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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 _smooth_the_residuals(self):
 """ Apply the MID_SPAN to the residuals of the primary smooths. "For stability reasons, it turns out to be a little better to smooth |r_{i}(J)| against xi" - [1] """

        for primary_smooth in self._primary_smooths:
            smooth = smoother.perform_smooth(self.x,
                                             primary_smooth.cross_validated_residual,
                                             MID_SPAN)
            self._residual_smooths.append(smooth.smooth_result)