reverse a 1 to n dictionary in python

Question

I would like to reverse a 1 to n dictionnary in python. Initial dictionnary:

initial = {'A1':'A','A2':'A','B1':'B'}

I would like to get the following result:

final = {'A':['A1','A2'],'B':['B1']}

Do you know how I could do that efficiently?

Many thanks