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```/**
* 124. Binary Tree Maximum Path Sum
* Hard
* 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 * 10^4].
* -1000 <= Node.val <= 1000
*/
class TreeNode {
val: number
left: TreeNode | null
right: TreeNode | null
constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
this.val = (val===undefined ? 0 : val)
this.left = (left===undefined ? null : left)
this.right = (right===undefined ? null : right)
}
}

function maxPathSum(root: TreeNode | null): number {

};

console.log(maxPathSum(new TreeNode(1, new TreeNode(2), new TreeNode(3))) === 6);
console.log(maxPathSum(new TreeNode(-10, new TreeNode(9), new TreeNode(20, new TreeNode(15), new TreeNode(7)))) === 42);
```