Given a binary tree, find the maximum path sum.

For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.

For example:
Given the below binary tree,

       1
      / \
     2   3

Return 6.

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    // Should use private, and declare maxSum as global variable.
    private int maxSum = Integer.MIN_VALUE;
    public int maxPathSum(TreeNode root) {
        helper(root);
        return maxSum;
    }
    private int helper(TreeNode root) {
        if (root == null) return 0;
        int max = root.val;
        int l = helper(root.left);
        int r = helper(root.right);
        if (l > 0) max += l;
        if (r > 0) max += r;
        maxSum = Math.max(maxSum, max);
        if (l > 0 || r > 0) return root.val + Math.max(l, r);
        return root.val;
    }
}

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