Binary Tree Maximum Path Sum

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. ### Constraints - The number of nodes in the tree is in the range `[1, 3 * 10^4]`. - `-1000 <= Node.val <= 1000` ### Input Format A single line containing space-separated integers representing the tree in level-order (-1 for null). ### Output Format Print a single integer representing the maximum path sum.