<p>A <strong>maximum tree</strong> is a tree where every node has a value greater than any other value in its subtree.</p>

<p>You are given the <code>root</code> of a maximum binary tree and an integer <code>val</code>.</p>

<p>Just as in the <a href="https://leetcode.com/problems/maximum-binary-tree/" target="_blank">previous problem</a>, the given tree was constructed from a list <code>a</code> (<code>root = Construct(a)</code>) recursively with the following <code>Construct(a)</code> routine:</p>

<ul>
	<li>If <code>a</code> is empty, return <code>null</code>.</li>
	<li>Otherwise, let <code>a[i]</code> be the largest element of <code>a</code>. Create a <code>root</code> node with the value <code>a[i]</code>.</li>
	<li>The left child of <code>root</code> will be <code>Construct([a[0], a[1], ..., a[i - 1]])</code>.</li>
	<li>The right child of <code>root</code> will be <code>Construct([a[i + 1], a[i + 2], ..., a[a.length - 1]])</code>.</li>
	<li>Return <code>root</code>.</li>
</ul>

<p>Note that we were not given <code>a</code> directly, only a root node <code>root = Construct(a)</code>.</p>

<p>Suppose <code>b</code> is a copy of <code>a</code> with the value <code>val</code> appended to it. It is guaranteed that <code>b</code> has unique values.</p>

<p>Return <code>Construct(b)</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/09/maxtree1.JPG" style="width: 376px; height: 235px;" />
<pre>
<strong>Input:</strong> root = [4,1,3,null,null,2], val = 5
<strong>Output:</strong> [5,4,null,1,3,null,null,2]
<strong>Explanation:</strong> a = [1,4,2,3], b = [1,4,2,3,5]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/09/maxtree21.JPG" style="width: 358px; height: 156px;" />
<pre>
<strong>Input:</strong> root = [5,2,4,null,1], val = 3
<strong>Output:</strong> [5,2,4,null,1,null,3]
<strong>Explanation:</strong> a = [2,1,5,4], b = [2,1,5,4,3]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/09/maxtree3.JPG" style="width: 404px; height: 180px;" />
<pre>
<strong>Input:</strong> root = [5,2,3,null,1], val = 4
<strong>Output:</strong> [5,2,4,null,1,3]
<strong>Explanation:</strong> a = [2,1,5,3], b = [2,1,5,3,4]
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 100]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 100</code></li>
	<li>All the values of the tree are <strong>unique</strong>.</li>
	<li><code>1 &lt;= 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 insertIntoMaxTree(self, root: Optional[TreeNode], val: int) -> Optional[TreeNode]:
        if root and root.val>val:
            root.right = self.insertIntoMaxTree(root.right, val)
            return root
        Node = TreeNode(val)
        Node.left = root
        return Node
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