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 Arabian Peninsula, simplified Arabia ("", « Arabian island ») is a peninsula of Western Asia situated northeast of Africa on the Arabian plate. From a geological perspective, it is considered a subcontinent of Asia., Yemen ('), officially known as the Republic of Yemen ('), is an Arab country in Western Asia, occupying South Arabia, the southern end of the Arabian Peninsula. Yemen is the second-largest country in the peninsula, occupying 527,970 km (203,850 sq mi). The coastline stretches for about 2,000 km (1,200 mi). It is bordered by Saudi Arabia to the north, the Red Sea to the west, the Gulf of Aden and Arabian Sea to the south, and Oman to the east-northeast. Although Yemen's constitutionally stated capital is the city of Sana'a, the city has been under rebel control since February 2015. Because of this, Yemen's capital has been temporarily relocated to the port city of Aden, on the southern coast. Yemen's territory includes more than 200 islands; the largest of these is Socotra., Socotra ('), also spelled Soqotra, is an island and a small archipelago of four islands in the Arabian Sea. The territory is part of Yemen, and had long been a subdivision of the Aden Governorate. In 2004, it became attached to the Hadhramaut Governorate, which is much closer to the island than Aden (although the nearest governorate was the Al Mahrah Governorate). In 2013, the archipelago became its own governorate, the Soqatra Governorate., Sana'a (also spelled Sanaa or Sana; "" ) is the largest city in Yemen and the centre of Sana'a Governorate. The city is not part of the Governorate, but forms the separate administrative district of "Amanat Al-Asemah". Under the Yemeni constitution, Sana'a is the capital of the country, although the seat of the internationally recognised government moved to Aden in the aftermath of the 201415 Yemeni coup d'état. Aden was declared as the temporary capital by President Abd Rabbuh Mansur Hadi in March 2015., Ash - Shihr ( Arabic :   ) ( transliteration al - Shir ) is a coastal town in Hadhramaut , southern Yemen . It is located at around 14 ° 45  39 `` N 49 ° 36  25 '' E. It was a part of the Qu'aiti Sultanate before the unified Yemen was formed . Ash Shihr was involved in the export of frankincense in ancient times , to places as far as China ., The Red Sea (also the Erythraean Sea) is a seawater inlet of the Indian Ocean, lying between Africa and Asia. The connection to the ocean is in the south through the Bab el Mandeb strait and the Gulf of Aden. To the north lie the Sinai Peninsula, the Gulf of Aqaba, and the Gulf of Suez (leading to the Suez Canal). The Red Sea is a Global 200 ecoregion. The sea is underlain by the Red Sea Rift which is part of the Great Rift Valley., The Gulf of Aden ("") is a gulf located in the Arabian Sea between Yemen, on the south coast of the Arabian Peninsula, and Somalia in the Horn of Africa. In the northwest, it connects with the Red Sea through the Bab-el-Mandeb strait, which is more than 20 miles wide. It shares its name with the port city of Aden in Yemen, which forms the northern shore of the gulf. Historically, the Gulf of Aden was known as "The Gulf of Berbera", named after the ancient Somali port city of Berbera on the south side of the gulf. However, as the city of Aden grew during the colonial era, the name of "Gulf of Aden" was popularised., The Arabian Sea is a region of the northern Indian Ocean bounded on the north by Pakistan and Iran, on the west by northeastern Somalia and the Arabian Peninsula, and on the east by India. Historically the sea has been known by other names including the Erythraean Sea and the Persian Sea. Its total area is and its maximum depth is . The Gulf of Aden is in the southwest, connecting the Arabian Sea to the Red Sea through the strait of Bab-el-Mandeb, and the Gulf of Oman is in the northwest, connecting it to the Persian Gulf., Oman (; ' ), officially the Sultanate of Oman, is an Arab country on the southeastern coast of the Arabian Peninsula. Holding a strategically important position at the mouth of the Persian Gulf, the nation is bordered by the United Arab Emirates to the northwest, Saudi Arabia to the west, and Yemen to the southwest, and shares marine borders with Iran and Pakistan. The coast is formed by the Arabian Sea on the southeast and the Gulf of Oman on the northeast. The Madha and Musandam exclaves are surrounded by the UAE on their land borders, with the Strait of Hormuz (which it shares with Iran) and Gulf of Oman forming Musandam's coastal boundaries., Aden (, ; "" ) is a port city in Yemen, located by the eastern approach to the Red Sea (the Gulf of Aden), some east of Bab-el-Mandeb. Its population is approximately 800,000 people. Aden's ancient, natural harbour lies in the crater of a dormant volcano which now forms a peninsula, joined to the mainland by a low isthmus. This harbour, Front Bay, was first used by the ancient Kingdom of Awsan between the 5th and 7th centuries BC. The modern harbour is on the other side of the peninsula. Aden gives its name to the Gulf of Aden., Western Asia, West Asia, Southwestern Asia or Southwest Asia is the westernmost subregion of Asia. The concept is in limited use, as it significantly overlaps with the Middle East (or Near East), the main difference being the exclusion of Egypt (which would be counted as part of North Africa). The term is sometimes used for the purposes of grouping countries in statistics., Saudi Arabia, officially known as the Kingdom of Saudi Arabia (KSA), is an Arab sovereign state in Western Asia constituting the bulk of the Arabian Peninsula. With a land area of approximately , Saudi Arabia is geographically the fifth-largest state in Asia and second-largest state in the Arab world after Algeria. Saudi Arabia is bordered by Jordan and Iraq to the north, Kuwait to the northeast, Qatar, Bahrain, and the United Arab Emirates to the east, Oman to the southeast, and Yemen to the south. It is separated from Israel and Egypt by the Gulf of Aqaba. It is the only nation with both a Red Sea coast and a Persian Gulf coast, and most of its terrain consists of arid desert or barren landforms., South Arabia is a historical region that consists of the southern region of the Arabian Peninsula, mainly centered in what is now the Republic of Yemen, yet it has historically also included Najran, Jizan, and 'Asir, which are presently in Saudi Arabia, and the Dhofar of present-day Oman., Subject: ash shihr, Relation: located_in_the_administrative_territorial_entity, Options: (A) aden (B) africa (C) gulf (D) hadhramaut governorate (E) india (F) indian ocean (G) iraq (H) jordan (I) kuwait (J) most (K) najran (L) near east (M) northern (N) northwest (O) of (P) oman (Q) qatar (R) red sea (S) saudi arabia (T) socotra (U) south (V) southern region (W) southwest (X) suez (Y) west (Z) yemen
[EX A]: hadhramaut governorate

[EX Q]: Context: General information.
Largely a residential area itself, Naniwa-ku is adjacent to and has in recent years blurred into the Namba district, which is south Osaka's transport hub and centre of commerce, entertainment, shopping, and culture., Name.
In Japanese, the city has been called Ky, Miyako, or Ky no Miyako. In the 11th century, the city was renamed Kyoto ("capital city"), after the Chinese word for capital city, '. After the city of Edo was renamed Tokyo (meaning "Eastern Capital") in 1868, and the seat of the Emperor was transferred there, Kyoto was known for a short time as Saiky (meaning "Western Capital")., Some of the most famous images of Osaka, including the Glico Man and the Kani Doraku Crab, are located around the Dtonbori canal in Namba. Namba is also known as an entertainment district, and hosts many of the city's most popular bars, restaurants, nightclubs, arcades, and pachinko parlors. The area is also known for shopping, with the Takashimaya department store (for older styles) and the sprawling underground Namba City shopping mall (for newer styles)., Historically a merchant city, Osaka has also been known as the and served as a center for the rice trade during the Edo period., The station is adjacent to Meitetsu Nagoya Station, the terminal of the Nagoya Railroad, and Kintetsu Nagoya Station, the terminal of the Kintetsu Nagoya Line., As of November 2012, the city has an estimated population of 50,230 and a population density of 263 persons per km². The total area is ., The Yamatoji Line (  Yamatoji - sen ) is the common name of the western portion of the Kansai Main Line . The line is owned and operated by West Japan Railway Company ( JR West ) , and starts at Kamo Station in Kyoto Prefecture and ends at JR Namba Station in Naniwa - ku , Osaka ., The is a railway line in Japan, which connects Nagoya Station with JR Namba Station in Osaka. It is jointly run by the Central Japan Railway Company (JR Central) and West Japan Railway Company (JR West), with the boundary between both companies being located at Kameyama Station in Kameyama, Mie., Honshu had a population of 103 million , mostly concentrated in the coastal lowlands, notably in the Kant plain where 25% of the total population resides in the Greater Tokyo Area. As the historical center of Japanese culture and political power, the island includes several past Japanese capitals, including Kyoto, Nara, and Kamakura. Much of the island's southern shore forms part of the Taiheiy Belt, a megalopolis that spans several of the Japanese islands., The Japan Railways Group, more commonly known as , consists of seven for-profit companies that took over most of the assets and operations of the government-owned Japanese National Railways on April 1, 1987. Most of the liability of the JNR was assumed by the JNR Settlement Corporation., The is the main railway company operating in the Chbu (Nagoya) region of central Japan. It is officially abbreviated in English as JR Central and in Japanese as . Its headquarters are located in the JR Central Towers in Nakamura-ku, Nagoya, Aichi Prefecture., Economy.
Kita-ku, particularly the Umeda area surrounding Osaka Station, is one of the main commercial centers of Osaka. Kita-ku is also a financial administration center, housing the headquarters of the Japan Mint and the Osaka branch of the Bank of Japan., JR Namba is the western terminus of the Kansai Main Line (Yamatoji Line)., History.
Until the Meiji Restoration, the area of Kyoto Prefecture was known as Yamashiro., , also referred to as , is one of the Japan Railways Group (JR Group) companies and operates in western Honshu. It has its headquarters in Kita-ku, Osaka., Subject: yamatoji line, Relation: instance_of, Options: (A) 1 (B) 25 (C) administration (D) april (E) area (F) bars (G) canal (H) capital (I) chinese (J) city (K) company (L) corporation (M) department store (N) district (O) economy (P) emperor (Q) government (R) group (S) headquarters (T) history (U) information (V) line (W) merchant (X) mint (Y) name (Z) november ([) part (\) plain (]) population (^) profit (_) railway company (`) railway line (a) seven (b) shopping mall (c) station (d) store (e) trade
[EX A]:
railway line