Given a non-empty 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.

Example 1:

Input: [1,2,3]

1
/ \
2 3

Output: 6
Example 2:

Input: [-10,9,20,null,null,15,7]

-10
/ \
9 20
/ \
15 7

Output: 42

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