instruction:
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).
question:
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
answer:
natural number


question:
Context: History.
Even after the emergence of the professional National Football League (NFL), college football remained extremely popular throughout the U.S. 
Although the college game has a much larger margin for talent than its pro counterpart, the sheer number of fans following major colleges provides a financial equalizer for the game, with Division I programs  the highest level  playing in huge stadiums, six of which have seating capacity exceeding 100,000. In many cases, college stadiums employ bench-style seating, as opposed to individual seats with backs and arm rests. This allows them to seat more fans in a given amount of space than the typical professional stadium, which tends to have more features and comforts for fans. (Only two stadiums owned by U.S. colleges or universities  Papa John's Cardinal Stadium at the University of Louisville and FAU Stadium at Florida Atlantic University  consist entirely of chairback seating.), The Sun Belt Conference is a collegiate athletic conference that has been affiliated with the NCAA's Division I since 1976. Originally a non-football conference, the Sun Belt began sponsoring football in 2001. Its football teams participate in the Division I Football Bowl Subdivision (FBS). The 12 member institutions of the Sun Belt are distributed primarily across the southern United States., The 2009 WKU Hilltoppers football ) team represented Western Kentucky University ( WKU ) during the 2009 NCAA Division I FBS football season . The team 's head coach was David Elson . WKU was an NCAA Division I FBS independent team in 2008 , before their move to the Sun Belt Conference in 2009 . 2009 was the first season where the Hilltoppers were eligible for a Sun Belt Conference championship and a postseason bowl game . The Hilltoppers played their home games at Houchens Industries -- L. T. Smith Stadium in Bowling Green , Kentucky . The Hilltopers were one of only two teams ( Eastern Michigan being the other ) to finish the 2009 season winless ., David Elson is an American football coach who is currently the defensive coordinator for Western Illinois University. Between 20032009 Elson was head coach of the WKU Hilltoppers football program representing Western Kentucky University (WKU). Elson oversaw the transition of WKU from a Football Championship Subdivision (formerly known as Division I-AA) to a Football Bowl Subdivision (formerly known as Division I-A) program, the highest division in college football; in his final season, the Hilltoppers joined the Sun Belt., An exhibition game (also known as a friendly, a scrimmage, a demonstration, a preseason game, a warmup match, or a preparation match, depending at least in part on the sport) is a sporting event whose prize money and impact on the player's or the team's rankings is either zero or otherwise greatly reduced. In team sports, matches of this type are often used to help coaches and managers select and condition players for the competitive matches of a league season or tournament. If the players usually play in different teams in other leagues, exhibition games offer an opportunity for the players to learn to work with each other. The games can be held between separate teams or between parts of the same team., A defensive coordinator is a member of the coaching staff of a gridiron football team who is in charge of the defense. Generally, along with the offensive coordinator, he represents the second level of command structure after the head coach. The defensive coordinator is generally in charge of managing all defensive players and assistant coaches, of developing a general defensive game plan, and of calling the plays for the defense during the game. At higher levels of football (college and professional), the defensive coordinator typically has a number of assistant coaches working under him who are responsible for the various defensive positions on the team (such as defensive line, linebackers, or defensive backs)., A county seat is an administrative center, seat of government, or capital city of a county or civil parish. The term is used in the United States, Canada, Romania, China and Taiwan. In the United Kingdom and Ireland, county towns have a similar function., Bowl eligibility in college football at the NCAA Division I FBS level is the standard through which teams become available for selection to participate in postseason bowl games. When a team achieves this state, it is described as "bowl-eligible"., The 2009 NCAA Division I FBS football season, or the college football season, began on September 2, 2009, progressed through the regular season and bowl season, and (aside from all-star exhibition games that followed the bowl games) concluded with the Bowl Championship Series (BCS) National Championship Game in Pasadena, California on January 7, 2010, featuring the Alabama Crimson Tide, defeating the Texas Longhorns for the National Championship by the score of 3721., Warren County is a county located in the U.S. state of Kentucky. As of 2014, the population was 120,460, making it the fifth-most populous county in Kentucky. The county seat is Bowling Green. Generally the county is dry, prohibiting the sale of alcohol, but retail alcohol sales are allowed in the "wet city" of Bowling Green; Warren County is classified as a moist county., Bowling Green is a city in and the county seat of Warren County, Kentucky, United States. As of 2015, its population of 63,616 made it the third most-populous city in the state after Louisville and Lexington; its metropolitan area had an estimated population of 165,732; and the combined statistical area it shares with Glasgow has an estimated population of 218,870., The Bowl Championship Series (BCS) was a selection system that created five bowl game match-ups involving ten of the top ranked teams in the National Collegiate Athletic Association (NCAA) Division I Football Bowl Subdivision (FBS) of American college football, including an opportunity for the top two teams to compete in the BCS National Championship Game. The system was in place for the 1998 through 2013 seasons and in 2014 was replaced by the College Football Playoff., Western Kentucky University is a public university in Bowling Green, Kentucky, United States. It was founded by the Commonwealth of Kentucky in 1906, though its roots reach back a quarter-century earlier. In the fall 2011 semester, enrollment was approximately 21,000., In North America, a bowl game is one of a number of post-season college football games that are primarily played by teams belonging to the NCAA's Division I Football Bowl Subdivision (FBS). Prior to 2002, bowl game statistics were not included in players' career totals and the games were mostly considered to be exhibition games involving a payout to participating teams. While teams once had to meet strict bowl eligibility requirements to receive an invitation to a bowl game, the number of bowl games has grown in recent years, climbing to 40 team-competitive games starting in the 201516 Bowl season. The increase in bowl games has necessitated the steady easing of the NCAA bowl eligibility rules since 2006, as teams with a losing record are often required to fill some of the 80 available bowl slots., A head coach, senior coach, or manager is a professional at training and developing athletes. They typically hold a more public profile and are paid more than other coaches. In some sports, the head coach is instead called the "manager", as in association football and professional baseball. In other sports such as Australian rules football, the head coach is generally termed a senior coach., Subject: 2009 wku hilltoppers football team, Relation: sport, Options: (A) american football (B) association football (C) bowling (D) climbing (E) football (F) national collegiate athletic association (G) sport (H) united kingdom
answer:
american football


question:
Context: Air Georgian Limited is a privately owned airline based at Toronto Pearson International Airport in Mississauga , Ontario , Canada . Its main business is its operation as Air Canada Express on a Tier III codeshare with Air Canada for scheduled services on domestic and trans - border routes . Its main base is Toronto Pearson International Airport , with hubs at Calgary International Airport and Montréal - Pierre Elliott Trudeau International Airport . It is an executive jet operator offering aircraft charter , aircraft maintenance , aircraft management , outsourced flight operations , flight crew scheduling , technical and airline pilot training services to major airlines , corporations and individuals at its hubs in Toronto ( CYYZ ) , Calgary ( CYYC ) , and Montreal ( CYUL ) . Air Georgian operates under the Commuter Operations Regulations Subpart 704 of the Canadian Aviation Regulations ( CAR 704 ) and has completed the IATA Operational Safety Audit . Air Georgian is a certified dealer of Pratt & Whitney ADAS systems and is the Canadian Service Ctr for the Hawker Premier . Air Georgian pilots are represented by an internal union , the Ontario Regional Employee Association ., Air Canada is the flag carrier and largest airline of Canada. The airline, founded in 1937, provides scheduled and charter air transport for passengers and cargo to 182 destinations worldwide. It is the world's tenth-largest passenger airline by fleet size, and is a founding member of the Star Alliance. Air Canada's corporate headquarters are located in Montreal, Quebec, while its largest hub is at Toronto Pearson International Airport. Air Canada had passenger revenues of CA$13.8 billion in 2015. The airline's regional service is Air Canada Express., Star Alliance is one of the world's largest global airline alliances. Founded on 14 May 1997, its current CEO is Mark Schwab and its headquarters is in Frankfurt am Main, Germany. , Star Alliance is the second largest global alliance by passenger count with 641.1 million, after SkyTeam (665.4 million) and ahead of Oneworld (557.4 million). Its slogan is "The Way The Earth Connects"., Subject: air georgian, Relation: airline_alliance, Options: (A) oneworld (B) star alliance
answer:

star alliance