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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 concat(cls, variables, dim='concat_dim', positions=None, shortcut=False):
 """Specialized version of Variable.concat for IndexVariable objects. This exists because we want to avoid converting Index objects to NumPy arrays, if possible. """

        if not isinstance(dim, str):
            dim, = dim.dims

        variables = list(variables)
        first_var = variables[0]

        if any(not isinstance(v, cls) for v in variables):
            raise TypeError('IndexVariable.concat requires that all input '
                            'variables be IndexVariable objects')

        indexes = [v._data.array for v in variables]

        if not indexes:
            data = []
        else:
            data = indexes[0].append(indexes[1:])

            if positions is not None:
                indices = nputils.inverse_permutation(
                    np.concatenate(positions))
                data = data.take(indices)

        attrs = OrderedDict(first_var.attrs)
        if not shortcut:
            for var in variables:
                if var.dims != first_var.dims:
                    raise ValueError('inconsistent dimensions')
                utils.remove_incompatible_items(attrs, var.attrs)

        return cls(first_var.dims, data, attrs)