from typing import Dict


class InvalidKeyError(Exception):
    def __init__(self, key):
        self.message = "Invalid key: {}".format(key)

        super().__init__(key)


class MissingKeyError(Exception):
    def __init__(self, key):
        self.message = "Missing key: {}".format(key)

        super().__init__(key)


def merge(*dicts: [Dict]) -> Dict:
    # Base cases
    if len(dicts) == 0:
        return {}

    if len(dicts) == 1:
        return dicts[0]

    # We merge the first two dicts
    d1, d2 = dicts[0], dicts[1]

    output = d1.copy()

    for key, value in d2.items():
        if type(value) == dict:
            # Merge the two sub-dictionaries
            output[key] = (
                merge(output[key], value)
                if type(output.get(key)) == dict
                else value
            )

        else:
            output[key] = value

    return merge(output, *dicts[2:])


def merge_with_skeleton(data: Dict, skel: Dict) -> Dict:
    """
    Compare a dict with a given skeleton dict, and fill in default values where
    needed.
    """

    # First, check for illegal keys
    for key in data:
        if key not in skel:
            raise InvalidKeyError(key)

    # Then, check the default values
    for key, value in skel.items():
        if key not in data:
            # Raise error if there's not default value
            if value is None:
                raise MissingKeyError(key)

            # Replace with default value
            data[key] = value

        # Error if value is not same type as default value
        elif type(data[key]) != type(value) and value is not None:
            raise TypeError("Invalid value type")

        # Recurse into dicts
        elif type(value) == dict:
            data[key] = merge_with_skeleton(data[key], value)

    return data