<p>Given the <code>root</code> of a binary tree, return <em>the length of the <strong>diameter</strong> of the tree</em>.</p>

<p>The <strong>diameter</strong> of a binary tree is the <strong>length</strong> of the longest path between any two nodes in a tree. This path may or may not pass through the <code>root</code>.</p>

<p>The <strong>length</strong> of a path between two nodes is represented by the number of edges between them.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/06/diamtree.jpg" style="width: 292px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5]
<strong>Output:</strong> 3
<strong>Explanation:</strong> 3 is the length of the path [4,2,1,3] or [5,2,1,3].
</pre>

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

<pre>
<strong>Input:</strong> root = [1,2]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>-100 &lt;= Node.val &lt;= 100</code></li>
</ul>

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def __init__(self):
        self.diameter = 0

    def depth(self, root: Optional[TreeNode]) -> int:
        left = self.depth(root.left) if root.left else 0
        right = self.depth(root.right) if root.right else 0
        self.diameter = max(self.diameter, left + right)

        return 1 + max(left, right)

    def diameterOfBinaryTree(self, root: Optional[TreeNode]) -> int:
        self.depth(root)
        return self.diameter
        
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