<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def default_sort_key(item, order=None):
 """Return a key that can be used for sorting. The key has the structure: (class_key, (len(args), args), exponent.sort_key(), coefficient) This key is supplied by the sort_key routine of Basic objects when ``item`` is a Basic object or an object (other than a string) that sympifies to a Basic object. Otherwise, this function produces the key. The ``order`` argument is passed along to the sort_key routine and is used to determine how the terms *within* an expression are ordered. (See examples below) ``order`` options are: 'lex', 'grlex', 'grevlex', and reversed values of the same (e.g. 'rev-lex'). The default order value is None (which translates to 'lex'). Examples ======== The following are equivalent ways of getting the key for an object: True Here are some examples of the key that is produced: ((0, 0, 'UndefinedFunction'), (1, ('f',)), ((1, 0, 'Number'), (0, ()), (), 1), 1) ((0, 0, 'str'), (1, ('1',)), ((1, 0, 'Number'), (0, ()), (), 1), 1) ((1, 0, 'Number'), (0, ()), (), 1) ((1, 0, 'Number'), (0, ()), (), 2) While sort_key is a method only defined for SymPy objects, default_sort_key will accept anything as an argument so it is more robust as a sorting key. For the following, using key= lambda i: i.sort_key() would fail because 2 doesn't have a sort_key method; that's why default_sort_key is used. Note, that it also handles sympification of non-string items likes ints: [2, -I, I] The returned key can be used anywhere that a key can be specified for 2 2 Note ---- The key returned is useful for getting items into a canonical order that will be the same across platforms. It is not directly useful for sorting lists of expressions: Since ``a`` has only 1 term, its value of sort_key is unaffected by ``order``: True If ``a`` and ``b`` are combined then the key will differ because there are terms that can be ordered: False [x, 1/x] [1/x, x] But since the keys for each of these terms are independent of ``order``'s value, they don't sort differently when they appear separately in a list: [1/x, x] [1/x, x] The order of terms obtained when using these keys is the order that would be obtained if those terms were *factors* in a product. See Also ======== sympy.core.expr.as_ordered_factors, sympy.core.expr.as_ordered_terms """


    from sympy.core import S, Basic
    from sympy.core.sympify import sympify, SympifyError
    from sympy.core.compatibility import iterable

    if isinstance(item, Basic):
        return item.sort_key(order=order)

    if iterable(item, exclude=string_types):
        if isinstance(item, dict):
            args = item.items()
            unordered = True
        elif isinstance(item, set):
            args = item
            unordered = True
        else:
            # e.g. tuple, list
            args = list(item)
            unordered = False

        args = [default_sort_key(arg, order=order) for arg in args]

        if unordered:
            # e.g. dict, set
            args = sorted(args)

        cls_index, args = 10, (len(args), tuple(args))
    else:
        if not isinstance(item, string_types):
            try:
                item = sympify(item)
            except SympifyError:
                # e.g. lambda x: x
                pass
            else:
                if isinstance(item, Basic):
                    # e.g int -> Integer
                    return default_sort_key(item)
                # e.g. UndefinedFunction

        # e.g. str
        cls_index, args = 0, (1, (str(item),))

    return (cls_index, 0, item.__class__.__name__
            ), args, S.One.sort_key(), S.One