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from collections import OrderedDict

class {typename}(tuple):
    '{typename}({arg_list})'

    __slots__ = ()

    _fields = {field_names!r}

    def __new__(_cls, {arg_list}):
        'Create new instance of {typename}({arg_list})'
        return _tuple.__new__(_cls, ({arg_list}))

    @classmethod
    def _make(cls, iterable, new=tuple.__new__, len=len):
        'Make a new {typename} object from a sequence or iterable'
        result = new(cls, iterable)
        if len(result) != {num_fields:d}:
            raise TypeError('Expected {num_fields:d} arguments, got %d' % len(result))
        return result

    def _replace(_self, **kwds):
        'Return a new {typename} 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' % list(kwds))
        return result

    def __repr__(self):
        'Return a nicely formatted representation string'
        return self.__class__.__name__ + '({repr_fmt})' % self

    def _asdict(self):
        'Return a new OrderedDict which maps field names to their values.'
        return OrderedDict(zip(self._fields, self))

    def __getnewargs__(self):
        'Return self as a plain tuple.  Used by copy and pickle.'
        return tuple(self)

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�	{name}=%r�W    {name} = _property(_itemgetter({index:d}), doc='Alias for field number {index:d}')
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    >>> 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 accessible 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)

    �,� �_�_%d�*Type names and field names must be strings�8Type names and field names must be valid identifiers: %r�2Type names and field names cannot be a keyword: %r�/Field names cannot start with an underscore: %r�$Encountered duplicate field name: %r�'�rG�, cs�|]}tj|d�VqdS)��nameN)�_repr_template�format)�.0r�r$r$r%�	<genexpr>���namedtuple.<locals>.<genexpr>�
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    >>> 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)]

    c�N|std��|^}}t|�dkr0tdt|���tt|�j�|j||�dS)�	Create a new, empty Counter object.  And if given, count elements
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        >>> 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

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        # 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
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�Counter.updatecO�|std��|^}}t|�dkr0tdt|���|r<|dnd}|dk	r�|j}t|t�r�xH|j�D]\}}||d�|||<qbWn x|D]}||d�d||<q�W|r�|j|�dS)�Like dict.update() but subtracts counts instead of replacing them.
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        >>> 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
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�Counter.__add__cC�|t|t�stSt�}x0|j�D]$\}}|||}|dkr|||<qWx0|j�D]$\}}||krP|dkrPd|||<qPW|S)�� Subtract count, but keep only results with positive counts.

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        Counter({'b': 2, 'a': 1})

        r)r�r	r�r�)r#r�r�r/rbr�r$r$r%�__sub__��
�Counter.__sub__cC�t|t�stSt�}x<|j�D]0\}}||}||kr:|n|}|dkr|||<qWx,|j�D] \}}||kr\|dkr\|||<q\W|S)��Union is the maximum of value in either of the input counters.

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�Counter.__or__cC�Vt|t�stSt�}x<|j�D]0\}}||}||kr:|n|}|dkr|||<qW|S)�� Intersection is the minimum of corresponding counts.

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�Counter.__and__cC�0t�}x$|j�D]\}}|dkr|||<qW|S)�EAdds an empty counter, effectively stripping negative and zero countsr)r	r�)r#r�r/rbr$r$r%�__pos__��
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�r6YnXed(k�rVd#dlZeej��dS)+��Heap queue algorithm (a.k.a. priority queue).

Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
all k, counting elements from 0.  For the sake of comparison,
non-existing elements are considered to be infinite.  The interesting
property of a heap is that a[0] is always its smallest element.

Usage:

heap = []            # creates an empty heap
heappush(heap, item) # pushes a new item on the heap
item = heappop(heap) # pops the smallest item from the heap
item = heap[0]       # smallest item on the heap without popping it
heapify(x)           # transforms list into a heap, in-place, in linear time
item = heapreplace(heap, item) # pops and returns smallest item, and adds
                               # new item; the heap size is unchanged

Our API differs from textbook heap algorithms as follows:

- We use 0-based indexing.  This makes the relationship between the
  index for a node and the indexes for its children slightly less
  obvious, but is more suitable since Python uses 0-based indexing.

- Our heappop() method returns the smallest item, not the largest.

These two make it possible to view the heap as a regular Python list
without surprises: heap[0] is the smallest item, and heap.sort()
maintains the heap invariant!
�oHeap queues

[explanation by François Pinard]

Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
all k, counting elements from 0.  For the sake of comparison,
non-existing elements are considered to be infinite.  The interesting
property of a heap is that a[0] is always its smallest element.

The strange invariant above is meant to be an efficient memory
representation for a tournament.  The numbers below are `k', not a[k]:

                                   0

                  1                                 2

          3               4                5               6

      7       8       9       10      11      12      13      14

    15 16   17 18   19 20   21 22   23 24   25 26   27 28   29 30


In the tree above, each cell `k' is topping `2*k+1' and `2*k+2'.  In
a usual binary tournament we see in sports, each cell is the winner
over the two cells it tops, and we can trace the winner down the tree
to see all opponents s/he had.  However, in many computer applications
of such tournaments, we do not need to trace the history of a winner.
To be more memory efficient, when a winner is promoted, we try to
replace it by something else at a lower level, and the rule becomes
that a cell and the two cells it tops contain three different items,
but the top cell "wins" over the two topped cells.

If this heap invariant is protected at all time, index 0 is clearly
the overall winner.  The simplest algorithmic way to remove it and
find the "next" winner is to move some loser (let's say cell 30 in the
diagram above) into the 0 position, and then percolate this new 0 down
the tree, exchanging values, until the invariant is re-established.
This is clearly logarithmic on the total number of items in the tree.
By iterating over all items, you get an O(n ln n) sort.

A nice feature of this sort is that you can efficiently insert new
items while the sort is going on, provided that the inserted items are
not "better" than the last 0'th element you extracted.  This is
especially useful in simulation contexts, where the tree holds all
incoming events, and the "win" condition means the smallest scheduled
time.  When an event schedule other events for execution, they are
scheduled into the future, so they can easily go into the heap.  So, a
heap is a good structure for implementing schedulers (this is what I
used for my MIDI sequencer :-).

Various structures for implementing schedulers have been extensively
studied, and heaps are good for this, as they are reasonably speedy,
the speed is almost constant, and the worst case is not much different
than the average case.  However, there are other representations which
are more efficient overall, yet the worst cases might be terrible.

Heaps are also very useful in big disk sorts.  You most probably all
know that a big sort implies producing "runs" (which are pre-sorted
sequences, which size is usually related to the amount of CPU memory),
followed by a merging passes for these runs, which merging is often
very cleverly organised[1].  It is very important that the initial
sort produces the longest runs possible.  Tournaments are a good way
to that.  If, using all the memory available to hold a tournament, you
replace and percolate items that happen to fit the current run, you'll
produce runs which are twice the size of the memory for random input,
and much better for input fuzzily ordered.

Moreover, if you output the 0'th item on disk and get an input which
may not fit in the current tournament (because the value "wins" over
the last output value), it cannot fit in the heap, so the size of the
heap decreases.  The freed memory could be cleverly reused immediately
for progressively building a second heap, which grows at exactly the
same rate the first heap is melting.  When the first heap completely
vanishes, you switch heaps and start a new run.  Clever and quite
effective!

In a word, heaps are useful memory structures to know.  I use them in
a few applications, and I think it is good to keep a `heap' module
around. :-)

--------------------
[1] The disk balancing algorithms which are current, nowadays, are
more annoying than clever, and this is a consequence of the seeking
capabilities of the disks.  On devices which cannot seek, like big
tape drives, the story was quite different, and one had to be very
clever to ensure (far in advance) that each tape movement will be the
most effective possible (that is, will best participate at
"progressing" the merge).  Some tapes were even able to read
backwards, and this was also used to avoid the rewinding time.
Believe me, real good tape sorts were quite spectacular to watch!
From all times, sorting has always been a Great Art! :-)
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This module provides regular expression matching operations similar to
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Regular expressions can contain both special and ordinary characters.
Most ordinary characters, like "A", "a", or "0", are the simplest
regular expressions; they simply match themselves.  You can
concatenate ordinary characters, so last matches the string 'last'.

The special characters are:
    "."      Matches any character except a newline.
    "^"      Matches the start of the string.
    "$"      Matches the end of the string or just before the newline at
             the end of the string.
    "*"      Matches 0 or more (greedy) repetitions of the preceding RE.
             Greedy means that it will match as many repetitions as possible.
    "+"      Matches 1 or more (greedy) repetitions of the preceding RE.
    "?"      Matches 0 or 1 (greedy) of the preceding RE.
    *?,+?,?? Non-greedy versions of the previous three special characters.
    {m,n}    Matches from m to n repetitions of the preceding RE.
    {m,n}?   Non-greedy version of the above.
    "\\"     Either escapes special characters or signals a special sequence.
    []       Indicates a set of characters.
             A "^" as the first character indicates a complementing set.
    "|"      A|B, creates an RE that will match either A or B.
    (...)    Matches the RE inside the parentheses.
             The contents can be retrieved or matched later in the string.
    (?aiLmsux) Set the A, I, L, M, S, U, or X flag for the RE (see below).
    (?:...)  Non-grouping version of regular parentheses.
    (?P<name>...) The substring matched by the group is accessible by name.
    (?P=name)     Matches the text matched earlier by the group named name.
    (?#...)  A comment; ignored.
    (?=...)  Matches if ... matches next, but doesn't consume the string.
    (?!...)  Matches if ... doesn't match next.
    (?<=...) Matches if preceded by ... (must be fixed length).
    (?<!...) Matches if not preceded by ... (must be fixed length).
    (?(id/name)yes|no) Matches yes pattern if the group with id/name matched,
                       the (optional) no pattern otherwise.

The special sequences consist of "\\" and a character from the list
below.  If the ordinary character is not on the list, then the
resulting RE will match the second character.
    \number  Matches the contents of the group of the same number.
    \A       Matches only at the start of the string.
    \Z       Matches only at the end of the string.
    \b       Matches the empty string, but only at the start or end of a word.
    \B       Matches the empty string, but not at the start or end of a word.
    \d       Matches any decimal digit; equivalent to the set [0-9] in
             bytes patterns or string patterns with the ASCII flag.
             In string patterns without the ASCII flag, it will match the whole
             range of Unicode digits.
    \D       Matches any non-digit character; equivalent to [^\d].
    \s       Matches any whitespace character; equivalent to [ \t\n\r\f\v] in
             bytes patterns or string patterns with the ASCII flag.
             In string patterns without the ASCII flag, it will match the whole
             range of Unicode whitespace characters.
    \S       Matches any non-whitespace character; equivalent to [^\s].
    \w       Matches any alphanumeric character; equivalent to [a-zA-Z0-9_]
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             In string patterns without the ASCII flag, it will match the
             range of Unicode alphanumeric characters (letters plus digits
             plus underscore).
             With LOCALE, it will match the set [0-9_] plus characters defined
             as letters for the current locale.
    \W       Matches the complement of \w.
    \\       Matches a literal backslash.

This module exports the following functions:
    match     Match a regular expression pattern to the beginning of a string.
    fullmatch Match a regular expression pattern to all of a string.
    search    Search a string for the presence of a pattern.
    sub       Substitute occurrences of a pattern found in a string.
    subn      Same as sub, but also return the number of substitutions made.
    split     Split a string by the occurrences of a pattern.
    findall   Find all occurrences of a pattern in a string.
    finditer  Return an iterator yielding a match object for each match.
    compile   Compile a pattern into a RegexObject.
    purge     Clear the regular expression cache.
    escape    Backslash all non-alphanumerics in a string.

Some of the functions in this module takes flags as optional parameters:
    A  ASCII       For string patterns, make \w, \W, \b, \B, \d, \D
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                   default).
                   For bytes patterns, this flag is the only available
                   behaviour and needn't be specified.
    I  IGNORECASE  Perform case-insensitive matching.
    L  LOCALE      Make \w, \W, \b, \B, dependent on the current locale.
    M  MULTILINE   "^" matches the beginning of lines (after a newline)
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                   "$" matches the end of lines (before a newline) as well
                   as the end of the string.
    S  DOTALL      "." matches any character at all, including the newline.
    X  VERBOSE     Ignore whitespace and comments for nicer looking RE's.
    U  UNICODE     For compatibility only. Ignored for string patterns (it
                   is the default), and forbidden for bytes patterns.

This module also defines an exception 'error'.

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