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# Max Sum Path in Binary Tree

Problem Description

Given a binary tree T, find the maximum path sum.

The path may start and end at any node in the tree.

Problem Constraints

1 <= Number of Nodes <= 7e4

-1000 <= Value of Node in T <= 1000

Input Format

The first and the only argument contains a pointer to the root of T, A.

Output Format

Return an integer representing the maximum sum path.

Example Input

Input 1:

```    1
/ \
2   3
```

Input 2:

```       20
/  \
-10   20
/  \
-10  -50
```

Example Output

Output 1:

``` 6
```

Output 2:

``` 40
```

Example Explanation

Explanation 1:

```     The path with maximum sum is: 2 -> 1 -> 3
```

Explanation 2:

```     The path with maximum sum is: 20 -> 20
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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