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: Wales is a country that is part of the United Kingdom and the island of Great Britain. It is bordered by England to the east, the Irish Sea to the north and west, and the Bristol Channel to the south. It had a population in 2011 of 3,063,456 and has a total area of . Wales has over of coastline and is largely mountainous, with its higher peaks in the north and central areas, including Snowdon, its highest summit. The country lies within the north temperate zone and has a changeable, maritime climate., The Isle of Wight is a county and the largest and second-most populous island in England. It is located in the English Channel, about 4 miles (6 km) off the coast of Hampshire, separated by the Solent. The island has resorts that have been holiday destinations since Victorian times, and is known for its mild climate, coastal scenery, and verdant landscape of fields, downland and chines., The English Channel ("the Sleeve" [hence ] "Sea of Brittany" "British Sea"), also called simply the Channel, is the body of water that separates southern England from northern France, and joins the southern part of the North Sea to the rest of the Atlantic Ocean., 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., John FitzAlan ( D ' Arundel ) , 1st Baron Arundel ( c. 1348 -- 16 December 1379 ) was a Lord Marshal or Marshal of England ., The Irish Sea (, , , Ulster-Scots: "Airish Sea"), separates the islands of Ireland and Great Britain. It is connected to the Celtic Sea in the south by St George's Channel, and to the Inner Seas off the West Coast of Scotland in the north by the North Channel. Anglesey is the largest island within the Irish Sea, followed by the Isle of Man. The sea is occasionally, but rarely, referred to as the Manx Sea., 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., Scotland (Scots: ) is a country that is part of the United Kingdom and covers the northern third of the island of Great Britain. It shares a border with England to the south, and is otherwise surrounded by the Atlantic Ocean, with the North Sea to the east and the North Channel and Irish Sea to the south-west. In addition to the mainland, the country is made up of more than 790 islands, including the Northern Isles and the Hebrides., The North Sea is a marginal sea of the Atlantic Ocean located between Great Britain, Scandinavia, Germany, the Netherlands, Belgium, and France. An epeiric (or "shelf") sea on the European continental shelf, it connects to the ocean through the English Channel in the south and the Norwegian Sea in the north. It is more than long and wide, with an area of around ., The Isles of Scilly (or "") are an archipelago off the south western tip of the Cornish peninsula of Great Britain. It is the southernmost location in England and the United Kingdom, as well as the most westerly in England., 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., The Celtic Sea (; ) is the area of the Atlantic Ocean off the south coast of Ireland bounded to the east by Saint George's Channel; other limits include the Bristol Channel, the English Channel, and the Bay of Biscay, as well as adjacent portions of Wales, Cornwall, Devon, and Brittany. The southern and western boundaries are delimited by the continental shelf, which drops away sharply. The Isles of Scilly are an archipelago of small islands in the sea., Subject: john fitzalan, Relation: place_of_death, Options: (A) anglesey (B) atlantic ocean (C) bristol (D) bristol channel (E) celtic sea (F) central (G) cornish (H) england (I) english channel (J) germany (K) ireland (L) irish sea (M) isle of man (N) isle of wight (O) isles of scilly (P) netherlands (Q) north atlantic ocean (R) north channel (S) north sea (T) northern ireland (U) scotland (V) sea (W) snowdon (X) southern england (Y) summit (Z) union ([) united kingdom (\) wales (]) westerly
[EX A]: atlantic ocean

[EX Q]: Context: A cay (or ), also spelled caye or key, is a small, low-elevation, sandy island on the surface of a coral reef. Cays occur in tropical environments throughout the Pacific, Atlantic and Indian Oceans (including in the Caribbean and on the Great Barrier Reef and Belize Barrier Reef)., Alaska is a U.S. state located in the northwest extremity of North America. The Canadian administrative divisions of British Columbia and Yukon border the state to the east; its most extreme western part is Attu Island; it has a maritime border with Russia to the west across the Bering Strait. To the north are the Chukchi and Beaufort seasthe southern parts of the Arctic Ocean. The Pacific Ocean lies to the south and southwest. Alaska is the largest state in the United States by area, the 3rd least populous and the least densely populated of the 50 United States. Approximately half of Alaska's residents (the total estimated at 738,432 by the U.S. Census Bureau in 2015) live within the Anchorage metropolitan area. Alaska's economy is dominated by the fishing, natural gas, and oil industries, resources which it has in abundance. Military bases and tourism are also a significant part of the economy., Seguam Island is a small volcanic island in the Andreanof Islands group in the Aleutian Islands of Alaska. The island is mountainous and oval shaped with a land area of . It is long and wide. The 2000 census reported a population of one person., A continent is one of several very large landmasses on Earth. Generally identified by convention rather than any strict criteria, up to seven regions are commonly regarded as continents. Ordered from largest in size to smallest, they are: Asia, Africa, North America, South America, Antarctica, Europe, and Australia. In geology, areas of continental crust include regions covered with water., Amukta Pass is a wide strait between the Bering Sea and the North Pacific Ocean in the Aleutian Islands in Alaska. It lies between Amukta Island to the east and Seguam Island to the west., The Andreanof Islands are a group of islands in the Aleutian Islands, in southwestern Alaska. They are located at about 52° North and 172°57' to 179°09' West., Lake Island is an island on the coast of the Canadian province of British Columbia. It is located between Mathieson Channel and Lady Trutch Passage, and is flanked by Dowager Island (to the northwest), Lady Douglas Island (to the west), and a long finger shaped peninsula of the Canadian mainland to the east. Ironically, Lake Island is not a lake island, as it is in an inlet of the Pacific Ocean, and lies only some 6 kilometres from the open sea., An islet is a very small island. Types. As suggested by its origin as "islette", an Old French diminutive of "isle", use of the term implies small size, but little attention is given to drawing an upper limit on its applicability., An archipelago, sometimes called an island group or island chain, is a chain, cluster or collection of islands. The word "archipelago" is derived from the Greek "-  arkhi-" ("chief") and "  pélagos" ("sea") through the Italian "arcipelago". In Italian, possibly following a tradition of antiquity, the Archipelago (from medieval Greek "*" and Latin "archipelagus") was the proper name for the Aegean Sea and, later, usage shifted to refer to the Aegean Islands (since the sea is remarkable for its large number of islands). It is now used to refer to any island group or, sometimes, to a sea containing a small number of scattered islands., Islands of Four Mountains is an island grouping of the Aleutian Islands in Alaska, United States. The chain includes, from west to east, Amukta, Chagulak, Yunaska, Herbert, Carlisle, Chuginadak, Uliaga, and Kagamil islands. This island chain is located between Amukta Pass and the Andreanof Islands to the west, and Samalga Pass and the Fox Islands to the east. These islands have a total land area of 210.656 sq mi (545.596 km²) and have no permanent population. The two largest islands are Yunaska and Chuginadak. Chuginadak is mainly made up of the active volcano Mount Cleveland., Water is a transparent and nearly colorless chemical substance that is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms. Its chemical formula is HO, meaning that its molecule contains one oxygen and two hydrogen atoms, that are connected by covalent bonds. Water strictly refers to the liquid state of that substance, that prevails at standard ambient temperature and pressure; but it often refers also to its solid state (ice) or its gaseous state (steam or water vapor). It also occurs in nature as snow, glaciers, ice packs and icebergs, clouds, fog, dew, aquifers, and atmospheric humidity., Amukta is a small yet mountainous island in the Islands of Four Mountains group lying between the Fox Islands and the Andreanof Islands in the Aleutian Islands . The nearest islands to it are Yunaska and Seguam Island ; it is separated from Seguam Island by Amukta Pass . The small island of Chagulak lies directly northeast of it . The island reaches a total height of 3,461 feet ( 1,055 m ) . The island measures 9 kilometres ( 5.6 mi ) long and 8.3 kilometres ( 5.2 mi ) wide ., The Bering Sea is a marginal sea of the Pacific Ocean. It comprises a deep water basin, which then rises through a narrow slope into the shallower water above the continental shelves., A strait is a naturally formed, narrow, typically navigable waterway that connects two larger bodies of water. Most commonly it is a channel of water that lies between two land masses. Some straits are not navigable, for example because they are too shallow, or because of an unnavigable reef or archipelago., An island or isle is any piece of sub-continental land that is surrounded by water. Very small islands such as emergent land features on atolls can be called islets, skerries, cays or keys. An island in a river or a lake island may be called an eyot or ait, and a small island off the coast may be called a holm. A grouping of geographically or geologically related islands is called an archipelago, e.g. the Philippines., The Philippines, officially the Republic of the Philippines, is a sovereign island country in Southeast Asia situated in the western Pacific Ocean. It consists of about 7,641 islands that are categorized broadly under three main geographical divisions from north to south: Luzon, Visayas, and Mindanao. The capital city of the Philippines is Manila and the most populous city is Quezon City, both part of Metro Manila. Bounded by the South China Sea on the west, the Philippine Sea on the east and the Celebes Sea on the southwest, the Philippines shares maritime borders with Taiwan to the north, Vietnam to the west, Palau to the east and Malaysia and Indonesia to the south., A volcano is a rupture in the crust of a planetary-mass object, such as Earth, that allows hot lava, volcanic ash, and gases to escape from a magma chamber below the surface., Subject: amukta, Relation: located_in_the_administrative_territorial_entity, Options: (A) africa (B) alaska (C) andreanof islands (D) australia (E) basin (F) belize (G) british columbia (H) caribbean (I) carlisle (J) china (K) earth (L) europe (M) fox islands (N) hot (O) indonesia (P) manila (Q) north (R) of (S) pacific ocean (T) palau (U) philippines (V) quezon (W) quezon city (X) river (Y) south (Z) southwest ([) taiwan (\) vietnam
[EX A]:
alaska