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Count Equal Numbers

Write a Python function `count_equal_numbers(a, b, c)` that takes three integers as input and returns the count of numbers that are equal among them. If all three numbers are different, the function should return `0`. If two numbers are equal, it should return `2`. If all three numbers are equal, it should return `3`.

#### Example Usage
```python [main.nopy]
count_equal_numbers(1, 1, 1)  # Output: 3
count_equal_numbers(1, 2, 3)  # Output: 0
count_equal_numbers(1, 2, 2)  # Output: 2
```
def count_equal_numbers(a: int, b: int, c: int) -> int:
    """
    Count the number of equal numbers among the three given integers.

    Args:
        a (int): The first integer.
        b (int): The second integer.
        c (int): The third integer.

    Returns:
        int: The count of equal numbers.
    """
    # Implement the logic to count equal numbers
    pass
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