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-\section{\module{itertools} ---
-         Functions creating iterators for efficient looping}
-
-\declaremodule{standard}{itertools}
-\modulesynopsis{Functions creating iterators for efficient looping.}
-\moduleauthor{Raymond Hettinger}{python@rcn.com}
-\sectionauthor{Raymond Hettinger}{python@rcn.com}
-\versionadded{2.3}
-
-
-This module implements a number of iterator building blocks inspired
-by constructs from the Haskell and SML programming languages.  Each
-has been recast in a form suitable for Python.
-
-The module standardizes a core set of fast, memory efficient tools
-that are useful by themselves or in combination.  Standardization helps
-avoid the readability and reliability problems which arise when many
-different individuals create their own slightly varying implementations,
-each with their own quirks and naming conventions.
-
-The tools are designed to combine readily with one another.  This makes
-it easy to construct more specialized tools succinctly and efficiently
-in pure Python.
-
-For instance, SML provides a tabulation tool: \code{tabulate(f)}
-which produces a sequence \code{f(0), f(1), ...}.  This toolbox
-provides \function{imap()} and \function{count()} which can be combined
-to form \code{imap(f, count())} and produce an equivalent result.
-
-Likewise, the functional tools are designed to work well with the
-high-speed functions provided by the \refmodule{operator} module.
-
-The module author welcomes suggestions for other basic building blocks
-to be added to future versions of the module.
-
-Whether cast in pure python form or compiled code, tools that use iterators
-are more memory efficient (and faster) than their list based counterparts.
-Adopting the principles of just-in-time manufacturing, they create
-data when and where needed instead of consuming memory with the
-computer equivalent of ``inventory''.
-
-The performance advantage of iterators becomes more acute as the number
-of elements increases -- at some point, lists grow large enough to
-severely impact memory cache performance and start running slowly.
-
-\begin{seealso}
-  \seetext{The Standard ML Basis Library,
-           \citetitle[http://www.standardml.org/Basis/]
-           {The Standard ML Basis Library}.}
-
-  \seetext{Haskell, A Purely Functional Language,
-           \citetitle[http://www.haskell.org/definition/]
-           {Definition of Haskell and the Standard Libraries}.}
-\end{seealso}
-
-
-\subsection{Itertool functions \label{itertools-functions}}
-
-The following module functions all construct and return iterators.
-Some provide streams of infinite length, so they should only be accessed
-by functions or loops that truncate the stream.
-
-\begin{funcdesc}{chain}{*iterables}
-  Make an iterator that returns elements from the first iterable until
-  it is exhausted, then proceeds to the next iterable, until all of the
-  iterables are exhausted.  Used for treating consecutive sequences as
-  a single sequence.  Equivalent to:
-
-  \begin{verbatim}
-     def chain(*iterables):
-         for it in iterables:
-             for element in it:
-                 yield element
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{count}{\optional{n}}
-  Make an iterator that returns consecutive integers starting with \var{n}.
-  If not specified \var{n} defaults to zero.  
-  Does not currently support python long integers.  Often used as an
-  argument to \function{imap()} to generate consecutive data points.
-  Also, used with \function{izip()} to add sequence numbers.  Equivalent to:
-
-  \begin{verbatim}
-     def count(n=0):
-         while True:
-             yield n
-             n += 1
-  \end{verbatim}
-
-  Note, \function{count()} does not check for overflow and will return
-  negative numbers after exceeding \code{sys.maxint}.  This behavior
-  may change in the future.
-\end{funcdesc}
-
-\begin{funcdesc}{cycle}{iterable}
-  Make an iterator returning elements from the iterable and saving a
-  copy of each.  When the iterable is exhausted, return elements from
-  the saved copy.  Repeats indefinitely.  Equivalent to:
-
-  \begin{verbatim}
-     def cycle(iterable):
-         saved = []
-         for element in iterable:
-             yield element
-             saved.append(element)
-         while saved:
-             for element in saved:
-                   yield element
-  \end{verbatim}
-
-  Note, this member of the toolkit may require significant
-  auxiliary storage (depending on the length of the iterable).
-\end{funcdesc}
-
-\begin{funcdesc}{dropwhile}{predicate, iterable}
-  Make an iterator that drops elements from the iterable as long as
-  the predicate is true; afterwards, returns every element.  Note,
-  the iterator does not produce \emph{any} output until the predicate
-  first becomes false, so it may have a lengthy start-up time.  Equivalent to:
-
-  \begin{verbatim}
-     def dropwhile(predicate, iterable):
-         iterable = iter(iterable)
-         for x in iterable:
-             if not predicate(x):
-                 yield x
-                 break
-         for x in iterable:
-             yield x
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{groupby}{iterable\optional{, key}}
-  Make an iterator that returns consecutive keys and groups from the
-  \var{iterable}. The \var{key} is a function computing a key value for each
-  element.  If not specified or is \code{None}, \var{key} defaults to an
-  identity function and returns  the element unchanged.  Generally, the
-  iterable needs to already be sorted on the same key function.
-
-  The operation of \function{groupby()} is similar to the \code{uniq} filter
-  in \UNIX{}.  It generates a break or new group every time the value
-  of the key function changes (which is why it is usually necessary
-  to have sorted the data using the same key function).  That behavior
-  differs from SQL's GROUP BY which aggregates common elements regardless
-  of their input order.
-
-  The returned group is itself an iterator that shares the underlying
-  iterable with \function{groupby()}.  Because the source is shared, when
-  the \function{groupby} object is advanced, the previous group is no
-  longer visible.  So, if that data is needed later, it should be stored
-  as a list:
-
-  \begin{verbatim}
-    groups = []
-    uniquekeys = []
-    data = sorted(data, key=keyfunc)
-    for k, g in groupby(data, keyfunc):
-        groups.append(list(g))      # Store group iterator as a list
-        uniquekeys.append(k)
-  \end{verbatim}
-
-  \function{groupby()} is equivalent to:
-
-  \begin{verbatim}
-    class groupby(object):
-        def __init__(self, iterable, key=None):
-            if key is None:
-                key = lambda x: x
-            self.keyfunc = key
-            self.it = iter(iterable)
-            self.tgtkey = self.currkey = self.currvalue = xrange(0)
-        def __iter__(self):
-            return self
-        def next(self):
-            while self.currkey == self.tgtkey:
-                self.currvalue = self.it.next() # Exit on StopIteration
-                self.currkey = self.keyfunc(self.currvalue)
-            self.tgtkey = self.currkey
-            return (self.currkey, self._grouper(self.tgtkey))
-        def _grouper(self, tgtkey):
-            while self.currkey == tgtkey:
-                yield self.currvalue
-                self.currvalue = self.it.next() # Exit on StopIteration
-                self.currkey = self.keyfunc(self.currvalue)
-  \end{verbatim}
-  \versionadded{2.4}
-\end{funcdesc}
-
-\begin{funcdesc}{ifilter}{predicate, iterable}
-  Make an iterator that filters elements from iterable returning only
-  those for which the predicate is \code{True}.
-  If \var{predicate} is \code{None}, return the items that are true.
-  Equivalent to:
-
-  \begin{verbatim}
-     def ifilter(predicate, iterable):
-         if predicate is None:
-             predicate = bool
-         for x in iterable:
-             if predicate(x):
-                 yield x
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{ifilterfalse}{predicate, iterable}
-  Make an iterator that filters elements from iterable returning only
-  those for which the predicate is \code{False}.
-  If \var{predicate} is \code{None}, return the items that are false.
-  Equivalent to:
-
-  \begin{verbatim}
-     def ifilterfalse(predicate, iterable):
-         if predicate is None:
-             predicate = bool
-         for x in iterable:
-             if not predicate(x):
-                 yield x
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{imap}{function, *iterables}
-  Make an iterator that computes the function using arguments from
-  each of the iterables.  If \var{function} is set to \code{None}, then
-  \function{imap()} returns the arguments as a tuple.  Like
-  \function{map()} but stops when the shortest iterable is exhausted
-  instead of filling in \code{None} for shorter iterables.  The reason
-  for the difference is that infinite iterator arguments are typically
-  an error for \function{map()} (because the output is fully evaluated)
-  but represent a common and useful way of supplying arguments to
-  \function{imap()}.
-  Equivalent to:
-
-  \begin{verbatim}
-     def imap(function, *iterables):
-         iterables = map(iter, iterables)
-         while True:
-             args = [i.next() for i in iterables]
-             if function is None:
-                 yield tuple(args)
-             else:
-                 yield function(*args)
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{islice}{iterable, \optional{start,} stop \optional{, step}}
-  Make an iterator that returns selected elements from the iterable.
-  If \var{start} is non-zero, then elements from the iterable are skipped
-  until start is reached.  Afterward, elements are returned consecutively
-  unless \var{step} is set higher than one which results in items being
-  skipped.  If \var{stop} is \code{None}, then iteration continues until
-  the iterator is exhausted, if at all; otherwise, it stops at the specified
-  position.  Unlike regular slicing,
-  \function{islice()} does not support negative values for \var{start},
-  \var{stop}, or \var{step}.  Can be used to extract related fields
-  from data where the internal structure has been flattened (for
-  example, a multi-line report may list a name field on every
-  third line).  Equivalent to:
-
-  \begin{verbatim}
-     def islice(iterable, *args):
-         s = slice(*args)
-         it = iter(xrange(s.start or 0, s.stop or sys.maxint, s.step or 1))
-         nexti = it.next()
-         for i, element in enumerate(iterable):
-             if i == nexti:
-                 yield element
-                 nexti = it.next()          
-  \end{verbatim}
-
-  If \var{start} is \code{None}, then iteration starts at zero.
-  If \var{step} is \code{None}, then the step defaults to one.
-  \versionchanged[accept \code{None} values for default \var{start} and
-                  \var{step}]{2.5}
-\end{funcdesc}
-
-\begin{funcdesc}{izip}{*iterables}
-  Make an iterator that aggregates elements from each of the iterables.
-  Like \function{zip()} except that it returns an iterator instead of
-  a list.  Used for lock-step iteration over several iterables at a
-  time.  Equivalent to:
-
-  \begin{verbatim}
-     def izip(*iterables):
-         iterables = map(iter, iterables)
-         while iterables:
-             result = [it.next() for it in iterables]
-             yield tuple(result)
-  \end{verbatim}
-
-  \versionchanged[When no iterables are specified, returns a zero length
-                  iterator instead of raising a \exception{TypeError}
-		  exception]{2.4}
-
-  Note, the left-to-right evaluation order of the iterables is guaranteed.
-  This makes possible an idiom for clustering a data series into n-length
-  groups using \samp{izip(*[iter(s)]*n)}.  For data that doesn't fit
-  n-length groups exactly, the last tuple can be pre-padded with fill
-  values using \samp{izip(*[chain(s, [None]*(n-1))]*n)}.
-         
-  Note, when \function{izip()} is used with unequal length inputs, subsequent
-  iteration over the longer iterables cannot reliably be continued after
-  \function{izip()} terminates.  Potentially, up to one entry will be missing
-  from each of the left-over iterables. This occurs because a value is fetched
-  from each iterator in-turn, but the process ends when one of the iterators
-  terminates.  This leaves the last fetched values in limbo (they cannot be
-  returned in a final, incomplete tuple and they are cannot be pushed back
-  into the iterator for retrieval with \code{it.next()}).  In general,
-  \function{izip()} should only be used with unequal length inputs when you
-  don't care about trailing, unmatched values from the longer iterables.
-\end{funcdesc}
-
-\begin{funcdesc}{izip_longest}{*iterables\optional{, fillvalue}}
-  Make an iterator that aggregates elements from each of the iterables.
-  If the iterables are of uneven length, missing values are filled-in
-  with \var{fillvalue}.  Iteration continues until the longest iterable
-  is exhausted.  Equivalent to:
-
-  \begin{verbatim}
-    def izip_longest(*args, **kwds):
-        fillvalue = kwds.get('fillvalue')
-        def sentinel(counter = ([fillvalue]*(len(args)-1)).pop):
-            yield counter()         # yields the fillvalue, or raises IndexError
-        fillers = repeat(fillvalue)
-        iters = [chain(it, sentinel(), fillers) for it in args]
-        try:
-            for tup in izip(*iters):
-                yield tup
-        except IndexError:
-            pass
-  \end{verbatim}
-
-  If one of the iterables is potentially infinite, then the
-  \function{izip_longest()} function should be wrapped with something
-  that limits the number of calls (for example \function{islice()} or
-  \function{take()}).
-  \versionadded{2.6}
-\end{funcdesc}
-
-\begin{funcdesc}{repeat}{object\optional{, times}}
-  Make an iterator that returns \var{object} over and over again.
-  Runs indefinitely unless the \var{times} argument is specified.
-  Used as argument to \function{imap()} for invariant parameters
-  to the called function.  Also used with \function{izip()} to create
-  an invariant part of a tuple record.  Equivalent to:
-
-  \begin{verbatim}
-     def repeat(object, times=None):
-         if times is None:
-             while True:
-                 yield object
-         else:
-             for i in xrange(times):
-                 yield object
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{starmap}{function, iterable}
-  Make an iterator that computes the function using arguments tuples
-  obtained from the iterable.  Used instead of \function{imap()} when
-  argument parameters are already grouped in tuples from a single iterable
-  (the data has been ``pre-zipped'').  The difference between
-  \function{imap()} and \function{starmap()} parallels the distinction
-  between \code{function(a,b)} and \code{function(*c)}.
-  Equivalent to:
-
-  \begin{verbatim}
-     def starmap(function, iterable):
-         iterable = iter(iterable)
-         while True:
-             yield function(*iterable.next())
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{takewhile}{predicate, iterable}
-  Make an iterator that returns elements from the iterable as long as
-  the predicate is true.  Equivalent to:
-
-  \begin{verbatim}
-     def takewhile(predicate, iterable):
-         for x in iterable:
-             if predicate(x):
-                 yield x
-             else:
-                 break
-  \end{verbatim}
-\end{funcdesc}
-
-\begin{funcdesc}{tee}{iterable\optional{, n=2}}
-  Return \var{n} independent iterators from a single iterable.
-  The case where \code{n==2} is equivalent to:
-
-  \begin{verbatim}
-     def tee(iterable):
-         def gen(next, data={}, cnt=[0]):
-             for i in count():
-                 if i == cnt[0]:
-                     item = data[i] = next()
-                     cnt[0] += 1
-                 else:
-                     item = data.pop(i)
-                 yield item
-         it = iter(iterable)
-         return (gen(it.next), gen(it.next))
-  \end{verbatim}
-
-  Note, once \function{tee()} has made a split, the original \var{iterable}
-  should not be used anywhere else; otherwise, the \var{iterable} could get
-  advanced without the tee objects being informed.
-
-  Note, this member of the toolkit may require significant auxiliary
-  storage (depending on how much temporary data needs to be stored).
-  In general, if one iterator is going to use most or all of the data before
-  the other iterator, it is faster to use \function{list()} instead of
-  \function{tee()}.
-  \versionadded{2.4}
-\end{funcdesc}
-
-
-\subsection{Examples \label{itertools-example}}
-
-The following examples show common uses for each tool and
-demonstrate ways they can be combined.
-
-\begin{verbatim}
-
->>> amounts = [120.15, 764.05, 823.14]
->>> for checknum, amount in izip(count(1200), amounts):
-...     print 'Check %d is for $%.2f' % (checknum, amount)
-...
-Check 1200 is for $120.15
-Check 1201 is for $764.05
-Check 1202 is for $823.14
-
->>> import operator
->>> for cube in imap(operator.pow, xrange(1,5), repeat(3)):
-...    print cube
-...
-1
-8
-27
-64
-
->>> reportlines = ['EuroPython', 'Roster', '', 'alex', '', 'laura',
-                  '', 'martin', '', 'walter', '', 'mark']
->>> for name in islice(reportlines, 3, None, 2):
-...    print name.title()
-...
-Alex
-Laura
-Martin
-Walter
-Mark
-
-# Show a dictionary sorted and grouped by value
->>> from operator import itemgetter
->>> d = dict(a=1, b=2, c=1, d=2, e=1, f=2, g=3)
->>> di = sorted(d.iteritems(), key=itemgetter(1))
->>> for k, g in groupby(di, key=itemgetter(1)):
-...     print k, map(itemgetter(0), g)
-...
-1 ['a', 'c', 'e']
-2 ['b', 'd', 'f']
-3 ['g']
-
-# Find runs of consecutive numbers using groupby.  The key to the solution
-# is differencing with a range so that consecutive numbers all appear in
-# same group.
->>> data = [ 1,  4,5,6, 10, 15,16,17,18, 22, 25,26,27,28]
->>> for k, g in groupby(enumerate(data), lambda (i,x):i-x):
-...     print map(operator.itemgetter(1), g)
-... 
-[1]
-[4, 5, 6]
-[10]
-[15, 16, 17, 18]
-[22]
-[25, 26, 27, 28]
-
-\end{verbatim}
-
-
-\subsection{Recipes \label{itertools-recipes}}
-
-This section shows recipes for creating an extended toolset using the
-existing itertools as building blocks.
-
-The extended tools offer the same high performance as the underlying
-toolset.  The superior memory performance is kept by processing elements one
-at a time rather than bringing the whole iterable into memory all at once.
-Code volume is kept small by linking the tools together in a functional style
-which helps eliminate temporary variables.  High speed is retained by
-preferring ``vectorized'' building blocks over the use of for-loops and
-generators which incur interpreter overhead.
-
-
-\begin{verbatim}
-def take(n, seq):
-    return list(islice(seq, n))
-
-def enumerate(iterable):
-    return izip(count(), iterable)
-
-def tabulate(function):
-    "Return function(0), function(1), ..."
-    return imap(function, count())
-
-def iteritems(mapping):
-    return izip(mapping.iterkeys(), mapping.itervalues())
-
-def nth(iterable, n):
-    "Returns the nth item or raise StopIteration"
-    return islice(iterable, n, None).next()
-
-def all(seq, pred=None):
-    "Returns True if pred(x) is true for every element in the iterable"
-    for elem in ifilterfalse(pred, seq):
-        return False
-    return True
-
-def any(seq, pred=None):
-    "Returns True if pred(x) is true for at least one element in the iterable"
-    for elem in ifilter(pred, seq):
-        return True
-    return False
-
-def no(seq, pred=None):
-    "Returns True if pred(x) is false for every element in the iterable"
-    for elem in ifilter(pred, seq):
-        return False
-    return True
-
-def quantify(seq, pred=None):
-    "Count how many times the predicate is true in the sequence"
-    return sum(imap(pred, seq))
-
-def padnone(seq):
-    """Returns the sequence elements and then returns None indefinitely.
-
-    Useful for emulating the behavior of the built-in map() function.
-    """
-    return chain(seq, repeat(None))
-
-def ncycles(seq, n):
-    "Returns the sequence elements n times"
-    return chain(*repeat(seq, n))
-
-def dotproduct(vec1, vec2):
-    return sum(imap(operator.mul, vec1, vec2))
-
-def flatten(listOfLists):
-    return list(chain(*listOfLists))
-
-def repeatfunc(func, times=None, *args):
-    """Repeat calls to func with specified arguments.
-    
-    Example:  repeatfunc(random.random)
-    """
-    if times is None:
-        return starmap(func, repeat(args))
-    else:
-        return starmap(func, repeat(args, times))
-
-def pairwise(iterable):
-    "s -> (s0,s1), (s1,s2), (s2, s3), ..."
-    a, b = tee(iterable)
-    try:
-        b.next()
-    except StopIteration:
-        pass
-    return izip(a, b)
-
-def grouper(n, iterable, padvalue=None):
-    "grouper(3, 'abcdefg', 'x') --> ('a','b','c'), ('d','e','f'), ('g','x','x')"
-    return izip(*[chain(iterable, repeat(padvalue, n-1))]*n)
-
-
-\end{verbatim}