reverse/inverse a mapping but with multiple values for each key

multi mappping dictionary , reverse/inverse

'''

mrg_dictionary: {15: {16, 19, 21, 23}, 22: {18}}

inv_merging_led_dict: {16: 15, 19: 15, 21: 15, 23: 15, 18: 22}

    mrg_dictionary --> inv_merging_led_dict

'''

mrg_dictionary = {15: {16, 19, 21, 23}, 22: {18}}

inv_merging_led_dict = {value:key for key in mrg_dictionary for value in mrg_dictionary[key]}

print(inv_merging_led_dict)

'''

inv_merging_led_dict: {16: 15, 19: 15, 21: 15, 23: 15, 18: 22}

mrg_dictionary: {15: {16, 19, 21, 23}, 22: {18}}

    inv_merging_led_dict --> mrg_dictionary

'''

valueset = set(inv_merging_led_dict.values())

mrg_dictionary = {k:set() for k in valueset}    # {15:set, 18:set()}

for key in mrg_dictionary.keys():

    pop_k_list = []

    for k in inv_merging_led_dict:

        if inv_merging_led_dict[k] == key:

            mrg_dictionary[key].add(k)

            pop_k_list.append(k)

    for k in pop_k_list:

        inv_merging_led_dict.pop(k)

print('mrg_dictionary', mrg_dictionary)