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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def add_functions(spec_dict: Mapping[str, Any]) -> Mapping[str, Any]: """Add function keys to spec_dict Args: spec_dict (Mapping[str, Any]):
 bel specification dictionary Returns: Mapping[str, Any]: bel specification dictionary with added function keys """


    # Class 'Mapping' does not define '__setitem__', so the '[]' operator cannot be used on its instances
    spec_dict["functions"]["list"] = []
    spec_dict["functions"]["list_long"] = []
    spec_dict["functions"]["list_short"] = []

    spec_dict["functions"]["primary"] = {}
    spec_dict["functions"]["primary"]["list_long"] = []
    spec_dict["functions"]["primary"]["list_short"] = []

    spec_dict["functions"]["modifier"] = {}
    spec_dict["functions"]["modifier"]["list_long"] = []
    spec_dict["functions"]["modifier"]["list_short"] = []

    spec_dict["functions"]["to_short"] = {}
    spec_dict["functions"]["to_long"] = {}

    for func_name in spec_dict["functions"]["info"]:

        abbreviated_name = spec_dict["functions"]["info"][func_name]["abbreviation"]

        spec_dict["functions"]["list"].extend((func_name, abbreviated_name))

        spec_dict["functions"]["list_long"].append(func_name)
        spec_dict["functions"]["list_short"].append(abbreviated_name)

        if spec_dict["functions"]["info"][func_name]["type"] == "primary":
            spec_dict["functions"]["primary"]["list_long"].append(func_name)
            spec_dict["functions"]["primary"]["list_short"].append(abbreviated_name)
        else:
            spec_dict["functions"]["modifier"]["list_long"].append(func_name)
            spec_dict["functions"]["modifier"]["list_short"].append(abbreviated_name)

        spec_dict["functions"]["to_short"][abbreviated_name] = abbreviated_name
        spec_dict["functions"]["to_short"][func_name] = abbreviated_name

        spec_dict["functions"]["to_long"][abbreviated_name] = func_name
        spec_dict["functions"]["to_long"][func_name] = func_name

    return spec_dict