__all__ = ['deque', 'defaultdict', 'namedtuple', 'UserDict', 'UserList',
            'UserString', 'Counter', 'OrderedDict']
# For bootstrapping reasons, the collection ABCs are defined in _abcoll.py.
# They should however be considered an integral part of collections.py.
from _abcoll import *
import _abcoll
__all__ += _abcoll.__all__

from _collections import deque, defaultdict
from operator import itemgetter as _itemgetter
from keyword import iskeyword as _iskeyword
import sys as _sys
import heapq as _heapq
from weakref import proxy as _proxy
from itertools import repeat as _repeat, chain as _chain, starmap as _starmap
from reprlib import recursive_repr as _recursive_repr

################################################################################
### OrderedDict
################################################################################

class _Link(object):
    __slots__ = 'prev', 'next', 'key', '__weakref__'

class OrderedDict(dict, MutableMapping):
    'Dictionary that remembers insertion order'
    # An inherited dict maps keys to values.
    # The inherited dict provides __getitem__, __len__, __contains__, and get.
    # The remaining methods are order-aware.
    # Big-O running times for all methods are the same as for regular dictionaries.

    # The internal self.__map dictionary maps keys to links in a doubly linked list.
    # The circular doubly linked list starts and ends with a sentinel element.
    # The sentinel element never gets deleted (this simplifies the algorithm).
    # The sentinel is stored in self.__hardroot with a weakref proxy in self.__root.
    # The prev/next links are weakref proxies (to prevent circular references).
    # Individual links are kept alive by the hard reference in self.__map.
    # Those hard references disappear when a key is deleted from an OrderedDict.

    def __init__(self, *args, **kwds):
        '''Initialize an ordered dictionary.  Signature is the same as for
        regular dictionaries, but keyword arguments are not recommended
        because their insertion order is arbitrary.

        '''
        if len(args) > 1:
            raise TypeError('expected at most 1 arguments, got %d' % len(args))
        try:
            self.__root
        except AttributeError:
            self.__hardroot = _Link()
            self.__root = root = _proxy(self.__hardroot)
            root.prev = root.next = root
            self.__map = {}
        self.update(*args, **kwds)

    def __setitem__(self, key, value,
                    dict_setitem=dict.__setitem__, proxy=_proxy, Link=_Link):
        'od.__setitem__(i, y) <==> od[i]=y'
        # Setting a new item creates a new link which goes at the end of the linked
        # list, and the inherited dictionary is updated with the new key/value pair.
        if key not in self:
            self.__map[key] = link = Link()
            root = self.__root
            last = root.prev
            link.prev, link.next, link.key = last, root, key
            last.next = link
            root.prev = proxy(link)
        dict_setitem(self, key, value)

    def __delitem__(self, key, dict_delitem=dict.__delitem__):
        'od.__delitem__(y) <==> del od[y]'
        # Deleting an existing item uses self.__map to find the link which is
        # then removed by updating the links in the predecessor and successor nodes.
        dict_delitem(self, key)
        link = self.__map.pop(key)
        link_prev = link.prev
        link_next = link.next
        link_prev.next = link_next
        link_next.prev = link_prev

    def __iter__(self):
        'od.__iter__() <==> iter(od)'
        # Traverse the linked list in order.
        root = self.__root
        curr = root.next
        while curr is not root:
            yield curr.key
            curr = curr.next

    def __reversed__(self):
        'od.__reversed__() <==> reversed(od)'
        # Traverse the linked list in reverse order.
        root = self.__root
        curr = root.prev
        while curr is not root:
            yield curr.key
            curr = curr.prev

    def clear(self):
        'od.clear() -> None.  Remove all items from od.'
        root = self.__root
        root.prev = root.next = root
        self.__map.clear()
        dict.clear(self)

    def popitem(self, last=True):
        '''od.popitem() -> (k, v), return and remove a (key, value) pair.
        Pairs are returned in LIFO order if last is true or FIFO order if false.

        '''
        if not self:
            raise KeyError('dictionary is empty')
        root = self.__root
        if last:
            link = root.prev
            link_prev = link.prev
            link_prev.next = root
            root.prev = link_prev
        else:
            link = root.next
            link_next = link.next
            root.next = link_next
            link_next.prev = root
        key = link.key
        del self.__map[key]
        value = dict.pop(self, key)
        return key, value

    def move_to_end(self, key, last=True):
        '''Move an existing element to the end (or beginning if last==False).

        Raises KeyError if the element does not exist.
        When last=True, acts like a fast version of self[key]=self.pop(key).

        '''
        link = self.__map[key]
        link_prev = link.prev
        link_next = link.next
        link_prev.next = link_next
        link_next.prev = link_prev
        root = self.__root
        if last:
            last = root.prev
            link.prev = last
            link.next = root
            last.next = root.prev = link
        else:
            first = root.next
            link.prev = root
            link.next = first
            root.next = first.prev = link

    def __reduce__(self):
        'Return state information for pickling'
        items = [[k, self[k]] for k in self]
        tmp = self.__map, self.__root, self.__hardroot
        del self.__map, self.__root, self.__hardroot
        inst_dict = vars(self).copy()
        self.__map, self.__root, self.__hardroot = tmp
        if inst_dict:
            return (self.__class__, (items,), inst_dict)
        return self.__class__, (items,)

    def __sizeof__(self):
        sizeof = _sys.getsizeof
        n = len(self) + 1                       # number of links including root
        size = sizeof(self.__dict__)            # instance dictionary
        size += sizeof(self.__map) * 2          # internal dict and inherited dict
        size += sizeof(self.__hardroot) * n     # link objects
        size += sizeof(self.__root) * n         # proxy objects
        return size

    setdefault = MutableMapping.setdefault
    update = MutableMapping.update
    pop = MutableMapping.pop
    keys = MutableMapping.keys
    values = MutableMapping.values
    items = MutableMapping.items
    __ne__ = MutableMapping.__ne__

    @_recursive_repr()
    def __repr__(self):
        'od.__repr__() <==> repr(od)'
        if not self:
            return '%s()' % (self.__class__.__name__,)
        return '%s(%r)' % (self.__class__.__name__, list(self.items()))

    def copy(self):
        'od.copy() -> a shallow copy of od'
        return self.__class__(self)

    @classmethod
    def fromkeys(cls, iterable, value=None):
        '''OD.fromkeys(S[, v]) -> New ordered dictionary with keys from S
        and values equal to v (which defaults to None).

        '''
        d = cls()
        for key in iterable:
            d[key] = value
        return d

    def __eq__(self, other):
        '''od.__eq__(y) <==> od==y.  Comparison to another OD is order-sensitive
        while comparison to a regular mapping is order-insensitive.

        '''
        if isinstance(other, OrderedDict):
            return len(self)==len(other) and \
                   all(p==q for p, q in zip(self.items(), other.items()))
        return dict.__eq__(self, other)


################################################################################
### namedtuple
################################################################################

def namedtuple(typename, field_names, verbose=False, rename=False):
    """Returns a new subclass of tuple with named fields.

    >>> Point = namedtuple('Point', 'x y')
    >>> Point.__doc__                   # docstring for the new class
    'Point(x, y)'
    >>> p = Point(11, y=22)             # instantiate with positional args or keywords
    >>> p[0] + p[1]                     # indexable like a plain tuple
    33
    >>> x, y = p                        # unpack like a regular tuple
    >>> x, y
    (11, 22)
    >>> p.x + p.y                       # fields also accessable by name
    33
    >>> d = p._asdict()                 # convert to a dictionary
    >>> d['x']
    11
    >>> Point(**d)                      # convert from a dictionary
    Point(x=11, y=22)
    >>> p._replace(x=100)               # _replace() is like str.replace() but targets named fields
    Point(x=100, y=22)

    """

    # Parse and validate the field names.  Validation serves two purposes,
    # generating informative error messages and preventing template injection attacks.
    if isinstance(field_names, str):
        field_names = field_names.replace(',', ' ').split() # names separated by whitespace and/or commas
    field_names = tuple(map(str, field_names))
    if rename:
        names = list(field_names)
        seen = set()
        for i, name in enumerate(names):
            if (not all(c.isalnum() or c=='_' for c in name) or _iskeyword(name)
                or not name or name[0].isdigit() or name.startswith('_')
                or name in seen):
                names[i] = '_%d' % i
            seen.add(name)
        field_names = tuple(names)
    for name in (typename,) + field_names:
        if not all(c.isalnum() or c=='_' for c in name):
            raise ValueError('Type names and field names can only contain alphanumeric characters and underscores: %r' % name)
        if _iskeyword(name):
            raise ValueError('Type names and field names cannot be a keyword: %r' % name)
        if name[0].isdigit():
            raise ValueError('Type names and field names cannot start with a number: %r' % name)
    seen_names = set()
    for name in field_names:
        if name.startswith('_') and not rename:
            raise ValueError('Field names cannot start with an underscore: %r' % name)
        if name in seen_names:
            raise ValueError('Encountered duplicate field name: %r' % name)
        seen_names.add(name)

    # Create and fill-in the class template
    numfields = len(field_names)
    argtxt = repr(field_names).replace("'", "")[1:-1]   # tuple repr without parens or quotes
    reprtxt = ', '.join('%s=%%r' % name for name in field_names)
    template = '''class %(typename)s(tuple):
        '%(typename)s(%(argtxt)s)' \n
        __slots__ = () \n
        _fields = %(field_names)r \n
        def __new__(_cls, %(argtxt)s):
            'Create new instance of %(typename)s(%(argtxt)s)'
            return _tuple.__new__(_cls, (%(argtxt)s)) \n
        @classmethod
        def _make(cls, iterable, new=tuple.__new__, len=len):
            'Make a new %(typename)s object from a sequence or iterable'
            result = new(cls, iterable)
            if len(result) != %(numfields)d:
                raise TypeError('Expected %(numfields)d arguments, got %%d' %% len(result))
            return result \n
        def __repr__(self):
            'Return a nicely formatted representation string'
            return self.__class__.__name__ + '(%(reprtxt)s)' %% self \n
        def _asdict(self):
            'Return a new OrderedDict which maps field names to their values'
            return OrderedDict(zip(self._fields, self)) \n
        def _replace(_self, **kwds):
            'Return a new %(typename)s object replacing specified fields with new values'
            result = _self._make(map(kwds.pop, %(field_names)r, _self))
            if kwds:
                raise ValueError('Got unexpected field names: %%r' %% kwds.keys())
            return result \n
        def __getnewargs__(self):
            'Return self as a plain tuple.  Used by copy and pickle.'
            return tuple(self) \n\n''' % locals()
    for i, name in enumerate(field_names):
        template += "        %s = _property(_itemgetter(%d), doc='Alias for field number %d')\n" % (name, i, i)
    if verbose:
        print(template)

    # Execute the template string in a temporary namespace and
    # support tracing utilities by setting a value for frame.f_globals['__name__']
    namespace = dict(_itemgetter=_itemgetter, __name__='namedtuple_%s' % typename,
                     OrderedDict=OrderedDict, _property=property, _tuple=tuple)
    try:
        exec(template, namespace)
    except SyntaxError as e:
        raise SyntaxError(e.msg + ':\n\n' + template)
    result = namespace[typename]

    # For pickling to work, the __module__ variable needs to be set to the frame
    # where the named tuple is created.  Bypass this step in enviroments where
    # sys._getframe is not defined (Jython for example) or sys._getframe is not
    # defined for arguments greater than 0 (IronPython).
    try:
        result.__module__ = _sys._getframe(1).f_globals.get('__name__', '__main__')
    except (AttributeError, ValueError):
        pass

    return result


########################################################################
###  Counter
########################################################################

def _count_elements(mapping, iterable):
    'Tally elements from the iterable.'
    mapping_get = mapping.get
    for elem in iterable:
        mapping[elem] = mapping_get(elem, 0) + 1

try:                                    # Load C helper function if available
    from _collections import _count_elements
except ImportError:
    pass

class Counter(dict):
    '''Dict subclass for counting hashable items.  Sometimes called a bag
    or multiset.  Elements are stored as dictionary keys and their counts
    are stored as dictionary values.

    >>> c = Counter('abracadabra')      # count elements from a string

    >>> c.most_common(3)                # three most common elements
    [('a', 5), ('r', 2), ('b', 2)]
    >>> sorted(c)                       # list all unique elements
    ['a', 'b', 'c', 'd', 'r']
    >>> ''.join(sorted(c.elements()))   # list elements with repetitions
    'aaaaabbcdrr'
    >>> sum(c.values())                 # total of all counts
    11

    >>> c['a']                          # count of letter 'a'
    5
    >>> for elem in 'shazam':           # update counts from an iterable
    ...     c[elem] += 1                # by adding 1 to each element's count
    >>> c['a']                          # now there are seven 'a'
    7
    >>> del c['r']                      # remove all 'r'
    >>> c['r']                          # now there are zero 'r'
    0

    >>> d = Counter('simsalabim')       # make another counter
    >>> c.update(d)                     # add in the second counter
    >>> c['a']                          # now there are nine 'a'
    9

    >>> c.clear()                       # empty the counter
    >>> c
    Counter()

    Note:  If a count is set to zero or reduced to zero, it will remain
    in the counter until the entry is deleted or the counter is cleared:

    >>> c = Counter('aaabbc')
    >>> c['b'] -= 2                     # reduce the count of 'b' by two
    >>> c.most_common()                 # 'b' is still in, but its count is zero
    [('a', 3), ('c', 1), ('b', 0)]

    '''
    # References:
    #   http://en.wikipedia.org/wiki/Multiset
    #   http://www.gnu.org/software/smalltalk/manual-base/html_node/Bag.html
    #   http://www.demo2s.com/Tutorial/Cpp/0380__set-multiset/Catalog0380__set-multiset.htm
    #   http://code.activestate.com/recipes/259174/
    #   Knuth, TAOCP Vol. II section 4.6.3

    def __init__(self, iterable=None, **kwds):
        '''Create a new, empty Counter object.  And if given, count elements
        from an input iterable.  Or, initialize the count from another mapping
        of elements to their counts.

        >>> c = Counter()                           # a new, empty counter
        >>> c = Counter('gallahad')                 # a new counter from an iterable
        >>> c = Counter({'a': 4, 'b': 2})           # a new counter from a mapping
        >>> c = Counter(a=4, b=2)                   # a new counter from keyword args

        '''
        self.update(iterable, **kwds)

    def __missing__(self, key):
        'The count of elements not in the Counter is zero.'
        # Needed so that self[missing_item] does not raise KeyError
        return 0

    def most_common(self, n=None):
        '''List the n most common elements and their counts from the most
        common to the least.  If n is None, then list all element counts.

        >>> Counter('abracadabra').most_common(3)
        [('a', 5), ('r', 2), ('b', 2)]

        '''
        # Emulate Bag.sortedByCount from Smalltalk
        if n is None:
            return sorted(self.items(), key=_itemgetter(1), reverse=True)
        return _heapq.nlargest(n, self.items(), key=_itemgetter(1))

    def elements(self):
        '''Iterator over elements repeating each as many times as its count.

        >>> c = Counter('ABCABC')
        >>> sorted(c.elements())
        ['A', 'A', 'B', 'B', 'C', 'C']

        # Knuth's example for prime factors of 1836:  2**2 * 3**3 * 17**1
        >>> prime_factors = Counter({2: 2, 3: 3, 17: 1})
        >>> product = 1
        >>> for factor in prime_factors.elements():     # loop over factors
        ...     product *= factor                       # and multiply them
        >>> product
        1836

        Note, if an element's count has been set to zero or is a negative
        number, elements() will ignore it.

        '''
        # Emulate Bag.do from Smalltalk and Multiset.begin from C++.
        return _chain.from_iterable(_starmap(_repeat, self.items()))

    # Override dict methods where necessary

    @classmethod
    def fromkeys(cls, iterable, v=None):
        # There is no equivalent method for counters because setting v=1
        # means that no element can have a count greater than one.
        raise NotImplementedError(
            'Counter.fromkeys() is undefined.  Use Counter(iterable) instead.')

    def update(self, iterable=None, **kwds):
        '''Like dict.update() but add counts instead of replacing them.

        Source can be an iterable, a dictionary, or another Counter instance.

        >>> c = Counter('which')
        >>> c.update('witch')           # add elements from another iterable
        >>> d = Counter('watch')
        >>> c.update(d)                 # add elements from another counter
        >>> c['h']                      # four 'h' in which, witch, and watch
        4

        '''
        # The regular dict.update() operation makes no sense here because the
        # replace behavior results in the some of original untouched counts
        # being mixed-in with all of the other counts for a mismash that
        # doesn't have a straight-forward interpretation in most counting
        # contexts.  Instead, we implement straight-addition.  Both the inputs
        # and outputs are allowed to contain zero and negative counts.

        if iterable is not None:
            if isinstance(iterable, Mapping):
                if self:
                    self_get = self.get
                    for elem, count in iterable.items():
                        self[elem] = count + self_get(elem, 0)
                else:
                    dict.update(self, iterable) # fast path when counter is empty
            else:
                _count_elements(self, iterable)
        if kwds:
            self.update(kwds)

    def subtract(self, iterable=None, **kwds):
        '''Like dict.update() but subtracts counts instead of replacing them.
        Counts can be reduced below zero.  Both the inputs and outputs are
        allowed to contain zero and negative counts.

        Source can be an iterable, a dictionary, or another Counter instance.

        >>> c = Counter('which')
        >>> c.subtract('witch')             # subtract elements from another iterable
        >>> c.subtract(Counter('watch'))    # subtract elements from another counter
        >>> c['h']                          # 2 in which, minus 1 in witch, minus 1 in watch
        0
        >>> c['w']                          # 1 in which, minus 1 in witch, minus 1 in watch
        -1

        '''
        if iterable is not None:
            self_get = self.get
            if isinstance(iterable, Mapping):
                for elem, count in iterable.items():
                    self[elem] = self_get(elem, 0) - count
            else:
                for elem in iterable:
                    self[elem] = self_get(elem, 0) - 1
        if kwds:
            self.subtract(kwds)

    def copy(self):
        'Like dict.copy() but returns a Counter instance instead of a dict.'
        return Counter(self)

    def __delitem__(self, elem):
        'Like dict.__delitem__() but does not raise KeyError for missing values.'
        if elem in self:
            dict.__delitem__(self, elem)

    def __repr__(self):
        if not self:
            return '%s()' % self.__class__.__name__
        items = ', '.join(map('%r: %r'.__mod__, self.most_common()))
        return '%s({%s})' % (self.__class__.__name__, items)

    # Multiset-style mathematical operations discussed in:
    #       Knuth TAOCP Volume II section 4.6.3 exercise 19
    #       and at http://en.wikipedia.org/wiki/Multiset
    #
    # Outputs guaranteed to only include positive counts.
    #
    # To strip negative and zero counts, add-in an empty counter:
    #       c += Counter()

    def __add__(self, other):
        '''Add counts from two counters.

        >>> Counter('abbb') + Counter('bcc')
        Counter({'b': 4, 'c': 2, 'a': 1})

        '''
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem in set(self) | set(other):
            newcount = self[elem] + other[elem]
            if newcount > 0:
                result[elem] = newcount
        return result

    def __sub__(self, other):
        ''' Subtract count, but keep only results with positive counts.

        >>> Counter('abbbc') - Counter('bccd')
        Counter({'b': 2, 'a': 1})

        '''
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem in set(self) | set(other):
            newcount = self[elem] - other[elem]
            if newcount > 0:
                result[elem] = newcount
        return result

    def __or__(self, other):
        '''Union is the maximum of value in either of the input counters.

        >>> Counter('abbb') | Counter('bcc')
        Counter({'b': 3, 'c': 2, 'a': 1})

        '''
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        for elem in set(self) | set(other):
            p, q = self[elem], other[elem]
            newcount = q if p < q else p
            if newcount > 0:
                result[elem] = newcount
        return result

    def __and__(self, other):
        ''' Intersection is the minimum of corresponding counts.

        >>> Counter('abbb') & Counter('bcc')
        Counter({'b': 1})

        '''
        if not isinstance(other, Counter):
            return NotImplemented
        result = Counter()
        if len(self) < len(other):
            self, other = other, self
        for elem in filter(self.__contains__, other):
            p, q = self[elem], other[elem]
            newcount = p if p < q else q
            if newcount > 0:
                result[elem] = newcount
        return result


################################################################################
### UserDict
################################################################################

class UserDict(MutableMapping):

    # Start by filling-out the abstract methods
    def __init__(self, dict=None, **kwargs):
        self.data = {}
        if dict is not None:
            self.update(dict)
        if len(kwargs):
            self.update(kwargs)
    def __len__(self): return len(self.data)
    def __getitem__(self, key):
        if key in self.data:
            return self.data[key]
        if hasattr(self.__class__, "__missing__"):
            return self.__class__.__missing__(self, key)
        raise KeyError(key)
    def __setitem__(self, key, item): self.data[key] = item
    def __delitem__(self, key): del self.data[key]
    def __iter__(self):
        return iter(self.data)

    # Modify __contains__ to work correctly when __missing__ is present
    def __contains__(self, key):
        return key in self.data

    # Now, add the methods in dicts but not in MutableMapping
    def __repr__(self): return repr(self.data)
    def copy(self):
        if self.__class__ is UserDict:
            return UserDict(self.data.copy())
        import copy
        data = self.data
        try:
            self.data = {}
            c = copy.copy(self)
        finally:
            self.data = data
        c.update(self)
        return c
    @classmethod
    def fromkeys(cls, iterable, value=None):
        d = cls()
        for key in iterable:
            d[key] = value
        return d


################################################################################
### UserList
################################################################################

class UserList(MutableSequence):
    """A more or less complete user-defined wrapper around list objects."""
    def __init__(self, initlist=None):
        self.data = []
        if initlist is not None:
            # XXX should this accept an arbitrary sequence?
            if type(initlist) == type(self.data):
                self.data[:] = initlist
            elif isinstance(initlist, UserList):
                self.data[:] = initlist.data[:]
            else:
                self.data = list(initlist)
    def __repr__(self): return repr(self.data)
    def __lt__(self, other): return self.data <  self.__cast(other)
    def __le__(self, other): return self.data <= self.__cast(other)
    def __eq__(self, other): return self.data == self.__cast(other)
    def __ne__(self, other): return self.data != self.__cast(other)
    def __gt__(self, other): return self.data >  self.__cast(other)
    def __ge__(self, other): return self.data >= self.__cast(other)
    def __cast(self, other):
        return other.data if isinstance(other, UserList) else other
    def __contains__(self, item): return item in self.data
    def __len__(self): return len(self.data)
    def __getitem__(self, i): return self.data[i]
    def __setitem__(self, i, item): self.data[i] = item
    def __delitem__(self, i): del self.data[i]
    def __add__(self, other):
        if isinstance(other, UserList):
            return self.__class__(self.data + other.data)
        elif isinstance(other, type(self.data)):
            return self.__class__(self.data + other)
        return self.__class__(self.data + list(other))
    def __radd__(self, other):
        if isinstance(other, UserList):
            return self.__class__(other.data + self.data)
        elif isinstance(other, type(self.data)):
            return self.__class__(other + self.data)
        return self.__class__(list(other) + self.data)
    def __iadd__(self, other):
        if isinstance(other, UserList):
            self.data += other.data
        elif isinstance(other, type(self.data)):
            self.data += other
        else:
            self.data += list(other)
        return self
    def __mul__(self, n):
        return self.__class__(self.data*n)
    __rmul__ = __mul__
    def __imul__(self, n):
        self.data *= n
        return self
    def append(self, item): self.data.append(item)
    def insert(self, i, item): self.data.insert(i, item)
    def pop(self, i=-1): return self.data.pop(i)
    def remove(self, item): self.data.remove(item)
    def count(self, item): return self.data.count(item)
    def index(self, item, *args): return self.data.index(item, *args)
    def reverse(self): self.data.reverse()
    def sort(self, *args, **kwds): self.data.sort(*args, **kwds)
    def extend(self, other):
        if isinstance(other, UserList):
            self.data.extend(other.data)
        else:
            self.data.extend(other)


################################################################################
### UserString
################################################################################

class UserString(Sequence):
    def __init__(self, seq):
        if isinstance(seq, str):
            self.data = seq
        elif isinstance(seq, UserString):
            self.data = seq.data[:]
        else:
            self.data = str(seq)
    def __str__(self): return str(self.data)
    def __repr__(self): return repr(self.data)
    def __int__(self): return int(self.data)
    def __float__(self): return float(self.data)
    def __complex__(self): return complex(self.data)
    def __hash__(self): return hash(self.data)

    def __eq__(self, string):
        if isinstance(string, UserString):
            return self.data == string.data
        return self.data == string
    def __ne__(self, string):
        if isinstance(string, UserString):
            return self.data != string.data
        return self.data != string
    def __lt__(self, string):
        if isinstance(string, UserString):
            return self.data < string.data
        return self.data < string
    def __le__(self, string):
        if isinstance(string, UserString):
            return self.data <= string.data
        return self.data <= string
    def __gt__(self, string):
        if isinstance(string, UserString):
            return self.data > string.data
        return self.data > string
    def __ge__(self, string):
        if isinstance(string, UserString):
            return self.data >= string.data
        return self.data >= string

    def __contains__(self, char):
        if isinstance(char, UserString):
            char = char.data
        return char in self.data

    def __len__(self): return len(self.data)
    def __getitem__(self, index): return self.__class__(self.data[index])
    def __add__(self, other):
        if isinstance(other, UserString):
            return self.__class__(self.data + other.data)
        elif isinstance(other, str):
            return self.__class__(self.data + other)
        return self.__class__(self.data + str(other))
    def __radd__(self, other):
        if isinstance(other, str):
            return self.__class__(other + self.data)
        return self.__class__(str(other) + self.data)
    def __mul__(self, n):
        return self.__class__(self.data*n)
    __rmul__ = __mul__
    def __mod__(self, args):
        return self.__class__(self.data % args)

    # the following methods are defined in alphabetical order:
    def capitalize(self): return self.__class__(self.data.capitalize())
    def center(self, width, *args):
        return self.__class__(self.data.center(width, *args))
    def count(self, sub, start=0, end=_sys.maxsize):
        if isinstance(sub, UserString):
            sub = sub.data
        return self.data.count(sub, start, end)
    def encode(self, encoding=None, errors=None): # XXX improve this?
        if encoding:
            if errors:
                return self.__class__(self.data.encode(encoding, errors))
            return self.__class__(self.data.encode(encoding))
        return self.__class__(self.data.encode())
    def endswith(self, suffix, start=0, end=_sys.maxsize):
        return self.data.endswith(suffix, start, end)
    def expandtabs(self, tabsize=8):
        return self.__class__(self.data.expandtabs(tabsize))
    def find(self, sub, start=0, end=_sys.maxsize):
        if isinstance(sub, UserString):
            sub = sub.data
        return self.data.find(sub, start, end)
    def format(self, *args, **kwds):
        return self.data.format(*args, **kwds)
    def index(self, sub, start=0, end=_sys.maxsize):
        return self.data.index(sub, start, end)
    def isalpha(self): return self.data.isalpha()
    def isalnum(self): return self.data.isalnum()
    def isdecimal(self): return self.data.isdecimal()
    def isdigit(self): return self.data.isdigit()
    def isidentifier(self): return self.data.isidentifier()
    def islower(self): return self.data.islower()
    def isnumeric(self): return self.data.isnumeric()
    def isspace(self): return self.data.isspace()
    def istitle(self): return self.data.istitle()
    def isupper(self): return self.data.isupper()
    def join(self, seq): return self.data.join(seq)
    def ljust(self, width, *args):
        return self.__class__(self.data.ljust(width, *args))
    def lower(self): return self.__class__(self.data.lower())
    def lstrip(self, chars=None): return self.__class__(self.data.lstrip(chars))
    def partition(self, sep):
        return self.data.partition(sep)
    def replace(self, old, new, maxsplit=-1):
        if isinstance(old, UserString):
            old = old.data
        if isinstance(new, UserString):
            new = new.data
        return self.__class__(self.data.replace(old, new, maxsplit))
    def rfind(self, sub, start=0, end=_sys.maxsize):
        if isinstance(sub, UserString):
            sub = sub.data
        return self.data.rfind(sub, start, end)
    def rindex(self, sub, start=0, end=_sys.maxsize):
        return self.data.rindex(sub, start, end)
    def rjust(self, width, *args):
        return self.__class__(self.data.rjust(width, *args))
    def rpartition(self, sep):
        return self.data.rpartition(sep)
    def rstrip(self, chars=None):
        return self.__class__(self.data.rstrip(chars))
    def split(self, sep=None, maxsplit=-1):
        return self.data.split(sep, maxsplit)
    def rsplit(self, sep=None, maxsplit=-1):
        return self.data.rsplit(sep, maxsplit)
    def splitlines(self, keepends=0): return self.data.splitlines(keepends)
    def startswith(self, prefix, start=0, end=_sys.maxsize):
        return self.data.startswith(prefix, start, end)
    def strip(self, chars=None): return self.__class__(self.data.strip(chars))
    def swapcase(self): return self.__class__(self.data.swapcase())
    def title(self): return self.__class__(self.data.title())
    def translate(self, *args):
        return self.__class__(self.data.translate(*args))
    def upper(self): return self.__class__(self.data.upper())
    def zfill(self, width): return self.__class__(self.data.zfill(width))


################################################################################
### Simple tests
################################################################################

if __name__ == '__main__':
    # verify that instances can be pickled
    from pickle import loads, dumps
    Point = namedtuple('Point', 'x, y', True)
    p = Point(x=10, y=20)
    assert p == loads(dumps(p))

    # test and demonstrate ability to override methods
    class Point(namedtuple('Point', 'x y')):
        __slots__ = ()
        @property
        def hypot(self):
            return (self.x ** 2 + self.y ** 2) ** 0.5
        def __str__(self):
            return 'Point: x=%6.3f  y=%6.3f  hypot=%6.3f' % (self.x, self.y, self.hypot)

    for p in Point(3, 4), Point(14, 5/7.):
        print (p)

    class Point(namedtuple('Point', 'x y')):
        'Point class with optimized _make() and _replace() without error-checking'
        __slots__ = ()
        _make = classmethod(tuple.__new__)
        def _replace(self, _map=map, **kwds):
            return self._make(_map(kwds.get, ('x', 'y'), self))

    print(Point(11, 22)._replace(x=100))

    Point3D = namedtuple('Point3D', Point._fields + ('z',))
    print(Point3D.__doc__)

    import doctest
    TestResults = namedtuple('TestResults', 'failed attempted')
    print(TestResults(*doctest.testmod()))