) > 0:
            # print('layer', layer)
            # print('nodes:', nodes)
            # print('dict:', self.relation)
            # print('='*80)
            new_layer = []
            for i in layer:      
                for j in nodes_dict[i]:
                    if j in nodes:
                        self.relation[i]['children'].append(j)
                        nodes.remove(j)
                        new_layer.append(j)
            layer = new_layer
        #print('final relation:', self.relation)

        # for i, j in edges:
        #     self.relation[i]['children'].append(j)
        self.helper(0)
        ans = []
        for i in range(n):
            if len(self.relation[i]['children']) in (0, 1):
                ans.append(i)
            else:
                equal = True
                node0 = self.relation[i]['children'][0]
                size0 = self.relation[node0]['size']
                for j in self.relation[i]['children'][1:]:
                    sizej = self.relation[j]['size']
                    if size0 != sizej:
                        equal = False
                        break
                if equal ==True:
                    ans.append(i)
        return len(ans)


                     


         
        
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