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The Lenstra β Pomerance β Wagstaff conjecture asserts that there are infinitely many Mersenne primes and predicts their order of growth . | Carl Pomerance , Samuel S. Wagstaff Jr. and Hendrik Lenstra developed a formula which they think should say about how many Mersenne primes there are under a given number . | [] |
A Soviet journalist dubbed her " The ' Iron Lady " , a nickname that became associated with her uncompromising politics and leadership style . | She was often known by the nickname , " The Iron Lady " , given to her by a Soviet journalist . | [] |
She studied chemistry at Somerville College , Oxford , and worked briefly as a research chemist , before becoming a barrister . | She took chemistry at Somerville College , Oxford . | [] |
Roberts became President of the Oxford University Conservative Association in 1946 . | She was already interested in politics , and became President of the Oxford University Conservative Association in 1946 . | [] |
She was influenced at university by political works such as Friedrich Hayek 's " The Road to Serfdom " ( 1944 ) , which condemned economic intervention by government as a precursor to an authoritarian state . | Roberts read political works such as Friedrich von Hayek 's " The Road to Serfdom " ( 1944 ) , which condemned economic intervention by government because it gave too much power to the state . | [] |
After graduating , Roberts moved to Colchester in Essex to work as a research chemist for BX Plastics near Manningtree . | After graduating , Roberts moved to Colchester in Essex to work as a research chemist for BX Plastics . | [] |
She was the longest-serving British prime minister of the 20th century and the first woman to hold that office . | She had the second longest single prime ministerial term in history . | [] |
It was a large complex of two wildfires , the River Fire and Ranch Fire , which burned in Mendocino , Lake , Colusa , and Glenn Counties in the U.S. State of California , with the Ranch Fire being California 's single-largest recorded wildfire . | The Mendocino Complex Fire is a large complex of two wildfires , the River Fire and Ranch Fire , currently burning in Mendocino , Lake , and Colusa counties in the U.S. state of California . | [] |
The Mendocino Complex Fire was the largest recorded fire complex in California history . | It is th largest fire complex in recorded US history . | [] |
The Ranch Fire burned eight miles northeast of Ukiah , and the River Fire burned six miles north of Hopland , to the south of the larger Ranch Fire . | The Ranch Fire is currently burning eight miles northeast of Ukiah and the River Fire is currently burning six miles north of Hopland . | [] |
First reported on July 27 , 2018 , both fires burned a combined total of 459,123 acre , before they were collectively 100 % contained on September 18 ; the Ranch Fire alone burned 410,203 acre , surpassing the Thomas Fire to become the single-largest modern California wildfire . | The fires were first reported on July 27 , 2018 . <SEP> Both fires have burned a combined total of 302,086 acre . | [] |
By late August 7 , the fire complex was 34 % contained . | By the night of August 7 , the fires were collectively 34 % contained . | [] |
Of the two fires , the Ranch and River Fires , the River Fire was 78 % contained , while Ranch Fire was only 20 % contained , with flames on the northern flank still pushing towards Snow Mountain Wilderness . | The River Fire was 78 % contained and the Ranch Fire was only 20 % contained , with flames on the northern flank still actively pushing towards Snow Mountain Wilderness . | [] |
The River and Ranch Fires impacted communities along the Mendocino and Lake County borders , causing the evacuations of Lakeport , Kelseyville , Lucerne , Upper Lake , Nice , Saratoga Springs , Witter Springs , Potter Valley , Finley , parts of Hopland , and the tribal communities of Hopland Rancheria and Big Valley Rancheria . | The River and Ranch Fires have affected communities along the Mendocino and Lake County borders . <SEP> People in these areas had to be evacuated : Lakeport , Kelseyville , Lucerne , Upper Lake , Nice , Saratoga Springs , Witter Springs , Potter Valley , and Finley , parts of Hopland , and the tribal communities Hopland Rancheria and Big Valley Rancheria . | [] |
The Annisquam Bridge is a historic bridge in Annisquam , Massachusetts , a village within the city of Gloucester . | Annisquam Bridge is a historic bridge in Annisquam , Massachusetts , a village within the city of Gloucester . | [] |
The bridge was built in 1861 to replace an earlier 1847 bridge that crossed Lobster Cove . | Built in 1861 to cross Lobster Cove , the bridge was added to the National Register of Historic Places in 1983 . | [] |
It is a wooden pile bridge , a type of which only two others were found in New England as part of a c . 1979 survey . | It is a wood pile bridge . | [] |
Ann Njogu is a Kenyan activist . | Ann Njogu is a lawyer and activist from Kenya . | [] |
In 2010 , she was the director of the Centre for Rights Education and Awareness , which among other things documented sexual- and gender-based violence after the Kenyan general election in December 2007 . | Njogu is the director of the Centre for Rights Education and Awareness . | [] |
In addition to her work on sexual and gender violence , Njogu was the Co-Chair of the Multi-Sectoral Committee on Constitutional Reform , the Co-Chair of the Joint Dialogue Forum on Constitutional Reform , and a delegate to the Bomas National Conference on Constitutional Reforms . | Njogu was also a leader in the Multi-Sectoral Committee on Constitutional Reform , the Joint Dialogue Forum on Constitutional Reform , and a delegate to the Bomas National Conference on Constitutional Reforms . | [] |
She was also a drafter of and lobbyist for Kenya β s Sexual Offences Act , which became law in 2006 . | Njogu helped write the law for Kenya β s Sexual Offenses Act . <SEP> This act became law in 2006 . | [] |
In 2007 , she was attacked and arrested by state security forces for demanding that Members of Parliament review their salaries , which were very large despite Kenya 's poverty . | In 2007 , Njogu wanted a review of the salaries of the members of parliament . | [] |
She and the others who were arrested filed a Constitutional reference popularly known as " Ann Njogu and others versus the State , " which was successful in limiting the time a Kenyan citizen could be held in custody to 24 hours . | Njoogu and the others who were arrested filed a Constitutional reference . <SEP> It was called " Ann Njogu and others versus the State . " | [] |
In 2008 , she was a co-convenor of the Civil Society Congress , which worked to improve politics after the violence in the wake of the December 2007 Kenyan elections . | In 2008 , Njokgu helped to start the Civil Society Congress . | [] |
In 2008 she was beaten and sexually molested by the police when they arrested her and others for suggesting corruption might have occurred in the sale of the Grand Regency Hotel . | In 2008 Njogu said there might be corrupttion in the sale of the Grand Regency Hotel . | [] |
Njogu received a 2010 International Women of Courage award . | Njogu received a 2010 International Women of Courage Award from the U.S. Department of State . | [] |
Nevada City ( originally , Ustumah , a Nisenan village ; later , Nevada , Deer Creek Dry Diggins , and Caldwell 's Upper Store ) is the county seat of Nevada County , California , United States , located 60 mi northeast of Sacramento , 84 mi southwest of Reno and 147 mi northeast of San Francisco . | Nevada City ( originally , Ustumah , a Nisenan Maidu village ; later , Nevada , Deer Creek Dry Diggins , and Caldwell 's Upper Store ) is the county seat of Nevada County , California , United States . | [] |
The population was 3,068 as of the 2010 Census . | At the 2010 United States Census , the population was 3,068 . | [] |
( ] ) is the largest industrial conglomerate in Turkey , and only company in the country to enter the Fortune Global 500 list . | Koc Μ§ Holding , the largest Turkish industrial conglomerate and Turkey 's largest group of companies . <SEP> Koc Μ§ Holding is the only Turkish company to be listed in Fortune Global 500 list . | [] |
The first firm that was to become Koc Μ§ Holding was established in 1926 by Vehbi Koc Μ§ . | Koc Μ§ Holding was founded in 1926 by Vehbi Koc Μ§ . | [] |
The company , headquartered in Nakkas Μ§ tepe , Istanbul . | Its headquarters in Nakkas Μ§ tepe , Istanbul . | [] |
Otto Frederick Warmbier ( December 12 , 1994 β June 19 , 2017 ) was an American college student who was imprisoned in North Korea in 2016 . | Otto Frederick Warmbier ( ; December 12 , 1994 β June 19 , 2017 ) was an American college student . <SEP> He was imprisoned in North Korea from March 2016 to June 2017 after being convicted of " hostile acts " against the country . | [] |
In June 2017 , he was released by North Korea in a vegetative state and died soon afterward . | Warmbier fell into a coma in North Korea and was released in June 2017 , after nearly 18 months in North Korea . | [] |
North Korean authorities did not disclose his medical condition until June 2017 , when they announced he had fallen into a coma as a result of botulism and a sleeping pill . | According to North Korean authorities , Warmbier 's coma was a result of botulism and a sleeping pill , but U.S. physicians cast doubt on that claim . | [] |
He was taken to University of Cincinnati Medical Center for immediate evaluation and treatment . | Warmbier arrived in Cincinnati on June 13 and was taken to University of Cincinnati Medical Center for immediate evaluation and treatment . | [] |
The Afar Triangle ( also called the Afar Depression ) is a geological depression caused by the Afar Triple Junction , which is part of the Great Rift Valley in East Africa . | The Afar Triangle ( or Afar Depression ) is a low area bordering on the Red Sea . <SEP> It is part of the Great Rift Valley in East Africa . | [] |
The Depression overlaps the borders of Eritrea , Djibouti and the entire Afar Region of Ethiopia ; and it contains the lowest point in Africa , Lake Asal , Djibouti , at 155 m ( or 509 ft ) below sea level . | The area overlaps the borders of Eritrea , Djibouti and the entire Afar region of Ethiopia . <SEP> The Triangle includes the lowest point in Africa , Lake Asal , Djibouti , at 155 m ( or 509 ft ) below sea level . | [] |
These sites have produced specimens of the earliest ( fossil ) hominins and of human tool culture , as well as many fossils of various flora and fauna . | Important fossil specimens of the earliest hominins have been found in this area . <SEP> These sites have produced specimens of the earliest ( fossil ) hominins and of human tool culture , as well as many fossils of flora and fauna . | [] |
The region has disclosed fossil specimens of the very earliest hominins , that is , the earliest of the human clade ; and it is thought by some paleontologists to be the cradle of the evolution of humans , see Middle Awash , Hadar . | The area is thought by some paleontologists to be the cradle of the evolution of humans . | [] |
Many important fossil localities exist in the Afar region , including the Middle Awash region and the sites of Hadar , Dikika , and Woranso-Mille . | Many important fossil localities exist in the Afar region . | [] |
He was the youngest child of his father Charles Emmanuel III of Sardinia and E Μ lisabeth The Μ re Μ se of Lorraine . | Chablais was born at the Palace of Venaria and was the was the youngest child of Charles Emmanuel III of Sardinia and Elisabeth Therese of Lorraine . | [] |
His maternal cousins included the future Queen of Naples and the famous " Marie Antoinette " . | His maternal cousin 's included the future Queen of Naples and the famous " Marie Antoinette " . | [] |
His uncle Francis I , Holy Roman Emperor proposed his daughter Archduchess Maria Christina of Austria as a prospective wife but the marriage between the two never materialised . | His uncle Francis I , Holy Roman Emperor wanted him to marry his daughter daughter Maria Christina of Austria as but it never happened . | [] |
In 1753 his father gave what is now the Palazzo Chiablese as his personal residence . | In 1753 his father gave what is now the Palazzo Chiablese as a home . | [] |
In 1763 his father granted him the Duchy of Chablais ( the prince having been styled Duke of Chablais since birth ) , with the subsidiary lands of Cureggio , Trino , Dezan , Crescentino , Riva di Chieri , Well , Ghemme Pollenzo Tricerro , and Apertole Centallo . | His father gave him the title of Duke of Chablais in 1763 . | [] |
He was born in Lisbon . | Dura Μ o was born in Lisbon . | [] |
Joaquim Manuel Dura Μ o ( 25 October 1930 β 21 May 2015 ) was a Portuguese chess player . | He died on 21 May 2015 , aged 84 . | [] |
For 40 years the band have been supported by their famous mascot , " Eddie " , who has appeared on almost all of their album and single covers , as well as in their live shows . | The mascot of the band is Eddie , a monster , who is present in the concerts and also appears on the album covers . | [] |
Their sixteenth studio album , " The Book of Souls " , was released on 4 September 2015 to similar success . | The band 's newest album , " The Book of Souls " , was released in the year 2015 . | [] |
Despite little radio or television support , Iron Maiden are considered one of the most successful heavy metal bands in history , with " The Sunday Times " reporting in 2017 that the band have sold over 100 million copies of their albums worldwide . | Iron Maiden has sold over 100 million copies of their albums world wide . | [] |
The racial makeup of the city was 98.9 % White and 1.1 % African American . | The racial makeup of the city was 98.9 % White and 1.1 % African-American . | [] |
The racial makeup of the city was 99.11 % White , and 0.89 % from two or more races . | The racial makeup of the city White and 0.89 % from two or more races . | [] |
The Cascade Volcanoes ( also known as the Cascade Volcanic Arc or the Cascade Arc ) are a number of volcanoes in a volcanic arc in western North America , extending from southwestern British Columbia through Washington and Oregon to Northern California , a distance of well over 700 mi . | The Cascade Volcanic Arc ( also known as the Cascade volcanoes or the Cascade Arc ) is a major range of volcanoes in southwestern British Columbia , Washington , Oregon and in northern California . | [] |
The Cascade Arc includes nearly 20 major volcanoes , among a total of over 4,000 separate volcanic vents including numerous stratovolcanoes , shield volcanoes , lava domes , and cinder cones , along with a few isolated examples of rarer volcanic forms such as tuyas . | It includes about 20 major volcanoes , among a total of over 4,000 separate volcanic vents . | [] |
Twelve volcanoes in the arc are over 10000 ft in elevation , and the two highest , Mount Rainier and Mount Shasta , exceed 14000 ft . | Twelve volcanoes in the arc are over 10,000 ft ( 3,000 m ) in height , and the two highest , Mount Rainier and Mount Shasta , are over 14,000 ft ( 4,300 m ) . | [] |
By volume , the two largest Cascade volcanoes are the broad shields of Medicine Lake Volcano and Newberry Volcano , which are about 145 cumi and 108 cumi respectively . | By volume , the two largest Cascade volcanoes are the broad shields of Medicine Lake Volcano and Newberry Volcano , which are about 145 mi3 ( 600 km3 ) and 108 mi3 ( 450 km3 ) respectively . | [] |
Volcanism in the arc began about 37 million years ago ; however , most of the present-day Cascade volcanoes are less than 2,000,000 years old , and the highest peaks are less than 100,000 years old . | The volcanism in the arc began about 37 million years ago , but most of the present-day Cascade volcanoes are less than 2 million years old . | [] |
Two most recent were Lassen Peak in 1914 to 1921 and a major eruption of Mount St. Helens in 1980 . | The most recent major catastrophic eruption in the arc was at Mount St. Helens on May 18 , 1980 . | [] |
Mary of Teck ( Victoria Mary Augusta Louise Olga Pauline Claudine Agnes ; 26 May 1867 β 24 March 1953 ) was Queen consort of the United Kingdom and the British Dominions and Empress consort of India as the wife of King George V. | Mary of Teck ( Victoria Mary Augusta Louise Olga Pauline Claudine Agnes ; 26 May 1867 β 24 March 1953 ) was the queen consort of King George V of the United Kingdom , who was also Emperor of India . | [] |
She was informally known as " May " , after her birth month . | Within her family , she was given the nickname " May " . | [] |
Princess Victoria Mary ( " May " ) of Teck was born on 26 May 1867 at Kensington Palace , London , in the same room where Queen Victoria , her first cousin once removed , was born 48 years earlier . | Princess Mary was born at Kensington Palace in London on 26 May 1867 . | [] |
Her mother was Princess Mary Adelaide of Cambridge , a granddaughter of King George III and the third child and younger daughter of Prince Adolphus , Duke of Cambridge , and Princess Augusta of Hesse-Kassel . | Her mother was Princess Mary Adelaide , a daughter of Prince Adolphus , Duke of Cambridge , and a granddaughter of King George III . | [] |
Her father , the Duke of Teck , had no inheritance or wealth and carried the lower royal style of Serene Highness because his parents ' marriage was morganatic . | Her father was Francis , Duke of Teck . | [] |
Prince Francis was deeply in debt and moved his family abroad with a small staff in 1883 , in order to economise . | Due to her parent 's financial troubles , Princess Mary spent much of her early life abroad in order to economise , the Tecks returned to London in 1883 , living at White Lodge in Richmond Park . | [] |
In December 1891 , May and Albert Victor were engaged . | In 1891 , Princess Mary , who was liked by Queen Victoria , became engaged to her double second cousin once removed Prince Albert Victor , the eldest son of Prince Albert Edward , Prince of Wales . | [] |
However , Albert Victor died six weeks later , in a recurrence of the worldwide 1889 β 90 influenza pandemic , before the date was fixed for their wedding . | However , a few weeks before the wedding , Prince Albert Victor died of influenza . | [] |
Albert Victor 's brother , Prince George , Duke of York , now second in line to the throne , evidently became close to May during their shared period of mourning , and Queen Victoria still favoured May as a suitable candidate to marry a future king . | Nevertheless , Queen Victoria still favoured Mary as a royal bride , and therefore arranged for her to marry Albert Victor 's brother , Prince George , created Duke of York . <SEP> This put his brother , Prince Albert , Duke of York , in his place as King George VI . | [] |
May married Prince George , Duke of York , in London on 6 July 1893 at the Chapel Royal , St James 's Palace . | They were married at St. James 's Palace , London , on 6 July 1893 . | [] |
On 6 May 1910 , Edward VII died . | In 1910 , Edward VII died , and Prince George ascended the throne as George V. Mary thus became Queen . | [] |
In 1935 , King George V and Queen Mary celebrated their silver jubilee , with celebrations taking place throughout the British Empire . | In 1935 , King George celebrated his Silver Jubilee , commemorating 25 years of his reign , and Queen Mary accompanied him during the official tours and visits that took place . | [] |
George V died on 20 January 1936 , after his physician , Lord Dawson of Penn , gave him an injection of morphine and cocaine that may have hastened his death . | In 1936 , King George V died . <SEP> His death was shortened by an injection of morphine and cocaine , administered by his doctor . | [] |
Queen Mary 's eldest son ascended the throne as Edward VIII . | Queen Mary supported her son , now King Edward VIII , during his reign . | [] |
A refrain ( from Vulgar Latin " refringere " , " to repeat " , and later from Old French " refraindre " ) is the line or lines that are repeated in music or in poetry ; the " chorus " of a song . | A refrain is a verse or group of verses that is repeated at intervals in a piece of music or poetry . <SEP> The word comes from Vulgar Latin word " refringere " , and later from Old French " refraindre " , both of which mean " to repeat " . | [] |
In popular music , the refrain or chorus may contrast with the verse melodically , rhythmically , and harmonically ; it may assume a higher level of dynamics and activity , often with added instrumentation . | It usually has a higher level of dynamics and activity , often with added instrumentation . <SEP> In popular music , the chorus contrasts with the verse , which leads into it , while the bridge contrasts with and leads into both . | [] |
The film stars Hrithik Roshan and Mrunal Thakur . | The movie stars Hrithik Roshan as Kumar and Mrunal Thakur . | [] |
The soundtrack is by Ajay-Atul and movie is co-produced by Sajid Nadiadwala . | The soundtrack was composed by Ajay-Atul . <SEP> The movie was co-produced by Ahmed khan | [] |
The film was shot in Ramnagar Fort and in Sambhar Lake Town which was shown as Kota , Rajasthan . | The movie was also shot for 10 days in Sambhar Lake Town which will be shown as Kota , Rajasthan . | [] |
The film was theatrically released in India on 12 July 2019 and received mixed reviews . | " Super 30 " was released on 12 July 2019 . | [] |
" Super 30 " was Phantom Film 's last production . | Super 30 will be Phantom Films 's last production . <SEP> " Super 30 " will be the last movie of Phantom Films . | [] |
Saxe-Weimar-Eisenach was created as a duchy in 1809 by the merger of the Ernestine duchies of Saxe-Weimar and Saxe-Eisenach , which had been in personal union since 1741 . | The Duchy of Saxe-Weimar-Eisenach was created in 1809 when the Ernestine duchies of Saxe-Weimar and Saxe-Eisenach were formally joined into one state . <SEP> The two duchies had shared the same ruler since 1741 , which is when the Saxe-Eisenach line had died out . | [] |
It was raised to a Grand duchy in 1815 by resolution of the Vienna Congress . | It became a Grand Duchy in 1815 . | [] |
The Grand Duchy came to an end in the German Revolution of 1918 β 19 with the other monarchies of the German Empire . | The Grand Duchy was abolished in 1918 with the other German monarchies , and the state joined others to form the new state of Thuringia in the Weimar Republic . | [] |
The king penguin ( " Aptenodytes patagonicus " ) is the second largest species of penguin , smaller , but somewhat similar in appearance to the emperor penguin . | The king penguin ( " Aptenodytes patagonicus " ) is a type of penguin . <SEP> It is the second largest species of penguin , as it is smaller and shorter than the emperor penguin . | [] |
The king penguin stands at 70 to tall and weighs from 9.3 to . | King penguins are usually 70 centimeters ( 0.7 meters / 30 inches ) tall and weigh 9 to 15 kilograms ( 20 to 30 pounds ) . | [] |
The chicks of both species are completely different from one another in appearance . | Males and females of the species look the same . | [] |
It was a powerful Cape Verde hurricane that formed during the 1985 Atlantic hurricane season , originating from a tropical wave on September 16 in the eastern Atlantic Ocean . | Hurricane Gloria was an Atlantic tropical cyclone in September 1985 . | [] |
Hurricane Gloria was the first significant tropical cyclone to strike the northeastern United States since Hurricane Agnes in 1972 and the first major storm to affect New York and Long Island directly since Hurricane Donna in 1960 . | The storm was the first major storm to affect Long Island and New York state directly since Hurricane Donna 25 years before . | [] |
After remaining a weak tropical cyclone for several days , Gloria intensified into a hurricane on September 22 north of the Lesser Antilles . | After being a weak tropical cyclone for several days , on September 22 , Gloria became a hurricane . | [] |
Gloria quickly intensified on September 24 , and the next day reached peak winds of 145 mph ( 230 km / h ) . | It quickly became stronger on September 24 ; the next day , its winds peaked at 145 mph . | [] |
At 1600 UTC on September 27 , the hurricane made landfall with a broad and poorly defined center between John F. Kennedy International Airport and Islip , New York , with winds of 85 mph ( 140 km / h ) on western Long Island . | Later that day , the storm struck western Long Island , with winds of 85 mph . | [] |
About an hour after striking Long Island , Gloria made its final landfall in western Connecticut near Westport , and proceeded to move through New England while weakening . | One hour after striking Long Island , it hit near Westport , Connecticut . | [] |
The storm continued to the northeast through Atlantic Canada passing south of Greenland on September 30 . | Gloria moved northeast through Atlantic Canada . | [] |
" On the Origin of Species " was first published on Thursday 24 November 1859 , priced at fifteen shillings with a first printing of 1250 copies . | It was published in London by John Murray in November 1859 . | [] |
The sixth edition was published by Murray on 19 February 1872 as " The Origin of Species " , with " On " dropped from the title . | The title since the 6th edition of 1872 has been " The Origin of Species " . <SEP> The sixth edition bore the title : " The origin of species " . | [] |
During Darwin 's lifetime the book went through six editions , with cumulative changes and revisions to deal with counter-arguments raised . | There were six editions of the " Origin " during Darwin 's life . | [] |
The fifth edition , published on 10 February 1869 , incorporated more changes and for the first time included the phrase " survival of the fittest " , which had been coined by the philosopher Herbert Spencer in his " Principles of Biology " ( 1864 ) . | In the fifth edition of 1869 Darwin used Herbert Spencer 's phrase ' survival of the fittest ' for the first time , in the heading of chapter 4 . | [] |
On the Origin of Species ( or , more completely , On the Origin of Species by Means of Natural Selection , or the Preservation of Favoured Races in the Struggle for Life ) , published on 24 November 1859 , is a work of scientific literature by Charles Darwin which is considered to be the foundation of evolutionary biology . | On the Origin of Species is the famous book by Charles Darwin . | [] |
It presented a body of evidence that the diversity of life arose by common descent through a branching pattern of evolution . | It gave evidence for evolution , and suggested what had caused evolution to happen . <SEP> First , it provided a great deal of evidence that evolution has taken place . | [] |
Darwin 's book introduced the scientific theory that populations evolve over the course of generations through a process of natural selection . | Darwin 's book did two things . <SEP> That theory is natural selection . | [] |
He knew that his readers were already familiar with the concept of transmutation of species from " Vestiges " , and his introduction ridicules that work as failing to provide a viable mechanism . | In his introduction Darwin ridicules that work as failing to provide a mechanism ( a way it could happen ) . | [] |
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