def dict_list_to_list_dict(dict_list):
    """Transform a list of dictionaries to a dictionary of list"""
    list_dict = {}
    key_list = set(key for d in dict_list for key in d)
    for dictionary in dict_list:
        for key in key_list:
            val = dictionary.get(key)
            if key in list_dict:
                list_dict[key].append(val)
            else:
                list_dict[key] = [val]

    return list_dict