We are given the root node of a maximum tree: a tree where every node has a value greater than any other value in its subtree.
Just as in the previous problem, the given tree was constructed from an list A (root = Construct(A)) recursively with the following Construct(A) routine:
If A is empty, return null.
Otherwise, let A[i] be the largest element of A.  Create a root node with value A[i].
The left child of root will be Construct([A[0], A[1], ..., A[i-1]])
The right child of root will be Construct([A[i+1], A[i+2], ..., A[A.length - 1]])
Return root.
Note that we were not given A directly, only a root node root = Construct(A).
Suppose B is a copy of A with the value val appended to it.  It is guaranteed that B has unique values.
Return Construct(B).
Example 1:
Input: root = [4,1,3,null,null,2], val = 5
Output: [5,4,null,1,3,null,null,2]
Explanation: A = [1,4,2,3], B = [1,4,2,3,5]
Example 2:
Input: root = [5,2,4,null,1], val = 3
Output: [5,2,4,null,1,null,3]
Explanation: A = [2,1,5,4], B = [2,1,5,4,3]
Example 3:
Input: root = [5,2,3,null,1], val = 4
Output: [5,2,4,null,1,3]
Explanation: A = [2,1,5,3], B = [2,1,5,3,4]
Constraints:
1 <= B.length <= 100
# 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: TreeNode, val: int) -> TreeNode:
        if root is None:
            return TreeNode(val)
        elif val > root.val:
            n = TreeNode(val)
            n.left = root
            return n
        else:
            n = root
            p = None
            while n is not None and val < n.val:
                n, p = n.right, n
            m = TreeNode(val)
            p.right = m
            m.left = n
            return root
# 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: TreeNode, val: int) -> TreeNode:
        if root is None:
            return TreeNode(val)
        elif val > root.val:
            n = TreeNode(val)
            n.left = root
            return n
        else:
            n = root
            p = None
            while n is not None and val < n.val:
                n, p = n.right, n
            m = TreeNode(val)
            p.right = m
            m.left = n
            return root