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: Google is an American multinational technology company specializing in Internet-related services and products that include online advertising technologies, search, cloud computing, software, and hardware., Kurt Friedrich Gödel (April 28, 1906  January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor., Rajeev Motwani ( Hindi :   ; March 26 , 1962 -- June 5 , 2009 ) was a professor of Computer Science at Stanford University whose research focused on theoretical computer science . He was an early advisor and supporter of companies including Google and PayPal , and a special advisor to Sequoia Capital . He was a winner of the Gödel Prize in 2001 ., Sequoia Capital is an American venture capital firm. The firm is located in Menlo Park, California and mainly focuses on the technology industry. It has backed companies that now control $1.4 trillion of the combined stock market value. Sequoia manages multiple investment funds including funds specific to India, Israel, and China., PayPal Holdings, Inc. is an American company operating a worldwide online payments system that supports online money transfers and serves as an electronic alternative to traditional paper methods like checks and money orders. PayPal is one of the world's largest Internet payment companies. The company operates as a payment processor for online vendors, auction sites and other commercial users, for which it charges a fee., The Gödel Prize is an annual prize for outstanding papers in the area of theoretical computer science, given jointly by European Association for Theoretical Computer Science (EATCS) and the Association for Computing Machinery Special Interest Group on Algorithms and Computational Theory (ACM SIGACT). The award is named in honor of Kurt Gödel. Gödel's connection to theoretical computer science is that he was the first to mention the "P versus NP" question, in a 1956 letter to John von Neumann in which Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time., A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. , Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California, adjacent to Palo Alto and between San Jose and San Francisco. Its campus is one of the largest in the United States. Stanford also has land and facilities elsewhere., The Internet is the global system of interconnected computer networks that use the Internet protocol suite (TCP/IP) to link devices worldwide. It is a "network of networks" that consists of private, public, academic, business, and government networks of local to global scope, linked by a broad array of electronic, wireless, and optical networking technologies. The Internet carries an extensive range of information resources and services, such as the inter-linked hypertext documents and applications of the World Wide Web (WWW), electronic mail, telephony, and peer-to-peer networks for file sharing., John von Neumann (; December 28, 1903  February 8, 1957) was a Hungarian-American mathematician, physicist, inventor, computer scientist, and polymath. He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics., Subject: rajeev motwani, Relation: country_of_citizenship, Options: (A) academic (B) american (C) india
[EX A]: india

[EX Q]: Context: He Poos Clouds is the second album by the Canadian indie rock artist Owen Pallett, released on June 13, 2006, on Blocks Recording Club in Canada and Tomlab internationally., Spectrum , 14th Century is an EP by the Canadian musician Owen Pallett , the second issued under the name of his project Final Fantasy . Pallett describes the songs as `` fake field recordings '' from the fictional country of Spectrum , which is also the setting of his 2010 album Heartland . Several musicians who play on the EP are also members of the indie band Beirut ., Michael James Owen Pallett (born September 7, 1979) is a Canadian composer, violinist, keyboardist, and vocalist, who performs solo as Owen Pallett or, before 2010, under the name Final Fantasy. As Final Fantasy, he won the 2006 Polaris Music Prize for the album "He Poos Clouds"., A knight is a person granted an honorary title of "knighthood" by a monarch or other political leader for service to the monarch or country, especially in a military capacity. Historically, in Europe, knighthood was conferred upon mounted warriors. During the High Middle Ages, knighthood was considered a class of lower nobility. By the Late Middle Ages, the rank had become associated with the ideals of chivalry, a code of conduct for the perfect courtly Christian warrior. Often, a knight was a vassal who served as a fighter for a lord, with payment in the form of land holdings. The lords trusted the knights, who were skilled in battle on horseback. Since the early modern period, the title of knight is purely honorific, usually bestowed by a monarch, as in the British honours system, often for non-military service to the country. The modern female equivalent in the United Kingdom is Dame., A baronet (or ; abbreviated Bart or Bt) or the rare female equivalent, a baronetess (, or ; abbreviation "Btss"), is the holder of a baronetcy, a hereditary title awarded by the British Crown. The practice of awarding baronetcies was originally introduced in England in the 14th century and was used by James I of England in 1611 as a means of raising funds., An earl is a member of the nobility. The title is Anglo-Saxon in origin, akin to the Scandinavian form jarl, and meant "chieftain", particularly a chieftain set to rule a territory in a king's stead. In Scandinavia, it became obsolete in the Middle Ages and was replaced by duke ("hertig"/"hertug"/"hertog"). In later medieval Britain, it became the equivalent of the continental count (in England in the earlier period, it was more akin to a duke; in Scotland it assimilated the concept of mormaer). However, earlier in Scandinavia, "jarl" could also mean a sovereign prince. For example, the rulers of several of the petty kingdoms of Norway had the title of "jarl" and in many cases they had no less power than their neighbours who had the title of king. Alternative names for the "Earl/Count" rank in the nobility structure are used in other countries, such as Hakushaku during the Japanese Imperial era., The Canadian titles debate has been ongoing since the presentation to the Canadian House of Commons of the Nickle Resolution in 1917. This resolution marked the earliest attempt to establish a Canadian government policy requesting the sovereign not to grant knighthoods, baronetcies, and peerages to Canadians and set the precedent for later policies restricting Canadians from accepting titles from foreign countries. Dissatisfaction with the British honours system led to the gradual creation of a separate system for Canada., The inaugural edition of the Canadian Polaris Music Prize presented on September 18, 2006, at Toronto's Phoenix Concert Theatre. The winning album was Final Fantasy's "He Poos Clouds"., Subject: spectrum, Relation: follows, Options: (A) 13 (B) 14th century (C) 1611 (D) 18 (E) 1917 (F) 1979 (G) 2006 (H) a (I) a class (J) ages (K) album (L) alternative (M) and (N) as (O) become (P) born (Q) earl (R) era (S) fighter (T) he poos clouds (U) is (V) king (W) knight (X) land (Y) michael (Z) middle ages ([) modern (\) music (]) name (^) neighbours (_) obsolete (`) on (a) or (b) perfect (c) phoenix (d) polaris (e) policy (f) power (g) rank (h) released (i) resolution (j) second (k) second album (l) september (m) solo (n) the album (o) the concept (p) the second (q) this (r) title (s) united kingdom
[EX A]:
he poos clouds