^^&&^^

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 <div class="section" id="module-itertools">
<h1>9.7. <a class="reference internal" href="#module-itertools" title="itertools: Functions creating iterators for efficient looping."><tt class="xref py py-mod docutils literal">itertools</tt></a> &#8212; Functions creating iterators for efficient looping<a class="headerlink" href="#module-itertools" title="Permalink to this headline">¶</a></h1>

New in version 2.3.
This module implements a number of <a class="reference internal" href="../glossary.html#term-iterator">iterator</a> building blocks inspired
by constructs from APL, Haskell, and SML. 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. Together, they form an &#8220;iterator
algebra&#8221; making it possible to construct specialized tools succinctly and
efficiently in pure Python.
For instance, SML provides a tabulation tool: <tt class="docutils literal">tabulate(f)</tt> which produces a
sequence <tt class="docutils literal">f(0), f(1), ...</tt>. The same effect can be achieved in Python
by combining <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a> and <a class="reference internal" href="#itertools.count" title="itertools.count"><tt class="xref py py-func docutils literal">count()</tt></a> to form <tt class="docutils literal">imap(f, count())</tt>.
These tools and their built-in counterparts also work well with the high-speed
functions in the <a class="reference internal" href="operator.html#module-operator" title="operator: Functions corresponding to the standard operators."><tt class="xref py py-mod docutils literal">operator</tt></a> module. For example, the multiplication
operator can be mapped across two vectors to form an efficient dot-product:
<tt class="docutils literal">sum(imap(operator.mul, vector1, vector2))</tt>.
Infinite Iterators:
<table border="1" class="docutils">
<colgroup>
<col width="14%" />
<col width="14%" />
<col width="39%" />
<col width="33%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Iterator</th>
<th class="head">Arguments</th>
<th class="head">Results</th>
<th class="head">Example</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><a class="reference internal" href="#itertools.count" title="itertools.count"><tt class="xref py py-func docutils literal">count()</tt></a></td>
<td>start, [step]</td>
<td>start, start+step, start+2*step, ...</td>
<td><tt class="docutils literal">count(10) --&gt; 10 11 12 13 14 ...</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.cycle" title="itertools.cycle"><tt class="xref py py-func docutils literal">cycle()</tt></a></td>
<td>p</td>
<td>p0, p1, ... plast, p0, p1, ...</td>
<td><tt class="docutils literal">cycle('ABCD') --&gt; A B C D A B C D ...</tt></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.repeat" title="itertools.repeat"><tt class="xref py py-func docutils literal">repeat()</tt></a></td>
<td>elem [,n]</td>
<td>elem, elem, elem, ... endlessly or up to n times</td>
<td><tt class="docutils literal">repeat(10, 3) --&gt; 10 10 10</tt></td>
</tr>
</tbody>
</table>
Iterators terminating on the shortest input sequence:
<table border="1" class="docutils">
<colgroup>
<col width="13%" />
<col width="18%" />
<col width="31%" />
<col width="39%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Iterator</th>
<th class="head">Arguments</th>
<th class="head">Results</th>
<th class="head">Example</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><a class="reference internal" href="#itertools.chain" title="itertools.chain"><tt class="xref py py-func docutils literal">chain()</tt></a></td>
<td>p, q, ...</td>
<td>p0, p1, ... plast, q0, q1, ...</td>
<td><tt class="docutils literal">chain('ABC', 'DEF') --&gt; A B C D E F</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.compress" title="itertools.compress"><tt class="xref py py-func docutils literal">compress()</tt></a></td>
<td>data, selectors</td>
<td>(d[0] if s[0]), (d[1] if s[1]), ...</td>
<td><tt class="docutils literal">compress('ABCDEF', [1,0,1,0,1,1]) --&gt; A C E F</tt></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.dropwhile" title="itertools.dropwhile"><tt class="xref py py-func docutils literal">dropwhile()</tt></a></td>
<td>pred, seq</td>
<td>seq[n], seq[n+1], starting when pred fails</td>
<td><tt class="docutils literal">dropwhile(lambda x: x&lt;5, [1,4,6,4,1]) --&gt; 6 4 1</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><tt class="xref py py-func docutils literal">groupby()</tt></a></td>
<td>iterable[, keyfunc]</td>
<td>sub-iterators grouped by value of keyfunc(v)</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.ifilter" title="itertools.ifilter"><tt class="xref py py-func docutils literal">ifilter()</tt></a></td>
<td>pred, seq</td>
<td>elements of seq where pred(elem) is True</td>
<td><tt class="docutils literal">ifilter(lambda x: x%2, range(10)) --&gt; 1 3 5 7 9</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.ifilterfalse" title="itertools.ifilterfalse"><tt class="xref py py-func docutils literal">ifilterfalse()</tt></a></td>
<td>pred, seq</td>
<td>elements of seq where pred(elem) is False</td>
<td><tt class="docutils literal">ifilterfalse(lambda x: x%2, range(10)) --&gt; 0 2 4 6 8</tt></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.islice" title="itertools.islice"><tt class="xref py py-func docutils literal">islice()</tt></a></td>
<td>seq, [start,] stop [, step]</td>
<td>elements from seq[start:stop:step]</td>
<td><tt class="docutils literal">islice('ABCDEFG', 2, None) --&gt; C D E F G</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a></td>
<td>func, p, q, ...</td>
<td>func(p0, q0), func(p1, q1), ...</td>
<td><tt class="docutils literal">imap(pow, (2,3,10), (5,2,3)) --&gt; 32 9 1000</tt></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.starmap" title="itertools.starmap"><tt class="xref py py-func docutils literal">starmap()</tt></a></td>
<td>func, seq</td>
<td>func(*seq[0]), func(*seq[1]), ...</td>
<td><tt class="docutils literal">starmap(pow, [(2,5), (3,2), (10,3)]) --&gt; 32 9 1000</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.tee" title="itertools.tee"><tt class="xref py py-func docutils literal">tee()</tt></a></td>
<td>it, n</td>
<td>it1, it2 , ... itn splits one iterator into n</td>
<td>&nbsp;</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.takewhile" title="itertools.takewhile"><tt class="xref py py-func docutils literal">takewhile()</tt></a></td>
<td>pred, seq</td>
<td>seq[0], seq[1], until pred fails</td>
<td><tt class="docutils literal">takewhile(lambda x: x&lt;5, [1,4,6,4,1]) --&gt; 1 4</tt></td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.izip" title="itertools.izip"><tt class="xref py py-func docutils literal">izip()</tt></a></td>
<td>p, q, ...</td>
<td>(p[0], q[0]), (p[1], q[1]), ...</td>
<td><tt class="docutils literal">izip('ABCD', 'xy') --&gt; Ax By</tt></td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.izip_longest" title="itertools.izip_longest"><tt class="xref py py-func docutils literal">izip_longest()</tt></a></td>
<td>p, q, ...</td>
<td>(p[0], q[0]), (p[1], q[1]), ...</td>
<td><tt class="docutils literal">izip_longest('ABCD', 'xy', fillvalue='-') --&gt; Ax By C- D-</tt></td>
</tr>
</tbody>
</table>
Combinatoric generators:
<table border="1" class="docutils">
<colgroup>
<col width="36%" />
<col width="16%" />
<col width="48%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Iterator</th>
<th class="head">Arguments</th>
<th class="head">Results</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td><a class="reference internal" href="#itertools.product" title="itertools.product"><tt class="xref py py-func docutils literal">product()</tt></a></td>
<td>p, q, ... [repeat=1]</td>
<td>cartesian product, equivalent to a nested for-loop</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.permutations" title="itertools.permutations"><tt class="xref py py-func docutils literal">permutations()</tt></a></td>
<td>p[, r]</td>
<td>r-length tuples, all possible orderings, no repeated elements</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#itertools.combinations" title="itertools.combinations"><tt class="xref py py-func docutils literal">combinations()</tt></a></td>
<td>p, r</td>
<td>r-length tuples, in sorted order, no repeated elements</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#itertools.combinations_with_replacement" title="itertools.combinations_with_replacement"><tt class="xref py py-func docutils literal">combinations_with_replacement()</tt></a></td>
<td>p, r</td>
<td>r-length tuples, in sorted order, with repeated elements</td>
</tr>
<tr class="row-even"><td><tt class="docutils literal">product('ABCD', repeat=2)</tt></td>
<td>&nbsp;</td>
<td><tt class="docutils literal">AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD</tt></td>
</tr>
<tr class="row-odd"><td><tt class="docutils literal">permutations('ABCD', 2)</tt></td>
<td>&nbsp;</td>
<td><tt class="docutils literal">AB AC AD BA BC BD CA CB CD DA DB DC</tt></td>
</tr>
<tr class="row-even"><td><tt class="docutils literal">combinations('ABCD', 2)</tt></td>
<td>&nbsp;</td>
<td><tt class="docutils literal">AB AC AD BC BD CD</tt></td>
</tr>
<tr class="row-odd"><td><tt class="docutils literal">combinations_with_replacement('ABCD', 2)</tt></td>
<td>&nbsp;</td>
<td><tt class="docutils literal">AA AB AC AD BB BC BD CC CD DD</tt></td>
</tr>
</tbody>
</table>
<div class="section" id="itertool-functions">
<h2>9.7.1. Itertool functions<a class="headerlink" href="#itertool-functions" title="Permalink to this headline">¶</a></h2>
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.
<dl class="function">
<dt id="itertools.chain">
<tt class="descclassname">itertools.</tt><tt class="descname">chain</tt><big>(</big>*iterables<big>)</big><a class="headerlink" href="#itertools.chain" title="Permalink to this definition">¶</a></dt>
<dd>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:
<div class="highlight-python"><div class="highlight"><pre>def chain(*iterables):
 # chain(&#39;ABC&#39;, &#39;DEF&#39;) --&gt; A B C D E F
 for it in iterables:
 for element in it:
 yield element
</pre></div>
</div>
</dd></dl>

<dl class="classmethod">
<dt id="itertools.chain.from_iterable">
classmethod <tt class="descclassname">chain.</tt><tt class="descname">from_iterable</tt><big>(</big>iterable<big>)</big><a class="headerlink" href="#itertools.chain.from_iterable" title="Permalink to this definition">¶</a></dt>
<dd>Alternate constructor for <a class="reference internal" href="#itertools.chain" title="itertools.chain"><tt class="xref py py-func docutils literal">chain()</tt></a>. Gets chained inputs from a
single iterable argument that is evaluated lazily. Roughly equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def from_iterable(iterables):
 # chain.from_iterable([&#39;ABC&#39;, &#39;DEF&#39;]) --&gt; A B C D E F
 for it in iterables:
 for element in it:
 yield element
</pre></div>
</div>

New in version 2.6.
</dd></dl>

<dl class="function">
<dt id="itertools.combinations">
<tt class="descclassname">itertools.</tt><tt class="descname">combinations</tt><big>(</big>iterable, r<big>)</big><a class="headerlink" href="#itertools.combinations" title="Permalink to this definition">¶</a></dt>
<dd>Return r length subsequences of elements from the input iterable.
Combinations are emitted in lexicographic sort order. So, if the
input iterable is sorted, the combination tuples will be produced
in sorted order.
Elements are treated as unique based on their position, not on their
value. So if the input elements are unique, there will be no repeat
values in each combination.
Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def combinations(iterable, r):
 # combinations(&#39;ABCD&#39;, 2) --&gt; AB AC AD BC BD CD
 # combinations(range(4), 3) --&gt; 012 013 023 123
 pool = tuple(iterable)
 n = len(pool)
 if r &gt; n:
 return
 indices = range(r)
 yield tuple(pool[i] for i in indices)
 while True:
 for i in reversed(range(r)):
 if indices[i] != i + n - r:
 break
 else:
 return
 indices[i] += 1
 for j in range(i+1, r):
 indices[j] = indices[j-1] + 1
 yield tuple(pool[i] for i in indices)
</pre></div>
</div>
The code for <a class="reference internal" href="#itertools.combinations" title="itertools.combinations"><tt class="xref py py-func docutils literal">combinations()</tt></a> can be also expressed as a subsequence
of <a class="reference internal" href="#itertools.permutations" title="itertools.permutations"><tt class="xref py py-func docutils literal">permutations()</tt></a> after filtering entries where the elements are not
in sorted order (according to their position in the input pool):
<div class="highlight-python"><div class="highlight"><pre>def combinations(iterable, r):
 pool = tuple(iterable)
 n = len(pool)
 for indices in permutations(range(n), r):
 if sorted(indices) == list(indices):
 yield tuple(pool[i] for i in indices)
</pre></div>
</div>
The number of items returned is <tt class="docutils literal">n! / r! / (n-r)!</tt> when <tt class="docutils literal">0 &lt;= r &lt;= n</tt>
or zero when <tt class="docutils literal">r &gt; n</tt>.

New in version 2.6.
</dd></dl>

<dl class="function">
<dt id="itertools.combinations_with_replacement">
<tt class="descclassname">itertools.</tt><tt class="descname">combinations_with_replacement</tt><big>(</big>iterable, r<big>)</big><a class="headerlink" href="#itertools.combinations_with_replacement" title="Permalink to this definition">¶</a></dt>
<dd>Return r length subsequences of elements from the input iterable
allowing individual elements to be repeated more than once.
Combinations are emitted in lexicographic sort order. So, if the
input iterable is sorted, the combination tuples will be produced
in sorted order.
Elements are treated as unique based on their position, not on their
value. So if the input elements are unique, the generated combinations
will also be unique.
Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def combinations_with_replacement(iterable, r):
 # combinations_with_replacement(&#39;ABC&#39;, 2) --&gt; AA AB AC BB BC CC
 pool = tuple(iterable)
 n = len(pool)
 if not n and r:
 return
 indices = [0] * r
 yield tuple(pool[i] for i in indices)
 while True:
 for i in reversed(range(r)):
 if indices[i] != n - 1:
 break
 else:
 return
 indices[i:] = [indices[i] + 1] * (r - i)
 yield tuple(pool[i] for i in indices)
</pre></div>
</div>
The code for <a class="reference internal" href="#itertools.combinations_with_replacement" title="itertools.combinations_with_replacement"><tt class="xref py py-func docutils literal">combinations_with_replacement()</tt></a> can be also expressed as
a subsequence of <a class="reference internal" href="#itertools.product" title="itertools.product"><tt class="xref py py-func docutils literal">product()</tt></a> after filtering entries where the elements
are not in sorted order (according to their position in the input pool):
<div class="highlight-python"><div class="highlight"><pre>def combinations_with_replacement(iterable, r):
 pool = tuple(iterable)
 n = len(pool)
 for indices in product(range(n), repeat=r):
 if sorted(indices) == list(indices):
 yield tuple(pool[i] for i in indices)
</pre></div>
</div>
The number of items returned is <tt class="docutils literal">(n+r-1)! / r! / (n-1)!</tt> when <tt class="docutils literal">n &gt; 0</tt>.

New in version 2.7.
</dd></dl>

<dl class="function">
<dt id="itertools.compress">
<tt class="descclassname">itertools.</tt><tt class="descname">compress</tt><big>(</big>data, selectors<big>)</big><a class="headerlink" href="#itertools.compress" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that filters elements from data returning only those that
have a corresponding element in selectors that evaluates to <tt class="docutils literal">True</tt>.
Stops when either the data or selectors iterables has been exhausted.
Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def compress(data, selectors):
 # compress(&#39;ABCDEF&#39;, [1,0,1,0,1,1]) --&gt; A C E F
 return (d for d, s in izip(data, selectors) if s)
</pre></div>
</div>

New in version 2.7.
</dd></dl>

<dl class="function">
<dt id="itertools.count">
<tt class="descclassname">itertools.</tt><tt class="descname">count</tt><big>(</big>start=0, step=1<big>)</big><a class="headerlink" href="#itertools.count" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that returns evenly spaced values starting with n. Often
used as an argument to <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a> to generate consecutive data points.
Also, used with <a class="reference internal" href="#itertools.izip" title="itertools.izip"><tt class="xref py py-func docutils literal">izip()</tt></a> to add sequence numbers. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def count(start=0, step=1):
 # count(10) --&gt; 10 11 12 13 14 ...
 # count(2.5, 0.5) -&gt; 2.5 3.0 3.5 ...
 n = start
 while True:
 yield n
 n += step
</pre></div>
</div>
When counting with floating point numbers, better accuracy can sometimes be
achieved by substituting multiplicative code such as: <tt class="docutils literal">(start + step * i
for i in count())</tt>.

Changed in version 2.7: added step argument and allowed non-integer arguments.
</dd></dl>

<dl class="function">
<dt id="itertools.cycle">
<tt class="descclassname">itertools.</tt><tt class="descname">cycle</tt><big>(</big>iterable<big>)</big><a class="headerlink" href="#itertools.cycle" title="Permalink to this definition">¶</a></dt>
<dd>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:
<div class="highlight-python"><div class="highlight"><pre>def cycle(iterable):
 # cycle(&#39;ABCD&#39;) --&gt; A B C D A B C D A B C D ...
 saved = []
 for element in iterable:
 yield element
 saved.append(element)
 while saved:
 for element in saved:
 yield element
</pre></div>
</div>
Note, this member of the toolkit may require significant auxiliary storage
(depending on the length of the iterable).
</dd></dl>

<dl class="function">
<dt id="itertools.dropwhile">
<tt class="descclassname">itertools.</tt><tt class="descname">dropwhile</tt><big>(</big>predicate, iterable<big>)</big><a class="headerlink" href="#itertools.dropwhile" title="Permalink to this definition">¶</a></dt>
<dd>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
any output until the predicate first becomes false, so it may have a lengthy
start-up time. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def dropwhile(predicate, iterable):
 # dropwhile(lambda x: x&lt;5, [1,4,6,4,1]) --&gt; 6 4 1
 iterable = iter(iterable)
 for x in iterable:
 if not predicate(x):
 yield x
 break
 for x in iterable:
 yield x
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.groupby">
<tt class="descclassname">itertools.</tt><tt class="descname">groupby</tt><big>(</big>iterable[, key]<big>)</big><a class="headerlink" href="#itertools.groupby" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that returns consecutive keys and groups from the iterable.
The key is a function computing a key value for each element. If not
specified or is <tt class="docutils literal">None</tt>, 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 <a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><tt class="xref py py-func docutils literal">groupby()</tt></a> is similar to the <tt class="docutils literal">uniq</tt> 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&#8217;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 <a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><tt class="xref py py-func docutils literal">groupby()</tt></a>. Because the source is shared, when the <a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><tt class="xref py py-func docutils literal">groupby()</tt></a>
object is advanced, the previous group is no longer visible. So, if that data
is needed later, it should be stored as a list:
<div class="highlight-python"><div class="highlight"><pre>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)
</pre></div>
</div>
<a class="reference internal" href="#itertools.groupby" title="itertools.groupby"><tt class="xref py py-func docutils literal">groupby()</tt></a> is equivalent to:
<div class="highlight-python"><div class="highlight"><pre>class groupby(object):
 # [k for k, g in groupby(&#39;AAAABBBCCDAABBB&#39;)] --&gt; A B C D A B
 # [list(g) for k, g in groupby(&#39;AAAABBBCCD&#39;)] --&gt; AAAA BBB CC D
 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 = object()
 def __iter__(self):
 return self
 def next(self):
 while self.currkey == self.tgtkey:
 self.currvalue = next(self.it) # 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 = next(self.it) # Exit on StopIteration
 self.currkey = self.keyfunc(self.currvalue)
</pre></div>
</div>

New in version 2.4.
</dd></dl>

<dl class="function">
<dt id="itertools.ifilter">
<tt class="descclassname">itertools.</tt><tt class="descname">ifilter</tt><big>(</big>predicate, iterable<big>)</big><a class="headerlink" href="#itertools.ifilter" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that filters elements from iterable returning only those for
which the predicate is <tt class="docutils literal">True</tt>. If predicate is <tt class="docutils literal">None</tt>, return the items
that are true. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def ifilter(predicate, iterable):
 # ifilter(lambda x: x%2, range(10)) --&gt; 1 3 5 7 9
 if predicate is None:
 predicate = bool
 for x in iterable:
 if predicate(x):
 yield x
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.ifilterfalse">
<tt class="descclassname">itertools.</tt><tt class="descname">ifilterfalse</tt><big>(</big>predicate, iterable<big>)</big><a class="headerlink" href="#itertools.ifilterfalse" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that filters elements from iterable returning only those for
which the predicate is <tt class="docutils literal">False</tt>. If predicate is <tt class="docutils literal">None</tt>, return the items
that are false. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def ifilterfalse(predicate, iterable):
 # ifilterfalse(lambda x: x%2, range(10)) --&gt; 0 2 4 6 8
 if predicate is None:
 predicate = bool
 for x in iterable:
 if not predicate(x):
 yield x
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.imap">
<tt class="descclassname">itertools.</tt><tt class="descname">imap</tt><big>(</big>function, *iterables<big>)</big><a class="headerlink" href="#itertools.imap" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that computes the function using arguments from each of the
iterables. If function is set to <tt class="docutils literal">None</tt>, then <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a> returns the
arguments as a tuple. Like <a class="reference internal" href="functions.html#map" title="map"><tt class="xref py py-func docutils literal">map()</tt></a> but stops when the shortest iterable is
exhausted instead of filling in <tt class="docutils literal">None</tt> for shorter iterables. The reason for
the difference is that infinite iterator arguments are typically an error for
<a class="reference internal" href="functions.html#map" title="map"><tt class="xref py py-func docutils literal">map()</tt></a> (because the output is fully evaluated) but represent a common and
useful way of supplying arguments to <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a>. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def imap(function, *iterables):
 # imap(pow, (2,3,10), (5,2,3)) --&gt; 32 9 1000
 iterables = map(iter, iterables)
 while True:
 args = [next(it) for it in iterables]
 if function is None:
 yield tuple(args)
 else:
 yield function(*args)
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.islice">
<tt class="descclassname">itertools.</tt><tt class="descname">islice</tt><big>(</big>iterable, stop<big>)</big><a class="headerlink" href="#itertools.islice" title="Permalink to this definition">¶</a></dt>
<dt>
<tt class="descclassname">itertools.</tt><tt class="descname">islice</tt><big>(</big>iterable, start, stop[, step]<big>)</big></dt>
<dd>Make an iterator that returns selected elements from the iterable. If start is
non-zero, then elements from the iterable are skipped until start is reached.
Afterward, elements are returned consecutively unless step is set higher than
one which results in items being skipped. If stop is <tt class="docutils literal">None</tt>, then iteration
continues until the iterator is exhausted, if at all; otherwise, it stops at the
specified position. Unlike regular slicing, <a class="reference internal" href="#itertools.islice" title="itertools.islice"><tt class="xref py py-func docutils literal">islice()</tt></a> does not support
negative values for start, stop, or 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:
<div class="highlight-python"><div class="highlight"><pre>def islice(iterable, *args):
 # islice(&#39;ABCDEFG&#39;, 2) --&gt; A B
 # islice(&#39;ABCDEFG&#39;, 2, 4) --&gt; C D
 # islice(&#39;ABCDEFG&#39;, 2, None) --&gt; C D E F G
 # islice(&#39;ABCDEFG&#39;, 0, None, 2) --&gt; A C E G
 s = slice(*args)
 it = iter(xrange(s.start or 0, s.stop or sys.maxint, s.step or 1))
 nexti = next(it)
 for i, element in enumerate(iterable):
 if i == nexti:
 yield element
 nexti = next(it)
</pre></div>
</div>
If start is <tt class="docutils literal">None</tt>, then iteration starts at zero. If step is <tt class="docutils literal">None</tt>,
then the step defaults to one.

Changed in version 2.5: accept <tt class="docutils literal">None</tt> values for default start and step.
</dd></dl>

<dl class="function">
<dt id="itertools.izip">
<tt class="descclassname">itertools.</tt><tt class="descname">izip</tt><big>(</big>*iterables<big>)</big><a class="headerlink" href="#itertools.izip" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that aggregates elements from each of the iterables. Like
<a class="reference internal" href="functions.html#zip" title="zip"><tt class="xref py py-func docutils literal">zip()</tt></a> except that it returns an iterator instead of a list. Used for
lock-step iteration over several iterables at a time. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def izip(*iterables):
 # izip(&#39;ABCD&#39;, &#39;xy&#39;) --&gt; Ax By
 iterators = map(iter, iterables)
 while iterators:
 yield tuple(map(next, iterators))
</pre></div>
</div>

Changed in version 2.4: When no iterables are specified, returns a zero length iterator instead of
raising a <a class="reference internal" href="exceptions.html#exceptions.TypeError" title="exceptions.TypeError"><tt class="xref py py-exc docutils literal">TypeError</tt></a> exception.
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 <tt class="docutils literal">izip(*[iter(s)]*n)</tt>.
<a class="reference internal" href="#itertools.izip" title="itertools.izip"><tt class="xref py py-func docutils literal">izip()</tt></a> should only be used with unequal length inputs when you don&#8217;t
care about trailing, unmatched values from the longer iterables. If those
values are important, use <a class="reference internal" href="#itertools.izip_longest" title="itertools.izip_longest"><tt class="xref py py-func docutils literal">izip_longest()</tt></a> instead.
</dd></dl>

<dl class="function">
<dt id="itertools.izip_longest">
<tt class="descclassname">itertools.</tt><tt class="descname">izip_longest</tt><big>(</big>*iterables[, fillvalue]<big>)</big><a class="headerlink" href="#itertools.izip_longest" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that aggregates elements from each of the iterables. If the
iterables are of uneven length, missing values are filled-in with fillvalue.
Iteration continues until the longest iterable is exhausted. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>class ZipExhausted(Exception):
 pass

def izip_longest(*args, **kwds):
 # izip_longest(&#39;ABCD&#39;, &#39;xy&#39;, fillvalue=&#39;-&#39;) --&gt; Ax By C- D-
 fillvalue = kwds.get(&#39;fillvalue&#39;)
 counter = [len(args) - 1]
 def sentinel():
 if not counter[0]:
 raise ZipExhausted
 counter[0] -= 1
 yield fillvalue
 fillers = repeat(fillvalue)
 iterators = [chain(it, sentinel(), fillers) for it in args]
 try:
 while iterators:
 yield tuple(map(next, iterators))
 except ZipExhausted:
 pass
</pre></div>
</div>
If one of the iterables is potentially infinite, then the
<a class="reference internal" href="#itertools.izip_longest" title="itertools.izip_longest"><tt class="xref py py-func docutils literal">izip_longest()</tt></a> function should be wrapped with something that limits
the number of calls (for example <a class="reference internal" href="#itertools.islice" title="itertools.islice"><tt class="xref py py-func docutils literal">islice()</tt></a> or <a class="reference internal" href="#itertools.takewhile" title="itertools.takewhile"><tt class="xref py py-func docutils literal">takewhile()</tt></a>). If
not specified, fillvalue defaults to <tt class="docutils literal">None</tt>.

New in version 2.6.
</dd></dl>

<dl class="function">
<dt id="itertools.permutations">
<tt class="descclassname">itertools.</tt><tt class="descname">permutations</tt><big>(</big>iterable[, r]<big>)</big><a class="headerlink" href="#itertools.permutations" title="Permalink to this definition">¶</a></dt>
<dd>Return successive r length permutations of elements in the iterable.
If r is not specified or is <tt class="docutils literal">None</tt>, then r defaults to the length
of the iterable and all possible full-length permutations
are generated.
Permutations are emitted in lexicographic sort order. So, if the
input iterable is sorted, the permutation tuples will be produced
in sorted order.
Elements are treated as unique based on their position, not on their
value. So if the input elements are unique, there will be no repeat
values in each permutation.
Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def permutations(iterable, r=None):
 # permutations(&#39;ABCD&#39;, 2) --&gt; AB AC AD BA BC BD CA CB CD DA DB DC
 # permutations(range(3)) --&gt; 012 021 102 120 201 210
 pool = tuple(iterable)
 n = len(pool)
 r = n if r is None else r
 if r &gt; n:
 return
 indices = range(n)
 cycles = range(n, n-r, -1)
 yield tuple(pool[i] for i in indices[:r])
 while n:
 for i in reversed(range(r)):
 cycles[i] -= 1
 if cycles[i] == 0:
 indices[i:] = indices[i+1:] + indices[i:i+1]
 cycles[i] = n - i
 else:
 j = cycles[i]
 indices[i], indices[-j] = indices[-j], indices[i]
 yield tuple(pool[i] for i in indices[:r])
 break
 else:
 return
</pre></div>
</div>
The code for <a class="reference internal" href="#itertools.permutations" title="itertools.permutations"><tt class="xref py py-func docutils literal">permutations()</tt></a> can be also expressed as a subsequence of
<a class="reference internal" href="#itertools.product" title="itertools.product"><tt class="xref py py-func docutils literal">product()</tt></a>, filtered to exclude entries with repeated elements (those
from the same position in the input pool):
<div class="highlight-python"><div class="highlight"><pre>def permutations(iterable, r=None):
 pool = tuple(iterable)
 n = len(pool)
 r = n if r is None else r
 for indices in product(range(n), repeat=r):
 if len(set(indices)) == r:
 yield tuple(pool[i] for i in indices)
</pre></div>
</div>
The number of items returned is <tt class="docutils literal">n! / (n-r)!</tt> when <tt class="docutils literal">0 &lt;= r &lt;= n</tt>
or zero when <tt class="docutils literal">r &gt; n</tt>.

New in version 2.6.
</dd></dl>

<dl class="function">
<dt id="itertools.product">
<tt class="descclassname">itertools.</tt><tt class="descname">product</tt><big>(</big>*iterables[, repeat]<big>)</big><a class="headerlink" href="#itertools.product" title="Permalink to this definition">¶</a></dt>
<dd>Cartesian product of input iterables.
Equivalent to nested for-loops in a generator expression. For example,
<tt class="docutils literal">product(A, B)</tt> returns the same as <tt class="docutils literal">((x,y) for x in A for y in B)</tt>.
The nested loops cycle like an odometer with the rightmost element advancing
on every iteration. This pattern creates a lexicographic ordering so that if
the input&#8217;s iterables are sorted, the product tuples are emitted in sorted
order.
To compute the product of an iterable with itself, specify the number of
repetitions with the optional repeat keyword argument. For example,
<tt class="docutils literal">product(A, repeat=4)</tt> means the same as <tt class="docutils literal">product(A, A, A, A)</tt>.
This function is equivalent to the following code, except that the
actual implementation does not build up intermediate results in memory:
<div class="highlight-python"><div class="highlight"><pre>def product(*args, **kwds):
 # product(&#39;ABCD&#39;, &#39;xy&#39;) --&gt; Ax Ay Bx By Cx Cy Dx Dy
 # product(range(2), repeat=3) --&gt; 000 001 010 011 100 101 110 111
 pools = map(tuple, args) * kwds.get(&#39;repeat&#39;, 1)
 result = [[]]
 for pool in pools:
 result = [x+[y] for x in result for y in pool]
 for prod in result:
 yield tuple(prod)
</pre></div>
</div>

New in version 2.6.
</dd></dl>

<dl class="function">
<dt id="itertools.repeat">
<tt class="descclassname">itertools.</tt><tt class="descname">repeat</tt><big>(</big>object[, times]<big>)</big><a class="headerlink" href="#itertools.repeat" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that returns object over and over again. Runs indefinitely
unless the times argument is specified. Used as argument to <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a> for
invariant function parameters. Also used with <a class="reference internal" href="#itertools.izip" title="itertools.izip"><tt class="xref py py-func docutils literal">izip()</tt></a> to create constant
fields in a tuple record. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def repeat(object, times=None):
 # repeat(10, 3) --&gt; 10 10 10
 if times is None:
 while True:
 yield object
 else:
 for i in xrange(times):
 yield object
</pre></div>
</div>
A common use for repeat is to supply a stream of constant values to imap
or zip:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; list(imap(pow, xrange(10), repeat(2)))
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.starmap">
<tt class="descclassname">itertools.</tt><tt class="descname">starmap</tt><big>(</big>function, iterable<big>)</big><a class="headerlink" href="#itertools.starmap" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that computes the function using arguments obtained from
the iterable. Used instead of <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a> when argument parameters are already
grouped in tuples from a single iterable (the data has been &#8220;pre-zipped&#8221;). The
difference between <a class="reference internal" href="#itertools.imap" title="itertools.imap"><tt class="xref py py-func docutils literal">imap()</tt></a> and <a class="reference internal" href="#itertools.starmap" title="itertools.starmap"><tt class="xref py py-func docutils literal">starmap()</tt></a> parallels the distinction
between <tt class="docutils literal">function(a,b)</tt> and <tt class="docutils literal">function(*c)</tt>. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def starmap(function, iterable):
 # starmap(pow, [(2,5), (3,2), (10,3)]) --&gt; 32 9 1000
 for args in iterable:
 yield function(*args)
</pre></div>
</div>

Changed in version 2.6: Previously, <a class="reference internal" href="#itertools.starmap" title="itertools.starmap"><tt class="xref py py-func docutils literal">starmap()</tt></a> required the function arguments to be tuples.
Now, any iterable is allowed.
</dd></dl>

<dl class="function">
<dt id="itertools.takewhile">
<tt class="descclassname">itertools.</tt><tt class="descname">takewhile</tt><big>(</big>predicate, iterable<big>)</big><a class="headerlink" href="#itertools.takewhile" title="Permalink to this definition">¶</a></dt>
<dd>Make an iterator that returns elements from the iterable as long as the
predicate is true. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def takewhile(predicate, iterable):
 # takewhile(lambda x: x&lt;5, [1,4,6,4,1]) --&gt; 1 4
 for x in iterable:
 if predicate(x):
 yield x
 else:
 break
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="itertools.tee">
<tt class="descclassname">itertools.</tt><tt class="descname">tee</tt><big>(</big>iterable[, n=2]<big>)</big><a class="headerlink" href="#itertools.tee" title="Permalink to this definition">¶</a></dt>
<dd>Return n independent iterators from a single iterable. Equivalent to:
<div class="highlight-python"><div class="highlight"><pre>def tee(iterable, n=2):
 it = iter(iterable)
 deques = [collections.deque() for i in range(n)]
 def gen(mydeque):
 while True:
 if not mydeque: # when the local deque is empty
 newval = next(it) # fetch a new value and
 for d in deques: # load it to all the deques
 d.append(newval)
 yield mydeque.popleft()
 return tuple(gen(d) for d in deques)
</pre></div>
</div>
Once <a class="reference internal" href="#itertools.tee" title="itertools.tee"><tt class="xref py py-func docutils literal">tee()</tt></a> has made a split, the original iterable should not be
used anywhere else; otherwise, the iterable could get advanced without
the tee objects being informed.
This itertool may require significant auxiliary storage (depending on how
much temporary data needs to be stored). In general, if one iterator uses
most or all of the data before another iterator starts, it is faster to use
<a class="reference internal" href="functions.html#list" title="list"><tt class="xref py py-func docutils literal">list()</tt></a> instead of <a class="reference internal" href="#itertools.tee" title="itertools.tee"><tt class="xref py py-func docutils literal">tee()</tt></a>.

New in version 2.4.
</dd></dl>

</div>
<div class="section" id="recipes">
<h2>9.7.2. Recipes<a class="headerlink" href="#recipes" title="Permalink to this headline">¶</a></h2>
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
&#8220;vectorized&#8221; building blocks over the use of for-loops and <a class="reference internal" href="../glossary.html#term-generator">generator</a>s
which incur interpreter overhead.
<div class="highlight-python"><div class="highlight"><pre>def take(n, iterable):
 &quot;Return first n items of the iterable as a list&quot;
 return list(islice(iterable, n))

def tabulate(function, start=0):
 &quot;Return function(0), function(1), ...&quot;
 return imap(function, count(start))

def consume(iterator, n):
 &quot;Advance the iterator n-steps ahead. If n is none, consume entirely.&quot;
 # Use functions that consume iterators at C speed.
 if n is None:
 # feed the entire iterator into a zero-length deque
 collections.deque(iterator, maxlen=0)
 else:
 # advance to the empty slice starting at position n
 next(islice(iterator, n, n), None)

def nth(iterable, n, default=None):
 &quot;Returns the nth item or a default value&quot;
 return next(islice(iterable, n, None), default)

def quantify(iterable, pred=bool):
 &quot;Count how many times the predicate is true&quot;
 return sum(imap(pred, iterable))

def padnone(iterable):
 &quot;&quot;&quot;Returns the sequence elements and then returns None indefinitely.

Useful for emulating the behavior of the built-in map() function.
 &quot;&quot;&quot;
 return chain(iterable, repeat(None))

def ncycles(iterable, n):
 &quot;Returns the sequence elements n times&quot;
 return chain.from_iterable(repeat(tuple(iterable), n))

def dotproduct(vec1, vec2):
 return sum(imap(operator.mul, vec1, vec2))

def flatten(listOfLists):
 &quot;Flatten one level of nesting&quot;
 return chain.from_iterable(listOfLists)

def repeatfunc(func, times=None, *args):
 &quot;&quot;&quot;Repeat calls to func with specified arguments.

Example: repeatfunc(random.random)
 &quot;&quot;&quot;
 if times is None:
 return starmap(func, repeat(args))
 return starmap(func, repeat(args, times))

def pairwise(iterable):
 &quot;s -&gt; (s0,s1), (s1,s2), (s2, s3), ...&quot;
 a, b = tee(iterable)
 next(b, None)
 return izip(a, b)

def grouper(iterable, n, fillvalue=None):
 &quot;Collect data into fixed-length chunks or blocks&quot;
 # grouper(&#39;ABCDEFG&#39;, 3, &#39;x&#39;) --&gt; ABC DEF Gxx
 args = [iter(iterable)] * n
 return izip_longest(fillvalue=fillvalue, *args)

def roundrobin(*iterables):
 &quot;roundrobin(&#39;ABC&#39;, &#39;D&#39;, &#39;EF&#39;) --&gt; A D E B F C&quot;
 # Recipe credited to George Sakkis
 pending = len(iterables)
 nexts = cycle(iter(it).next for it in iterables)
 while pending:
 try:
 for next in nexts:
 yield next()
 except StopIteration:
 pending -= 1
 nexts = cycle(islice(nexts, pending))

def powerset(iterable):
 &quot;powerset([1,2,3]) --&gt; () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)&quot;
 s = list(iterable)
 return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

def unique_everseen(iterable, key=None):
 &quot;List unique elements, preserving order. Remember all elements ever seen.&quot;
 # unique_everseen(&#39;AAAABBBCCDAABBB&#39;) --&gt; A B C D
 # unique_everseen(&#39;ABBCcAD&#39;, str.lower) --&gt; A B C D
 seen = set()
 seen_add = seen.add
 if key is None:
 for element in ifilterfalse(seen.__contains__, iterable):
 seen_add(element)
 yield element
 else:
 for element in iterable:
 k = key(element)
 if k not in seen:
 seen_add(k)
 yield element

def unique_justseen(iterable, key=None):
 &quot;List unique elements, preserving order. Remember only the element just seen.&quot;
 # unique_justseen(&#39;AAAABBBCCDAABBB&#39;) --&gt; A B C D A B
 # unique_justseen(&#39;ABBCcAD&#39;, str.lower) --&gt; A B C A D
 return imap(next, imap(itemgetter(1), groupby(iterable, key)))

def iter_except(func, exception, first=None):
 &quot;&quot;&quot; Call a function repeatedly until an exception is raised.

Converts a call-until-exception interface to an iterator interface.
 Like __builtin__.iter(func, sentinel) but uses an exception instead
 of a sentinel to end the loop.

Examples:
 bsddbiter = iter_except(db.next, bsddb.error, db.first)
 heapiter = iter_except(functools.partial(heappop, h), IndexError)
 dictiter = iter_except(d.popitem, KeyError)
 dequeiter = iter_except(d.popleft, IndexError)
 queueiter = iter_except(q.get_nowait, Queue.Empty)
 setiter = iter_except(s.pop, KeyError)

&quot;&quot;&quot;
 try:
 if first is not None:
 yield first()
 while 1:
 yield func()
 except exception:
 pass

def random_product(*args, **kwds):
 &quot;Random selection from itertools.product(*args, **kwds)&quot;
 pools = map(tuple, args) * kwds.get(&#39;repeat&#39;, 1)
 return tuple(random.choice(pool) for pool in pools)

def random_permutation(iterable, r=None):
 &quot;Random selection from itertools.permutations(iterable, r)&quot;
 pool = tuple(iterable)
 r = len(pool) if r is None else r
 return tuple(random.sample(pool, r))

def random_combination(iterable, r):
 &quot;Random selection from itertools.combinations(iterable, r)&quot;
 pool = tuple(iterable)
 n = len(pool)
 indices = sorted(random.sample(xrange(n), r))
 return tuple(pool[i] for i in indices)

def random_combination_with_replacement(iterable, r):
 &quot;Random selection from itertools.combinations_with_replacement(iterable, r)&quot;
 pool = tuple(iterable)
 n = len(pool)
 indices = sorted(random.randrange(n) for i in xrange(r))
 return tuple(pool[i] for i in indices)

def tee_lookahead(t, i):
 &quot;&quot;&quot;Inspect the i-th upcomping value from a tee object
 while leaving the tee object at its current position.

Raise an IndexError if the underlying iterator doesn&#39;t
 have enough values.

&quot;&quot;&quot;
 for value in islice(t.__copy__(), i, None):
 return value
 raise IndexError(i)
</pre></div>
</div>
Note, many of the above recipes can be optimized by replacing global lookups
with local variables defined as default values. For example, the
dotproduct recipe can be written as:
<div class="highlight-python"><div class="highlight"><pre>def dotproduct(vec1, vec2, sum=sum, imap=imap, mul=operator.mul):
 return sum(imap(mul, vec1, vec2))
</pre></div>
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