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).

[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 to1, 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, and2048 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
[A]: natural number

[Q]: Context: Solomon Islands is a sovereign country consisting of six major islands and over 900 smaller islands in Oceania lying to the east of Papua New Guinea and northwest of Vanuatu and covering a land area of . The country's capital, Honiara, is located on the island of Guadalcanal. The country takes its name from the Solomon Islands archipelago, which is a collection of Melanesian islands that also includes the North Solomon Islands (part of Papua New Guinea), but excludes outlying islands, such as Rennell and Bellona, and the Santa Cruz Islands., Sydney is the state capital of New South Wales and the most populous city in Australia and Oceania. Located on Australia's east coast, the metropolis surrounds the world's largest natural harbour, and sprawls towards the Blue Mountains to the west. Residents of Sydney are known as "Sydneysiders". Sydney is the second official seat and second official residence of the Governor-General of Australia and the Prime Minister of Australia and many federal ministries maintain substantial presences in Sydney., South Holland is a province in the midwestern Netherlands. It has a population of just over 3.6 million (as of 2015) and a population density of about , making it the country's most populous province and one of the world's most densely populated areas. Situated on the North Sea in the west of the Netherlands, South Holland covers an area of , of which is water. It borders North Holland to the north, Utrecht and Gelderland to the east, and North Brabant and Zeeland to the south. The provincial capital is The Hague, while its largest city is Rotterdam., East Timor or Timor-Leste (Tetum: "Timor Lorosa'e"), officially the Democratic Republic of Timor-Leste, is a sovereign state in Maritime Southeast Asia. It comprises the eastern half of the island of Timor; the nearby islands of Atauro and Jaco; and Oecusse, an exclave on the northwestern side of the island surrounded by Indonesian West Timor. The country's size is about 15,410km (5,400 sqmi)., Atlanta is the capital of and the most populous city in the U.S. state of Georgia, with an estimated 2015 population of 463,878. Atlanta is the cultural and economic center of the Atlanta metropolitan area, home to 5,710,795 people and the ninth largest metropolitan area in the United States. Atlanta is the county seat of Fulton County, and a small portion of the city extends eastward into DeKalb County., Belgium , officially the Kingdom of Belgium, is a sovereign state in Western Europe bordered by France, the Netherlands, Germany, Luxembourg, and the North Sea. It is a small, densely populated country which covers an area of and has a population of about 11million people. Straddling the cultural boundary between Germanic and Latin Europe, Belgium is home to two main linguistic groups: the Dutch-speaking, mostly Flemish community, which constitutes about 59% of the population, and the French-speaking, mostly Walloon population, which comprises 41% of all Belgians. Additionally, there is a small group of German-speakers who live in the East Cantons located around the High Fens area, and bordering Germany., The Netherlands is the main constituent country of the Kingdom of the Netherlands. It is a densely populated country located in Western Europe with three island territories in the Caribbean. The European part of the Netherlands borders Germany to the east, Belgium to the south, and the North Sea to the northwest, sharing maritime borders with Belgium, the United Kingdom, and Germany. The largest cities in the Netherlands are Amsterdam, Rotterdam, The Hague and Utrecht. Amsterdam is the country's capital, while The Hague holds the Dutch seat of government and parliament. The name "Holland" is used to refer informally to the whole of the country of the Netherlands., Pepijn Aardewijn (born 15 June 1970 in Amsterdam, North Holland) is a former rower from the Netherlands, who competed for his native country in two consecutive Summer Olympics, starting in 1996. He won the silver medal in the men's lightweight double sculls event in Atlanta, Georgia, alongside Maarten van der Linden., Voorburg is a Dutch town and former municipality in the western part of the province of South Holland, the Netherlands. Together with Leidschendam and Stompwijk, it makes up the municipality Leidschendam-Voorburg. It has a population of approximately 39,000 people. It is considered to be the oldest city in The Netherlands and celebrated its 2000th year of existence in 1988., Tasmania (abbreviated as Tas and known colloquially as "Tassie") is an island state of the Commonwealth of Australia. It is located to the south of the Australian mainland, separated by Bass Strait. The state encompasses the main island of Tasmania, the 26th-largest island in the world, and the surrounding 334 islands. The state has a population of around 518,500, just over forty percent of which resides in the Greater Hobart precinct, which forms the metropolitan area of the state capital and largest city, Hobart., 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., Metro Atlanta, designated by the United States Office of Management and Budget as the Atlanta-Sandy Springs-Roswell, GA Metropolitan Statistical Area, is the most populous metro area in the US state of Georgia and the ninth-largest metropolitan statistical area (MSA) in the United States. Its economic, cultural and demographic center is Atlanta, and it had a 2015 estimated population of 5.7 million people according to the U.S. Census Bureau. The metro area forms the core of a broader trading area, the AtlantaAthens-ClarkeSandy Springs Combined Statistical Area. The Combined Statistical Area spans up to 39 counties in north Georgia and had an estimated 2015 population of 6.3 million people. Atlanta is considered an "alpha(-) world city". It is the third largest metropolitan region in the Southeast behind Greater Washington and South Florida., Everwijn Johan Maarten van der Linden (born 9 March 1969 in Voorburg, Zuid-Holland) is a former rower from the Netherlands, who competed for his native country in two consecutive Summer Olympics, starting in 1996. He won the silver medal in the men's lightweight double sculls event in Atlanta, United States, alongside Pepijn Aardewijn. The pair came in 12th in 2000 in Sydney, Australia., Everwijn Johan Maarten van der Linden ( born March 9 , 1969 in Voorburg , Zuid - Holland ) is a former rower from the Netherlands , who competed for his native country in two consecutive Summer Olympics , starting in 1996 . He won the silver medal in the men 's lightweight double sculls event in Atlanta , United States , alongside Pepijn Aardewijn . The pair came in 12th in 2000 in Sydney , Australia ., North Holland (, West Frisian: "Noard-Holland") is a province in the northwest of the Netherlands. It is situated on the North Sea, north of South Holland and Utrecht, and west of Friesland and Flevoland. As of 2015, it has a population of 2,762,163 and a total area of ., Australia, officially the Commonwealth of Australia, is a country comprising the mainland of the Australian continent, the island of Tasmania and numerous smaller islands. It is the world's sixth-largest country by total area. The neighbouring countries are Papua New Guinea, Indonesia and East Timor to the north; the Solomon Islands and Vanuatu to the north-east; and New Zealand to the south-east. Australia's capital is Canberra, and its largest urban area is Sydney., Rotterdam is a city in the Netherlands, located in South Holland, within the RhineMeuseScheldt river delta at the North Sea. Its history goes back to 1270 when a dam was constructed in the Rotte river by people settled around it for safety. In 1340 Rotterdam was granted city rights by the Count of Holland and slowly grew into a major logistic and economic centre. Nowadays it is home to Europe's largest port and has a population of 633,471 (city proper), ranking second in the Netherlands. The Greater Rijnmond area is home to approximately 1.4 million people and the Rotterdam The Hague Metropolitan Area makes for the 168th most populous urban area in the world. Rotterdam is part of the yet larger Randstad conurbation with a total population of 7,100,000., Indonesia (or ; Indonesian: ), officially the Republic of Indonesia, is a unitary sovereign state and transcontinental country located mainly in Southeast Asia with some territories in Oceania. Situated between the Indian and Pacific oceans, it is the world's largest island country, with more than seventeen thousand islands. At , Indonesia is the world's 14th-largest country in terms of land area and world's 7th-largest country in terms of combined sea and land area. It has an estimated population of over 260 million people and is the world's fourth most populous country, the most populous Austronesian nation, as well as the most populous Muslim-majority country. The world's most populous island of Java contains more than half of the country's population., Canberra (or )
is the capital city of Australia. With a population of 381,488, it is Australia's largest inland city and the eighth-largest city overall. The city is located at the northern end of the Australian Capital Territory (ACT), south-west of Sydney, and north-east of Melbourne. A resident of Canberra is known as a "Canberran"., Amsterdam is the capital and most populous municipality of the Kingdom of the Netherlands. Its status as the capital is mandated by the Constitution of the Netherlands, although it is not the seat of the government, which is The Hague. Amsterdam has a population of 847,176 within the city proper, 1,343,647 in the urban area, and 2,431,000 in the Amsterdam metropolitan area. The city is located in the province of North Holland in the west of the country. The metropolitan area comprises much of the northern part of the Randstad, one of the larger conurbations in Europe, with a population of approximately 7million., A country is a region that is identified as a distinct national entity in political geography. A country may be an independent sovereign state or one that is occupied by another state, as a non-sovereign or formerly sovereign political division, or a geographic region associated with sets of previously independent or differently associated people with distinct political characteristics. Regardless of the physical geography, in the modern internationally accepted legal definition as defined by the League of Nations in 1937 and reaffirmed by the United Nations in 1945, a resident of a country is subject to the independent exercise of legal jurisdiction., New South Wales (abbreviated as NSW) is a state on the east coast of :Australia. It borders Queensland to the north, Victoria to the south, and South Australia to the west. It has a coast line with the Tasman Sea on its east side. The Australian Capital Territory is an enclave within the state. New South Wales' state capital is Sydney, which is also Australia's most populous city. , the estimated population of New South Wales was 7.5 million, making it Australia's most populous state. Just under two-thirds of the state's population, 4.67 million, live in the Greater Sydney area. Inhabitants of New South Wales are referred to as "New South Welshmen"., Subject: maarten van der linden, Relation: date_of_birth, Options: (A) 1 (B) 100 (C) 11 (D) 1270 (E) 1340 (F) 15 (G) 163 (H) 176 (I) 1937 (J) 1969 (K) 1970 (L) 1988 (M) 1996 (N) 2 (O) 260 (P) 3 (Q) 334 (R) 343 (S) 381 (T) 39 (U) 4 (V) 41 (W) 410 (X) 463 (Y) 5 (Z) 500 ([) 6 (\) 65 (]) 7 (^) 710 (_) 762 (') 795 (a) 847 (b) 878 (c) 9 march 1969 (d) 900
[A]: 9 march 1969

[Q]: Context: Iraq (, or ; '; '), officially known as the Republic of Iraq ('; ') is a country in Western Asia, bordered by Turkey to the north, Iran to the east, Kuwait to the southeast, Saudi Arabia to the south, Jordan to the southwest, and Syria to the west. The capital, and largest city, is Baghdad. The main ethnic groups are Arabs and Kurds; others include Assyrians, Turkmen, Shabakis, Yazidis, Armenians, Mandeans, Circassians, and Kawliya. Around 95% of the country's 36 million citizens are Muslims, with Christianity, Yarsan, Yezidism, and Mandeanism also present. The official languages of Iraq are Arabic and Kurdish., Mahmud Ghazan (1271 11 May 1304) (, sometimes referred to as Casanus by Westerners) was the seventh ruler of the Mongol Empire's Ilkhanate division in modern-day Iran from 1295 to 1304. He was the son of Arghun and Quthluq Khatun, continuing a long line of rulers who were direct descendants of Genghis Khan. Considered the most prominent of the Ilkhans, he is best known for making a political conversion to Islam in 1295 when he took the throne, marking a turning point for the dominant religion of Mongols in West Asia (Iran, Iraq, Anatolia and Trans-Caucassia). His principal wife was Kokochin, a Mongol princess (originally betrothed to Ghazan's father Arghun before his death) sent by his Khagan Kublai Khan, and escorted from the Mongol capital to the Ilkhanate by Marco Polo., The Ilkhanate, also spelled Il-khanate ("Ilkhnn" "Hulagu-yn Ulus"), was established as a khanate that formed the southwestern sector of the Mongol Empire, ruled by the Mongol House of Hulagu. It was founded in the 13th century and was based primarily in Iran as well as neighboring territories, such as present-day Azerbaijan and the central and eastern parts of present-day Turkey. The Ilkhanate was originally based on the campaigns of Genghis Khan in the Khwarazmian Empire in 121924 and was founded by Hulagu Khan, a grandson of Genghis Khan. With the fragmentation of the Mongol Empire after 1259 it became a functionally separate khanate. At its greatest extent, the state expanded into territories that today comprise most of Iran, Iraq, Armenia, Azerbaijan, Georgia, Turkmenistan, Turkey, western Afghanistan, and southwestern Pakistan. Later Ilkhanate rulers, beginning with Ghazan in 1295, would convert to Islam., Hulagu Khan, also known as Hulegu or Hulegu ( 8 February 1265), was a Mongol ruler who conquered much of Western Asia. Son of Tolui and the Keraite princess Sorghaghtani Beki, he was a grandson of Genghis Khan and brother of Ariq Boke, Mongke Khan, and Kublai Khan., Islam (' ;) is a religion articulated by the Quran, a text considered by its adherents to be the verbatim word of God ('), and, for the vast majority of adherents, the teachings and normative example (called the "sunnah", composed of accounts called "hadith") of Muhammad (5708 June 632 CE). It is the world's second-largest religion and the fastest-growing major religion in the world, with over 1.7 billion followers or 23% of the global population, known as Muslims. Islam is an Abrahamic monotheistic religion that upholds that God is one and incomparable and that the purpose of existence is to worship God. Muslims consider Muhammad to be the last prophet of God., Genghis Khan (often pronounced ; c. 1162 August 18, 1227), born Temujin, was the founder and Great Khan (Emperor) of the Mongol Empire, which became the largest contiguous empire in history after his death., Ahmed Tekuder ( Mongolian : Togoldor / , meaning '' perfect '' ) , also known as Sultan Ahmad ( reigned 1282 -- 1284 ) , was the sultan of the Persian - based Ilkhanate , son of Hulegu and brother of Abaqa . He was eventually succeeded by his nephew Arghun Khan ., 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., Subject: tekuder, Relation: father, Options: (A) arghun (B) genghis khan (C) hulagu khan (D) include (E) kublai khan (F) muhammad (G) persian gulf
[A]:
hulagu khan