A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.

The path sum of a path is the sum of the node's values in the path.

Given the `root` of a binary tree, return the maximum path sum of any non-empty path.

Example 1:

    Input: root = [1,2,3]
    Output: 6
    Explanation: The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.

Example 2:

    Input: root = [-10,9,20,null,null,15,7]
    Output: 42
    Explanation: The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.

Constraints:

- The number of nodes in the tree is in the range `[1, 3 * 104]`.
- `-1000 <= Node.val <= 1000`