<p>You are given the <code>root</code> of a binary tree.</p>

<p>A ZigZag path for a binary tree is defined as follow:</p>

<ul>
	<li>Choose <strong>any </strong>node in the binary tree and a direction (right or left).</li>
	<li>If the current direction is right, move to the right child of the current node; otherwise, move to the left child.</li>
	<li>Change the direction from right to left or from left to right.</li>
	<li>Repeat the second and third steps until you can&#39;t move in the tree.</li>
</ul>

<p>Zigzag length is defined as the number of nodes visited - 1. (A single node has a length of 0).</p>

<p>Return <em>the longest <strong>ZigZag</strong> path contained in that tree</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/22/sample_1_1702.png" style="width: 221px; height: 383px;" />
<pre>
<strong>Input:</strong> root = [1,null,1,1,1,null,null,1,1,null,1,null,null,null,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Longest ZigZag path in blue nodes (right -&gt; left -&gt; right).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/01/22/sample_2_1702.png" style="width: 157px; height: 329px;" />
<pre>
<strong>Input:</strong> root = [1,1,1,null,1,null,null,1,1,null,1]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Longest ZigZag path in blue nodes (left -&gt; right -&gt; left -&gt; right).
</pre>

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

<pre>
<strong>Input:</strong> root = [1]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 5 * 10<sup>4</sup>]</code>.</li>
	<li><code>1 &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 longestZigZag(self, root: Optional[TreeNode]) -> int:
        return max(self.helper(root.right, False, 0), self.helper(root.left, True, 0))
    def helper(self, root, isLeft, depth):
        if not root:
            return depth
        if isLeft:
            depth = max(depth, self.helper(root.right, False, depth + 1), self.helper(root.left, True, 0))
        else:
            depth = max(depth, self.helper(root.left, True, depth + 1), self.helper(root.right, False, 0))
        return depth
        
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