<p>Given the <code>root</code> of a binary tree, the depth of each node is <strong>the shortest distance to the root</strong>.</p>

<p>Return <em>the smallest subtree</em> such that it contains <strong>all the deepest nodes</strong> in the original tree.</p>

<p>A node is called <strong>the deepest</strong> if it has the largest depth possible among any node in the entire tree.</p>

<p>The <strong>subtree</strong> of a node is a tree consisting of that node, plus the set of all descendants of that node.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/07/01/sketch1.png" style="width: 600px; height: 510px;" />
<pre>
<strong>Input:</strong> root = [3,5,1,6,2,0,8,null,null,7,4]
<strong>Output:</strong> [2,7,4]
<strong>Explanation:</strong> We return the node with value 2, colored in yellow in the diagram.
The nodes coloured in blue are the deepest nodes of the tree.
Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest subtree among them, so we return it.
</pre>

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

<pre>
<strong>Input:</strong> root = [1]
<strong>Output:</strong> [1]
<strong>Explanation:</strong> The root is the deepest node in the tree.
</pre>

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

<pre>
<strong>Input:</strong> root = [0,1,3,null,2]
<strong>Output:</strong> [2]
<strong>Explanation:</strong> The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 and 0 but the subtree of node 2 is the smallest.
</pre>

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

<ul>
	<li>The number of nodes in the tree will be in the range <code>[1, 500]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 500</code></li>
	<li>The values of the nodes in the tree are <strong>unique</strong>.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Note:</strong> This question is the same as 1123: <a href="https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/" target="_blank">https://leetcode.com/problems/lowest-common-ancestor-of-deepest-leaves/</a></p>

# 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 subtreeWithAllDeepest(self, root: TreeNode) -> TreeNode:
        
        def dfs(node: Optional[TreeNode]) -> tuple[int, Optional[TreeNode]]:
            if node is None:
                return 0, None

            left_max, left_tree = dfs(node.left)
            right_max, right_tree = dfs(node.right)

            if left_max > right_max:
                return 1+left_max, left_tree
            elif left_max < right_max:
                return 1+right_max, right_tree
            else:
                return 1+left_max, node
        
        _, node = dfs(root)
        return node
16700