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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 _unpickle_sparse_frame_compat(self, state):
 """ Original pickle format """

        series, cols, idx, fv, kind = state

        if not isinstance(cols, Index):  # pragma: no cover
            from pandas.io.pickle import _unpickle_array
            columns = _unpickle_array(cols)
        else:
            columns = cols

        if not isinstance(idx, Index):  # pragma: no cover
            from pandas.io.pickle import _unpickle_array
            index = _unpickle_array(idx)
        else:
            index = idx

        series_dict = DataFrame()
        for col, (sp_index, sp_values) in series.items():
            series_dict[col] = SparseSeries(sp_values, sparse_index=sp_index,
                                            fill_value=fv)

        self._data = to_manager(series_dict, columns, index)
        self._default_fill_value = fv
        self._default_kind = kind