__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

################################################################################
### 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 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.__root = root = _Link()    # sentinel node for the doubly linked list
            root.prev = root.next = root
            self.__map = {}
        self.update(*args, **kwds)

    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 __setitem__(self, key, value):
        '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 = root.prev = _proxy(link)
        dict.__setitem__(self, key, value)

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

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

    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')
        key = next(reversed(self) if last else iter(self))
        value = self.pop(key)
        return key, value

    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)

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

        '''
        return not 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):
            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 '%(typename)s(%(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 tuple(self) \n\n''' % locals()
    for i, name in enumerate(field_names):
        template += '        %s = _property(_itemgetter(%d))\n' % (name, 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' + template) from e
    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
########################################################################

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:
                    for elem, count in iterable.items():
                        self[elem] += count
                else:
                    dict.update(self, iterable) # fast path when counter is empty
            else:
                for elem in iterable:
                    self[elem] += 1
        if kwds:
            self.update(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):
        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()))
