In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).
--------
Question: Context: Latin (Latin: ) is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets., In mathematics, a rational number is any number that can be expressed as the quotient or fraction "p"/"q" of two integers, a numerator "p" and a non-zero denominator "q". Since "q" may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", is usually denoted by a boldface Q (or blackboard bold formula_1, Unicode ); it was thus denoted in 1895 by Giuseppe Peano after "quoziente", Italian for "quotient"., In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization., A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests "prove" that a number is prime, while others like MillerRabin prove that a number is composite. Therefore, the latter might be called "compositeness tests" instead of primality tests., Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers)., A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3., Paul Leyland is a British number theorist who has studied integer factorization and primality testing., Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts. This was a recognizable category of mathematical activity from the 19th century onwards, at variance with the trend towards meeting the needs of navigation, astronomy, physics, economics, engineering, and so on., In number theory , a Leyland number is a number of the form x ^ y + y ^ x where x and y are integers greater than 1 . They are named after the mathematician Paul Leyland . The first few Leyland numbers are 8 , 17 , 32 , 54 , 57 , 100 , 145 , 177 , 320 , 368 , 512 , 593 , 945 , 1124 ( sequence A076980 in OEIS ) . The requirement that x and y both be greater than 1 is important , since without it every positive integer would be a Leyland number of the form x1 + 1x . Also , because of the commutative property of addition , the condition x  y is usually added to avoid double - covering the set of Leyland numbers ( so we have 1 < y  x ) . The first prime Leyland numbers are 17 , 593 , 32993 , 2097593 , 8589935681 , 59604644783353249 , 523347633027360537213687137 , 43143988327398957279342419750374600193 ( A094133 ) corresponding to 32 +23 , 92 +29 , 152 +215 , 212 +221 , 332 +233 , 245 +524 , 563 +356 , 3215 +1532 . One can also fix the value of y and consider the sequence of x values that gives Leyland primes , for example x2 + 2x is prime for x = 3 , 9 , 15 , 21 , 33 , 2007 , 2127 , 3759 , ... ( A064539 ) . By November 2012 , the largest Leyland number that had been proven to be prime was 51226753 + 67535122 with 25050 digits . From January 2011 to April 2011 , it was the largest prime whose primality was proved by elliptic curve primality proving . In December 2012 , this was improved by proving the primality of the two numbers 311063 + 633110 ( 5596 digits ) and 86562929 + 29298656 ( 30008 digits ) , the latter of which surpassed the previous record . There are many larger known probable primes such as 3147389 + 9314738 , but it is hard to prove primality of large Leyland numbers . Paul Leyland writes on his website : `` More recently still , it was realized that numbers of this form are ideal test cases for general purpose primality proving programs . They have a simple algebraic description but no obvious cyclotomic properties which special purpose algorithms can exploit . '' There is a project called XYYXF to factor composite Leyland numbers ., An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and 2048 are integers, while 9.75, , and  are not., In Algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in formula_1 (the set of integers). The set of all algebraic integers, , is closed under addition and multiplication and therefore is a commutative subring of the complex numbers. The ring is the integral closure of regular integers formula_1 in complex numbers., Subject: leyland number, Relation: subclass_of, Options: (A) algorithm (B) blackboard (C) branch (D) category (E) complex number (F) decomposition (G) economics (H) engineering (I) integer (J) language (K) latin (L) mathematics (M) meeting (N) natural (O) natural number (P) number (Q) out (R) polynomial (S) problem (T) process (U) rational number (V) ring (W) set (X) test (Y) theorem (Z) theory ([) thought (\) time

Answer: natural number


Question: Context: Bezirk Mürzzuschlag is a former district of the state of Styria in Austria. Mürzzuschlag merged with the district of Bruck an der Mur to form the new district Bruck-Mürzzuschlag on January 1, 2013., In rail transport, track gauge is the spacing of the rails on a railway track and is measured between the inner faces of the load-bearing rails., The standard gauge (also Stephenson gauge after George Stephenson, International gauge, or normal gauge) is a widely used railway track gauge. Approximately 55% of the lines in the world are this gauge. All high-speed rail lines (except those in Russia, Uzbekistan, and Finland) are standard gauge. The distance between the inside edges of the rails is defined to be (except in the United States, where it is still defined in Imperial and US customary units as ). It is also called the UIC gauge or UIC track gauge, the European gauge in the EU and Russia, or uniform gauge in Queensland, Australia., The Semmering railway ( German : Semmeringbahn ) in Austria , which starts at Gloggnitz and leads over the Semmering to Mürzzuschlag was the first mountain railway in Europe built with a standard gauge track . It is commonly referred to as the world 's first true mountain railway , given the very difficult terrain and the considerable altitude difference that was mastered during its construction . It is still fully functional as a part of the Southern Railway which is operated by the Austrian Federal Railways ., Gloggnitz is a mountain town in the Neunkirchen district of Lower Austria, Austria., The Austrian Federal Railways (German: Österreichische Bundesbahnen or ÖBB, formerly the Bundesbahn Österreich or BBÖ) is the national railway system of Austria, and the administrator of Liechtenstein's railways. The ÖBB group is owned entirely by the Republic of Austria and is divided into several separate businesses that manage the infrastructure and operate passenger and freight services., A ski resort is a resort developed for skiing, snowboarding, and other winter sports. In Europe, most ski resorts are towns or villages in or adjacent to a ski area  a mountainous area with pistes, ski trails and a ski lift system. In North America, it is more common for ski areas to exist well away from towns, so ski resorts usually are destination resorts, often purpose-built and self-contained, where skiing is the main activity., Mürzzuschlag is a town in northeastern Styria, Austria, the capital of the former Mürzzuschlag District. It is located on the Mürz river near the Semmering Pass, the border with the state of Lower Austria, about southwest of Vienna. The population is. Originally an industrial area, the nearby mountains are today a popular ski resort., George Stephenson (9 June 1781  12 August 1848) was an English civil engineer and mechanical engineer who built the first public inter-city railway line in the world to use steam locomotives, the Liverpool and Manchester Railway which opened in 1830. Renowned as the "Father of Railways", the Victorians considered him a great example of diligent application and thirst for improvement, with self-help advocate Samuel Smiles particularly praising his achievements. His rail gauge of , sometimes called "Stephenson gauge", is the standard gauge by name and by convention for most of the world's railways., The Mürz is a river in Austria. It begins north of the Schneealpe in Lower Austria, flows into Styria, and meets the Mur River after 98 km in Bruck an der Mur. Its headwaters end at Mürzzuschlag. Along its course are the tracks of the Southern Railway as well as the Semmering Highway., Lower Austria (; ) is the northeasternmost state of the nine states in Austria. The capital of Lower Austria since 1986 is Sankt Pölten, the most recently designated capital town in Austria. The capital of Lower Austria had formerly been Vienna, even though Vienna has not officially been part of Lower Austria since 1921. With a land area of and a population of 1.612 million people, it is the largest state in Austria, and in terms of population second only to the federal state of Vienna., Styria (, Slovene/) is a state or "Bundesland", located in the southeast of Austria. In area it is the second largest of the nine Austrian federated states, covering . It borders Slovenia and the Austrian states of Upper Austria, Lower Austria, Salzburg, Burgenland, and Carinthia. The population (as of ) was . The capital city is Graz which had 276,526 inhabitants at the beginning of 2015., Liechtenstein , officially the Principality of Liechtenstein, is a doubly landlocked German-speaking microstate in Central Europe. It is a constitutional monarchy with the rank of principality, headed by the Prince of Liechtenstein., Ö, or ö, is a character that represents either a letter from several extended Latin alphabets, or the letter O modified with an umlaut mark or diaeresis. In many languages, the letter ö, or the O modified with what is known as an "umlaut mark", is used to denote the non-close front rounded vowels or . In languages without such vowels, the character is known as an "O with diaeresis" and denotes a syllable break, wherein its pronunciation remains an unmodified ., High-speed rail is a type of rail transport that operates significantly faster than traditional rail traffic, using an integrated system of specialized rolling stock and dedicated tracks. While there is no single standard that applies worldwide, new lines in excess of and existing lines in excess of are widely considered to be high-speed, with some extending the definition to include lower speeds in areas for which these speeds still represent significant improvements. The first such system began operations in Japan in 1964 and was widely known as the bullet train. High-speed trains normally operate on standard gauge tracks of continuously welded rail on grade-separated right-of-way that incorporates a large turning radius in its design., "For the town of the same name, see Semmering, Austria.", Vienna is the capital and largest city of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.8 million (2.6 million within the metropolitan area, nearly one third of Austria's population), and its cultural, economic, and political centre. It is the 7th-largest city by population within city limits in the European Union. Until the beginning of the 20th century, it was the largest German-speaking city in the world, and before the splitting of the Austro-Hungarian Empire in World War I, the city had 2 million inhabitants. Today, it has the second largest number of German speakers after Berlin. Vienna is host to many major international organizations, including the United Nations and OPEC. The city is located in the eastern part of Austria and is close to the borders of the Czech Republic, Slovakia, and Hungary. These regions work together in a European Centrope border region. Along with nearby Bratislava, Vienna forms a metropolitan region with 3 million inhabitants. In 2001, the city centre was designated a UNESCO World Heritage Site., Subject: semmering railway, Relation: instance_of, Options: (A) 12 (B) administrator (C) application (D) area (E) august (F) bearing (G) berlin (H) bezirk (I) border (J) capital (K) character (L) city (M) city centre (N) constitutional monarchy (O) course (P) definition (Q) distance (R) district (S) grade (T) hungary (U) infrastructure (V) june (W) letter (X) line (Y) mountain (Z) name ([) nine (\) number (]) people (^) population (_) principality (`) railway line (a) railway system (b) rank (c) river (d) rolling stock (e) ski resort (f) skiing (g) standard (h) state (i) syllable (j) system (k) town (l) track (m) transport (n) work (o) world heritage site (p) world war

Answer: railway line


Question: Context: Moscow (or ) is the capital and most populous city of Russia, with 12.2 million residents within the city limits and 16.8 million within the urban area. Moscow has the status of a Russian federal city., The Venera series space probes were developed by the Soviet Union between 1961 and 1984 to gather data from Venus, Venera being the Russian name for Venus. As with some of the Soviet Union's other planetary probes, the later versions were launched in pairs with a second vehicle being launched soon after the first of the pair., Earth, otherwise known as the world, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets., A space probe is a robotic spacecraft that leaves Earth orbit and explores space. It may approach the Moon; enter interplanetary space; flyby, orbit, or land on other planetary bodies; or approach interstellar space., The Moon is an astronomical body that orbits planet Earth, being Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, and the largest among planetary satellites relative to the size of the planet that it orbits (its primary). Following Jupiter's satellite Io, the Moon is second-densest satellite among those whose densities are known. , Eurasia is the combined continental landmass of Europe and Asia. The term is a portmanteau of its constituent continents. Located primarily in the Northern and Eastern Hemispheres, it is bordered by the Atlantic Ocean to the west, the Pacific Ocean to the east, the Arctic Ocean to the north, and by Africa, the Mediterranean Sea, and the Indian Ocean to the south. The division between Europe and Asia as two different continents is a historical and cultural construct, with no clear physical separation between them; thus, in some parts of the world, Eurasia is recognized as the largest of five or six continents. In geology, Eurasia is often considered as a single rigid megablock. However, the rigidity of Eurasia is debated based on the paleomagnet data., Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. It has the longest rotation period (243 days) of any planet in the Solar System and rotates in the opposite direction to most other planets. It has no natural satellite. It is named after the Roman goddess of love and beauty. It is the second-brightest natural object in the night sky after the Moon, reaching an apparent magnitude of 4.6, bright enough to cast shadows. Because Venus orbits within Earth's orbit it is an inferior planet and never appears to venture far from the Sun; its maximum angular distance from the Sun (elongation) is 47.8°., A natural satellite or moon is, in the most common usage, an astronomical body that orbits a planet or minor planet (or sometimes another Small Solar System Body)., The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process.<ref name="doi10.1146/annurev-astro-081913-040012"></ref> It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99.86% of the total mass of the Solar System.
About three quarters of the Sun's mass consists of hydrogen (~73%); the rest is mostly helium (~25%), with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron., The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value (i.e. inverse relation). The Sun, at apparent magnitude of 27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere. Furthermore, the magnitude scale is logarithmic; a difference of one in magnitude corresponds to a change in brightness by a factor of , or about 2.512., The Soviet Union, officially the Union of Soviet Socialist Republics (USSR " ) was a socialist state in Eurasia that existed from 1922 to 1991. A union of multiple subnational republics, its government and economy were highly centralized. The Soviet Union was a one-party federation, governed by the Communist Party with Moscow as its capital., A planet is an astronomical body orbiting a star or stellar remnant that
The term "planet" is ancient, with ties to history, astrology, science, mythology, and religion. Several planets in the Solar System can be seen with the naked eye. These were regarded by many early cultures as divine, or as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, incorporating a number of disparate objects. In 2006, the International Astronomical Union (IAU) officially adopted a resolution defining planets within the Solar System. This definition is controversial because it excludes many objects of planetary mass based on where or what they orbit. Although eight of the planetary bodies discovered before 1950 remain "planets" under the modern definition, some celestial bodies, such as Ceres, Pallas, Juno and Vesta (each an object in the solar asteroid belt), and Pluto (the first trans-Neptunian object discovered), that were once considered planets by the scientific community, are no longer viewed as such., Venera 1 ( Russian :  - 1 meaning Venus 1 ) , also known as Venera - 1VA No.2 and occasionally in the West as Sputnik 8 was the first spacecraft to fly past Venus , as part of the Soviet Union 's Venera programme . Launched in February 1961 , it flew past Venus on 19 May of the same year ; however , radio contact with the probe was lost before the flyby , resulting in it returning no data ., The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those objects that orbit the Sun directly, the largest eight are the planets, with the remainder being significantly smaller objects, such as dwarf planets and small Solar System bodies. Of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury., In astronomy, the rotation period of a celestial object is the time that it takes to complete one revolution around its axis of rotation relative to the background stars. It differs from the planet's solar day, which includes an extra fractional rotation needed to accommodate the portion of the planet's orbital period during one day., Subject: venera 1, Relation: instance_of, Options: (A) belt (B) capital (C) city (D) direction (E) distance (F) division (G) eight (H) federal city (I) federation (J) five (K) geology (L) government (M) harbor (N) hydrogen (O) landmass (P) magnitude (Q) mass (R) may (S) mediterranean sea (T) minor planet (U) motion (V) mythology (W) natural satellite (X) object (Y) ocean (Z) orbit ([) perception (\) period (]) planet (^) relation (_) robotic spacecraft (`) scale (a) science (b) sea (c) series (d) single (e) six (f) size (g) soviet (h) space (i) space probe (j) spacecraft (k) sphere (l) star (m) state (n) system (o) term (p) the city (q) three (r) two (s) urban area (t) value

Answer:
space probe