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).

[EX Q]: 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
[EX A]: natural number

[EX Q]: Context: The Normans (Norman: "Nourmands"; ) were the people who, in the 10th and 11th centuries, gave their name to Normandy, a region in France. They were descended from Norse ("Norman" comes from "Norseman") raiders and pirates from Denmark, Iceland and Norway who, under their leader Rollo, agreed to swear fealty to King Charles III of West Francia. Through generations of assimilation and mixing with the native Frankish and Gallo-Roman populations, their descendants would gradually adopt the Carolingian-based cultures of West Francia, ultimately resulting in their own assimilation into the Romance society. The distinct cultural and ethnic identity of the Normans emerged initially in the first half of the 10th century, and it continued to evolve over the succeeding centuries., The Church of England (C of E) is the Anglican Christian state church of England. Headed by the Archbishop of Canterbury (currently Justin Welby) and primarily governed from London with the monarch as the supreme governor, the Church of England is also the mother church of the international Anglican Communion. The church dates its formal establishment as a national church to the 6th-century Gregorian mission in Kent led by Augustine of Canterbury, with considerable features introduced and established during and following the English Reformation in the 16th century., 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., Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam about north of London. At the United Kingdom Census 2011, its population was 123,867, including 24,488 students., Ridley Hall is a theological college located in Sidgwick Avenue in Cambridge in the United Kingdom, which trains men and women intending to take Holy Orders, as deacon or priest of the Church of England and the ministry of other churches. It was founded in 1881 and named in memory of Nicholas Ridley, a leading Protestant theologian of the sixteenth century. The first principal was theologian Handley Moule, later Bishop of Durham., A census of the population of the United Kingdom is taken every ten years. The 2011 census was held in all countries of the UK on 27 March 2011. It was the first UK census which could be completed online via the Internet. The Office for National Statistics (ONS) is responsible for the census in England and Wales, the General Register Office for Scotland (GROS) is responsible for the census in Scotland, and the Northern Ireland Statistics and Research Agency (NISRA) is responsible for the census in Northern Ireland., In the Christian churches, Holy Orders are ordained ministries such as bishop, priest or deacon. In the Roman Catholic (Latin: "sacri ordines"), Eastern Catholic, Eastern Orthodox ( ["hiersyn"],  ["hierateuma"],  ["Svyashchenstvo"]), Oriental Orthodox, Anglican, Assyrian, Old Catholic, Independent Catholic and some Lutheran churches, holy orders is comprised is the three ministerial orders of bishop, priest and deacon, or the sacrament or rite by which candidates are ordained to those orders. Except for Lutherans and some Anglicans, these churches regard ordination as a sacrament (the "sacramentum ordinis"). The Anglo-Catholic tradition within Anglicanism identifies more with the Roman Catholic position about the sacramental nature of ordination., Handley Carr Glyn Moule (23 December 1841  8 May 1920) was an evangelical Anglican theologian, writer, poet, and Bishop of Durham from 1901-1920. , 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 Bishop of Durham is the Anglican bishop responsible for the Diocese of Durham in the Province of York. The diocese is one of the oldest in England and its bishop is a member of the House of Lords. Paul Butler has been the Bishop of Durham since his election was confirmed at York Minster on 20 January 2014. The previous bishop was Justin Welby, Archbishop of Canterbury. The bishop is one of two (the other is the Bishop of Bath and Wells) who escort the sovereign at the coronation., The Bishop of Thetford is an episcopal title which takes its name after the market town of Thetford in Norfolk, England. The title was originally used by the Normans in the 11th century, and is now used by a Church of England suffragan bishop., Hugo Ferdinand de Waal ( 16 March 1935 -- 6 January 2007 ) was Principal of Ridley Hall , Cambridge from 1978 to 1991 and the suffragan Bishop of Thetford from 1992 until 2000 . He was born at Jember on East Java and educated at Tonbridge School and Pembroke College , Cambridge before embarking on an ecclesiastical career with a curacy at St Martin in the Bull Ring after which he was Chaplain at his old college then Rector of Dry Drayton . Following this he was Vicar of St John the Evangelist , Blackpool and then ( his final appointment before elevation to the Episcopate ) Principal of Ridley Hall theological college in Cambridge ( 1978 -- 91 ) . In retirement he continued to serve the Church as an honorary assistant bishop within the Diocese in Europe until his death ., The River Cam is the main river flowing through Cambridge in eastern England. After leaving Cambridge, it flows north and east into the Great Ouse to the south of Ely at Pope's Corner. The Great Ouse connects the Cam to the North Sea at King's Lynn: The total distance from Cambridge to the sea is about and is navigable for punts, small boats, and rowing craft. The Great Ouse also connects to England's canal system via the Middle Level Navigations and the River Nene. In total, the Cam runs for around from its furthest source (near Debden in Essex) to its confluence with the Great Ouse. , Subject: hugo de waal, Relation: occupation, Options: (A) archbishop (B) bishop (C) butler (D) deacon (E) general (F) king (G) leader (H) member (I) monarch (J) poet (K) priest (L) research (M) theologian (N) united kingdom
[EX A]: priest

[EX Q]: Context: A pub, or public house, is an establishment licensed to sell alcoholic drinks, which traditionally include beer, ale and other brewed alcoholic drinks. It is a relaxed, social drinking establishment and a prominent part of British culture, Irish culture, New Zealand culture and Australian culture. In many places, especially in villages, a pub is the focal point of the community. In his 17th century diary Samuel Pepys described the pub as "the heart of England.", Inns are generally establishments or buildings where travelers can seek lodging and, usually, food and drink. They are typically located in the country or along a highway; before the advent of motorized transportation they also provided accommodation for horses., A taberna (plural tabernae) was a single room shop covered by a barrel vault within great indoor markets of ancient Rome. Each taberna had a window above it to let light into a wooden attic for storage and had a wide doorway.
A famous example is the Markets of Trajan in Rome, built in the early 1st century by Apollodorus of Damascus., Hoar Tavern is a historic tavern northeast of downtown Lincoln on MA 2 in Lincoln , Massachusetts . Also known as the Hoar Homestead , it is now known as Hobbs Brook Farm . It was built in 1680 and added to the National Register of Historic Places in 1973 ., Lincoln is a town in the historic area of Middlesex County, Massachusetts, United States. The population was 6,362 at the 2010 census, including residents of Hanscom Air Force Base that live within town limits., A tavern is a place of business where people gather to drink alcoholic beverages and be served food, and in most cases, where travelers receive lodging. An inn is a tavern which has a license to put up guests as lodgers. The word derives from the Latin "taberna" whose original meaning was a shed, workshop, stall, or pub., A census is the procedure of systematically acquiring and recording information about the members of a given population. It is a regularly occurring and official count of a particular population. The term is used mostly in connection with national population and housing censuses; other common censuses include agriculture, business, and traffic censuses. The United Nations defines the essential features of population and housing censuses as "individual enumeration, universality within a defined territory, simultaneity and defined periodicity", and recommends that population censuses be taken at least every 10 years. United Nations recommendations also cover census topics to be collected, official definitions, classifications and other useful information to co-ordinate international practice., Massachusetts ; officially the Commonwealth of Massachusetts, is the most populous state in the New England region of the northeastern United States. It is bordered by the Atlantic Ocean to the east, the states of Connecticut and Rhode Island to the south, New Hampshire and Vermont to the north, and New York to the west. The state is named for the Massachusett tribe, which once inhabited the area. The capital of Massachusetts and the most populous city in New England is Boston. Over 80% of Massachusetts' population lives in the Greater Boston metropolitan area, a region influential upon American history, academia, and industry. Originally dependent on agriculture, fishing and trade, Massachusetts was transformed into a manufacturing center during the Industrial Revolution. During the 20th century, Massachusetts' economy shifted from manufacturing to services. Modern Massachusetts is a global leader in biotechnology, engineering, higher education, finance, and maritime trade., A shed is typically a simple, single-storey roofed structure in a back garden or on an allotment that is used for storage, hobbies, or as a workshop. Sheds vary considerably in the complexity of their construction and their size, from small open-sided tin-roofed structures to large wood-framed sheds with shingled roofs, windows, and electrical outlets. Sheds used on farms or in industry can be large structures. The main types of shed construction are metal sheathing over a metal frame, plastic sheathing and frame, all-wood construction (the roof may be asphalt shingled or sheathed in tin), and vinyl-sided sheds built over a wooden frame., Hanscom Air Force Base (AFB) is a United States Air Force base located predominantly within Bedford, Massachusetts, with portions extending into the adjoining towns of Concord and Lincoln. The facility is adjacent to Hanscom Field which provides general aviation and charter service., Food is any substance consumed to provide nutritional support for the body. It is usually of plant or animal origin, and contains essential nutrients, such as carbohydrates, fats, proteins, vitamins, or minerals. The substance is ingested by an organism and assimilated by the organism's cells to provide energy, maintain life, or stimulate growth., Travel is the movement of people between relatively distant geographical locations, and can involve travel by foot, bicycle, automobile, train, boat, airplane, or other means, with or without luggage, and can be one way or round trip. Travel can also include relatively short stays between successive movements., Lodging or a holiday accommodation is a type of residential accommodation. People who travel and stay away from house for more than a day need lodging for sleep, rest, food, safety, shelter from cold temperatures or rain, storage of luggage and access to common household functions., Subject: hoar tavern, Relation: instance_of, Options: (A) air force (B) ancient rome (C) animal (D) area (E) automobile (F) barrel (G) base (H) bicycle (I) boat (J) census (K) century (L) charter (M) construction (N) country (O) day (P) diary (Q) drink (R) education (S) energy (T) england (U) facility (V) finance (W) food (X) force (Y) garden (Z) geographical ([) highway (\) holiday (]) information (^) inn (_) island (`) may (a) metal (b) organism (c) people (d) plant (e) point (f) population (g) practice (h) pub (i) public (j) region (k) roof (l) service (m) shelter (n) shop (o) single (p) size (q) state (r) tavern (s) term (t) territory (u) town (v) travel (w) tribe (x) word
[EX A]:
construction