instruction:
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).
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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


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Context: Telotroch is the free-swimming stage of members of the order Sessilida. Sessilida are ciliates of the subclass Peritrichia., The ciliates are a group of protozoans characterized by the presence of hair-like organelles called cilia, which are identical in structure to eukaryotic flagella, but are in general shorter and present in much larger numbers, with a different undulating pattern than flagella. Cilia occur in all members of the group (although the peculiar Suctoria only have them for part of the life-cycle) and are variously used in swimming, crawling, attachment, feeding, and sensation. All behavioral patterns are coordinated by signaling processes., The peritrichs ( Latin : Peritrichia ) are a large and distinctive group of ciliate protozoa . They are usually bell or disc shaped , with a prominent paroral membrane arising from the oral cavity and circling counter-clockwise around the anterior of the cell , accompanied by a smaller series of membranelles . The oral cavity is apical and funnel shaped , with a contractile vacuole discharging directly into it . When disturbed , the anterior of the cell can contract . The rest of the body is unciliated , except for a telotroch band circling the posterior in mobile species and stages . The larger order of peritrichia are the Sessilida . Most of these have modified posterior kinetosomes which secrete a contractile stalk . The unattached stage , called a telotroch , is mouthless . These are common in both freshwater and marine environments , and many live attached to aquatic plants and animals . They are either solitary or produce branched colonies . A few secrete a lorica . Vorticella is one of the best - known genera . Stalks may be as long as 2 mm , and in some cases where they are highly contractile can be extended up to 3 mm. The other peritrichia make up the order Mobilida . In these the posterior of the cell is enlarged and modified to form a complex holdfast , allowing the cell to temporarily attach to some host organism . Most live on the integument or gills of freshwater and marine invertebrates , but other hosts occur , including fish and even other ciliates , and other locations as well . Some can be pathenogenic in high populations . The peritrichs were first defined by Friedrich von Stein in 1859 . Initially they were considered spirotrichs , then treated as a separate category , before receiving their modern placement ., Subject: peritrich, Relation: taxon_rank, Options: (A) group (B) order (C) subclass
answer:
subclass


question:
Context: East Hertfordshire is a local government district in Hertfordshire, England. Its council has offices in Bishop's Stortford and Hertford (Hertfordshire's traditional county town)., England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west. The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain (which lies in the North Atlantic) in its centre and south; and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight., In England, a civil parish is a territorial designation which is the lowest tier of local government below districts and counties, or their combined form, the unitary authority. It is an administrative parish, in contrast to an ecclesiastical parish., Bedford is the county town of Bedfordshire, England. It had a population of 107,590 in 2011 together with Kempston but the urban area has a population of about 122,943., Bedfordshire (or /bdfd/; abbreviated Beds.) is a county in the East of England. It is a ceremonial county and a historic county, covered by three unitary authorities: Bedford, Central Bedfordshire, and Luton., Heath Mount School is a Church of England co-educational independent prep school near Watton - at - Stone , Hertfordshire admitting pupils aged 3 to 13 . Originally founded as Heath Mount Academy in Hampstead in 1796 it was not until later in 1934 that it relocated to the Georgian Mansion , on the Woodhall Estate in rural Hertfordshire . As of 2014 there are 442 children in attendance at the school and this figure is split between boarding pupils and day pupils and girls and boys ., The East of England is one of nine official regions of England at the first level of NUTS for statistical purposes. It was created in 1994 and was adopted for statistics from 1999. It includes the ceremonial counties of Bedfordshire, Cambridgeshire, Essex, Hertfordshire, Norfolk and Suffolk. Essex has the highest population in the region., Hertford is the county town of Hertfordshire, England, and is also a civil parish in the East Hertfordshire district of the county. Forming a civil parish, the 2011 census put the population of Hertford at about 26,000., London is the capital and most populous city of England and the United Kingdom, as well as the most populous city proper in the European Union. Standing on the River Thames in the south east of the island of Great Britain, London has been a major settlement for two millennia. It was founded by the Romans, who named it "Londinium". London's ancient core, the City of London, largely retains its medieval boundaries. Since at least the 19th century, "London" has also referred to the metropolis around this core, historically split between Middlesex, Essex, Surrey, Kent, and Hertfordshire, which today largely makes up Greater London, governed by the Mayor of London and the London Assembly., The River Beane is a short river in the county of Hertfordshire, England. A tributary of the River Lea, it rises to the south-west of Sandon in the hills northeast of Stevenage and joins the Lea at Hartham Common in Hertford., Southern England, or the South of England, also known as the South, refers roughly to the southern counties of England. The extent of this area can take a number of different interpretations depending on the context, including geographical, cultural, political and economic., Hampstead (or ), commonly known as Hampstead Village, is an area of London, England, northwest of Charing Cross. Part of the London Borough of Camden, it is known for its intellectual, liberal, artistic, musical and literary associations and for Hampstead Heath, a large, hilly expanse of parkland. It has some of the most expensive housing in the London area. The village of Hampstead has more millionaires within its boundaries than any other area of the United Kingdom., Hampstead Heath (locally known as "the heath") is a large, ancient London park, covering . This grassy public space sits astride a sandy ridge, one of the highest points in London, running from Hampstead to Highgate, which rests on a band of London Clay. The heath is rambling and hilly, embracing ponds, recent and ancient woodlands, a lido, playgrounds, and a training track, and it adjoins the former stately home of Kenwood House and its estate. The south-east part of the heath is Parliament Hill, from which the view over London is protected by law., Charing Cross denotes the junction of Strand, Whitehall and Cockspur Street, just south of Trafalgar Square in central London. It gives its name to several landmarks, including Charing Cross railway station, one of the main London rail terminals., Stevenage is a town and borough in Hertfordshire, England. It is situated to the east of junctions 7 and 8 of the A1(M), and is between Letchworth Garden City to the north, and Welwyn Garden City to the south., Hertfordshire (often abbreviated Herts) is a county in southern England, bordered by Bedfordshire to the north, Cambridgeshire to the north-east, Essex to the east, Buckinghamshire to the west and Greater London to the south. For government statistical purposes, it is placed in the East of England region., Watton-at-Stone is a village in the English county of Hertfordshire, situated midway between the towns of Stevenage and Hertford in the valley of the River Beane. The 2011 census showed a population of 2,272 living in 946 households. Watton-at-Stone is also a civil parish in East Hertfordshire District Council., Cambridgeshire (or ; abbreviated Cambs.), archaically known as the County of Cambridge, is an East Anglian county in England, bordering Lincolnshire to the north, Norfolk to the north-east, Suffolk to the east, Essex and Hertfordshire to the south, and Bedfordshire and Northamptonshire to the west. The city of Cambridge is the county town. Modern Cambridgeshire was formed in 1974 as an amalgamation of the counties of Cambridgeshire and Isle of Ely and Huntingdon and Peterborough, which had been created in 1965 from the historic counties of Cambridgeshire, Huntingdonshire, the Isle of Ely and the Soke of Peterborough. It contains most of the region known as Silicon Fen., Buckinghamshire (or ), abbreviated Bucks, is a county in South East England which borders Greater London to the south east, Berkshire to the south, Oxfordshire to the west, Northamptonshire to the north, Bedfordshire to the north east and Hertfordshire to the east., Subject: heath mount school, Relation: located_in_the_administrative_territorial_entity, Options: (A) bedford (B) bedfordshire (C) buckinghamshire (D) cambridge (E) cambridgeshire (F) cambridgeshire and isle of ely (G) cross (H) east (I) east hertfordshire (J) east of england (K) england (L) essex (M) european union (N) greater london (O) hertfordshire (P) highgate (Q) huntingdonshire (R) london (S) luton (T) norfolk (U) northwest (V) of (W) peterborough (X) river (Y) scotland (Z) soke of peterborough ([) south (\) south east england (]) southwest (^) split (_) stevenage (`) strand (a) street (b) suffolk (c) surrey (d) the valley (e) whitehall (f) woodlands
answer:

east hertfordshire