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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 added(self):
        '''
        Returns all keys that have been added.

        If the keys are in child dictionaries they will be represented with
        . notation
        '''
        def _added(diffs, prefix):
            keys = []
            for key in diffs.keys():
                if isinstance(diffs[key], dict) and 'old' not in diffs[key]:
                    keys.extend(_added(diffs[key],
                                       prefix='{0}{1}.'.format(prefix, key)))
                elif diffs[key]['old'] == self.NONE_VALUE:
                    if isinstance(diffs[key]['new'], dict):
                        keys.extend(
                            _added(diffs[key]['new'],
                                   prefix='{0}{1}.'.format(prefix, key)))
                    else:
                        keys.append('{0}{1}'.format(prefix, key))
            return keys

        return sorted(_added(self._diffs, prefix=''))