#!/usr/bin/env python
import string
from bitarray import bitarray
PARTLEN = 5 # 5 bits per character
CHARS = (string.ascii_lowercase + string.digits)[:2 ** PARTLEN]
# 'abcdefghijklmnopqrstuvwxyz012345'
PARTS = {}
for i, char in enumerate(CHARS):
    PARTS[char] = bitarray(bin(i).lstrip('-0b').rjust(PARTLEN, '0'), endian='big')
# {
#   'a': bitarray('00000'),
#   ...
#   '5': bitarray('11111')
# }
def encode_set(ids):
    times, more = divmod(max(ids) + 1, PARTLEN)
    length = PARTLEN * (times + bool(more))
    ba = bitarray(length, endian='big')
    ba.setall(0)
    
    for id in ids:
        ba[id] = 1
    
    return ''.join(ba.decode(PARTS))
def decode_set(string):
    result = bitarray(endian='big')
    result.encode(PARTS, string)
    return set(result.search(bitarray('1')))
print(encode_set({1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16})) # Buttons in an elevator in Shanghai
# 'o52y'
print(encode_set({1, 4, 11, 16, 24, 29, 33, 35, 39, 45, 47, 51, 56, 58, 62, 64})) # Aronson's sequence
# 'jaiibbcrauikf'
print(decode_set('5'))
# {0, 1, 2, 3, 4}
print(decode_set('choices'))
# {3, 7, 8, 9, 11, 12, 13, 16, 23, 27, 30, 33}