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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 merge_variables( list_of_variables_dicts, # type: List[Mapping[Any, Variable]] priority_vars=None, # type: Optional[Mapping[Any, Variable]] compat='minimal', # type: str ):
 """Merge dicts of variables, while resolving conflicts appropriately. Parameters lists_of_variables_dicts : list of mappings with Variable values List of mappings for which each value is a xarray.Variable object. priority_vars : mapping with Variable or None values, optional If provided, variables are always taken from this dict in preference to the input variable dictionaries, without checking for conflicts. compat : {'identical', 'equals', 'broadcast_equals', 'minimal', 'no_conflicts'}, optional Type of equality check to use when checking for conflicts. Returns ------- OrderedDict with keys taken by the union of keys on list_of_variable_dicts, and Variable values corresponding to those that should be found on the merged result. """
  # noqa
    if priority_vars is None:
        priority_vars = {}

    _assert_compat_valid(compat)
    dim_compat = min(compat, 'equals', key=_VALID_COMPAT.get)

    lookup = OrderedDefaultDict(list)
    for variables in list_of_variables_dicts:
        for name, var in variables.items():
            lookup[name].append(var)

    # n.b. it's important to fill up merged in the original order in which
    # variables appear
    merged = OrderedDict()  # type: OrderedDict[Any, Variable]

    for name, var_list in lookup.items():
        if name in priority_vars:
            # one of these arguments (e.g., the first for in-place arithmetic
            # or the second for Dataset.update) takes priority
            merged[name] = priority_vars[name]
        else:
            dim_variables = [var for var in var_list if (name,) == var.dims]
            if dim_variables:
                # if there are dimension coordinates, these must be equal (or
                # identical), and they take priority over non-dimension
                # coordinates
                merged[name] = unique_variable(name, dim_variables, dim_compat)
            else:
                try:
                    merged[name] = unique_variable(name, var_list, compat)
                except MergeError:
                    if compat != 'minimal':
                        # we need more than "minimal" compatibility (for which
                        # we drop conflicting coordinates)
                        raise

    return merged