------
## 最终结论
```python
def prod_signs(arr):
    if not arr:
        return None
    
    sign_product = 1
    for num in arr:
        if num > 0:
            sign_product *= 1
        elif num < 0:
            sign_product *= -1
        else:
            sign_product = 0
            break

    magnitude_sum = sum(abs(num) for num in arr)
    
    return magnitude_sum * sign_product
```