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Maximum Sum of Bitonic Subsequence

Write a function `max_sum_bitonic_subsequence(arr: List[int]) -> int` that takes an array of integers and finds the maximum sum of a bitonic subsequence for the given array. A sequence is bitonic if it is first increasing and then decreasing.

#### Example Usage:
```python [main.nopy]
max_sum_bitonic_subsequence([1, 15, 51, 45, 33, 100, 12, 18, 9])
# Output: 194

max_sum_bitonic_subsequence([80, 60, 30, 40, 20, 10])
# Output: 210

max_sum_bitonic_subsequence([2, 3, 14, 16, 21, 23, 29, 30])
# Output: 138
```
from typing import List

def max_sum_bitonic_subsequence(arr: List[int]) -> int:
    """
    Calculate the maximum sum of a bitonic subsequence in the given array.
    
    Args:
    arr (List[int]): The input array of integers.
    
    Returns:
    int: The maximum sum of a bitonic subsequence.
    """
    # Placeholder for the solution
    pass
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