------
## 最终结论
```python
def min_steps_to_n_A(n: int) -> int:
    steps = 0
    factor = 2
    
    while n > 1:
        if n % factor == 0:
            steps += factor
            n //= factor
        else:
            factor += 1
            
    return steps

# Example usage:
n = 3
print(min_steps_to_n_A(n))
```