"""
Miscellaneous function (re)definitions from the Py3.4+ standard library
for Python 2.6/2.7.

- math.ceil                (for Python 2.7)
- collections.OrderedDict  (for Python 2.6)
- collections.Counter      (for Python 2.6)
- collections.ChainMap     (for all versions prior to Python 3.3)
- itertools.count          (for Python 2.6, with step parameter)
- subprocess.check_output  (for Python 2.6)
- reprlib.recursive_repr   (for Python 2.6+)
- functools.cmp_to_key     (for Python 2.6)
"""

from __future__ import absolute_import

import subprocess
from math import ceil as oldceil

from operator import itemgetter as _itemgetter, eq as _eq
import sys
import heapq as _heapq
from _weakref import proxy as _proxy
from itertools import repeat as _repeat, chain as _chain, starmap as _starmap
from socket import getaddrinfo, SOCK_STREAM, error, socket

from future.utils import iteritems, itervalues, PY2, PY26, PY3

if PY2:
    from collections import Mapping, MutableMapping
else:
    from collections.abc import Mapping, MutableMapping


def ceil(x):
    """
    Return the ceiling of x as an int.
    This is the smallest integral value >= x.
    """
    return int(oldceil(x))


########################################################################
###  reprlib.recursive_repr decorator from Py3.4
########################################################################

from itertools import islice

if PY3:
    try:
        from _thread import get_ident
    except ImportError:
        from _dummy_thread import get_ident
else:
    try:
        from thread import get_ident
    except ImportError:
        from dummy_thread import get_ident


def recursive_repr(fillvalue='...'):
    'Decorator to make a repr function return fillvalue for a recursive call'

    def decorating_function(user_function):
        repr_running = set()

        def wrapper(self):
            key = id(self), get_ident()
            if key in repr_running:
                return fillvalue
            repr_running.add(key)
            try:
                result = user_function(self)
            finally:
                repr_running.discard(key)
            return result

        # Can't use functools.wraps() here because of bootstrap issues
        wrapper.__module__ = getattr(user_function, '__module__')
        wrapper.__doc__ = getattr(user_function, '__doc__')
        wrapper.__name__ = getattr(user_function, '__name__')
        wrapper.__annotations__ = getattr(user_function, '__annotations__', {})
        return wrapper

    return decorating_function


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

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

class OrderedDict(dict):
    '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 regular dictionaries.

    # The internal self.__map dict 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 in self.__hardroot with a weakref proxy in self.__root.
    # The prev 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__(*args, **kwds):
        '''Initialize an ordered dictionary.  The signature is the same as
        regular dictionaries, but keyword arguments are not recommended because
        their insertion order is arbitrary.

        '''
        if not args:
            raise TypeError("descriptor '__init__' of 'OrderedDict' object "
                            "needs an argument")
        self = args[0]
        args = args[1:]
        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 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 gets
        # 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 __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

    update = __update = MutableMapping.update
    keys = MutableMapping.keys
    values = MutableMapping.values
    items = MutableMapping.items
    __ne__ = MutableMapping.__ne__

    __marker = object()

    def pop(self, key, default=__marker):
        '''od.pop(k[,d]) -> v, remove specified key and return the corresponding
        value.  If key is not found, d is returned if given, otherwise KeyError
        is raised.

        '''
        if key in self:
            result = self[key]
            del self[key]
            return result
        if default is self.__marker:
            raise KeyError(key)
        return default

    def setdefault(self, key, default=None):
        'od.setdefault(k[,d]) -> od.get(k,d), also set od[k]=d if k not in od'
        if key in self:
            return self[key]
        self[key] = default
        return default

    @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 __reduce__(self):
        'Return state information for pickling'
        inst_dict = vars(self).copy()
        for k in vars(OrderedDict()):
            inst_dict.pop(k, None)
        return self.__class__, (), inst_dict or None, None, iter(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.
        If not specified, the value defaults to None.

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

    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 dict.__eq__(self, other) and all(map(_eq, self, other))
        return dict.__eq__(self, other)


# {{{ http://code.activestate.com/recipes/576611/ (r11)

try:
    from operator import itemgetter
    from heapq import nlargest
except ImportError:
    pass

########################################################################
###  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

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('abcdeabcdabcaba')  # count elements from a string

    >>> c.most_common(3)                # three most common elements
    [('a', 5), ('b', 4), ('c', 3)]
    >>> sorted(c)                       # list all unique elements
    ['a', 'b', 'c', 'd', 'e']
    >>> ''.join(sorted(c.elements()))   # list elements with repetitions
    'aaaaabbbbcccdde'
    >>> sum(c.values())                 # total of all counts
    15

    >>> 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['b']                      # remove all 'b'
    >>> c['b']                          # now there are zero 'b'
    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__(*args, **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

        '''
        if not args:
            raise TypeError("descriptor '__init__' of 'Counter' object "
                            "needs an argument")
        self = args[0]
        args = args[1:]
        if len(args) > 1:
            raise TypeError('expected at most 1 arguments, got %d' % len(args))
        super(Counter, self).__init__()
        self.update(*args, **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('abcdeabcdabcaba').most_common(3)
        [('a', 5), ('b', 4), ('c', 3)]

        '''
        # 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(*args, **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 not args:
            raise TypeError("descriptor 'update' of 'Counter' object "
                            "needs an argument")
        self = args[0]
        args = args[1:]
        if len(args) > 1:
            raise TypeError('expected at most 1 arguments, got %d' % len(args))
        iterable = args[0] if args else None
        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:
                    super(Counter, self).update(iterable) # fast path when counter is empty
            else:
                _count_elements(self, iterable)
        if kwds:
            self.update(kwds)

    def subtract(*args, **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 not args:
            raise TypeError("descriptor 'subtract' of 'Counter' object "
                            "needs an argument")
        self = args[0]
        args = args[1:]
        if len(args) > 1:
            raise TypeError('expected at most 1 arguments, got %d' % len(args))
        iterable = args[0] if args else None
        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):
        'Return a shallow copy.'
        return self.__class__(self)

    def __reduce__(self):
        return self.__class__, (dict(self),)

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

    def __repr__(self):
        if not self:
            return '%s()' % self.__class__.__name__
        try:
            items = ', '.join(map('%r: %r'.__mod__, self.most_common()))
            return '%s({%s})' % (self.__class__.__name__, items)
        except TypeError:
            # handle case where values are not orderable
            return '{0}({1!r})'.format(self.__class__.__name__, dict(self))

    # 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, count in self.items():
            newcount = count + other[elem]
            if newcount > 0:
                result[elem] = newcount
        for elem, count in other.items():
            if elem not in self and count > 0:
                result[elem] = count
        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, count in self.items():
            newcount = count - other[elem]
            if newcount > 0:
                result[elem] = newcount
        for elem, count in other.items():
            if elem not in self and count < 0:
                result[elem] = 0 - count
        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, count in self.items():
            other_count = other[elem]
            newcount = other_count if count < other_count else count
            if newcount > 0:
                result[elem] = newcount
        for elem, count in other.items():
            if elem not in self and count > 0:
                result[elem] = count
        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()
        for elem, count in self.items():
            other_count = other[elem]
            newcount = count if count < other_count else other_count
            if newcount > 0:
                result[elem] = newcount
        return result

    def __pos__(self):
        'Adds an empty counter, effectively stripping negative and zero counts'
        return self + Counter()

    def __neg__(self):
        '''Subtracts from an empty counter.  Strips positive and zero counts,
        and flips the sign on negative counts.

        '''
        return Counter() - self

    def _keep_positive(self):
        '''Internal method to strip elements with a negative or zero count'''
        nonpositive = [elem for elem, count in self.items() if not count > 0]
        for elem in nonpositive:
            del self[elem]
        return self

    def __iadd__(self, other):
        '''Inplace add from another counter, keeping only positive counts.

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

        '''
        for elem, count in other.items():
            self[elem] += count
        return self._keep_positive()

    def __isub__(self, other):
        '''Inplace subtract counter, but keep only results with positive counts.

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

        '''
        for elem, count in other.items():
            self[elem] -= count
        return self._keep_positive()

    def __ior__(self, other):
        '''Inplace union is the maximum of value from either counter.

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

        '''
        for elem, other_count in other.items():
            count = self[elem]
            if other_count > count:
                self[elem] = other_count
        return self._keep_positive()

    def __iand__(self, other):
        '''Inplace intersection is the minimum of corresponding counts.

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

        '''
        for elem, count in self.items():
            other_count = other[elem]
            if other_count < count:
                self[elem] = other_count
        return self._keep_positive()


def check_output(*popenargs, **kwargs):
    """
    For Python 2.6 compatibility: see
    http://stackoverflow.com/questions/4814970/
    """

    if 'stdout' in kwargs:
        raise ValueError('stdout argument not allowed, it will be overridden.')
    process = subprocess.Popen(stdout=subprocess.PIPE, *popenargs, **kwargs)
    output, unused_err = process.communicate()
    retcode = process.poll()
    if retcode:
        cmd = kwargs.get("args")
        if cmd is None:
            cmd = popenargs[0]
        raise subprocess.CalledProcessError(retcode, cmd)
    return output


def count(start=0, step=1):
    """
    ``itertools.count`` in Py 2.6 doesn't accept a step
    parameter. This is an enhanced version of ``itertools.count``
    for Py2.6 equivalent to ``itertools.count`` in Python 2.7+.
    """
    while True:
        yield start
        start += step


########################################################################
###  ChainMap (helper for configparser and string.Template)
###  From the Py3.4 source code. See also:
###    https://github.com/kkxue/Py2ChainMap/blob/master/py2chainmap.py
########################################################################

class ChainMap(MutableMapping):
    ''' A ChainMap groups multiple dicts (or other mappings) together
    to create a single, updateable view.

    The underlying mappings are stored in a list.  That list is public and can
    accessed or updated using the *maps* attribute.  There is no other state.

    Lookups search the underlying mappings successively until a key is found.
    In contrast, writes, updates, and deletions only operate on the first
    mapping.

    '''

    def __init__(self, *maps):
        '''Initialize a ChainMap by setting *maps* to the given mappings.
        If no mappings are provided, a single empty dictionary is used.

        '''
        self.maps = list(maps) or [{}]          # always at least one map

    def __missing__(self, key):
        raise KeyError(key)

    def __getitem__(self, key):
        for mapping in self.maps:
            try:
                return mapping[key]             # can't use 'key in mapping' with defaultdict
            except KeyError:
                pass
        return self.__missing__(key)            # support subclasses that define __missing__

    def get(self, key, default=None):
        return self[key] if key in self else default

    def __len__(self):
        return len(set().union(*self.maps))     # reuses stored hash values if possible

    def __iter__(self):
        return iter(set().union(*self.maps))

    def __contains__(self, key):
        return any(key in m for m in self.maps)

    def __bool__(self):
        return any(self.maps)

    # Py2 compatibility:
    __nonzero__ = __bool__

    @recursive_repr()
    def __repr__(self):
        return '{0.__class__.__name__}({1})'.format(
            self, ', '.join(map(repr, self.maps)))

    @classmethod
    def fromkeys(cls, iterable, *args):
        'Create a ChainMap with a single dict created from the iterable.'
        return cls(dict.fromkeys(iterable, *args))

    def copy(self):
        'New ChainMap or subclass with a new copy of maps[0] and refs to maps[1:]'
        return self.__class__(self.maps[0].copy(), *self.maps[1:])

    __copy__ = copy

    def new_child(self, m=None):                # like Django's Context.push()
        '''
        New ChainMap with a new map followed by all previous maps. If no
        map is provided, an empty dict is used.
        '''
        if m is None:
            m = {}
        return self.__class__(m, *self.maps)

    @property
    def parents(self):                          # like Django's Context.pop()
        'New ChainMap from maps[1:].'
        return self.__class__(*self.maps[1:])

    def __setitem__(self, key, value):
        self.maps[0][key] = value

    def __delitem__(self, key):
        try:
            del self.maps[0][key]
        except KeyError:
            raise KeyError('Key not found in the first mapping: {0!r}'.format(key))

    def popitem(self):
        'Remove and return an item pair from maps[0]. Raise KeyError is maps[0] is empty.'
        try:
            return self.maps[0].popitem()
        except KeyError:
            raise KeyError('No keys found in the first mapping.')

    def pop(self, key, *args):
        'Remove *key* from maps[0] and return its value. Raise KeyError if *key* not in maps[0].'
        try:
            return self.maps[0].pop(key, *args)
        except KeyError:
            raise KeyError('Key not found in the first mapping: {0!r}'.format(key))

    def clear(self):
        'Clear maps[0], leaving maps[1:] intact.'
        self.maps[0].clear()


# Re-use the same sentinel as in the Python stdlib socket module:
from socket import _GLOBAL_DEFAULT_TIMEOUT
# Was: _GLOBAL_DEFAULT_TIMEOUT = object()


def create_connection(address, timeout=_GLOBAL_DEFAULT_TIMEOUT,
                      source_address=None):
    """Backport of 3-argument create_connection() for Py2.6.

    Connect to *address* and return the socket object.

    Convenience function.  Connect to *address* (a 2-tuple ``(host,
    port)``) and return the socket object.  Passing the optional
    *timeout* parameter will set the timeout on the socket instance
    before attempting to connect.  If no *timeout* is supplied, the
    global default timeout setting returned by :func:`getdefaulttimeout`
    is used.  If *source_address* is set it must be a tuple of (host, port)
    for the socket to bind as a source address before making the connection.
    An host of '' or port 0 tells the OS to use the default.
    """

    host, port = address
    err = None
    for res in getaddrinfo(host, port, 0, SOCK_STREAM):
        af, socktype, proto, canonname, sa = res
        sock = None
        try:
            sock = socket(af, socktype, proto)
            if timeout is not _GLOBAL_DEFAULT_TIMEOUT:
                sock.settimeout(timeout)
            if source_address:
                sock.bind(source_address)
            sock.connect(sa)
            return sock

        except error as _:
            err = _
            if sock is not None:
                sock.close()

    if err is not None:
        raise err
    else:
        raise error("getaddrinfo returns an empty list")

# Backport from Py2.7 for Py2.6:
def cmp_to_key(mycmp):
    """Convert a cmp= function into a key= function"""
    class K(object):
        __slots__ = ['obj']
        def __init__(self, obj, *args):
            self.obj = obj
        def __lt__(self, other):
            return mycmp(self.obj, other.obj) < 0
        def __gt__(self, other):
            return mycmp(self.obj, other.obj) > 0
        def __eq__(self, other):
            return mycmp(self.obj, other.obj) == 0
        def __le__(self, other):
            return mycmp(self.obj, other.obj) <= 0
        def __ge__(self, other):
            return mycmp(self.obj, other.obj) >= 0
        def __ne__(self, other):
            return mycmp(self.obj, other.obj) != 0
        def __hash__(self):
            raise TypeError('hash not implemented')
    return K

# Back up our definitions above in case they're useful
_OrderedDict = OrderedDict
_Counter = Counter
_check_output = check_output
_count = count
_ceil = ceil
__count_elements = _count_elements
_recursive_repr = recursive_repr
_ChainMap = ChainMap
_create_connection = create_connection
_cmp_to_key = cmp_to_key

# Overwrite the definitions above with the usual ones
# from the standard library:
if sys.version_info >= (2, 7):
    from collections import OrderedDict, Counter
    from itertools import count
    from functools import cmp_to_key
    try:
        from subprocess import check_output
    except ImportError:
        # Not available. This happens with Google App Engine: see issue #231
        pass
    from socket import create_connection

if sys.version_info >= (3, 0):
    from math import ceil
    from collections import _count_elements

if sys.version_info >= (3, 3):
    from reprlib import recursive_repr
    from collections import ChainMap