Partition a list of strings into n number of partitions which are deterministically reproducible, given n can change

Question

I have this requirement wherein I need to assign every string in a list, a partition in the range [1,n] randomly. These partitions should be reproducible and should not change on varying n.

I am able to achieve the first requirement pretty easily using hashlib in python. The issue is the second requirement.

For eg:

import hashlib
string = "johndoe"
digest = hashlib.md5(string.encode()).hexdigest()
print("Partition id:", int(digest,16)%8)

This gives me 7 for n = 8. But if n = 9, the partition id changes to 4

How can I retain and reproduce the partitions for a given string on varying n?

The number of partitions n is a number in [8,50] The size of the list is < 200,000

If reproducing is not possible, is a solution with minimum movement of strings between the partitions on the cards?