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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 uniqued(layer, column=0):
 """Group inputs to a layer, so that the layer only has to compute for the unique values. The data is transformed back before output, and the same transformation is applied for the gradient. Effectively, this is a cache local to each minibatch. The uniqued wrapper is useful for word inputs, because common words are seen often, but we may want to compute complicated features for the words, using e.g. character LSTM. """


    def uniqued_fwd(X, drop=0.0):
        keys = X[:, column]
        keys = layer.ops.xp.ascontiguousarray(keys)
        if not isinstance(keys, numpy.ndarray):
            keys = keys.get()
        uniq_keys, ind, inv, counts = numpy.unique(
            keys, return_index=True, return_inverse=True, return_counts=True
        )
        X_uniq = layer.ops.xp.ascontiguousarray(X[ind])
        Y_uniq, bp_Y_uniq = layer.begin_update(X_uniq, drop=drop)
        Y = Y_uniq[inv].reshape((X.shape[0],) + Y_uniq.shape[1:])

        def uniqued_bwd(dY, sgd=None):
            dY_uniq = layer.ops.allocate(Y_uniq.shape, dtype="f")
            layer.ops.scatter_add(dY_uniq, layer.ops.asarray(inv, dtype="i"), dY)
            d_uniques = bp_Y_uniq(dY_uniq, sgd=sgd)
            if d_uniques is not None:
                dX = (d_uniques / counts)[inv]
                return dX
            else:
                return None

        return Y, uniqued_bwd

    model = wrap(uniqued_fwd, layer)
    return model