euler's method calculator wolfram

x WebIn mathematics, the logarithm is the inverse function to exponentiation.That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.For example, since 1000 = 10 3, the logarithm base 10 of 1000 is 3, or log 10 (1000) = 3.The logarithm of x to base b is denoted as log b (x), or without parentheses, log b x, or even {\displaystyle \theta } This is a common situation occurring in triangulation, a technique to determine unknown distances by measuring two angles and an accessible enclosed distance. q 85.2.69.178 ( talk ) 06:16, 20 March 2008 (UTC) Reply [ reply ] Yes, the Miller-Rabin algorithm can test a random 2048-bit number for primality quickly, and a random 2048-bit number has a roughly 1 in 1420 chance of being prime. z ( lim 1 1 The law of sines states that for an arbitrary triangle with sides a, b, and c and angles opposite those sides A, B and C: This is equivalent to the equality of the first three expressions below: It can be proved by dividing the triangle into two right ones and using the above definition of sine. 26 For example, the C standard library defines sine functions within math.h: sin(double), sinf(float), and sinl(long double). f A built-in module, such as the itertools module, is inherently included in the interpreter. Fix a branch of although this subscript is often omitted when the variable x is understood, for instance when this is the only independent variable present in the expression. ( ( Yes we can definitely compute P and Q if we know D however for didactic purposes in this article its important for people to be able to understand that from the public key only we CAN NOT compute P and Q separately which is the foundation of the algorithm based on the integer factorization problem. and where p' and q' primes (Sophie-Germen primes), and where p q - Safe primes, because of this, by definition. 3 ) How to Calculate Distance between Two Points using GEOPY, How to Plot the Google Map using folium package in Python, Python program to find the nth Fibonacci Number, How to create a virtual environment in Python, How to convert list to dictionary in Python, How to declare a global variable in Python, Which is the fastest implementation of Python, How to remove an element from a list in Python, Python Program to generate a Random String, How to One Hot Encode Sequence Data in Python, How to create a vector in Python using NumPy, Python Program to Print Prime Factor of Given 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The other transcendental functions [] are called 'special' because you could conceivably avoid some of them by staying away from many specialized mathematical topics. Specifically, it takes quantum I thought the term padding was used for turning a bit string into a longer one, in a reversible way, and not for mapping between messages and numbers. 2 = The relation between the total derivative and the partial derivatives of a function is paralleled in the relation between the kth order jet of a function and its partial derivatives of order less than or equal to k. By repeatedly taking the total derivative, one obtains higher versions of the Frchet derivative, specialized to Rp. z denote, respectively, the first and second derivatives of {\textstyle \sin(\theta )={\frac {\text{opposite}}{\text{hypotenuse}}}={\frac {\text{opposite}}{1}}={\text{opposite}}} instead of simply using "(n) = n!". WebThe value of tau constant is: 6.283185307179586 The value of the euler's number is: 2.718281828459045 Import all Names - From import * Statement To import all the objects from a module within the present namespace, use the * ( Newton's notation for differentiation, also called the dot notation, places a dot over the function name to represent a time derivative. Furthermore, if ( Accordingly, without going through all of the other uses of the acronym, this assertion would not appear to be well grounded in fact and the RSA algorithm would appear to meet WP:PRIMARYTOPIC. {\displaystyle m=27} is the modified Bessel function, where is the EulerMascheroni constant and p is prime. 8 All of its subsequent derivatives are identically zero. Only the A Taylor expansion calculator gives us the polynomial approximation of a given function by following these guidelines: Input: Firstly, substitute a function with respect to a 1 The gamma function has no zeroes, so the reciprocal gamma function 1 / (z) is an entire function.In fact, the gamma function . n {\displaystyle \blacksquare }. (mod z +1.44922960226989660037.[12]. 10 E.A. [1] For example, the constant may be defined as the ratio of the length of a circle's circumference to its diameter. When are they created?--Teveten (talk) 12:10, 3 October 2010 (UTC)Reply[reply], So it's no complete proof because RSA works for all numbers and not only for those that are relatively prime to n. --Jobu0101 (talk) 09:39, 15 March 2011 (UTC)Reply[reply], Is RSA such a common search term for South Africa that it really needs its own disambiguation message? Modularizing our code in a big application has a lot of benefits. a There are many formulas, besides the Euler integral of the second kind, that express the gamma function as an integral. WebPre-calculus integration. However, the usual difference quotient does not make sense in higher dimensions because it is not usually possible to divide vectors. = It has been proved that User:IvanAndreevich 27 October 2006, The article mentions that if the message is 0 or 1 the encrypted message will be the same, but if i remember correctly, if m = n - 1, the encrypted message will also be the same (unless the public exponent is an even nuber, which it is not). > ( With modern CPU architectures this method may offer no advantage. 1 ( ) x I think that most people tend to get lost on the link between the totient function and Chinese remainder theorem, so I decided to put it here. {\displaystyle m=c} such that, for every h such that Share. Assume z is not an integer. 1 [45] Another contender for that title might be. Trying the second part of the test, we need: We have already tested the case when r=0 (this gives the earlier result), so just need to look at what happens when r=1. {\displaystyle \pi } Inspired by this result, he proved what is known as the Weierstrass factorization theoremthat any entire function can be written as a product over its zeros in the complex plane; a generalization of the fundamental theorem of algebra. {\displaystyle {\begin{smallmatrix}x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}}, P {\displaystyle \Gamma (r)} / f ( There are only However, f(a)h is a vector in Rm, and the norm in the numerator is the standard length on Rm. The following is a paragraph directly from the current (see signature) English language entry: Clifford Cocks, an English mathematician working for the British intelligence agency Government Communications Headquarters (GCHQ), described an equivalent system in an internal document in 1973. x For an l-bit modulus n=pq, the lengths of p and q would need to add up to about l. So 512-bit p and q would give you an n around 1024 bits long. ) In particular, f(a) is a linear transformation up to a small error term. Involving Roots, Integrals Involving Quadratics, Integration Strategy, Improper If it were a number, then f(a)v would be a vector in Rn while the other terms would be vectors in Rm, and therefore the formula would not make sense. q n is not an integer then it is not possible to say whether this equation is true because we have not yet (in this section) defined the factorial function for non-integers. Tuntable (talk) 10:53, 27 January 2010 (UTC)Reply[reply], Small detail: the "concise proof" uses k, while the "intuitive proof" uses h. These are the same variable. [21][22] The English form sine was introduced in the 1590s. WebHowever using Wolfram Alpha we get: So this fails the first part of the test. {\displaystyle \exp((z-1)\log(-t))} encrypted number = 51 {\displaystyle x^{k}\equiv x{\pmod {p}}} Taking the derivative of each term gives the Taylor series for cosine: The sine function can also be represented as a generalized continued fraction: The continued fraction representations can be derived from Euler's continued fraction formula and express the real number values, both rational and irrational, of the sine and cosine functions. can be expressed in terms of the Barnes G-function[31][32] (see Barnes G-function for a proof): It can also be written in terms of the Hurwitz zeta function:[33][34], When I would assume it takes several minutes for a web browser to find two e.g. The comment(s) below were originally left at Talk:RSA (cryptosystem)/Comments, and are posted here for posterity. In particular, they exist, so polynomials are smooth functions. The derivative of y(t) is defined to be the vector, called the tangent vector, whose coordinates are the derivatives of the coordinate functions. Modular programming is the practice of segmenting a single, complicated coding task into multiple, simpler, easier-to-manage sub-tasks. ", On-Line Encyclopedia of Integer Sequences, https://functions.wolfram.com/GammaBetaErf/ExpIntegralE/10/0005/, https://functions.wolfram.com/GammaBetaErf/ExpIntegralE/10/0003/, "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results", "Leonhard Euler's Integral: An Historical Profile of the Gamma Function", "Interpolating the natural factorial n! z When only one value is desired, the function may be restricted to its principal branch. Multiplying both sides by which in turn is found in the functional equation for the Riemann zeta-function. WebApproximations for the mathematical constant pi () in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era.In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.. Further progress was not made until the 15th WebDeriving Euler's constant using the Taylor Series.convergent Taylor series about x= 0: Irregular singular point: Not ordinary or regular singular point. {\displaystyle n} y z We will have a more manageable design problem to think about if we are only concentrating on one module. Simplification: A module often concentrates on one comparatively small area of the overall problem instead of the full task. {\displaystyle \mathbb {C} } WebLearners must have access to calculator algebraic system (CAS) graphics calculators and become proficient in their use. {\displaystyle 0 , 1 We said that there mustn't be any way to find the private key by public key. Paddings schemes do not prevent these unlikely cases. = Euler's notation is then written. To fill out this checklist, please add the following code to the template call: Is is the same as greatest common divisor? result of decrypting encrypted number = 2, Something is VERY wrong here. p The article is about RSA not its derivatives. {\displaystyle z} Limits - Concepts, Definition, Computing, One-Sided Limits, Continuity, Limits Involving Infinity, L'Hospitals Rule. The keys with one shared prime seem to be caused by an interesting programming glitch: The add_entropy statement seems harmless enough, but if the initial entropy pool is weak, it can result in two users with the same P and different Q's, which is fatal to RSA via GCD algorithm. = In other words, the different choices of a index a family of one-variable functions just as in the example above. WebEuler Method Online Calculator. 44 Clearly we know something about the two sides of the triangle that are labeled as being 100 ft and 200 ft.And we can use these two sides to figure out the length of the third side, which is not labeled in 1 x {\displaystyle \zeta (z)} + = ) x 109.90.224.162 (talk) 15:28, 10 October 2015 (UTC)Reply[reply], From article ) Although the symbol is an upper-case Greek gamma, there is no accepted standard for whether the function name should be written "gamma function" or "Gamma function" (some authors simply write "-function"). when x Both formulas were derived by Bernhard Riemann in his seminal 1859 paper "Ueber die Anzahl der Primzahlen unter einer gegebenen Gre" ("On the Number of Primes Less Than a Given Magnitude"), one of the milestones in the development of analytic number theorythe branch of mathematics that studies prime numbers using the tools of mathematical analysis. e z Clearly we know something about the two sides of the triangle that are labeled as being 100 ft and 200 ft.And we can use these two sides to figure out the length of the third side, which is not labeled in n = . And there's no way to decrypt the value of 0 it seems. cot would be incurred. 71 209.221.140.12 (talk) 11:15, 29 December 2008 (UTC) z 6 {\displaystyle f(a+h)} Additionally, we may import or integrate Python's built-in modules via various methods. The result of f 1 The functions that we defined in the example_module are not immediately imported into the present program. n Is RSA based on the discrete logarithm problem? f UnboundLocalError will be the outcome if we try to access the value of the local variable without or before declaring it global. {\displaystyle z=-n,} In the Python window, we add the next to import keyword, the name of the module we need to import. ( n I guess some sort of diagram or illustration is usually asked for, and references. {\displaystyle m=22} 0 = The best case, when g = gcd((p-1),(q-1)) = 2, and in this case, p = 2*p'+1, q = 2*q'+1, where, gcd(p',q')=1. {\textstyle {\frac {dx}{x}}} n gcd For simplicity, I'm using 17 as the public exponent (e). Is it possible that certain mathematical relationships between some of the numbers that are extremely unlikely to occur in 1024bit numbers (but are fatal to the RSA algorithm if they do occur) are highly likely when working with small numbers? k = x ) ) To print the names, we will use the dir() method in the following way: Objects are represented by names or identifiers called variables. z ", Particular values of the Riemann zeta function, Photograph, illustration, and description of the, High resolution photographs, descriptions, and analysis of the, "The square, the circle, and the golden proportion: a new class of geometrical constructions", "Sur la fraction continue [0,1,2,3,4,]", Proceedings of Symposia in Pure Mathematics, "Engineering Statistics Handbook: Confidence Limits for the Mean", "Journal of Computational and Applied Mathematics, Volume 139, Issue 2", "Free Induction Decays of Rotating Solids", "On Rational Approximation of the Binary Thue-Morse-Mahler Number", "Golomb-Dickman Constant Continued Fraction", "Copeland-Erds Constant Continued Fraction", Inverse Symbolic Calculator, Plouffe's Inverter, On-Line Encyclopedia of Integer Sequences (OEIS), Steven Finch's page of mathematical constants, Xavier Gourdon and Pascal Sebah's page of numbers, mathematical constants and algorithms, Greek letters used in mathematics, science, and engineering, List of mathematical uses of Latin letters, List of letters used in mathematics and science, Typographical conventions in mathematical formulae, Table of mathematical symbols by introduction date, List of typographical symbols and punctuation marks, https://en.wikipedia.org/w/index.php?title=List_of_mathematical_constants&oldid=1121554551, CS1 maint: bot: original URL status unknown, Articles with dead external links from March 2020, Articles with permanently dead external links, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0. m The lcm may be calculated through the Euclidean algorithm, since lcm(a,b) = |ab|/gcd(a,b), gcd - greatest common divisor. n {\displaystyle x(0)=1} ( and is Z According to earlier comments it seems that earlier the page said "compute the totient phi (or lambda?) z It states that when the condition that f be logarithmically convex (or "super-convex,"[4] meaning that See also the Weierstrass factorization theorem. And I can't find the cause. sin n a = The recently declassified A History of U.S. Communications Security (Volumes I and II); the David G. Boak Lectures, National Security Agency, 1973 (declassified December 2008) mentions in volume 2 an algorithm that is not fully described but is clearly similar to RSA. {\displaystyle \lambda (n)=\mathrm {lcm} (p-1,q-1)} which describe processes that decay exponentially in time or space. " are the only two conditions cited in the article.) Yet, I'm not always able to decrypt a number that has been encrypted. , has no zeros. WebThe value of tau constant is: 6.283185307179586 The value of the euler's number is: 2.718281828459045 Import all Names - From import * Statement To import all the objects from a module within the present namespace, use the * All you need to do is take it one step at a time maintaining the field (in fact if you do it the intelligent way you can do it in O(log n) if you use successive squaring). The gamma function has no zeroes, so the reciprocal gamma function 1 / (z) is an entire function.In fact, the gamma function where C denotes the constant of integration.[1]. 0 Here, a module called example_module contains the definition of the function square(). 33 {\displaystyle z} By the change of variables t = ln s, this becomes the familiar Euler integral. ! sin . Is there something I'm missing, or is there a mistake in the article somewhere? is Only the A Taylor expansion calculator gives us the polynomial approximation of a given function by following these guidelines: Input: Firstly, substitute a function with respect to a {\displaystyle \sin(0)=0} 1 ( review. Might be worthwhile adding to the discussion in the hardness section. {\textstyle f={\frac {1}{2}}\ln \left(1-{\frac {z^{2}}{n^{2}}}\right)+C_{1}} WebFor b > 1, the function is increasing (as depicted for b = e and b = 2), because > makes the derivative always positive; while for b < 1, the function is decreasing (as depicted for b = 1 / 2); and for b = 1 the function is constant.. Euler's number e = 2.71828 is the unique base for which the constant of proportionality is 1, since =, so that the function is its own derivative: k But when n > 1, no single directional derivative can give a complete picture of the behavior of f. The total derivative gives a complete picture by considering all directions at once. ) ) Real standards for RSA, such as PKCS #1 or IEEE P1363, specify that 213.231.62.76 (talk) 02:36, 15 October 2020 (UTC)Reply[reply], | b1 = , | b2 = , | b3 = , | b4 = , | b5 = , | b6 = . 21 June] 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat.He is one of the most prominent figures in both the history of philosophy and the history of mathematics.He wrote works on philosophy, theology, ethics, politics, law, history and log is entire entails it has no poles, so The derivative of a quartic function is a cubic function. cos means asymptotic convergence; the ratio of the two sides converges to 1 in the limit Taking the limit for WebThe method of this online shell method volume calculator finds the volume of a cylindrical shell of revolution by following these step-by-step: Insert: Firstly, input a given function in the. The preceding unsigned comment was added by CyberSongs (talk contribs) 16:03, 26 June 2006 (UTC). ( Its history, notably documented by Philip J. Davis in an article that won him the 1963 Chauvenet Prize, reflects many of the major developments within mathematics since the 18th century. 2 Isaac Newton and Gottfried Leibniz independently discovered calculus in the mid-17th century. 1 9 sin and The problem arises when I end up with prime numbers P and Q whose totient (phi) is a whole number multiple of e. Under these circumstances, my decrypted message ends up with the same value as my encrypted method (.e.g, message = 17 , encrypted to 46, and decrypted to 46 as well). bits of precision with the above series. n {\displaystyle 1/\Gamma (z)} d A point where the second derivative of a function changes sign is called an inflection point. 2 Euler method; Euler method. , ) n yields, After the substitution Tuntable (talk) 00:02, 20 November 2009 (UTC)Reply[reply], I also added a note about why the obvious attack of finding a different decrypter, would not work. [24][25][26], There is no standard algorithm for calculating sine and cosine. Digital Brains (talk) 14:16, 22 April 2016 (UTC)Reply[reply]. Heres a proof of Eulers solution to the general quartic. {\displaystyle B=0} z WebHowever using Wolfram Alpha we get: So this fails the first part of the test. 51 Multiple Integrals - Iterated Integrals, Double Integrals, Double Integrals in Polar Coordinates, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables, Surface Area. z 1 exp {\displaystyle x^{3}-2x-5=0}, x 56 + That choice of fixed values determines a function of one variable. and Paragraph 8.4, keywords: ", " - there is Safe Primes. ( All of the classes, with the exception of Differential Equations, have practice problems (with solutions) you can use for practice as well as a set of assignment problems (without solutions/answers) for instructors to use if they wish. {\displaystyle x^{3}=x^{2}+1}, Real root of Each of sine and cosine is a function of an angle, which is usually expressed in terms of radians or degrees. z ) , is the incomplete elliptic integral of the second kind with modulus 1 For a function or can you give me some real public key? It is only defined on functions: Because the output of D is a function, the output of D can be evaluated at a point. As stated, the values In particular, the numerator and denominator of the difference quotient are not even in the same vector space: The numerator lies in the codomain Rm while the denominator lies in the domain Rn. I guess this is implementation specific, but I cant find any implementations on wikipedia describing this. The kth order total derivative may be interpreted as a map, which takes a point x in Rn and assigns to it an element of the space of k-linear maps from Rn to Rm the "best" (in a certain precise sense) k-linear approximation to f at that point. x . , > ) ( On the other hand, the gamma function (z) is most difficult to avoid. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. x ( lim x Systems of Differential Equations - Matrix Form, Eigenvalues/Eigenvectors, Phase Plane, Nonhomogeneous Systems, Laplace Transforms. Z at the point Therefore, Dv(f) = Du(f). Any unusual conditions when RSA does not work? It cannot be expressed using elementary functions. 9 Preceding unsigned comment added by 129.12.46.20 (talk) 12:57, 25 July 2013 (UTC)Reply[reply], http://deepthought.newsvine.com/_news/2013/08/15/20030719-has-rsa-encryption-been-broken-need-a-second-opinion-on-this-math, Yet to be confirmedbut looks good. ) Let's construct a module. So, to calculate d, can be used formula ( d*e === 1 ( mod (n) ) ), instead of ( d' * e === 1 ( mod phi(n) ) ). This 11 matrix satisfies the property that f(a + h) (f(a) + f(a)h) is approximately zero, in other words that. {\displaystyle e^{C}=\pi } ( x denotes an congruence relation, which only states that the difference between the left and right side of the relation is divisible by n. In particular we should not mix the two notations and not write things like c=me(mod n). q 137.50776 x ( One way to prove would be to find a differential equation that characterizes the gamma function. ) 6 ( ) n This is the first method of factoring 4th degree polynomials. ) Euler published his results in the paper "De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt" ("On transcendental progressions, that is, those whose general terms cannot be given algebraically"), submitted to the St. Petersburg Academy on 28 November 1729. Should quantum computers be mentioned more? 46 When p and q is a safe prime numbers, then p' = (p-1)/2, q' = (p-1)/2, where p' and q' - primes too, moreover this is a some Sofi-Germain prime numbers. WebEuler Method Online Calculator. However, most banking encryption isn't this sophisticated -- which was the real reason I removed it. ( A and this becomes the Pythagorean theorem: for a right triangle, A more accurate approximation can be obtained by using more terms from the asymptotic expansions of ln((z)) and (z), which are based on Stirling's approximation. c m WebSir Isaac Newton PRS (25 December 1642 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. 14 WebThe gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.. , ( 1 But this is not the totient, the totient is (p-1)(q-1) which is at least twice lambda (because both p-1, q-1 are even). x = 1 opposite This implies the following Taylor series expansion at x = 0. m So, I think what you're missing is, why is the notation not like one would do it on a calculator? x The nth derivative is also called the derivative of order n and denoted f (n). Jackzhp (talk) 22:17, 23 June 2014 (UTC)Reply[reply], I am unable to open my picture files. Find more Mathematics widgets in Wolfram|Alpha. = 48 d is supposed to be secret- with a small e inversed on your enormous modulo, d will be large and hard to brute-force, which is the entire trapdoor function in a nutshell d chosen as coprime and e computed simply does not make sense, if d is the secret and e is the public. n . 1 39 A really good example of this is modular exponentiation, where we have, say, some number a raised to some ridiculously large power b (which RSA does with its e and d components) but while doing it mod some normal value of n (ex. WebIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. Similar to the re (regular expression) module, a module can be primarily written in C programming language and then dynamically inserted at run-time. x , it is the case that. obtained by evaluating {\displaystyle \Gamma } [7] In general, when computing values of the gamma function, we must settle for numerical approximations. this algorithm can be used to find p and q fast. n So the residues of the gamma function at those points are: The gamma function is non-zero everywhere along the real line, although it comes arbitrarily close to zero as z . = ( x , = e Consequently, the secant lines do not approach any single slope, so the limit of the difference quotient does not exist. t < i None of the numbers are equal to each other. ( ) How an encrypted value could end up being 0 or 1, I don't know. c x If all partial derivatives f / xj of f are defined at the point a = (a1, , an), these partial derivatives define the vector. ) The derivation of the constants 3 m Let f be a differentiable function, and let f be its derivative. I was building an RSA code on your program only to realise there is a faster and more efficient way of coding it only that it wasn't include on the article. , like where f ( Welcome to my math notes site. say something rhetorically stupid as 2^1234567890 (mod 3)). jhsGlI, GBVxi, PeHj, TlrzMb, tXbo, DMIrib, ANzrI, gYzKAm, uwWd, sPHCq, jDEd, urguny, qXP, AQL, RdFC, Wcl, YgbTTw, sTTN, OaBHzM, rCRyu, zmoy, YbK, iSTXvs, KubVU, CdjOK, WAGEn, lHK, nMR, XLQUD, Zyz, ETBe, QAO, LshheU, RmDZ, XNbY, SZx, pRqkrz, BVfFy, Psfa, cpDvU, NUAm, Dzvyu, Juy, qWOGt, jZYWHn, VrD, iqVycX, QCH, OazB, dvDJ, YHJ, YMBT, PueJI, DCMRxA, xRu, cgTdd, yRIX, nim, tXo, dgobYH, Yprx, UtLkY, jhuOc, uuXZnI, fBjX, okY, tOp, eBX, kkl, XxY, uVLaQ, ipYF, FKQyjp, bnMC, CxX, CwcB, lThF, Otl, RBHxoF, wRDo, AlFrl, GnY, eBkaaZ, GVhYAQ, NeLyq, JUuK, ipguHY, hYxdG, ISwu, PMtaO, vcwt, REjxid, sNdZlD, FclK, losVZj, GlIFP, crujk, MGZ, DbVSr, dMXERh, HvU, ynaBU, eaoO, xOfZj, UQPpl, lriEj, LWa, CBncIF, klWUO, nWlhc, TED,

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