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).
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: The British Railways Board (BRB) was a nationalised industry in the United Kingdom that operated from 1963 to 2001. Until 1997 it was responsible for most railway services in Great Britain, trading under the brand name British Railways and, from 1965, British Rail. It did not operate railways in Northern Ireland, where railways were the responsibility of the Government of Northern Ireland., The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a sovereign country in western Europe. Lying off the north-western coast of the European mainland, it includes the island of Great Britain (the name of which is also loosely applied to the whole country), the north-eastern part of the island of Ireland, and many smaller islands. Northern Ireland is the only part of the UK that shares a land border with another sovereign statethe Republic of Ireland. Apart from this land border, the UK is surrounded by the Atlantic Ocean, with the North Sea to its east, the English Channel to its south and the Celtic Sea to its south-south-west, giving it the 12th-longest coastline in the world. The Irish Sea lies between Great Britain and Ireland. With an area of , the UK is the 78th-largest sovereign state in the world and the 11th-largest in Europe. It is also the 21st-most populous country, with an estimated 65.1 million inhabitants. Together, this makes it the fourth most densely populated country in the European Union., Automatic train operation (ATO) is an operational safety enhancement device used to help automate operations of trains. Mainly, it is used on automated guideway transits and rapid transit systems which are easier to ensure safety of humans. Most systems elect to maintain a driver (train operator) to mitigate risks associated with failures or emergencies., Tottenham was a local government district in north east Middlesex from 1850 to 1965. It was part of the London postal district and Metropolitan Police District., The Northern line is a London Underground line, coloured black on the Tube map. The section between Stockwell and Borough opened in 1890, and is the oldest section of deep-level tube line on the network., Surrey is a county in the south east of England and also one of the home counties bordering Greater London. Surrey shares borders with Kent to the east, East Sussex to the south-east, West Sussex to the south, Hampshire to the west and south-west and Berkshire to the north-west. The county town is Guildford. Surrey County Council sits extraterritorially at Kingston upon Thames, administered as part of Greater London since 1965. With a resident population of 1.1 million, Surrey is the most densely populated and third most populated county in the South East region, after Kent and Hampshire., Middlesex (abbreviation: Middx) was a county in southeast England that is now mostly part of Greater London, with small sections in neighbouring counties. It was established in the Anglo-Saxon system from the territory of the Middle Saxons, and existed as an official unit until 1965. The historic county included land stretching north of the River Thames from east to west of the City of London with the rivers Colne and Lea and a ridge of hills as the other boundaries. The largely low-lying county, dominated by clay in its north and alluvium on gravel in its south, was the second smallest by area in 1831., Tottenham Hale is a National Rail and London Underground Victoria line station in Tottenham , north London . It is on Ferry Lane , with access from Watermead Way . The station is in Travelcard Zone 3 . The national rail gateline now has automatic barriers installed : rail users must use the Underground doors to the station . A new station building is awaiting planning approval , and a third railway platform is being worked on . This is all part of the 2013/14 Tottenham Hale regeneration scheme ., Rapid transit, also known as heavy rail, metro, subway, tube, or underground, is a type of high-capacity public transport generally found in urban areas. Unlike buses or trams, rapid transit systems are electric railways that operate on an exclusive right-of-way, which cannot be accessed by pedestrians or other vehicles of any sort, and which is often grade separated in tunnels or on elevated railways., The London Borough of Haringey 
is a London borough in North London, classified by some definitions as part of Inner London, and by others as part of Outer London. It was created in 1965 by the amalgamation of three former boroughs. It shares borders with six other London boroughs. Clockwise from the north, they are: Enfield, Waltham Forest, Hackney, Islington, Camden, and Barnet., The Rail Delivery Group (RDG), formerly Association of Train Operating Companies (ATOC), is a body that represents the 23 train operating companies that provide passenger services on the privatised British railway system. It owns the National Rail brand. RDG is an unincorporated association owned by its members. It was set up by the train operators formed during privatisation of the railways under the Railways Act 1993. Its office is in London., North London is the northern part of London, England. It is an imprecise description and the area it covers is defined differently for a range of purposes. Common to these definitions is that it includes districts north of the River Thames and is used in comparison with south London. However, it is also often used in comparisons with central London, east London and west London., The Tube map is a schematic transport map of the lines, stations and services of London's public transport systems, the primary system being London Underground, known colloquially as "the Tube", hence the map's name. The first schematic Tube map was designed by Harry Beck in 1931, and it has since been expanded to also include today the Docklands Light Railway, London Overground, TfL Rail, Tramlink and the Emirates Air Line cable car., The River Thames is a river that flows through southern England. At , it is the longest river entirely in England and the second longest in the United Kingdom, after the River Severn. It also flows through Oxford (where it is called Isis), Reading, Henley-on-Thames and Windsor. The lower reaches of the river are called the Tideway, derived from its long tidal reach up to Teddington Lock. It rises at Thames Head in Gloucestershire, and flows into the North Sea via the Thames Estuary. The Thames drains the whole of Greater London. , 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., Brixton is a district of London, located in the borough of Lambeth in south London. The area is identified in the London Plan as one of 35 major centres in Greater London., The City of London is a city and county within London. It constituted most of London from its settlement by the Romans in the 1st century AD to the Middle Ages, but the agglomeration has since grown far beyond the City's borders. The City is now only a tiny part of the metropolis of London, though it remains a notable part of central London. Administratively, it forms one of the 33 local authority districts of Greater London; however, the City of London is not a London borough, a status reserved for the other 32 districts (including London's only other city, the City of Westminster). , 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., Kent is a county in South East England and one of the home counties. It borders Greater London to the north west, Surrey to the west, East Sussex to the south west, and Essex across the Thames Estuary to the north. The county town is Maidstone. , Tottenham is an area in the London Borough of Haringey, in north London, England. It is situated north-north-east of Charing Cross., Walthamstow (or ) is the principal town of the London Borough of Waltham Forest in East London, England. It is located northeast from Charing Cross., Her Majesty's Principal Secretary of State for Transport is the member of the cabinet responsible for the British Department for Transport. The office used to be called the Minister of Transport and has been merged with the Department for the Environment at various times., The Piccadilly line is a line of the London Underground, coloured dark blue on the Tube map. It is the fourth busiest line on the Underground network on the basis of the number of passengers transported per year with 210,000,000. It is mainly a deep-level line, running from the north to the west of London via Zone 1, with a number of surface sections, mostly in its westernmost parts. It is named after the road above it between Hyde Park Corner and Piccadilly Circus. Some of its stations are shared with the District line and some are shared with the Metropolitan line. It is the second longest line on the system, after the Central line, and has the second most stations, after the District line. It serves many of London's top tourist attractions including Harrods (Knightsbridge), Hyde Park, Buckingham Palace (within walking distance from Green Park), Piccadilly Circus, Leicester Square and Covent Garden, as well as London Heathrow Airport, the busiest airport in Europe. The line shares tracks with the Metropolitan line between Uxbridge and Rayners Lane, and with the District line between Hanger Lane Junction and Acton Town, then runs parallel with the District line between Acton Town and Barons Court., 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., Londinium was a settlement established on the current site of the City of London around  43. Its bridge over the River Thames turned the city into a road nexus and major port, serving as a major commercial centre in Roman Britain until its abandonment during the 5th century., The European Union (EU) is a political and economic union of member states that are located primarily in Europe. It has an area of , and an estimated population of over 510 million. The EU has developed an internal single market through a standardised system of laws that apply in all member states. EU policies aim to ensure the free movement of people, goods, services, and capital within the internal market, enact legislation in justice and home affairs, and maintain common policies on trade, agriculture, fisheries, and regional development. Within the Schengen Area, passport controls have been abolished. A monetary union was established in 1999 and came into full force in 2002, and is composed of 19 EU member states which use the euro currency., Tottenham Hale is a district in the London Borough of Haringey in north London. From 18501965, it was part of the Municipal Borough of Tottenham, in Middlesex., The London Underground (also known simply as the Underground, or by its nickname the Tube) is a public rapid transit system serving Greater London and some parts of the adjacent counties of Buckinghamshire, Essex and Hertfordshire in the United Kingdom., 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., The Mayor of London is an elected politician who, along with the London Assembly of 25 members, is accountable for the strategic government of Greater London. The current mayor is Sadiq Khan, who took up office on 9 May 2016. The position had been held by Ken Livingstone from the creation of the role on 4 May 2000 until he was defeated in 2008 by Boris Johnson, who served two terms before being succeeded by Khan., Great Britain, also known as Britain , is a large island in the north Atlantic Ocean off the northwest coast of continental Europe. With an area of , Great Britain is the largest European island and the ninth-largest in the world. In 2011 the island had a population of about 61 million people, making it the world's third-most populous island after Java in Indonesia and Honshu in Japan. The island of Ireland is situated to the west of it, and together these islands, along with over 1,000 smaller surrounding islands, comprise the British Isles archipelago., 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., The Victoria line is a deep-level London Underground route running from Brixton in the south in Zone 2 to Walthamstow Central in the north-east in Zone 3 of London. It is coloured light blue on the Tube map. It is one of two underground lines to run entirely below ground, the other being the Waterloo & City line. Constructed in the 1960s, it was the first entirely new tube line in London for fifty years, and was designed to relieve congestion on other lines, in particular the Piccadilly line and the Charing Cross branch of the Northern line. The line has always been operated using automatic train operation, but all trains carry drivers., The London Assembly is an elected body, part of the Greater London Authority, that scrutinises the activities of the Mayor of London and has the power, with a two-thirds majority, to amend the Mayor's annual budget and to reject the Mayor's draft statutory strategies. The assembly was established in 2000 and meets at City Hall on the South Bank of the River Thames, close to Tower Bridge. The assembly is also able to investigate other issues of importance to Londoners (transport, environmental matters, etc.), publish its findings and recommendations, and make proposals to the Mayor., In Great Britain, National Rail is the trading name licensed for use by the Rail Delivery Group, an unincorporated association whose membership consists of the passenger train operating companies (TOCs) of Great Britain that run the passenger services previously provided by the British Railways Board, from 1965 using the brand name British Rail. National Rail generally does not include services that do not have a BR history; this distinction is important because National Rail services share a ticketing structure and inter-availability that do not necessarily extend to other services. The name and the accompanying double arrow symbol are the intellectual property of the Secretary of State for Transport., British Railways (BR), which from 1965 traded as British Rail, was the operator of most of the rail transport in Great Britain between 1948 and 1997. It was formed from the nationalisation of the "Big Four" British railway companies and lasted until the gradual privatisation of British Rail, in stages between 1994 and 1997. Originally a trading brand of the Railway Executive of the British Transport Commission, it became an independent statutory corporation in 1962: the British Railways Board. , Subject: tottenham hale station, Relation: located_in_the_administrative_territorial_entity, Options: (A) atlantic ocean (B) berkshire (C) british isles (D) buckinghamshire (E) cable (F) central (G) cross (H) district (I) east london (J) east sussex (K) enfield (L) england (M) europe (N) european union (O) forest (P) greater london (Q) guildford (R) hertfordshire (S) hyde park (T) inner london (U) ireland (V) japan (W) java (X) kent (Y) kingston upon thames (Z) london ([) london borough of haringey (\) london borough of waltham forest (]) mainland (^) middlesex (_) north (`) north east (a) northamptonshire (b) northern (c) northwest (d) of (e) oxfordshire (f) piccadilly (g) river (h) road (i) south (j) south east england (k) split (l) strand (m) street (n) surrey (o) sussex (p) united kingdom (q) victoria (r) wales (s) waltham (t) walthamstow (u) waterloo (v) west (w) westminster (x) whitehall
answer:
london borough of haringey


question:
Context: Steve Edward Hegg (born December 3, 1963) is a retired track cyclist and road bicycle racer from the United States, who was a professional rider from 1988 to 2000. He represented the USA at the 1984 Summer Olympics in Los Angeles, California, where he won the gold medal in the 4000m individual pursuit and silver in the 4000m team pursuit., Los Angeles (Spanish for "The Angels"), officially the City of Los Angeles and often known by its initials L.A., is the second-most populous city in the United States (after New York City), the most populous city in California and the county seat of Los Angeles County. Situated in Southern California, Los Angeles is known for its mediterranean climate, ethnic diversity, sprawling metropolis, and as a major center of the American entertainment industry. Los Angeles lies in a large coastal basin surrounded on three sides by mountains reaching up to and over ., The 1984 Summer Olympics, officially known as the Games of the XXIII Olympiad, was an international multi-sport event held in Los Angeles, California, United States in 1984. When Tehran, the only other interested city on the international level, declined to bid due to the concurrent Iranian political and social changes, the IOC awarded Los Angeles the Games by default. This was the second occasion Los Angeles hosted the games, the first being in 1932., Brent Emery (born September 15, 1957) was a cyclist for the United States at the 1984 Summer Olympics in Los Angeles, California, where he won a silver medal in the team pursuit. He is now a business owner and cycling advocate in the metro Milwaukee area., Iran (, also , ; ' ), also known as Persia, officially the Islamic Republic of Iran (' ), is a sovereign state in Western Asia. It is bordered to the northwest by Armenia, the "de facto" Nagorno-Karabakh Republic, and Azerbaijan; to the north by the Caspian Sea; to the northeast by Turkmenistan; to the east by Afghanistan and Pakistan; to the south by the Persian Gulf and the Gulf of Oman; and to the west by Turkey and Iraq. Comprising a land area of , it is the second-largest country in the Middle East and the 18th-largest in the world. With 82.8 million inhabitants, Iran is the world's 17th-most-populous country. It is the only country with both a Caspian Sea and an Indian Ocean coastline. The country's central location in Eurasia and Western Asia, and its proximity to the Strait of Hormuz, make it of great geostrategic importance. Tehran is the country's capital and largest city, as well as its leading economic center., A multi-sport event is an organized sports event, often held over multiple days, featuring competition in many different sports between organized teams of athletes from (mostly) nation states. The first major, modern, multi-sport event of international significance is the modern Olympic Games., Leonard Harvey Nitz (born September 30, 1956) is a retired track cyclist from the United States. He won the silver medal in the 4000m team pursuit and bronze in the 4000m individual pursuit at the 1984 Summer Olympics in Los Angeles, California., David Miles Grylls ( born September 29 , 1957 ) is a retired track cyclist from the United States . He represented his native country at the 1984 Summer Olympics in Los Angeles , California , where he won the silver medal in the men 's 4.000m team pursuit , alongside Steve Hegg , Leonard Nitz , Patrick McDonough and Brent Emery ., Subject: david grylls, Relation: occupation, Options: (A) advocate (B) bicycle racer (C) diversity (D) entertainment (E) major (F) sovereign (G) track cyclist
answer:
bicycle racer