------
## 最终结论
```python
def count_Intgral_Points(x1, y1, x2, y2):
    # Calculate the number of integral coordinates inside the square
    if x1 >= x2 or y1 >= y2:
        return 0  # If the coordinates do not form a valid square
    
    # The number of integral points strictly inside the square
    return (x2 - x1 - 1) * (y2 - y1 - 1)
```