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 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

A: natural number
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Q: Context: Tahiti is the largest island in the Windward group of French Polynesia; this overseas collectivity of the French Republic is sometimes referred to as an overseas country. The island is located in the archipelago of the Society Islands in the central Southern Pacific Ocean, and is divided into two parts: The bigger, northwestern part "Tahiti Nui" and the smaller, southeastern part "Tahiti Iti". The island was formed from volcanic activity and is high and mountainous with surrounding coral reefs. The population is 183,645 inhabitants (2012 census), making it the most populous island of French Polynesia and accounting for 68.5 percent of its total population., Coral reefs are diverse underwater ecosystems held together by calcium carbonate structures secreted by corals. Coral reefs are built by colonies of tiny animals found in marine waters that contain few nutrients. Most coral reefs are built from stony corals, which in turn consist of polyps that cluster in groups. The polyps belong to a group of animals known as Cnidaria, which also includes sea anemones and jellyfish. Unlike sea anemones, corals secrete hard carbonate exoskeletons which support and protect the coral polyps. Most reefs grow best in warm, shallow, clear, sunny and agitated waters., Western Europe, also West Europe, is the region comprising the western part of the European continent. There may be differences between the geopolitical and purely geographic definitions of the term., Makemo, Rangi-kemo or Te Paritua, is one of the larger of the Tuamotu atolls in French Polynesia., Tikehau (meaning "Peaceful Landing" in Tuamotuan) or Porutu-kai is a coral atoll in the Palliser Islands group, part of the Tuamotu Archipelago in French Polynesia. It is included in the commune of Rangiroa., The Maldives (, or ), officially the Republic of Maldives (""), is a South Asian island country, located in the Indian Ocean. It lies southwest of India and Sri Lanka. The chain of twenty-six atolls stretches from Ihavandhippolhu Atoll in the north to the Addu City in the south. Comprising a territory spanning roughly , the Maldives is one of the world's most geographically dispersed countries, as well as the smallest Asian country by both land area and population, with a little over 393,500 inhabitants. Malé is the capital and most populated city, traditionally called the "King's Island" for its central location., The Tuamotus or the Tuamotu Archipelago (officially "") are a French Polynesian chain of almost 80 islands and atolls, stretching from the northwest to the southeast over an area of the southern Pacific Ocean roughly the size of Western Europe, with a land area of and 16,000 inhabitants, forming the largest chain of atolls in the world. Its major islands are Anaa, Fakarava, Hao and Makemo., Nukutavake or Nukutuvake is an island in the Tuamotu group in French Polynesia. It lies 1125 km from Tahiti. The closest land is small Pinaki Atoll, located 15 km to the southeast. Vairaatea Atoll lies 38 km to the west of Nukutavake., The French overseas collectivities (or "COM"), like the French regions, are first-order administrative divisions of France. The COMs include some former French overseas territories and other French overseas entities with a particular status, all of which became COMs by constitutional reform on 28 March 2003. The COMs should not be confused with the overseas regions and overseas departments which have no particular status.
As integral parts of France, overseas collectivities are represented in the National Assembly, Senate and Economic and Social Council. Only one COM, Saint Martin, is part of the European Union and can vote to elect members of the European Parliament (MEP). The Pacific COMs use the CFP franc, a currency pegged to the euro, whereas the Atlantic COMs use the euro directly. 
As of 31 March 2011, there were five COMs:, French Polynesia  is an overseas collectivity of the French Republic; " (COM)", sometimes unofficially referred to as an overseas country; " (POM)". It is composed of 118 geographically dispersed islands and atolls stretching over an expanse of more than in the South Pacific Ocean. Its total land area is ., The Marshall Islands, officially the Republic of the Marshall Islands, is an island country located near the equator in the Pacific Ocean, slightly west of the International Date Line. Geographically, the country is part of the larger island group of Micronesia. The country's population of 53,158 people (at the 2011 Census) is spread out over 29 coral atolls, comprising 1,156 individual islands and islets. The islands share maritime boundaries with the Federated States of Micronesia to the west, Wake Island to the north, Kiribati to the south-east, and Nauru to the south. About 27,797 of the islanders (at the 2011 Census) live on Majuro, which contains the capital., 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)., The Pacific Ocean is the largest of the Earth's oceanic divisions. It extends from the Arctic Ocean in the north to the Southern Ocean (or, depending on definition, to Antarctica) in the south and is bounded by Asia and Australia in the west and the Americas in the east., Rangiroa (meaning "Vast Sky" in Tuamotuan) or Te Kokta ("Hyades" in Mori), is the largest atoll in the Tuamotus, and one of the largest in the world (although it is smaller than Kwajalein in the Marshall Islands and Huvadhu in the Maldives). It is part of the Palliser group. The nearest atoll is Tikehau, located only 12 km to the west. It is about 355 km northeast of Tahiti., Anaa, Nganaa-nui (or Ara-ura) is an atoll in the Tuamotu archipelago, in French Polynesia. It is located in the north-west of the archipelago, 350 km to the east of Tahiti. It is oval in shape, 29.5 km in length and 6.5 km wide, with a total land area of 38 km² and a population of 500. The atoll is made up by eleven small barren islands with deeper and more fertile soil than other atolls in the Tuamotus. The lagoon is shallow, without entrance, and formed by three main basins. Although it does not have any navigable access, the water of the lagoon renews by several small channels that can be crossed walking., Makatea , or Mangaia - te - vai - tamae , is a raised coral atoll in the northwestern part of the Tuamotus , which is a part of the French overseas collectivity of French Polynesia . It is located 79 km southwest from Rangiroa to the west of the Palliser group , which also is in French Polynesia . Makatea is surrounded by spectacular cliffs , rising to a plateau 80 m above sea level . This island is 7.5 km long , with a maximum width of 7 km in the south . It is 24 km² in area . Makatea is one of the only four islands of the Tuamotu Archipelago ( along with Nukutavake , Tikei , and Tepoto Nord ) that do not take the form of a typical atoll ., Corals are marine invertebrates in the class Anthozoa of phylum Cnidaria. They typically live in compact colonies of many identical individual polyps. The group includes the important reef builders that inhabit tropical oceans and secrete calcium carbonate to form a hard skeleton., Tikei, also known as Manu, Tikai and Tiku is an island in the Tuamotu group in French Polynesia. Tikei is not a typical Tuamotu atoll, but a separate island. The island is long, wide, and has a land area of . Its highest elevation is above sea level, 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., An atoll (, , , or ), sometimes called a coral atoll, is a ring-shaped coral reef including a coral rim that encircles a lagoon partially or completely. There may be coral islands/cays on the rim., Fakarava, Havaiki-te-araro, Havai'i or Farea is an atoll in the west of the Tuamotu group in French Polynesia. It is the second largest of the Tuamotu atolls. The nearest land is Toau Atoll, which lies to the northwest., A lagoon is a shallow body of water separated from a larger body of water by barrier islands or reefs. Lagoons are commonly divided into coastal lagoons and atoll lagoons. They have also been identified as occurring on mixed-sand and gravel coastlines. There is an overlap between bodies of water classified as coastal lagoons and bodies of water classified as estuaries. Lagoons are common coastal features around many parts of the world., A coral island is a type of island formed from coral detritus and associated organic material. They occur in tropical and sub-tropical areas, typically as part of coral reefs which have grown to cover a far larger area under the sea., Vairaatea is a small atoll of the Tuamotu group in French Polynesia. Geographically Vairaatea Atoll is part of the East-central subgroup of the Tuamotus, which includes Ahunui, Amanu, Fangatau, Hao and Nukutavake. Nukutavake, the closest land, lies to the east., Subject: makatea, Relation: part_of, Options: (A) animals (B) australia (C) belize barrier reef (D) body (E) caribbean (F) class (G) country (H) earth (I) europe (J) european parliament (K) european union (L) french (M) india (N) islands (O) national assembly (P) ocean (Q) order (R) palliser islands (S) part (T) phylum (U) ring (V) river (W) sky (X) society islands (Y) the americas (Z) the republic ([) tuamotus

A: palliser islands
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Q: Context: Purple is a color intermediate between blue and red. It is similar to violet, but unlike violet, which is a spectral color with its own wavelength on the visible spectrum of light, purple is a composite color made by combining red and blue. According to surveys In Europe and the U.S., purple is the color most often associated with royalty, magic, mystery and piety. When combined with pink, it is associated with eroticism, femininity and seduction., Thrombocytopenic purpura are purpura associated with a reduction in circulating blood platelets which can result from a variety of causes , such as kaposi sarcoma ., Scurvy is a disease resulting from a lack of vitamin C. Early symptoms include weakness, feeling tired, curly hair, and sore arms and legs. Without treatment, decreased red blood cells, gum disease, and bleeding from the skin may occur. As scurvy worsens there can be poor wound healing, personality changes, and finally death from infection or bleeding.
Scurvy is caused by not enough vitamin C in the diet. It typically takes at least a month of little to no vitamin C before symptoms occur. In modern times, it occurs most commonly in people with mental disorders, unusual eating habits, alcoholism, and old people who live alone. Other risk factors include intestinal malabsorption and dialysis. Humans and certain other animals require vitamin C in their diets to make the building blocks for collagen. Diagnosis is typically based on physical signs, X-rays, and improvement after treatment.
Treatment is with vitamin C supplements taken by mouth. Improvement often begins in a few days with complete recovery in a few weeks. Sources of vitamin C in the diet include citrus fruit and a number of vegetables such as tomatoes and potatoes. Cooking often decreases vitamin C in foods.
Scurvy is currently rare. It occurs more often in the developing world in association with malnutrition. Rates among refugees are reported at 5% to 45%. Scurvy was described as early as the time of ancient Egypt. It was a limiting factor in long distance sea travel, often killing large numbers of people. A Scottish surgeon in the Royal Navy, James Lind, was the first to prove it could be treated with citrus fruit in a 1753 publication. His experiments represented the first controlled trial. It took another 40 years before the British Navy began giving out lemon juice routinely., Purpura is a condition of red or purple discolored spots on the skin that do not blanch on applying pressure. The spots are caused by bleeding underneath the skin usually secondary to vasculitis or dietary deficiency of vitamin C (scurvy). They measure 0.31 cm (310 mm), whereas petechiae measure less than 3 mm, and ecchymoses greater than 1 cm., Skin is the soft outer covering of vertebrates. Other animal coverings, such as the arthropod exoskeleton have different developmental origin, structure and chemical composition. The adjective cutaneous means "of the skin" (from Latin "cutis", skin). In mammals, the skin is an organ of the integumentary system made up of multiple layers of ectodermal tissue, and guards the underlying muscles, bones, ligaments and internal organs. Skin of a different nature exists in amphibians, reptiles, and birds. All mammals have some hair on their skin, even marine mammals like whales, dolphins, and porpoises which appear to be hairless.
The skin interfaces with the environment and is the first line of defense from external factors. For example, the skin plays a key role in protecting the body against pathogens and excessive water loss. Its other functions are insulation, temperature regulation, sensation, and the production of vitamin D folates. Severely damaged skin may heal by forming scar tissue. This is sometimes discoloured and depigmented. The thickness of skin also varies from location to location on an organism. In humans for example, the skin located under the eyes and around the eyelids is the thinnest skin in the body at 0.5 mm thick, and is one of the first areas to show signs of aging such as "crows feet" and wrinkles. The skin on the palms and the soles of the feet is 4 mm thick and the back is 14 mm thick and is the thickest skin in the body. The speed and quality of wound healing in skin is promoted by the reception of estrogen., A petechia, plural petechiae, is a small (12 mm) red or purple spot on the skin, caused by a minor bleed from broken capillary blood vessels., Vasculitis (plural: "vasculitides") is a group of disorders that destroy blood vessels by inflammation. Both arteries and veins are affected. Lymphangitis is sometimes considered a type of vasculitis. Vasculitis is primarily caused by leukocyte migration and resultant damage., Bleeding, also known as hemorrhaging or haemorrhaging, is blood escaping from the circulatory system. Bleeding can occur internally, where blood leaks from blood vessels inside the body, or externally, either through a natural opening such as the mouth, nose, ear, urethra, vagina or anus, or through a break in the skin.
Hypovolemia is a massive decrease in blood volume, and death by excessive loss of blood is referred to as exsanguination. Typically, a healthy person can endure a loss of 1015% of the total blood volume without serious medical difficulties (by comparison, blood donation typically takes 810% of the donor's blood volume). The stopping or controlling of bleeding is called hemostasis and is an important part of both first aid and surgery., Subject: thrombocytopenic purpura, Relation: instance_of, Options: (A) 1 (B) adjective (C) animal (D) association (E) chemical (F) citrus (G) color (H) composition (I) condition (J) damage (K) diet (L) disease (M) environment (N) fruit (O) group (P) inflammation (Q) key (R) killing (S) magic (T) month (U) navy (V) number (W) opening (X) organ (Y) part (Z) person ([) production (\) quality (]) sea (^) skin (_) system (`) temperature (a) tissue (b) trial (c) vitamin (d) volume (e) water

A:
disease
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