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).

Input: Consider Input: 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

Output: natural number


Input: Consider Input: Context: The Mass of Paul VI also known as the Ordinary Form of the Roman Rite is a form of Mass in the Catholic Church, promulgated by Pope Paul VI in 1969 after the Second Vatican Council (19621965). It is now the ordinary or standard form of the Roman Rite Mass., The Eastern Orthodox Church, also known as the Orthodox Church, or officially as the Orthodox Catholic Church, is the second largest Christian church and one of the oldest current religious institutions in the world. The Eastern Orthodox Church teaches that it is the One, Holy, Catholic and Apostolic Church established by Jesus Christ in his Great Commission to the apostles. It practices what it understands to be the original Christian faith and maintains the sacred tradition passed down from the apostles., Constantinople  was the capital city of the Roman/Byzantine Empire (3301204 and 12611453), and also of the brief Latin (12041261), and the later Ottoman (14531923) empires. It was reinaugurated in 324 AD from ancient Byzantium as the new capital of the Roman Empire by Emperor Constantine the Great, after whom it was named, and dedicated on 11 May 330 AD., Constantine the Great (27 February 272 AD  22 May 337 AD), also known as Constantine I or Saint Constantine (in the Orthodox Church as Saint Constantine the Great, Equal-to-the-Apostles), was a Roman Emperor from 306 to 337 AD. Constantine was the son of Flavius Valerius Constantius, a Roman Army officer, and his consort Helena. His father became "Caesar", the deputy emperor in the west, in 293 AD. Constantine was sent east, where he rose through the ranks to become a military tribune under the emperors Diocletian and Galerius. In 305, Constantius was raised to the rank of "Augustus", senior western emperor, and Constantine was recalled west to campaign under his father in Britannia (Britain). Acclaimed as emperor by the army at Eboracum (modern-day York) after his father's death in 306 AD, Constantine emerged victorious in a series of civil wars against the emperors Maxentius and Licinius to become sole ruler of both west and east by 324 AD., The Roman Empire (Koine and Medieval Greek:   , tr. ) was the post-Roman Republic period of the ancient Roman civilization, characterized by government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, Africa and Asia. The city of Rome was the largest city in the world BC AD, with Constantinople (New Rome) becoming the largest around 500 AD, and the Empire's populace grew to an estimated 50 to 90 million inhabitants (roughly 20% of the world's population at the time). The 500-year-old republic which preceded it was severely destabilized in a series of civil wars and political conflict, during which Julius Caesar was appointed as perpetual dictator and then assassinated in 44 BC. Civil wars and executions continued, culminating in the victory of Octavian, Caesar's adopted son, over Mark Antony and Cleopatra at the Battle of Actium in 31 BC and the annexation of Egypt. Octavian's power was then unassailable and in 27 BC the Roman Senate formally granted him overarching power and the new title "Augustus", effectively marking the end of the Roman Republic., Jesus (; c. 4 BC  c. AD 30/33), also referred to as Jesus of Nazareth or Jesus Christ, was a Jewish preacher and religious leader who became the central figure of Christianity. Christians believe him to be the Son of God and the awaited Messiah (Christ) prophesied in the Old Testament.
Virtually all modern scholars of antiquity agree that Jesus existed historically, although the quest for the historical Jesus has produced little agreement on the historical reliability of the Gospels and on how closely the biblical Jesus reflects the historical Jesus. Jesus was a Galilean Jew who was baptized by John the Baptist and subsequently began his own ministry, preaching his message orally and often being referred to as "rabbi". He was arrested and tried by the Jewish authorities, and was crucified by the order of Pontius Pilate, the Roman prefect. Jesus debated fellow Jews on how to best follow God, performed healings, taught in parables and gathered followers. After his death, his followers believed he rose from the dead, and the community they formed eventually became the Christian Church., Sacred tradition or holy tradition is a theological term used in some Christian traditions, primarily those claiming apostolic succession such as the Eastern Orthodox, Oriental Orthodox, Assyrian, Catholic and Anglican traditions, to refer to the foundation of the doctrinal and spiritual authority of the Christian Church and of the scriptures., The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with more than 1.27 billion members worldwide. As one of the oldest religious institutions in the world, it has played a prominent role in the history of Western civilisation. Headed by the Bishop of Rome, known as the pope, its doctrines are summarised in the Nicene Creed. The Catholic Church is notable within Western Christianity for its sacred tradition and seven sacraments., Byzantium ("Byzántion") was an ancient Greek colony on the site that later became Constantinople, and later still Istanbul. Byzantium was colonised by the Greeks from Megara in ., The Eucharist (also called Holy Communion, the Lord's Supper, and other names) is a Christian rite that is considered a sacrament in most churches. According to the New Testament, It was instituted by Jesus Christ during his Last Supper. Giving his disciples bread and wine during the Passover meal, Jesus commanded his followers to "do this in memory of Me" while referring to the bread as "My Body" and the wine as "My Blood". Through the Eucharistic celebration Christians remember Christ's sacrifice of himself on the cross., In Christianity, the Great Commission is the instruction of the resurrected Jesus Christ to his disciples to spread his teachings to all the nations of the world. The most famous version of the Great Commission is in , where on a mountain in Galilee Jesus calls on his followers to baptize all nations in the name of the Father, the Son, and the Holy Spirit., The Tridentine Mass, also known as the Traditional Latin Mass (abbr. TLM) or the Extraordinary Form of the Roman Rite (Extraordinary Form for short), is the Roman Rite Mass which appears in typical editions of the Roman Missal published from 1570 to 1962. The most widely used Mass liturgy in the world until the introduction of the Mass of Paul VI in 1969, it is celebrated in ecclesiastical Latin., The Byzantine Empire, also referred to as the Eastern Roman Empire, was the continuation of the Roman Empire in the East during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, which had been founded as Byzantium). It survived the fragmentation and fall of the Western Roman Empire in the 5th century AD and continued to exist for an additional thousand years until it fell to the Ottoman Turks in 1453. During most of its existence, the empire was the most powerful economic, cultural, and military force in Europe. Both "Byzantine Empire" and "Eastern Roman Empire" are historiographical terms created after the end of the realm; its citizens continued to refer to their empire as the "Roman Empire" (tr. ), or "Romania", and to themselves as "Romans"., The Roman Rite ("Ritus Romanus") the most widespread liturgical rite in the Catholic Church, is one of the Latin rites used in the Western or Latin Church. The Roman Rite has been adapted over the centuries and its Eucharistic liturgy can be divided into three stages: the Pre-Tridentine Mass, Tridentine Mass and Mass of Paul VI., The term Pre-Tridentine Mass here refers to the variants of the liturgical rite of Mass in Rome before 1570, when, with his bull "Quo primum", Pope Pius V made the Roman Missal, as revised by him, obligatory throughout the Latin-Rite or Western Church, except for those places and congregations whose distinct rites could demonstrate an antiquity of 200 years or more., The Byzantine Rite , also known as the Greek Rite , Rite of Constantinople or Constantinopolitan Rite , is the liturgical rite currently used by the Eastern Orthodox Church and some Eastern Catholic churches . Its development began during the third century in Constantinople and it is now the second most - used rite in Christendom after the Roman Rite . The rite consists of the divine liturgies , canonical hours , forms for the administration of sacred mysteries ( sacraments ) and the numerous prayers , blessings and exorcisms developed by the Church of Constantinople . Also involved are the specifics of architecture , icons , liturgical music , vestments and traditions which have evolved over the centuries in the practice of this rite . Traditionally , the congregation stands throughout the whole service , and an iconostasis separates the sanctuary from the nave of the church . The faithful are very active in their worship , making frequent bows and prostrations , and feeling free to move about the temple ( church building ) during the services . Also , traditionally , the major clergy and monks neither shave nor cut their hair or beards . Scripture plays a large role in Byzantine worship , with not only daily readings but also many quotes from the Bible throughout the services . The entire psalter is read each week , and twice weekly during great lent . Fasting is stricter than in the West . On fast days , the faithful give up not only meat , but also dairy products , and on many fast days they also give up fish , wine and the use of oil in cooking . The rite observes four fasting seasons : Great Lent , Nativity Fast , Apostles ' Fast and Dormition Fast . In addition , most Wednesdays and Fridays throughout the year are fast days and many monasteries also observe Monday as a fast day ., A capital city (or simply capital) is the municipality exercising primary status in a country, state, province, or other region, usually as its seat of government. A capital is typically a city that physically encompasses the offices and meeting places of its respective government; the status as capital is often designated by its law or constitution. In some jurisdictions, including several countries, the different branches of government are located in different settlements. In some cases, a distinction is made between the official (constitutional) capital and the seat of government, which is in another place., Subject: byzantine rite, Relation: subclass_of, Options: (A) ancient greek (B) army (C) being (D) c (E) capital (F) christian church (G) christian rite (H) christianity (I) church (J) city (K) colony (L) community (M) conflict (N) country (O) creed (P) cross (Q) deputy (R) faith (S) force (T) government (U) greek (V) greeks (W) history (X) latin (Y) mass (Z) meal ([) memory (\) message (]) mountain (^) municipality (_) officer (`) order (a) own (b) pope (c) preacher (d) rabbi (e) rank (f) religious (g) religious leader (h) republic (i) rite (j) role (k) sacrament (l) saint (m) sea (n) seat (o) second (p) series (q) spread (r) term (s) time (t) tradition (u) western (v) wine (w) world

Output: christian rite


Input: Consider Input: Context: Engineers design materials, structures, and systems while considering the limitations imposed by practicality, regulation, safety, and cost. The word "engineer ("from the Latin "ingeniator"")" is derived from the Latin words "ingeniare" ("to contrive, devise") and "ingenium" ("cleverness"). The foundation education of an engineer is typically a 4-year bachelor's degree or in some countries, a master's degree in an engineering discipline plus 46 years peer-reviewed professional practice culminating in a project report or thesis. Engineers who seek a professional engineer license in N. America will be required to take further exams in ethics, law and professional practice., Gertrude S. Rogallo ( January 13 , 1914 -- January 28 , 2008 ) was one of the co-inventors of the flexible wing . These wings are now known as Rogallo wings . She and her husband , Francis Rogallo , invented the wing and obtained two United States patents on different versions of it in the early 1950s . Rogallo wings are commonly used today in kites , hang gliders and powered hang gliders ., A kite is traditionally a tethered heavier-than-air craft with wing surfaces that react against the air to create lift and drag. A kite consists of wings, tethers, and anchors. Kites often have a bridle to guide the face of the kite at the correct angle so the wind can lift it. A kite's wing also may be so designed so a bridle is not needed; when kiting a sailplane for launch, the tether meets the wing at a single point. A kite may have fixed or moving anchors. Untraditionally in technical kiting, a kite consists of tether-set-coupled wing sets; even in technical kiting, though, a wing in the system is still often called the kite., The Rogallo wing is a flexible type of airfoil. In 1948, Gertrude Rogallo, and her husband Francis Rogallo, a NASA engineer, invented a self-inflating flexible wing they called the Parawing, also known after them as the "Rogallo Wing" and flexible wing. NASA considered Rogallo's flexible wing as an alternative recovery system for the Mercury and Gemini space capsules, and for possible use in other spacecraft landings, but the idea was dropped from Gemini in 1964 in favor of conventional parachutes., Francis Melvin Rogallo (January 27, 1912  September 1, 2009) was an American aeronautical engineer inventor born in Sanger, California, U.S.; he is credited with the invention of the Rogallo wing, or "flexible wing", a precursor to the modern hang glider and paraglider. His patents were ranged over mechanical utility patents and ornamental design patents for wing controls, airfoils, target kite, flexible wing, and advanced configurations for flexible wing vehicles., Subject: gertrude rogallo, Relation: occupation, Options: (A) engineer (B) guide (C) master (D) peer


Output: engineer