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Count Array Inversions

An inversion in an array is a pair of elements `(arr[i], arr[j])` such that `i < j` and `arr[i] > arr[j]`. Write a Python function `count_inversions` that takes a list of integers as input and returns the number of inversions in the array.

#### Example Usage
```python [main.nopy]
print(count_inversions([1, 20, 6, 4, 5]))  # Output: 5
print(count_inversions([1, 2, 1]))         # Output: 1
print(count_inversions([1, 2, 5, 6, 1]))  # Output: 3
```

#### Constraints
- The input list will contain integers.
- The list can be empty, in which case the function should return `0`.
def count_inversions(arr):
    """
    Count the number of inversions in the array.

    Args:
        arr (list): A list of integers.

    Returns:
        int: The number of inversions in the array.
    """
    # Initialize the inversion count
    inversion_count = 0

    # Implement the logic to count inversions
    # Placeholder for the solution

    return inversion_count
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