Hi @asehmi,
thank you so much. This is great.
I always got a “was created with a default value but also had its value set via the Session State API.” warning because I tried value=session.n, key='n'. I didn’t realize the warning would not appear if you used another key within session_state as value. 
Regarding the init() function: You are totally right. I just copied a MWE from my code and deleted non-relevant lines. In my actual app I am doing some more work and checks inside this init() function.
Again, thank you!