What is the ruling on introducing water into the tip of the penis when cleaning oneself (istinja') during fasting?

It was previously stated that introducing water into the male organ (penis) to remove impurity does not invalidate the fast, even though introducing water is not required. And if it is confirmed that the water returned and did not go inside, then it does not affect the fast. As for instilling water into the urethra, scholars have differed as to whether it breaks the fast or not. The Malikis held that it does not break the fast because it does not reach the stomach, while the prevalent opinion among the Shafi'is is that it invalidates the fast.