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The full point, full stop (Commonwealth English) or period (North American English) is a punctuation mark. It is used for several purposes, the most frequent of which is to mark the end of a declaratory sentence (as opposed to a question or exclamation); this sentence-terminal use is properly, or the precise meaning of, full stop. The full stop is also often used alone to indicate omitted characters (or in an ellipsis, "..." to indicate omitted words). It may be placed after an initial letter used to stand for a name, or sometimes after each individual letter in an initialism or acronym, for example, "U.S.A."; however, this style is declining, and many initialisms like UK or NATO have individually become accepted norms. A full stop is also frequently used at the end of word abbreviations – in British usage, primarily truncations like Rev., but not after contractions like Revd; however, in American English it is used in both cases. The full point also has multiple contexts in mathematics and computing, where
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Truncated octahedron (Click here for rotating model) Type Archimedean solidUniform polyhedron Elements F = 14, E = 36, V = 24 (χ = 2) Faces by sides 6{4}+8{6} Conway notation tObT Schläfli symbols t{3,4}tr{3,3} or t { 3 3 } {\displaystyle t{\begin{Bmatrix}3\\3\end{Bmatrix}}} t{3,4} or t{3,3} Wythoff symbol 2 4 | 33 3 2 | Coxeter diagram Symmetry group O, B, [4,3], (*432), order 48T, [3,3] and (*332), order 24 Rotation group O, [4,3]+, (432), order 24 Dihedral angle 4-6: arccos(−1/√3) = 125°15′51″6-6: arccos(−1/3) = 109°28′16″ References U, C, W Properties Semiregular convex parallelohedronpermutohedron Colored faces 4.6.6(Vertex figure) Tetrakis hexahedron(dual polyhedron) Net In geometry, the truncated octahedron is an Archimedean solid. It has 14 faces (8 regular hexagonal and 6 square), 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron. It is also the Goldberg polyhed
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Graphs of vertices 24
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Roger von Oech (born February 16, 1948) is an American speaker, conference organizer, author, and toy-maker whose focus has been on the study of creativity.[1][2][3] Professional life In 1975, von Oech earned his Ph.D. from Stanford University in the self-created interdisciplinary program "History of Ideas"[2] Shortly afterwards, he began providing services in creativity consulting, working with companies such as Apple, IBM, Disney, Sony, and Intel. In the 1980s, he created and produced the "Innovation in Industry" conference series in Palo Alto, which included Silicon Valley entrepreneurs such as Steve Jobs, Bill Gates, Bob Metcalfe, Charles Schwab, Alan Kay, and Nolan Bushnell of Atari.[4] Decks Creative Whack Pack In 1989, von Oech created the Creative Whack Pack, a deck of 64 cards with illustrations and strategies for stimulating creativity. It was designed to be a portable version of his creativity workshops, and it has sold over a million copies. Creative Whack Company In 2004, he started the Cr
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In the early afternoon of October 6, 2018, a stretch limousine crashed at the junction of New York state routes 30 and 30A north of Schoharie ( skoh-HAIR-ee), 30 miles (48 km) west of Albany, killing 20—the driver, all 17 passengers, and two pedestrians who were in a nearby parking lot.[1][2] The passengers were mostly from communities around the Capital District, primarily Amsterdam, where they had gathered to begin their trip. They were on their way to celebrate a 30th birthday at Brewery Ommegang near Cooperstown. Among them were four sisters and two recently married couples. It was the deadliest transportation-related disaster in the United States since the 2009 Colgan Air Flight 3407 crash outside Buffalo killed 50;[3] it was also the deadliest road transportation disaster in the U.S. since a 2005 bus fire in Wilmer, Texas, killed 23 nursing home residents evacuating from the path of Hurricane Rita.[4] Investigation of the accident has revealed pre-existing problems with the limousine, the driver and t
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An 8.3 filename[1] (also called a short filename or SFN) is a filename convention used by old versions of DOS and versions of Microsoft Windows prior to Windows 95 and Windows NT 3.5. It is also used in modern Microsoft operating systems as an alternate filename to the long filename for compatibility with legacy programs. The filename convention is limited by the FAT file system. Similar 8.3 file naming schemes have also existed on earlier CP/M, TRS-80, Atari, and some Data General and Digital Equipment Corporation minicomputer operating systems. Overview 8.3 filenames are limited to at most eight characters (after any directory specifier), followed optionally by a filename extension consisting of a period . and at most three further characters. For systems that only support 8.3 filenames, excess characters are ignored and if a file name has no extension, the ., if present, has no significance (that is, myfile and myfile. are equivalent). Furthermore, in these systems file and directory names are uppercase,
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Fractional approximations to π. The name Milü (Chinese: 密率; pinyin: mì lǜ; "close ratio"), also known as Zulü (Zu's ratio), is given to an approximation to π (pi) found by Chinese mathematician and astronomer, Zǔ Chōngzhī (祖沖之). Using Liu Hui's algorithm (which is based on the areas of regular polygons approximating a circle), Zu famously computed π to be between 3.1415926 and 3.1415927 and gave two rational approximations of π, 22/7 and 355/113, naming them respectively Yuelü 约率 (approximate ratio) and Milü. 355/113 is the best rational approximation of π with a denominator of four digits or fewer, being accurate to 6 decimal places. It is within 0.000009% of the value of π, or in terms of common fractions overestimates π by less than 1/3748629. The next rational number (ordered by size of denominator) that is a better rational approximation of π is 52163/16604, still only correct to 6 decimal places and hardly closer to π than 355/113. To be accurate to 7 decimal places, one needs to go as far as 86953/27
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The domain name org is a generic top-level domain (gTLD) of the Domain Name System (DNS) used in the Internet. The name is truncated from organization. It was one of the original domains established in 1985, and has been operated by the Public Interest Registry since 2003. The domain was originally intended for non-profit entities, but this restriction was not enforced and has been removed. The domain is commonly used by schools, open-source projects, and communities, but also by some for-profit entities. The number of registered domains in org has increased from fewer than one million in the 1990s, to ten million as of June 2013. History The domain ".org" was one of the original top-level domains,[1] with com, us, edu, gov, mil and net, established in January 1985. It was originally intended for non-profit organizations or organizations of a non-commercial character that did not meet the requirements for other gTLDs. The MITRE Corporation was the first group to register an org domain with mitre.org in July
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Hoplomorpha caminodes is a moth in the Oecophoridae family. It was described by Turner in 1916.[1] It is found in Australia, where it has been recorded from Queensland.[2] The wingspan is 13–15 mm. The forewings are pale reddish-ochreous, darker towards the costa and with a dark reddish dorsal streak, edged with whitish, from one-fifth to four-fifth, abruptly truncated posteriorly. A fuscous spot, indented posteriorly, is found before the tornus, from this a reddish-ochreous suffusion containing two minute fuscous dots extends more than half across the disc beyond the middle, and is preceded by a whitish dot. There is a short, outwardly oblique, reddish-ochreous streak from three-fourth of the costa and an interrupted, fuscous line from beneath the costa to the termen above the tornus. There is also a fine, fuscous terminal line. The hindwings are dark grey, towards the base ochreous-whitish.[3] References Beccaloni, G.; Scoble, M.; Kitching, I.; Simonsen, T.; Robinson, G.; Pitkin, B.; Hine, A.; Lyal, C
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A typical 7-segment LED display component, with decimal point in a DIP-10 package A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays. Seven-segment displays are widely used in digital clocks, electronic meters, basic calculators, and other electronic devices that display numerical information.[1] History A multiplexed 4-digit, seven-segment display with only 12 pins Seven-segment representation of figures can be found in patents as early as 1903 (in U.S. Patent 1,126,641), when Carl Kinsley invented a method of telegraphically transmitting letters and numbers and having them printed on tape in a segmented format. In 1908, F. W. Wood invented an 8-segment display, which displayed the number 4 using a diagonal bar (U.S. Patent 974,943). In 1910, a seven-segment display illuminated by incandescent bulbs was used on a power-plant boiler room signal panel.[2] They were also used to show the dialed tele
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In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation,[1][2] is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program. Automatic differentiation is neither: Figure 1: How automatic differentiation relates to symbolic differentiation Symbolic differentiation, nor Numerical differentiation (the method of finite differences). Symbolic differentiation can lead to inefficient code and
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Periclimenes soror, also called the starfish shrimp, is a species of shrimp that lives as a symbiont with sea stars. Periclimenes soror is a species of little shrimp with a truncated rostris, and showing a wide variety of coats, but often with a distinctive white stripe or white dots pattern on the back. The rest of the body varies with the host starfish: it is often "a deep purple red" when living on Culcita, Protoreaster or Pentaceraster, but red with a white dorsal stripe when living on Acanthaster, and can also be transparent[1] Adults reach up to 15 millimetres (0.6 in) long.[2] On an Acanthaster planci On a Culcita schmideliana Ecology and behaviour It lives commensally on starfishes, including the "crown-of-thorns" starfish, Acanthaster planci. Distribution This species has a wide distribution across the Indo-Pacific and in the Gulf of Panama.[1] References A. J. Bruce (1982). "The shrimps associated with Indo-West Pacific echinoderms, with the description of a new species in t
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Palaemonoidea
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Hypatima verticosa is a moth in the Gelechiidae family. It was described by Meyrick in 1913.[1] It is found in southern India.[2] The wingspan is about 14 mm. The forewings are ochreous-whitish, irrorated with light brownish and fuscous and with a black white-circled dot near the base above the middle and a blackish white-edged triangular patch occupying more than the median third of the costa, its costal extremities cut off by a line oblique white strigulae, the apex truncate and reaching half across the wing. A black elongate mark rests on the termen beneath the apex. The hindwings are grey, thinly scaled and subhyaline anteriorly, with the veins and termen suffused with dark fuscous.[3] References Beccaloni, G.; Scoble, M.; Kitching, I.; Simonsen, T.; Robinson, G.; Pitkin, B.; Hine, A.; Lyal, C., eds. (2003). "Hypatima verticosa". The Global Lepidoptera Names Index. Natural History Museum. Retrieved May 25, 2018. Hypatima at funet J. Bombay nat. hist. Soc. 22 (1): 166
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Bethlehem Pike is a historic 42.21 mi (67.93 km) long road in the U.S. state of Pennsylvania, connecting Philadelphia and Bethlehem, Pennsylvania. It began as a Native American path called the Minsi Trail which developed into a colonial highway called the King's Road in the 1760s. Most of the route later became part of U.S. Route 309, now Pennsylvania Route 309. History Colonial Age The Bethlehem Pike originated from a Native American pathway known as the Minsi Trail. Named after the Minsi Indians, the trail was routed between the Blue Mountains and the lands to the south.[6] In December 1740, David Nitschmann and his party went to Bethlehem and Nazareth along this trail. A year later, a second party joined the first, traversing the same pathway. Nicolaus Zinzendorf, was included in the second party who visited the pioneers in the cabin along the banks of the Monocacy Creek. On Christmas Eve, Zinzendorf celebrated a famous love-feast service, during which the new settlement was named Bethlehem.[4] After th
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Transportation in Montgomery County, Pennsylvania
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In control theory, the cross Gramian ( W X {\displaystyle W_{X}} , also referred to by W C O {\displaystyle W_{CO}} ) is a Gramian matrix used to determine how controllable and observable a linear system is.[1][2] For the stable time-invariant linear system x ˙ = A x + B u {\displaystyle {\dot {x}}=Ax+Bu\,} y = C x {\displaystyle y=Cx\,} the cross Gramian is defined as: W X := ∫ 0 ∞ e A t B C e A t d t {\displaystyle W_{X}:=\int _{0}^{\infty }e^{At}BCe^{At}dt\,} and thus also given by the solution to the Sylvester equation: A W X + W X A = − B C {\displaystyle AW_{X}+W_{X}A=-BC\,} The triple ( A , B , C ) {\displaystyle (A,B,C)} is controllable and observable if and only if the matrix W X {\displaystyle W_{X}} is nonsingular, (i.e. W X {\displaystyle W_{X}} has full rank, for any t > 0 {\displaystyle t>0} ). If the associated system ( A , B , C ) {\displaystyle (A,B,C)} is furthe
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Diagram of one version of the derivation of the Arabic word muslim in autosegmental phonology, with root consonants associating (shown by dotted grey lines). Nonconcatenative morphology, also called discontinuous morphology and introflection, is a form of word formation in which the root is modified and which does not involve stringing morphemes together sequentially.[1] Types Ablaut In English, for example, while plurals are usually formed by adding the suffix -s, certain words use nonconcatenative processes for their plural forms: foot → feet ; and many irregular verbs form their past tenses, past participles, or both in this manner: freeze → froze , frozen . This specific form of nonconcatenative morphology is known as base modification or ablaut, a form in which part of the root undergoes a phonological change without necessarily adding new phonological material. (In traditional Indo-Europeanist usage, these changes are termed ablaut only when they result from vowel gradations in Proto-Indo-Europea
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Callionima denticulata is a species of moth in the family Sphingidae, which is known from Panama, Mexico, Costa Rica, Nicaragua, Bolivia, Peru and western Venezuela. It was originally described by Schaus as Calliomma denticulata, in 1895.[1] The wingspan is 59–72 mm. Adults are on wing year round in Costa Rica.[2] It is extremely similar to Callionima pan pan, but the forewing apex is strongly truncate, the outer margin strongly excavate below the apex and markedly dentate. The basal half of the forewing underside is distinctly orange, contrasting with the greyish-brown distal part. The hindwing upperside is as in Callionima pan pan, but the black anal spot is at least 1.5 mm wide. The larvae feed on Tabernaemontana alba and probably other Apocynaceae species. They are green with reddish orange spiracles and a longitudinal, dotted black line down the back and an orange, thick anal horn. References "Callionima denticulata (Schaus, 1895) sec CATE Sphingidae, 2009". Cate-sphingidae.org. Archived from the
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A wave packet without dispersion (real or imaginary part) A wave packet with dispersion In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.[1] Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating. Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation
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The gun barrel sequence is the signature device featured in nearly every James Bond film.[1] Shot from the point of view of a presumed assassin, it features James Bond walking, turning, and then shooting directly at camera, causing blood to run down the screen. The visuals are usually accompanied by the "James Bond Theme", written by Monty Norman. Originally designed by Maurice Binder, the sequence has featured in every James Bond film produced by Eon Productions, and while retaining the same basic elements, has evolved noticeably throughout the series.[2] It is one of the most immediately recognisable elements of the franchise and has featured heavily in marketing material for the films and their spin-offs. The British media historian James Chapman suggests that the sequence is a significant part of the James Bond mythos because it "foregrounds the motif of looking, which is central to the spy genre."[3] Description In all but a couple of films, the sequence begins with a white dot blinking across the sc
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Great icosahedron Type Kepler–Poinsot polyhedron Stellation core icosahedron Elements F = 20, E = 30V = 12 (χ = 2) Faces by sides 20{3} Schläfli symbol {3,5/2} Face configuration V(53)/2 Wythoff symbol 5/2 | 2 3 Coxeter diagram Symmetry group I, H, [5,3], (*532) References U, C, W Properties Regular nonconvex deltahedron (35)/2(Vertex figure) Great stellated dodecahedron(dual polyhedron) In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,5/2} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence. The great icosahedron can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of the (n-1)-D simplex faces of the core nD polytope (equilateral triangles for the great icosahedron, and line segments for the pentagram) until the figure regains reg
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Excommatica is a genus of moth in the family Gelechiidae. It contains the species Excommatica compsotoma, which is found in Mozambique and Zimbabwe.[1][2] The wingspan is about 10 mm. The forewings are pale ochreous with an irregular blackish patch extending along the dorsum from near the base to near the tornus, widest before the middle of the wing, where it extends half across, the edge sinuate before and beyond this, narrow towards the posterior extremity, the apex truncate and followed by slight whitish suffusion. There is a broad blackish streak along the costa from before the middle to the apex, pointed anteriorly, cut by an oblique whitish strigula at two-thirds and a less oblique grey-whitish strigula at three-fourths, the lower edge between this and the apex semicircularly excavated. There is also an oval silvery-white spot on the middle of the termen containing an elongate black dot. The hindwings are grey, lighter and bluish-tinged anteriorly.[3] References funet.fi Afro Moths Ann. Tran
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In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles. The equation for an s-particle distribution function (probability density function) in the BBGKY hierarchy includes the (s + 1)-particle distribution function thus forming a coupled chain of equations. This formal theoretic result is named after Bogoliubov, Born, Green, Kirkwood, and Yvon. Formulation The evolution of an N-particle system in absence of quantum fluctuations is given by the Liouville equation for the probability density function f N = f N ( q 1 … q N , p 1 … p N , t ) {\displaystyle f_{N}=f_{N}(\mathbf {q} _{1}\dots \mathbf {q} _{N},\mathbf {p} _{1}\dots \mathbf {p} _{N},t)} in 6N dimensional phase space (3 space and 3 momentum coordinates per particle) ∂ f N ∂ t + ∑ i = 1 N p i m ∂ f N
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Srinivasa Ramanujan FRS ([1] listen ; 22 December 1887 – 26 April 1920)[2] was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered".[3] Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Ramanujan had produced g
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Cantharidus marmoreus is a species of sea snail, a marine gastropod mollusk in the family Trochidae, the top snails.[2][3] Description The height of the shell attains 8 mm, its diameter 5 mm. The rather solid shell has an elongate-conical shape. It is imperforate, but with a groove and pit or even a slight perforation at the place of the umbilicus. It is whitish, longitudinally clouded with brown or pink, often showing white opaque scattered dots. The surface is polished. The sculpture consists of numerous broad flat smooth spirals, separated by impressed lines. There are seven of these flat spiral ribs on the upper surface of the body whorl, the peripheral one larger. The base of the shell has numerous concentric striae, and about 4 spaced, more impressed grooves. The spire is high with its lateral outlines nearly straight . There are about 8 whorls, each one a trifle convex, the last angular at the periphery. The base of the shell is a little convex. The aperture is quadrate. The columella is vertical and
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The vertical bar ( | ) is a computer character and glyph with various uses in mathematics, computing, and typography. It has many names, often related to particular meanings: Sheffer stroke (in logic), verti-bar, vbar, stick, vertical line, vertical slash, bar, pike, or pipe, and several variants on these names. It is occasionally considered an allograph of broken bar (see below). Usage Mathematics The vertical bar is used as a mathematical symbol in numerous ways: absolute value: | x | {\displaystyle |x|} , read "the absolute value of x" cardinality: | S | {\displaystyle |S|} , read "the cardinality of the set S" conditional probability: P ( X | Y ) {\displaystyle P(X|Y)} , reads "the probability of X given Y" determinant: | A | {\displaystyle |A|} , read "the determinant of the matrix A". When the matrix entries are written out, the determinant is denoted by surrounding the matrix entries by vertical bars instead of the usual brackets or parentheses of the ma
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Dendrotriton xolocalcae, commonly known as the Xolocalca bromeliad salamander or Xolocalco bromeliad salamander, is a species of salamander in the family Plethodontidae. It is endemic to Chiapas, Mexico, and only known from its type locality, Cerro Ovando, at an elevation of about 2,000 m (6,600 ft) asl.[1][3] The specific name xolocalcae is derived from the Indian name of Cerro Ovando, Xolocalco.[2] Description The holotype (sex unspecified) measures 37 mm (1.5 in) in snout–vent length and 56 mm (2.2 in) in total length. The body and head are flattened, and the head is much broader than the body. The hands and feet are large. Only the first finger and toe are webbed; the digits are broad and truncate. The tail is slender and attenuated. There are three distinct color patters: most specimens are mottled brownish-lavender above, with a black, triangular head marking. Some specimens have a pair of cream dorsolateral lines that start from the eyelid and continue back. The third variety has pinkish cream back a
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