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).

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
natural number

Context: Razadarit ( Burmese :  ( jàzad ) ; Thai :  , rtgs : Rachathirat ; Sanskrit :  Rjdhirja `` King of Kings '' ; 1368 -- 1421 ) was the ninth king of the Hanthawaddy Pegu Kingdom in Burma from 1384 to 1421 . Considered one of the greatest kings in Burmese history , he successfully reunified all three Mon - speaking regions of southern Burma ( Myanmar ) , and fended off major assaults by the Burmese - speaking northern Kingdom of Ava ( Inwa ) in the Forty Years ' War ( 1385 -- 1424 ) . When Razadarit became the ruler of Hanthawaddy in 1384 , the 16 - year - old boy - king held just the Pegu ( Bago ) province while the other two major Mon - speaking regions of the Irrawaddy delta and Martaban ( Mottama ) were in open rebellion . By his sheer will and military leadership , he defeated Ava 's first wave of invasions in the 1380s , and by 1390 , was able to reunify all three Mon regions . During the second half of the Forty Years ' War , he met Minkhaung I of Ava and his son Minyekyawswa head - on in Lower Burma , Upper Burma , and Arakan . Razadarit is remembered as a complex figure : a brave military commander , who defeated Minkhaung I in single combat , and kept the kingdom independent ; an able administrator who organized the kingdom ; and a ruthless paranoid figure , who drove his first love Talamidaw to commit suicide , and ordered the execution of their innocent son Bawlawkyantaw . The king died of injuries received in hunting a wild elephant in 1421 at age 53 . He left a strong , independent kingdom for the Mon people that would prosper for another 118 years . Three of his offspring later became rulers of Hanthawaddy . His daughter Shin Sawbu was the first and only female regent , and one of the most enlightened rulers in Burmese history . The story of Razadarit 's reign is recorded in a classic epic that exists in Mon , Burmese and Thai language forms . Razadarit 's struggles against Minkhaung I and Minyekyawswa are retold as classic stories of legend in Burmese popular culture ., The Kingdom of Pagan (, lit. "Pagan Period"; also commonly known as the Pagan Dynasty and the Pagan Empire) was the first kingdom to unify the regions that would later constitute modern-day Burma (Myanmar). Pagan's 250-year rule over the Irrawaddy valley and its periphery laid the foundation for the ascent of Burmese language and culture, the spread of Burman ethnicity in Upper Burma, and the growth of Theravada Buddhism in Burma and in mainland Southeast Asia., The Ava Kingdom was the dominant kingdom that ruled upper Burma (Myanmar) from 1364 to 1555. Founded in 1364, the kingdom was the successor state to the petty kingdoms of Myinsaing, Pinya and Sagaing that had ruled central Burma since the collapse of the Pagan Kingdom in the late 13th century., Myanmar, officially the Republic of the Union of Myanmar and also known as Burma, is a sovereign state in South East Asia bordered by Bangladesh, India, China, Laos and Thailand. About one third of Myanmar's total perimeter of 5,876 km (3,651 miles), forms an uninterrupted coastline of 1,930 km (1,200 miles) along the Bay of Bengal and the Andaman Sea. The country's 2014 census revealed a much lower population than expected, with 51 million people recorded. Myanmar is 676,578 square kilometres (261,227 sq mi) in size. Its capital city is Naypyidaw and its largest city is Yangon (Rangoon)., Subject: razadarit, Relation: religion, Options: (A) india (B) theravada
theravada

Context: The Pauli exclusion principle is the quantum mechanical principle that states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. In the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: "n", the principal quantum number, ', the angular momentum quantum number, "m", the magnetic quantum number, and "m", the spin quantum number. For example, if two electrons reside in the same orbital, and if their "n", ', and "m" values are the same, then their "m" must be different, and thus the electrons must have opposite half-integer spins of 1/2 and -1/2. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin-statistics theorem of 1940., Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 GHz to as low as 3 kHz, though some definitions describe waves above 1 or 3 GHz as microwaves, or include waves of any lower frequency. At 300 GHz, the corresponding wavelength is , and at 3 kHz is . Like all other electromagnetic waves, they travel at the speed of light. Naturally occurring radio waves are generated by lightning, or by astronomical objects. , A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the elemental (baryonic) mass of the universe., Red is the color at the longer-wavelengths end of the spectrum of visible light next to orange, at the opposite end from violet. Red color has a predominant light wavelength of roughly 620740 nanometers.
Light with a longer wavelength than red but shorter than terahertz radiation and microwave is called infrared., Ultraviolet (UV) is an electromagnetic radiation with a wavelength from 10 nm (30 PHz) to 400 nm (750 THz), shorter than that of visible light but longer than X-rays. UV radiation constitutes about 10% of the total light output of the Sun, and is thus present in sunlight. It is also produced by electric arcs and specialized lights such as mercury-vapor lamps, tanning lamps, and black lights. Although it is not considered an ionizing radiation because its photons lack the energy to ionize atoms, long-wavelength ultraviolet radiation can cause chemical reactions and causes many substances to glow or fluoresce. Consequently, biological effects of UV are greater than simple heating effects, and many practical applications of UV radiation derive from its interactions with organic molecules., Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its periodthe time interval between beatsis half a second (that is, 60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio (sound) signals, radio waves, and light., The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on 5 November 1888., Microwaves are a form of electromagnetic radiation with wavelengths ranging from one meter to one millimeter; with frequencies between and . This broad definition includes both UHF and EHF (millimeter wave) bands, and various sources use different boundaries. In all cases, microwaves include the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum, with RF engineering often restricting the range between 1 and 100 GHz (300 and 3 mm). Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, K, K, or K band, or by similar NATO or EU designations., In physics, energy is the property that must be transferred to an object in order to perform work on  or to heat  the object, and can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton., A chemical element or element is a species of atoms having the same number of protons in their atomic nuclei (i.e. the same atomic number, "Z"). There are 118 elements that have been identified, of which the first 94 occur naturally on Earth with the remaining 24 being synthetic elements. There are 80 elements that have at least one stable isotope and 38 that have exclusively radioactive isotopes, which decay over time into other elements. Iron is the most abundant element (by mass) making up Earth, while oxygen is the most common element in the Earth's crust., Johannes ( Janne ) Robert Rydberg ( November 8 , 1854 -- December 28 , 1919 ) was a Swedish physicist mainly known for devising the Rydberg formula , in 1888 , which is used to predict the wavelengths of photons ( of light and other electromagnetic radiation ) emitted by changes in the energy level of an electron in a hydrogen atom . The physical constant known as the Rydberg constant is named after him , as is the Rydberg unit . Excited atoms with very high values of the principal quantum number , represented by n in the Rydberg formula , are called Rydberg atoms . Rydberg 's anticipation that spectral studies could assist in a theoretical understanding of the atom and its chemical properties was justified in 1913 by the work of Niels Bohr ( see hydrogen spectrum ) . An important spectroscopic constant based on a hypothetical atom of infinite mass is called the Rydberg ( R ) in his honour . He was active at Lund University , Sweden , for all of his working life . The crater Rydberg on the Moon and asteroid 10506 Rydberg are named in his honour . There is a pub night held in Rydberg 's honour every Wednesday at the Department of Physics at Lund University ., A proton is a subatomic particle, symbol or , with a positive electric charge of +1"e" elementary charge and mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collectively referred to as "nucleons". One or more protons are present in the nucleus of every atom. They are a necessary part of the nucleus. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol Z). Since each element has a unique number of protons, each element has its own unique atomic number. The word "proton" is Greek for "first", and this name was given to the hydrogen nucleus by Ernest Rutherford in 1920. In previous years, Rutherford had discovered that the hydrogen nucleus (known to be the lightest nucleus) could be extracted from the nuclei of nitrogen by atomic collisions. Protons were therefore a candidate to be a fundamental particle, and hence a building block of nitrogen and all other heavier atomic nuclei., An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are very small; typical sizes are around 100 picometers (a ten-billionth of a meter, in the short scale)., The electron is a subatomic particle, symbol or , with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, "". As it is a fermion, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all matter, electrons have properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a larger De Broglie wavelength for a given energy., Hydrogen is a chemical element with chemical symbol H and atomic number 1. With an atomic weight of , hydrogen is the lightest element on the periodic table. Its monatomic form (H) is the most abundant chemical substance in the Universe, constituting roughly 75% of all baryonic mass. Non-remnant stars are mainly composed of hydrogen in the plasma state. The most common isotope of hydrogen, termed "protium" (name rarely used, symbol H), has one proton and no neutrons., Johannes (Janne) Robert Rydberg (8 November 1854  28 December 1919) was a Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to predict the wavelengths of photons (of light and other electromagnetic radiation) emitted by changes in the energy level of an electron in a hydrogen atom., In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-, and gamma radiation., Infrared radiation, or simply infrared or IR, is electromagnetic radiation (EMR) with longer wavelengths than those of visible light, and is therefore invisible, although it is sometimes loosely called infrared light. It extends from the nominal red edge of the visible spectrum at 700 nanometers (frequency 430 THz), to 1000000 nm (300 GHz) (although people can see infrared up to at least 1050 nm in experiments). Most of the thermal radiation emitted by objects near room temperature is infrared. Like all EMR, IR carries radiant energy, and behaves both like a wave and like its quantum particle, the photon. , The human eye is an organ which reacts to light and pressure. As a sense organ, the mammalian eye allows vision. Human eyes help provide a three dimensional, moving image, normally coloured in daylight. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth. The human eye can differentiate between about 10 million colors and is possibly capable of detecting a single photon., Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400700 nanometres (nm), or 4.00 × 10 to 7.00 × 10 m, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). This wavelength means a frequency range of roughly 430750 terahertz (THz)., Subject: johannes rydberg, Relation: date_of_birth, Options: (A) 1 (B) 10 (C) 100 (D) 120 (E) 1888 (F) 1925 (G) 1940 (H) 2 (I) 3 (J) 30 (K) 300 (L) 38 (M) 4 (N) 400 (O) 430 (P) 5 november 1888 (Q) 620 (R) 700 (S) 740 (T) 75 (U) 8 (V) 8 november 1854 (W) 80 (X) 94

8 november 1854