+ hrcsRt^RIt^RIt^RIHt^RIHt^RIHtH t ^RI H t H t H t HtHtHtHtHtHtHtHtHt^RIHtHtHt^RIHt.RNR NR NR NR NR NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5Nt]!4t] !R6R77]!] R6R77t!]#!]R8R94t$R:t%RuR;lt&R<t'RvR=lt(RvR>lt)RvR?lt*]+3R@lt,RAt-]-t.RBt/RCt0RDt1RvRElt2RFt3^RGI H4t5RHt4]3P]4n!RIRJ]74t8RKt9RLt:RwRMlt;RNtRvRQlt?RvRRlt@RxRTltARvRUltBRyRVltCRW^/RXltDRvRYltERZtFR[tGR\tHR]tIR^tJR_tKR`tLRatMRbtNRctORdtPRetQRzRfltRRgtSRhRS/RiltT]Rj8d^RkI HUtVRhRS/RlltUM]TtU]TP]UnRmtWRntXRotYRptZRqt[Rrt\Rst]Rtt^R# ]"d] t!EL!i;i ]6d]3t4Li;i){aImported from the recipes section of the itertools documentation. All functions taken from the recipes section of the itertools library docs [1]_. Some backward-compatible usability improvements have been made. .. [1] http://docs.python.org/library/itertools.html#recipes N)deque)Sized)partialreduce) chain combinationscompresscountcyclegroupbyisliceproductrepeatstarmaptee zip_longest) randrangesamplechoice) hexversion all_equalbatchedbefore_and_afterconsumeconvolve dotproduct first_truefactorflattengrouper iter_except iter_indexmatmulncyclesnthnth_combinationpadnonepad_nonepairwise partitionpolynomial_evalpolynomial_from_rootspolynomial_derivativepowersetprependquantifyreshape#random_combination_with_replacementrandom_combinationrandom_permutationrandom_product repeatfunc roundrobinsievesliding_window subslicessum_of_squarestabulatetailtaketotient transpose triplewiseuniqueunique_everseenunique_justseenTstrictZsumprodcs\W4#N)r)xZy&&;/usr/lib/python3.14/site-packages/more_itertools/recipes.pyrH_s A1Ac*\\W44#)zReturn first *n* items of the iterable as a list. >>> take(3, range(10)) [0, 1, 2] If there are fewer than *n* items in the iterable, all of them are returned. >>> take(10, range(3)) [0, 1, 2] )listr niterablerFrGr;r;bs x# $$rIcs,\V\V44#)aReturn an iterator over the results of ``func(start)``, ``func(start + 1)``, ``func(start + 2)``... *func* should be a function that accepts one integer argument. If *start* is not specified it defaults to 0. It will be incremented each time the iterator is advanced. >>> square = lambda x: x ** 2 >>> iterator = tabulate(square, -3) >>> take(4, iterator) [9, 4, 1, 0] )mapr)ZfunctionstartrFrGr9r9rs xu &&rIc #s"\V\4'd2\V\^\ V4V, 4R4RjxL R#\ \ WR74RjxL R#L%L5i)zsReturn an iterator over the last *n* items of *iterable*. >>> t = tail(3, 'ABCDEFG') >>> list(t) ['E', 'F', 'G'] NZmaxlen)Z isinstancerr ZmaxleniterrrLrFrGr:r:sR(E""(C3x=1+<$=tDDDh1222 E2s$AA-A)A-"A+#A-+A-csXVf\V^R7R#\\WV4R4R#)aAdvance *iterable* by *n* steps. If *n* is ``None``, consume it entirely. Efficiently exhausts an iterator without returning values. Defaults to consuming the whole iterator, but an optional second argument may be provided to limit consumption. >>> i = (x for x in range(10)) >>> next(i) 0 >>> consume(i, 3) >>> next(i) 4 >>> consume(i) >>> next(i) Traceback (most recent call last): File "", line 1, in StopIteration If the iterator has fewer items remaining than the provided limit, the whole iterator will be consumed. >>> i = (x for x in range(3)) >>> consume(i, 5) >>> next(i) Traceback (most recent call last): File "", line 1, in StopIteration NrQ)rnextr )iteratorrMrFrGrrs'@ y hq! VH #T*rIcs.\\WR4V4#)zmReturns the nth item or a default value. >>> l = range(10) >>> nth(l, 3) 3 >>> nth(l, 20, "zebra") 'zebra' N)rTr )rNrMdefault&&&rGr"r"s xD)7 33rIcsF\W4pVFpVFpR# R# R#)aw Returns ``True`` if all the elements are equal to each other. >>> all_equal('aaaa') True >>> all_equal('aaab') False A function that accepts a single argument and returns a transformed version of each input item can be specified with *key*: >>> all_equal('AaaA', key=str.casefold) True >>> all_equal([1, 2, 3], key=lambda x: x < 10) True FT)r )rNkeyrUfirstZsecond&& rGrrs-$x%HF rIcrJ)zWReturn the how many times the predicate is true. >>> quantify([True, False, True]) 2 )sumrO)rNpredrFrGr-r-s s4" ##rIcs,\V\R44#)zReturns the sequence of elements and then returns ``None`` indefinitely. >>> take(5, pad_none(range(3))) [0, 1, 2, None, None] Useful for emulating the behavior of the built-in :func:`map` function. See also :func:`padded`. N)rr rN&rGr%r%s 6$< ((rIcsT\P!\\V4V44#)zjReturns the sequence elements *n* times >>> list(ncycles(["a", "b"], 3)) ['a', 'b', 'a', 'b', 'a', 'b'] )r from_iterabler tuplerNrMrFrGr!r!s    veHoq9 ::rIcsH\\\PW44#)zWReturns the dot product of the two iterables. >>> dotproduct([10, 10], [20, 20]) 400 )r[rOoperatormul)Zvec1Zvec2rFrGrr s s8<<, --rIcs.\P!V4#)zReturn an iterator flattening one level of nesting in a list of lists. >>> list(flatten([[0, 1], [2, 3]])) [0, 1, 2, 3] See also :func:`collapse`, which can flatten multiple levels of nesting. )rr_)Z listOfListsr^rGrrs   { ++rIcs^Vf\V\V44#\V\W!44#)a Call *func* with *args* repeatedly, returning an iterable over the results. If *times* is specified, the iterable will terminate after that many repetitions: >>> from operator import add >>> times = 4 >>> args = 3, 5 >>> list(repeatfunc(add, times, *args)) [8, 8, 8, 8] If *times* is ``None`` the iterable will not terminate: >>> from random import randrange >>> times = None >>> args = 1, 11 >>> take(6, repeatfunc(randrange, times, *args)) # doctest:+SKIP [2, 4, 8, 1, 8, 4] )r r )funcZtimesargss&&*rGr3r3 s,, }tVD\** 4, --rIcsJ\V4wr\VR4\W4#)zReturns an iterator of paired items, overlapping, from the original >>> take(4, pairwise(count())) [(0, 1), (1, 2), (2, 3), (3, 4)] On Python 3.10 and above, this is an alias for :func:`itertools.pairwise`. NrrTzip)rNZaZb& rG _pairwiseri;s" x=DADM q9rI)r&cs\V4#rD)itertools_pairwiser]r^rGr&r&Os !(++rIcs6aa]tRtRtoRV3RlltRtVtV;t#)UnequalIterablesErroriUcs`<RpVeVRP!V!, p\SV` V4R#)z Iterables have different lengthsNz/: index 0 has length {}; index {} has length {})ZformatZsuper__init__)ZselfdetailsZmsg __class__s&& rGrlZUnequalIterablesError.__init__Vs80   EMM C rIrD)Z__name__Z __module__Z __qualname__Z__firstlineno__rlZ__static_attributes__Z__classdictcell__Z __classcell__)rnZ __classdict__s@@rGrkrkUsrIrkc#s|"\VR\/F$pVFpV\JgK\4h VxK& R#5i) fillvalueN)r_markerrk) iterablesZcomboZvalrhrG_zip_equal_generatorrs`s:i;7;Cg~+-- >> list(grouper('ABCDEF', 3)) [('A', 'B', 'C'), ('D', 'E', 'F')] The keyword arguments *incomplete* and *fillvalue* control what happens for iterables whose length is not a multiple of *n*. When *incomplete* is `'fill'`, the last group will contain instances of *fillvalue*. >>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x')) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')] When *incomplete* is `'ignore'`, the last group will not be emitted. >>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x')) [('A', 'B', 'C'), ('D', 'E', 'F')] When *incomplete* is `'strict'`, a subclass of `ValueError` will be raised. >>> it = grouper('ABCDEFG', 3, incomplete='strict') >>> list(it) # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... UnequalIterablesError fillrprCZignorez Expected fill, strict, or ignore)rSrrzrg ValueError)rNrMZ incompleterpres&&&& rGrrxs^: N a DVD6I66X4  XDz;<>> list(roundrobin('ABC', 'D', 'EF')) ['A', 'D', 'E', 'B', 'F', 'C'] This function produces the same output as :func:`interleave_longest`, but may perform better for some inputs (in particular when the number of iterables is small). N)rOrSrangerRrr rT)rr iteratorsZ num_actives* rGr4r4sLD)$IC NAr2 &78 tY'''3'sAA A A csVf\p\V^4wr#p\\W44wrV\V\\P V44\W643#)aw Returns a 2-tuple of iterables derived from the input iterable. The first yields the items that have ``pred(item) == False``. The second yields the items that have ``pred(item) == True``. >>> is_odd = lambda x: x % 2 != 0 >>> iterable = range(10) >>> even_items, odd_items = partition(is_odd, iterable) >>> list(even_items), list(odd_items) ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9]) If *pred* is None, :func:`bool` is used. >>> iterable = [0, 1, False, True, '', ' '] >>> false_items, true_items = partition(None, iterable) >>> list(false_items), list(true_items) ([0, False, ''], [1, True, ' ']) )boolrrOrrbZnot_)r\rNt1t2pZp1Zp2s&& rGr'r'sP( |Ha IBA T FB RX]]B/ 0(22B CCrIcsa\V4o\P!V3Rl\\ S4^,444#)aYields all possible subsets of the iterable. >>> list(powerset([1, 2, 3])) [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)] :func:`powerset` will operate on iterables that aren't :class:`set` instances, so repeated elements in the input will produce repeated elements in the output. >>> seq = [1, 1, 0] >>> list(powerset(seq)) [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)] For a variant that efficiently yields actual :class:`set` instances, see :func:`powerset_of_sets`. c3s<<"TFp\SV4xK R#5irD)r).0rs& rG Zpowerset..sM;La|Aq11;Ls)rKrr_r~rR)rNrs&@rGr+r+s2" XA   M5Q!;LM MMrIc#s "\4pVPp.pVPpVRJpVF*pV'd V!V4MTpW9dV!V4VxK*K, R# \dY9dT!T4TxKPKSi;i5i)aJ Yield unique elements, preserving order. >>> list(unique_everseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D'] >>> list(unique_everseen('ABBCcAD', str.lower)) ['A', 'B', 'C', 'D'] Sequences with a mix of hashable and unhashable items can be used. The function will be slower (i.e., `O(n^2)`) for unhashable items. Remember that ``list`` objects are unhashable - you can use the *key* parameter to transform the list to a tuple (which is hashable) to avoid a slowdown. >>> iterable = ([1, 2], [2, 3], [1, 2]) >>> list(unique_everseen(iterable)) # Slow [[1, 2], [2, 3]] >>> list(unique_everseen(iterable, key=tuple)) # Faster [[1, 2], [2, 3]] Similarly, you may want to convert unhashable ``set`` objects with ``key=frozenset``. For ``dict`` objects, ``key=lambda x: frozenset(x.items())`` can be used. N)setZaddappendrw) rNrXZseensetZ seenset_addZseenlistZ seenlist_addZuse_keyelementks && rGr@r@s6eG++KH??LoG#CL A     Q ! s*ABABB:BBBc sVf*\\P!^4\V44#\\\\P!^4\W444#)zYields elements in order, ignoring serial duplicates >>> list(unique_justseen('AAAABBBCCDAABBB')) ['A', 'B', 'C', 'D', 'A', 'B'] >>> list(unique_justseen('ABBCcAD', str.lower)) ['A', 'B', 'C', 'A', 'D'] )rOrbZ itemgetterr rT)rNrXrFrGrArAsJ {8&&q)78+<== tS,,Q/1GH IIrIFcs2\\WVR7VR7#)aYields unique elements in sorted order. >>> list(unique([[1, 2], [3, 4], [1, 2]])) [[1, 2], [3, 4]] *key* and *reverse* are passed to :func:`sorted`. >>> list(unique('ABBcCAD', str.casefold)) ['A', 'B', 'c', 'D'] >>> list(unique('ABBcCAD', str.casefold, reverse=True)) ['D', 'c', 'B', 'A'] The elements in *iterable* need not be hashable, but they must be comparable for sorting to work. )rXreverse)rX)rAsorted)rNrXrrWrGr?r?s 6(WE3 OOrIc#sZ"Ve V!4xV!4xK TdR#i;i5i)aYields results from a function repeatedly until an exception is raised. Converts a call-until-exception interface to an iterator interface. Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel to end the loop. >>> l = [0, 1, 2] >>> list(iter_except(l.pop, IndexError)) [2, 1, 0] Multiple exceptions can be specified as a stopping condition: >>> l = [1, 2, 3, '...', 4, 5, 6] >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) [7, 6, 5] >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) [4, 3, 2] >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError))) [] Nro)rdZ exceptionrYrWrGrr2s2,  'M&L    s+(+(+cs,\\W 4V4#)ad Returns the first true value in the iterable. If no true value is found, returns *default* If *pred* is not None, returns the first item for which ``pred(item) == True`` . >>> first_true(range(10)) 1 >>> first_true(range(10), pred=lambda x: x > 5) 6 >>> first_true(range(10), default='missing', pred=lambda x: x > 9) 'missing' )rTZfilter)rNrVr\rWrGrrQs" t& 00rIr csVUu.uFp\V4NK upV,p\;QJd.RV4FNK 5#!RV44#uupi)aDraw an item at random from each of the input iterables. >>> random_product('abc', range(4), 'XYZ') # doctest:+SKIP ('c', 3, 'Z') If *repeat* is provided as a keyword argument, that many items will be drawn from each iterable. >>> random_product('abcd', range(4), repeat=2) # doctest:+SKIP ('a', 2, 'd', 3) This equivalent to taking a random selection from ``itertools.product(*args, **kwarg)``. c3s8"TFp\V4xK R#5irD)r)rpool& rGrZ!random_product..vs0%$%s)r`)r rerZpoolss$* rGr2r2esH &* *TTU4[T *V 3E 50%05050%0 00 +sAcsb\V4pVf \V4MTp\\W!44#)aFReturn a random *r* length permutation of the elements in *iterable*. If *r* is not specified or is ``None``, then *r* defaults to the length of *iterable*. >>> random_permutation(range(5)) # doctest:+SKIP (3, 4, 0, 1, 2) This equivalent to taking a random selection from ``itertools.permutations(iterable, r)``. )r`rRr)rNrr&& rGr1r1ys+ ?DYD AA  !!rIcsa\V4o\S4p\\\ V4V44p\;QJd.V3RlV4FNK 5#!V3RlV44#)zReturn a random *r* length subsequence of the elements in *iterable*. >>> random_combination(range(5), 3) # doctest:+SKIP (2, 3, 4) This equivalent to taking a random selection from ``itertools.combinations(iterable, r)``. c36<"TFpSV,xK R#5irDrorrxrrrGrZ%random_combination..*'Qa')r`rRrrr~)rNrrMindicesrs&& @rGr0r0sN ?D D AVE!Ha()G 5*'*5*5*'* **rIcsaa\V4o\S4o\V3Rl\V444p\;QJd.V3RlV4FNK 5#!V3RlV44#)a;Return a random *r* length subsequence of elements in *iterable*, allowing individual elements to be repeated. >>> random_combination_with_replacement(range(3), 5) # doctest:+SKIP (0, 0, 1, 2, 2) This equivalent to taking a random selection from ``itertools.combinations_with_replacement(iterable, r)``. c3s:<"TFp\S4xK R#5irD)r)rrxrMrrGr6random_combination_with_replacement..s48aYq\\8sc3rrDrorrrGrrrr)r`rRrr~)rNrrrMrs&& @@rGr/r/sM ?D D A45844G 5*'*5*5*'* **rIcs6\V4p\V4pV^8gW8d\h^p\WV, 4p\ ^V^,4F pWTV, V,,V,pK" V^8d W%, pV^8gW%8d\ h.pV'dpWQ,V,V^, V^, rpW%8d)W%,pWTV, ,V,V^, rEK.VP VRV, ,4Kw\V4#)aEquivalent to ``list(combinations(iterable, r))[index]``. The subsequences of *iterable* that are of length *r* can be ordered lexicographically. :func:`nth_combination` computes the subsequence at sort position *index* directly, without computing the previous subsequences. >>> nth_combination(range(5), 3, 5) (0, 3, 4) ``ValueError`` will be raised If *r* is negative or greater than the length of *iterable*. ``IndexError`` will be raised if the given *index* is invalid. r})r`rRr|Zminr~Z IndexErrorr) rNrindexrrMZcrrxZresults &&& rGr#r#s ?D D A A15 A A1u A 1a!e_ QOq  qy   uz F %1*a!eQUaj JEA;!#QUq d26l# =rIcs\V.V4#)aYield *value*, followed by the elements in *iterator*. >>> value = '0' >>> iterator = ['1', '2', '3'] >>> list(prepend(value, iterator)) ['0', '1', '2', '3'] To prepend multiple values, see :func:`itertools.chain` or :func:`value_chain`. )r)valuerUrFrGr,r,s %( ##rIc#s"\V4RRR1,p\V4p\^.VR7V,p\V\ ^V^, 44F!pVP V4\ W4xK# R#5i)a&Convolve the iterable *signal* with the iterable *kernel*. >>> signal = (1, 2, 3, 4, 5) >>> kernel = [3, 2, 1] >>> list(convolve(signal, kernel)) [3, 8, 14, 20, 26, 14, 5] Note: the input arguments are not interchangeable, as the *kernel* is immediately consumed and stored. NrQr})r`rRrrr r_sumprod)ZsignalZkernelrMwindowrErZrGrrsh6]4R4 F F A A3q !A %F 66!QU+ , av&&-sA:A<cs\aaa\S4o.oVVV3Rlp\SS4pV!4V3#)aA variant of :func:`takewhile` that allows complete access to the remainder of the iterator. >>> it = iter('ABCdEfGhI') >>> all_upper, remainder = before_and_after(str.isupper, it) >>> ''.join(all_upper) 'ABC' >>> ''.join(remainder) # takewhile() would lose the 'd' 'dEfGhI' Note that the first iterator must be fully consumed before the second iterator can generate valid results. c3sn<"SF)pS!V4'dVxKSPV4R# R#5irD)r)Zelemry predicate transitions rG true_iteratorZ'before_and_after..true_iterator s/D !!$' s25)rSr)rryrZremainder_iteratorrsff @rGrrs5 bBJz2. ?. ..rIcs\V^4wrp\VR4\VR4\VR4\WV4#)zReturn overlapping triplets from *iterable*. >>> list(triplewise('ABCDE')) [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')] Nrf)rNrrZt3s& rGr>r>s;Xq!JBBTNTNTN rr?rIcs~\W4p\V4Fwr4\\WCV4R4K \ V!#rD)rrvrTr rg)rNrMrrxrUrZrG_sliding_window_islicer,s8H I +  VH #T*,  ?rIc#s"\V4p\\W!^, 4VR7pVF!pVPV4\ V4xK# R#5i)rurQN)rSrr rr`)rNrMryrrErZrG_sliding_window_dequer4sC hB 6"!e$Q /F  aFmsAAcsV^8d \W4#V^8d \W4#V^8Xd \V4#V^8Xd \V4#\ RV 24h)a=Return a sliding window of width *n* over *iterable*. >>> list(sliding_window(range(6), 4)) [(0, 1, 2, 3), (1, 2, 3, 4), (2, 3, 4, 5)] If *iterable* has fewer than *n* items, then nothing is yielded: >>> list(sliding_window(range(3), 4)) [] For a variant with more features, see :func:`windowed`. zn should be at least one, not )rrr&rgr|rarFrGr6r6=s^ 2v$X11 Q%h22 a!! a8}9!=>>rIc s\V4p\\\\ \ V4^,4^44p\ \P\V4V4#)zReturn all contiguous non-empty subslices of *iterable*. >>> list(subslices('ABC')) [['A'], ['A', 'B'], ['A', 'B', 'C'], ['B'], ['B', 'C'], ['C']] This is similar to :func:`substrings`, but emits items in a different order. ) rKr Zslicerr~rRrOrbZgetitemr )rNZseqZslicesrhrGr7r7VsF x.C ULs3x!|)>> roots = [5, -4, 3] # (x - 5) * (x + 4) * (x - 3) >>> polynomial_from_roots(roots) # x^3 - 4 * x^2 - 17 * x + 60 [1, -4, -17, 60] )rgr rOrbZnegrKrr)ZrootsZfactorsrrGr)r)ds5&)Su56G x1#. //rIc#s"\VRR4pVf4\WV4p\WR4FwrgWqJg Wq8XgKVxK R#Vf \V4MTpV^, pV!W^,V4;pxK \dR#i;i5i)aYield the index of each place in *iterable* that *value* occurs, beginning with index *start* and ending before index *stop*. >>> list(iter_index('AABCADEAF', 'A')) [0, 1, 4, 7] >>> list(iter_index('AABCADEAF', 'A', 1)) # start index is inclusive [1, 4, 7] >>> list(iter_index('AABCADEAF', 'A', 1, 7)) # stop index is not inclusive [1, 4] The behavior for non-scalar *values* matches the built-in Python types. >>> list(iter_index('ABCDABCD', 'AB')) [0, 4] >>> list(iter_index([0, 1, 2, 3, 0, 1, 2, 3], [0, 1])) [] >>> list(iter_index([[0, 1], [2, 3], [0, 1], [2, 3]], [0, 1])) [0, 2] See :func:`locate` for a more general means of finding the indexes associated with particular values. rN)getattrr rvrRr|)rNrrPZstopZ seq_indexryrxrs&&&& rGrros2'40I HT *#B.JA7#3/ !% s8}$ AI %eUD99q:   s(6B $B "A99 BB BB c #s"V^8d^x^p\R4V^,,p\P!V4^,p\V^W4Fdp\V^WV,4RjxL \ \ \ WD,WV,444W$V,WV,1&WD,pKf \V^V4RjxL R#LdL5i)zXYield the primes less than n. >>> list(sieve(30)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] N)rtru)Z bytearraymathisqrtrZbytesrRr~)rMrPZdataZlimitrs& rGr5r5s  1u E V Q 'D JJqMA E a .dAu!e444"'E!%E,B(C"DUQQ /$5))) 5*s%A+C-C.AC C CCrCc#s"V^8d \R4h\V4p\\W144;p'd*V'd\ V4V8wd \R4hVxKER#5i)arBatch data into tuples of length *n*. If the number of items in *iterable* is not divisible by *n*: * The last batch will be shorter if *strict* is ``False``. * :exc:`ValueError` will be raised if *strict* is ``True``. >>> list(batched('ABCDEFG', 3)) [('A', 'B', 'C'), ('D', 'E', 'F'), ('G',)] On Python 3.13 and above, this is an alias for :func:`itertools.batched`. zn must be at least onezbatched(): incomplete batchN)r|rSr`r rR)rNrMrCryZbatchs&&$ rG_batchedrsZ 1u122 hB' '% ' c%jAo:; ;  (s AA'#A'i )rcs\WVR7#)rB)itertools_batched)rNrMrCs&&$rGrrs V<>> list(transpose([(1, 2, 3), (11, 22, 33)])) [(1, 11), (2, 22), (3, 33)] The caller should ensure that the dimensions of the input are compatible. If the input is empty, no output will be produced. ) _zip_strictryr^rGr=r=s  rIcsB\\P!V4V4#)zReshape the 2-D input *matrix* to have a column count given by *cols*. >>> matrix = [(0, 1), (2, 3), (4, 5)] >>> cols = 3 >>> list(reshape(matrix, cols)) [(0, 1, 2), (3, 4, 5)] )rrr_)ZmatrixZcolsrFrGr.r.s 5&&v. 55rIc s\V^,4p\\\\ V\ V444V4#)zMultiply two matrices. >>> list(matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)])) [(49, 80), (41, 60)] The caller should ensure that the dimensions of the input matrices are compatible with each other. )rRrr rr r=)Zm1Zm2rMrrGr r s0 BqE A 78WR2%?@! DDrIc#s"\\P!V4^,4F)pW,'dKVxW,pV^8XgK%R# V^8dVxR#R#5i)zHYield the prime factors of n. >>> list(factor(360)) [2, 2, 2, 3, 3, 5] N)r5rrrMZprimerrGrrsS tzz!}q()))K KAAv *  1u s5A%A%A%c s\V4pV^8Xd V^,#\\\V4\ \ V444p\ W4#)zEvaluate a polynomial at a specific value. Example: evaluating x^3 - 4 * x^2 - 17 * x + 60 at x = 2.5: >>> coefficients = [1, -4, -17, 60] >>> x = 2.5 >>> polynomial_eval(coefficients, x) 8.125 )rRrOZpowr reversedr~r) coefficientsrErMpowerss&& rGr(r(sD LAAv1u fQi%(!3 4F L ))rIcs&\\V4!#)zZReturn the sum of the squares of the input values. >>> sum_of_squares([10, 20, 30]) 1400 )rrrr^rGr8r8s SW rIcs\V4p\\^V44p\\ \ P W44#)aCompute the first derivative of a polynomial. Example: evaluating the derivative of x^3 - 4 * x^2 - 17 * x + 60 >>> coefficients = [1, -4, -17, 60] >>> derivative_coefficients = polynomial_derivative(coefficients) >>> derivative_coefficients [3, -8, -17] )rRrr~rKrOrbrc)rrMrrhrGr*r*s4 LA eAqk "F HLL,7 88rIcsZ\\V44FpWV,,pK V#)zmReturn the count of natural numbers up to *n* that are coprime with *n*. >>> totient(9) 6 >>> totient(12) 4 )rrrrrGr<r<)s&VAY %Z HrI)rtrD)r{N)NF)NN)rtN)_Z__doc__rrbZ collectionsrZcollections.abcrZ functoolsrrZ itertoolsrrrrrr r r r r rrZrandomrrrZsysrZ__all__Zobjectrqrgrrwrrr;r9r:rr"rrr-r%r$r!rrr3rir&rjZ ImportErrorr|rkrsrzrr4r'r+r@rAr?rrr2r1r0r/r#r,rrr>rrr6r7r)rr5rrrr=r.r rr(r8r*r<rorIrGrs !%    -,/ /  / /  /   /   / /  / / / / /  / /  /  !/ "#/ $%/ &'/ ()/ *+/ ,-/ .// 01/ 23/ 45/ 67/ 8*9/ :;/ <=/ >?/ @A/ BC/ D E/ FG/ HI/ JK/ LM/ N O/ P Q/ RS/ TU/ VW/ X Y/ Z[/ \]/ b (,t#d+K 4$A B % '$3$%+P 44!$ ) ;. ,.6  )8 ,!((HJ / %=P($D8N**Z JP& >1(11("$ + +"'T $',/B  ?2 60(V*$E(6=u=G&&GO 6 E  *" 9  aKdHs$1 GG) G&%G&) G54G5