Paragraph 1: When New York Law School reopened in 1919, it was located in another building at 215 West 23rd Street, in Midtown. However, George Chase contracted an illness that resulted in him running New York Law School for the last three years of his life from his bed; he died in 1924. New York Law School continued without Chase, seeing its enrollment peak in the mid-1920s, but it saw a steady decline after that. At the onset of the Great Depression, the law school began seeing a serious decline in enrollment, which forced the law school to accept a much lower quality of students than they had previously accepted. With much fewer and poorer performing students, the law school moved to smaller facilities at 253 Broadway, just opposite City Hall. In 1936, the law school moved to another location at 63 Park Row, on the opposite side of City Hall Park; it also became coeducational that same year. However, as enrollment was still declining, both because of the Great Depression and because of the military draft started in 1940, and the school closed in 1941. The remaining students that were still enrolled finished their studies at St. John's University School of Law, in Brooklyn.

Paragraph 2: Dam construction comes with several impacts that can affect the economy and the environment. In specific, there are several ways in which the environment can be affected from dam construction. Species richness is usually measured to determine the effect of a dam on the ecosystems surrounding dams. To observe the species richness, scientists collect data on the fish and animal populations before and after construction of the dam. With that data, they are able to see how the population size increased or decreased. In some cases, it was found that the species richness was less downstream from a dam compared to further upstream. Inhibiting the volume of water was shown to be detrimental to species diversity and richness. Also, at the entrance of dams, there is less nutrients due to the high-water flow reducing the ecosystems reproduction standard. Along with the species richness, plankton diversity can be an indicator of the ecosystems ability to handle the newly built dam. It has been shown that dams can have an effect on the migration of fish leading to less reproduction.  There are many small factors that can have relatively large impacts that effect the river ecosystems, such as the species richness, volume of water and nutrient levels. Different experiments have been done that look into each of these individually and were able to determine why some dams cause such impacts. While there is substantial evidence and case studies that point to dam construction having environmental impacts, there are also studies that show less damage than expected. Looking at plankton near some dams has shown that plankton are able to continue to live although changes to their habitats. Changes such as the pH levels near dams have been recorded and plankton were minimally affected. Other species, however, such as trout, are more affected due to the physical dam inhibiting their migration and reproduction paths. Barrage dams control the amount of water going through them, leading to differences in the amount of water up and downstream from the dam. This discrepancy has different effects on different species native to the area. While there can be reduced flow downstream, there can also be problems upstream. Dams can have buildup of pressure that fish are not accustomed to and they migrate further upstream causing that part of the river to have reduced population sizes. Although there are environmental impacts that come with building new dams, there are also many economies that benefit from a dam. Without dams, it would be much harder to farm and grow livestock. The irrigation technology that comes with building a dam can exceed the risk factor.

Paragraph 3: Eric von Hippel and his colleagues have conducted a series of national surveys to identify the amount and importance of innovation being developed by consumers for their own use.  These nationally-representative surveys have been conducted in ten nations to date. An important, top-level finding from these studies is that the level of household sector innovation development by consumers, thought in Schumpeterian economics to be minimal, is in fact massive in scale.  The fraction of citizens innovating for their own use ranges from 1.5% in China, to 5.2% in the US, to 9.6% in Russia. In aggregate across the 10 nations surveyed to date, 65 million citizen innovators - consumers - have been documented to be spending tens of billions of dollars per year to develop novel products for themselves.  A second major finding is that more than 90% of the innovation developments by citizens are "free" - freely revealed by their citizen-developers to both peer consumers and commercializing producers without any intellectual property protections. Free citizen innovators are willing to openly reveal their innovation designs because they justify their development costs in terms of direct "self-rewards" they gain from innovating rather than from sales of their innovations to others. These self-rewards importantly include benefits from personal use of their innovations, plus the learning and enjoyment they gained by engaging in the innovation development process. The remaining 10% of household sector innovators are consumer-entrepreneurs. These individuals do hope to commercialize their innovations and so generally do not freely reveal their developments.

Paragraph 4: Eric von Hippel and his colleagues have conducted a series of national surveys to identify the amount and importance of innovation being developed by consumers for their own use.  These nationally-representative surveys have been conducted in ten nations to date. An important, top-level finding from these studies is that the level of household sector innovation development by consumers, thought in Schumpeterian economics to be minimal, is in fact massive in scale.  The fraction of citizens innovating for their own use ranges from 1.5% in China, to 5.2% in the US, to 9.6% in Russia. In aggregate across the 10 nations surveyed to date, 65 million citizen innovators - consumers - have been documented to be spending tens of billions of dollars per year to develop novel products for themselves.  A second major finding is that more than 90% of the innovation developments by citizens are "free" - freely revealed by their citizen-developers to both peer consumers and commercializing producers without any intellectual property protections. Free citizen innovators are willing to openly reveal their innovation designs because they justify their development costs in terms of direct "self-rewards" they gain from innovating rather than from sales of their innovations to others. These self-rewards importantly include benefits from personal use of their innovations, plus the learning and enjoyment they gained by engaging in the innovation development process. The remaining 10% of household sector innovators are consumer-entrepreneurs. These individuals do hope to commercialize their innovations and so generally do not freely reveal their developments.

Paragraph 5: Author James Riordan translated a tale from the Tatar people with the title Shaitan the Devil and His Forty Daughters, a man named Safa looks for adventure and rescues a swan in a lake from a black witch. In gratitude, the bird takes Safa to visit her sisters. He is given a little box and a warning not to open it until he reaches home. However, on his way, curiosity takes the better of him and he opens the box: a retinue of market sellers, wares, jades and money comes out of the box. At first, Safa is astonished by the wondrous contents of the box, but, after trying to shut them all back, regrets his decision. Suddenly, a mysterious gray-bearded man offers to help the man, in exchange for what Safa does not know he has at home. Safa closes the box and returns home, only to find his wife gave birth to a son, and immediately regrets his deal. Years later, Safa's son, a jigit, decides to fulfill his father's deal, and stops by a lakeside, waiting for the coming of Shaitan the Devil. He sees a flock of 40 swans coming to the lake and bathing in the water. The jigit creeps behind one of the birds and snatches it, while the other swans fly away. The bird in the jigit's hands shakes off her feathers and becomes a human maiden. She reveals that she is one of Shaitan's daughter, and her father plans to eat him, but he can delay this fate by asking to do chores for him. She flies back to the skies and Shaitan appears soon after to take the boy to his lair in the depths of the forest. the jigit offers to do chores for him, and Shaitan sets three tasks: first, to chop down the forest and sell the wood, then buy rye, plant it and harvest it, grind the corn and store hay - all in one night; secondly, to draw water from a lake to another with a sieve; thirdly, to bridle a wild stallion from Shaitan's stables (which is Shaitan metamorphosed). The jigit fulfills the tasks with the help of the swan girl. Shaitan agrees to marry the jigit to one of his daughters, after the youth passes more tests: to identify his daughter among 40 doves; then, to identify who is his daughter among her sisters, each playing a kurai. After succeeding twice more, Shaitan locks his youngest daughter and the jigit in the dungeons, but the swan girl takes the jigit with her and both escape in a "Magic Flight" sequence.

Paragraph 6: Gunmajin (ガンマジン Ganmajin, 37, 38, 40, 41, 44, 48 & Ohranger vs. Kakuranger) is an ancient warrior known for his honor and courage. According to Riki, Gunmajin appeared once 600 million years ago. Imprisoned within the form of a tiny tiki, the only way to unlock his power is by placing a key into his forehead and reciting the magic words "Gunma Gunma Dondoko Gunma" (ガンマガンマ ドンドコガンマ Ganma Ganma Dondoko Ganma). For some reason, the key always ended up in the hands of a child and everyone knew the magic words after hearing them. When awakened, Gunmajin would grant a single wish to his discoverer as long as it didn't mean harm to anyone. There were times in which he simply didn't like the wish and refused to grant it or punished his awakener for lying to him. Gunmajin possessed the Mazin Saber (マジンサーベル Majin Sāberu) through which he focused his power into the Majin One Sword Style (マジン一刀流 Majin Ittō Ryū) of Majin One Sword Fencing (Fire, Lightning, Wind, and Light). His back can act as a shield to defend himself and others (even King Pyramider's beam). In the series finale, he took Acha, Kocha, and Buldont, Jr. to his care. In Ohranger vs. Kakuranger, he is revealed to be terrified of Youkai (monsters fought by the Kakurangers).

Paragraph 7: Taking stock and looking forward – on the desirability of the continuation of the Forum: 45 speakers and nine written statements supported a continuation of the Forum. Many speakers emphasized the usefulness of the IGF as a platform for dialogue, free from the pressures of negotiations. A majority of speakers and written submissions supported an extension of the mandate as it is, that is, to continue the IGF as a multi-stakeholder platform that brings people together to discuss issues, exchange information and share best practices, but not to make decisions, nor to have highly visible outputs. The other speakers, while supporting a continuation of the IGF along similar lines to its current form, called for some change, ranging from small operational improvements to major changes in its functioning, such as adding provisions that would allow it to produce outputs, recommendations and decisions on a multi-stakeholder consensus basis, or to finance the IGF through the regular UN budget. Most of those who supported the continuation of the forum would like to do so for at least another five-year term. Two speakers, while welcoming the success of the IGF and not opposing an extension, said it had not met expectations as regards ‘enhanced cooperation’ in the area of Internet governance. They also linked the IGF to unilateral control of critical Internet resource, an issue that needed to be addressed in the future. Egypt, the host country, supported the continuation of the forum, while stressing at the same time the need to review its modalities of work, to increase institutional and financial capacity of its secretariat. The Chairman, Mr. Sha Zukang, Under-Secretary-General for Economic and Social Affairs, concluded the meeting by stating that he would now report back to the Secretary-General on the discussions held in Sharm El Sheikh and the Secretary-General would then make his recommendations to the UN Membership, as requested by the Tunis Agenda.

Paragraph 8: Eric von Hippel and his colleagues have conducted a series of national surveys to identify the amount and importance of innovation being developed by consumers for their own use.  These nationally-representative surveys have been conducted in ten nations to date. An important, top-level finding from these studies is that the level of household sector innovation development by consumers, thought in Schumpeterian economics to be minimal, is in fact massive in scale.  The fraction of citizens innovating for their own use ranges from 1.5% in China, to 5.2% in the US, to 9.6% in Russia. In aggregate across the 10 nations surveyed to date, 65 million citizen innovators - consumers - have been documented to be spending tens of billions of dollars per year to develop novel products for themselves.  A second major finding is that more than 90% of the innovation developments by citizens are "free" - freely revealed by their citizen-developers to both peer consumers and commercializing producers without any intellectual property protections. Free citizen innovators are willing to openly reveal their innovation designs because they justify their development costs in terms of direct "self-rewards" they gain from innovating rather than from sales of their innovations to others. These self-rewards importantly include benefits from personal use of their innovations, plus the learning and enjoyment they gained by engaging in the innovation development process. The remaining 10% of household sector innovators are consumer-entrepreneurs. These individuals do hope to commercialize their innovations and so generally do not freely reveal their developments.

Paragraph 9: Taking stock and looking forward – on the desirability of the continuation of the Forum: 45 speakers and nine written statements supported a continuation of the Forum. Many speakers emphasized the usefulness of the IGF as a platform for dialogue, free from the pressures of negotiations. A majority of speakers and written submissions supported an extension of the mandate as it is, that is, to continue the IGF as a multi-stakeholder platform that brings people together to discuss issues, exchange information and share best practices, but not to make decisions, nor to have highly visible outputs. The other speakers, while supporting a continuation of the IGF along similar lines to its current form, called for some change, ranging from small operational improvements to major changes in its functioning, such as adding provisions that would allow it to produce outputs, recommendations and decisions on a multi-stakeholder consensus basis, or to finance the IGF through the regular UN budget. Most of those who supported the continuation of the forum would like to do so for at least another five-year term. Two speakers, while welcoming the success of the IGF and not opposing an extension, said it had not met expectations as regards ‘enhanced cooperation’ in the area of Internet governance. They also linked the IGF to unilateral control of critical Internet resource, an issue that needed to be addressed in the future. Egypt, the host country, supported the continuation of the forum, while stressing at the same time the need to review its modalities of work, to increase institutional and financial capacity of its secretariat. The Chairman, Mr. Sha Zukang, Under-Secretary-General for Economic and Social Affairs, concluded the meeting by stating that he would now report back to the Secretary-General on the discussions held in Sharm El Sheikh and the Secretary-General would then make his recommendations to the UN Membership, as requested by the Tunis Agenda.

Paragraph 10: In February, Spud started an alliance with his former rival Ethan Carter III in order to even things with Hardy and Tyrus, defeating them in a tag-team match on 16 February episode of Impact Wrestling. At 2016 Lockdown, Spud came out, supposedly to stop Reby Sky from attacking EC3. However, he would close the cage door on EC3 to help Matt Hardy retain his TNA World Heavyweight Championship, turning heel once again in the process. He would follow up, with encouragement from Matt Hardy, by delivering a conchairto to EC3 with his head on the steps. On 9 March 2016 episode of Impact Wrestling, Spud aligned with Matt Hardy and Tyrus to form a stable, after explaining his actions as getting revenge against Carter for his cruel treatment of him last year. The trio would go on to face EC3 and Jeff Hardy in a losing effort. On 29 March episode of Impact Wrestling, Matt Hardy, Rockstar Spud, Tyrus and Reby Hardy were defeated by Carter by disqualification in a Four On One Handicap match. On 10 May episode of Impact Wrestling, he was defeated by Carter in a Six Sides of Steel match.  At May Mayhem, Spud and Tyrus were defeated by Jeff Hardy in a Ladder match. On 31 May episode of Impact Wrestling, Spud and Tyrus were defeated by The BroMans in a number one contendership match to challenge Decay for the TNA World Tag Team Championship at Slammiversary. On 21 June 2016 episode of Impact Wrestling, he challenged Braxton Sutter, Spud interrupting him when Sutter scheduled match against indy wrestler Balam. Sutter went on to defeat Spud and following his victory, was viciously attacked by Spud. During several months, Rockstar Spud and Braxton Sutter have many confrontation, during X Division matches. On 1 September edition of Impact Wrestling, Rockstar Spud viciously attacked Sutter with a chair during an Ultimate X match, and attacked him once again on 8 September edition of Impact Wrestling after his match against Drew Galloway, breaking one of his teeth. The feud ended in "Empty Arena, No Turnbuckles" match 15 September edition of Impact Wrestling, which was won by Sutter. At Bound for Glory, he participated in the Bound for Gold but was eliminated by Tyrus.

Paragraph 11: In February, Spud started an alliance with his former rival Ethan Carter III in order to even things with Hardy and Tyrus, defeating them in a tag-team match on 16 February episode of Impact Wrestling. At 2016 Lockdown, Spud came out, supposedly to stop Reby Sky from attacking EC3. However, he would close the cage door on EC3 to help Matt Hardy retain his TNA World Heavyweight Championship, turning heel once again in the process. He would follow up, with encouragement from Matt Hardy, by delivering a conchairto to EC3 with his head on the steps. On 9 March 2016 episode of Impact Wrestling, Spud aligned with Matt Hardy and Tyrus to form a stable, after explaining his actions as getting revenge against Carter for his cruel treatment of him last year. The trio would go on to face EC3 and Jeff Hardy in a losing effort. On 29 March episode of Impact Wrestling, Matt Hardy, Rockstar Spud, Tyrus and Reby Hardy were defeated by Carter by disqualification in a Four On One Handicap match. On 10 May episode of Impact Wrestling, he was defeated by Carter in a Six Sides of Steel match.  At May Mayhem, Spud and Tyrus were defeated by Jeff Hardy in a Ladder match. On 31 May episode of Impact Wrestling, Spud and Tyrus were defeated by The BroMans in a number one contendership match to challenge Decay for the TNA World Tag Team Championship at Slammiversary. On 21 June 2016 episode of Impact Wrestling, he challenged Braxton Sutter, Spud interrupting him when Sutter scheduled match against indy wrestler Balam. Sutter went on to defeat Spud and following his victory, was viciously attacked by Spud. During several months, Rockstar Spud and Braxton Sutter have many confrontation, during X Division matches. On 1 September edition of Impact Wrestling, Rockstar Spud viciously attacked Sutter with a chair during an Ultimate X match, and attacked him once again on 8 September edition of Impact Wrestling after his match against Drew Galloway, breaking one of his teeth. The feud ended in "Empty Arena, No Turnbuckles" match 15 September edition of Impact Wrestling, which was won by Sutter. At Bound for Glory, he participated in the Bound for Gold but was eliminated by Tyrus.

Paragraph 12: Dam construction comes with several impacts that can affect the economy and the environment. In specific, there are several ways in which the environment can be affected from dam construction. Species richness is usually measured to determine the effect of a dam on the ecosystems surrounding dams. To observe the species richness, scientists collect data on the fish and animal populations before and after construction of the dam. With that data, they are able to see how the population size increased or decreased. In some cases, it was found that the species richness was less downstream from a dam compared to further upstream. Inhibiting the volume of water was shown to be detrimental to species diversity and richness. Also, at the entrance of dams, there is less nutrients due to the high-water flow reducing the ecosystems reproduction standard. Along with the species richness, plankton diversity can be an indicator of the ecosystems ability to handle the newly built dam. It has been shown that dams can have an effect on the migration of fish leading to less reproduction.  There are many small factors that can have relatively large impacts that effect the river ecosystems, such as the species richness, volume of water and nutrient levels. Different experiments have been done that look into each of these individually and were able to determine why some dams cause such impacts. While there is substantial evidence and case studies that point to dam construction having environmental impacts, there are also studies that show less damage than expected. Looking at plankton near some dams has shown that plankton are able to continue to live although changes to their habitats. Changes such as the pH levels near dams have been recorded and plankton were minimally affected. Other species, however, such as trout, are more affected due to the physical dam inhibiting their migration and reproduction paths. Barrage dams control the amount of water going through them, leading to differences in the amount of water up and downstream from the dam. This discrepancy has different effects on different species native to the area. While there can be reduced flow downstream, there can also be problems upstream. Dams can have buildup of pressure that fish are not accustomed to and they migrate further upstream causing that part of the river to have reduced population sizes. Although there are environmental impacts that come with building new dams, there are also many economies that benefit from a dam. Without dams, it would be much harder to farm and grow livestock. The irrigation technology that comes with building a dam can exceed the risk factor.

Paragraph 13: Author James Riordan translated a tale from the Tatar people with the title Shaitan the Devil and His Forty Daughters, a man named Safa looks for adventure and rescues a swan in a lake from a black witch. In gratitude, the bird takes Safa to visit her sisters. He is given a little box and a warning not to open it until he reaches home. However, on his way, curiosity takes the better of him and he opens the box: a retinue of market sellers, wares, jades and money comes out of the box. At first, Safa is astonished by the wondrous contents of the box, but, after trying to shut them all back, regrets his decision. Suddenly, a mysterious gray-bearded man offers to help the man, in exchange for what Safa does not know he has at home. Safa closes the box and returns home, only to find his wife gave birth to a son, and immediately regrets his deal. Years later, Safa's son, a jigit, decides to fulfill his father's deal, and stops by a lakeside, waiting for the coming of Shaitan the Devil. He sees a flock of 40 swans coming to the lake and bathing in the water. The jigit creeps behind one of the birds and snatches it, while the other swans fly away. The bird in the jigit's hands shakes off her feathers and becomes a human maiden. She reveals that she is one of Shaitan's daughter, and her father plans to eat him, but he can delay this fate by asking to do chores for him. She flies back to the skies and Shaitan appears soon after to take the boy to his lair in the depths of the forest. the jigit offers to do chores for him, and Shaitan sets three tasks: first, to chop down the forest and sell the wood, then buy rye, plant it and harvest it, grind the corn and store hay - all in one night; secondly, to draw water from a lake to another with a sieve; thirdly, to bridle a wild stallion from Shaitan's stables (which is Shaitan metamorphosed). The jigit fulfills the tasks with the help of the swan girl. Shaitan agrees to marry the jigit to one of his daughters, after the youth passes more tests: to identify his daughter among 40 doves; then, to identify who is his daughter among her sisters, each playing a kurai. After succeeding twice more, Shaitan locks his youngest daughter and the jigit in the dungeons, but the swan girl takes the jigit with her and both escape in a "Magic Flight" sequence.

Paragraph 14: Rodney Young named the largest burial mound at the site Tumulus MM—for “Midas Mound,” after the famous Phrygian king Midas, who ruled at Gordion during the second half of the eighth century B.C. Young eventually came to believe that the tomb’s occupant was not Midas but rather his father, although in either case the wooden finds from the burial can be associated with King Midas. When Midas took the throne on the death of his father, he surely would have officiated at the funeral, with the grave goods provided by him for the deposition. The historical King Midas was a contemporary of the Assyrian king Sargon II (r. 721–705 BC) and was also well known to the Greeks. Midas was the first foreigner to make an offering at the sanctuary of Apollo at Delphi, according to the Greek historian Herodotus, who wrote that the king had dedicated his throne, which was “well worth seeing.” Unfortunately, this tantalizing comment tells us little about the appearance of the throne of Midas. However, the magnificent wooden furniture from Tumulus MM at Gordion suggests that the throne was likely made from beautiful woods with carved and inlaid decoration, including a complex of geometric patterns that reflected the power of the Phrygian royal house and its connection to the Phrygian mother goddess Matar (Kybele).Tumulus MM produced an array of priceless artifacts: 170 bronze vessels, some with deposits of organic residues; 10 bronze-and-leather belts; more than 180 bronze fibulae (ancient safety pins); pottery vessels containing the remains of food; and 15 pieces of fine wooden furniture. The exact nature of the furniture was not clear to Young and his team when they entered the chamber in 1957, as many of the objects had broken along the lines of the joinery, with their constituent parts dispersed on the tomb floor. The first thing the excavators saw was the skeleton of the king lying on a mass of textiles, covering what Young thought was a four-poster bed. To the east of the “bed” were several furniture legs scattered among remnants of cloth. Leaning against the east wall were two ornate, inlaid objects, called “screens” by Young and initially identified as “throne backs.” To the south of these, a fancy inlaid table had collapsed with its frame intact, and nearby were the tops and legs of eight “plain” tables. Most of the bronze vessels found in the tomb had once been hung on the walls or placed on the tables, but all had fallen to the floor.

Paragraph 15: In February, Spud started an alliance with his former rival Ethan Carter III in order to even things with Hardy and Tyrus, defeating them in a tag-team match on 16 February episode of Impact Wrestling. At 2016 Lockdown, Spud came out, supposedly to stop Reby Sky from attacking EC3. However, he would close the cage door on EC3 to help Matt Hardy retain his TNA World Heavyweight Championship, turning heel once again in the process. He would follow up, with encouragement from Matt Hardy, by delivering a conchairto to EC3 with his head on the steps. On 9 March 2016 episode of Impact Wrestling, Spud aligned with Matt Hardy and Tyrus to form a stable, after explaining his actions as getting revenge against Carter for his cruel treatment of him last year. The trio would go on to face EC3 and Jeff Hardy in a losing effort. On 29 March episode of Impact Wrestling, Matt Hardy, Rockstar Spud, Tyrus and Reby Hardy were defeated by Carter by disqualification in a Four On One Handicap match. On 10 May episode of Impact Wrestling, he was defeated by Carter in a Six Sides of Steel match.  At May Mayhem, Spud and Tyrus were defeated by Jeff Hardy in a Ladder match. On 31 May episode of Impact Wrestling, Spud and Tyrus were defeated by The BroMans in a number one contendership match to challenge Decay for the TNA World Tag Team Championship at Slammiversary. On 21 June 2016 episode of Impact Wrestling, he challenged Braxton Sutter, Spud interrupting him when Sutter scheduled match against indy wrestler Balam. Sutter went on to defeat Spud and following his victory, was viciously attacked by Spud. During several months, Rockstar Spud and Braxton Sutter have many confrontation, during X Division matches. On 1 September edition of Impact Wrestling, Rockstar Spud viciously attacked Sutter with a chair during an Ultimate X match, and attacked him once again on 8 September edition of Impact Wrestling after his match against Drew Galloway, breaking one of his teeth. The feud ended in "Empty Arena, No Turnbuckles" match 15 September edition of Impact Wrestling, which was won by Sutter. At Bound for Glory, he participated in the Bound for Gold but was eliminated by Tyrus.

Paragraph 16: Another example where we can use the more general version of Hensel's lemma but not the basic version is a proof that any 3-adic integer c ≡ 1 mod 9 is a cube in  Let  and take initial approximation a = 1. The basic Hensel's lemma cannot be used to find roots of f(x) since  for every r. To apply the general version of Hensel's lemma we want  which means  That is, if c ≡ 1 mod 27 then the general Hensel's lemma tells us f(x) has a 3-adic root, so c is a 3-adic cube. However, we wanted to have this result under the weaker condition that c ≡ 1 mod 9. If c ≡ 1 mod 9 then c ≡ 1, 10, or 19 mod 27. We can apply the general Hensel's lemma three times depending on the value of c mod 27: if c ≡ 1 mod 27 then use a = 1, if c ≡ 10 mod 27 then use a = 4 (since 4 is a root of f(x) mod 27), and if c ≡ 19 mod 27 then use a = 7. (It is not true that every c ≡ 1 mod 3 is a 3-adic cube, e.g., 4 is not a 3-adic cube since it is not a cube mod 9.)

Paragraph 17: Gunmajin (ガンマジン Ganmajin, 37, 38, 40, 41, 44, 48 & Ohranger vs. Kakuranger) is an ancient warrior known for his honor and courage. According to Riki, Gunmajin appeared once 600 million years ago. Imprisoned within the form of a tiny tiki, the only way to unlock his power is by placing a key into his forehead and reciting the magic words "Gunma Gunma Dondoko Gunma" (ガンマガンマ ドンドコガンマ Ganma Ganma Dondoko Ganma). For some reason, the key always ended up in the hands of a child and everyone knew the magic words after hearing them. When awakened, Gunmajin would grant a single wish to his discoverer as long as it didn't mean harm to anyone. There were times in which he simply didn't like the wish and refused to grant it or punished his awakener for lying to him. Gunmajin possessed the Mazin Saber (マジンサーベル Majin Sāberu) through which he focused his power into the Majin One Sword Style (マジン一刀流 Majin Ittō Ryū) of Majin One Sword Fencing (Fire, Lightning, Wind, and Light). His back can act as a shield to defend himself and others (even King Pyramider's beam). In the series finale, he took Acha, Kocha, and Buldont, Jr. to his care. In Ohranger vs. Kakuranger, he is revealed to be terrified of Youkai (monsters fought by the Kakurangers).

Paragraph 18: Eric von Hippel and his colleagues have conducted a series of national surveys to identify the amount and importance of innovation being developed by consumers for their own use.  These nationally-representative surveys have been conducted in ten nations to date. An important, top-level finding from these studies is that the level of household sector innovation development by consumers, thought in Schumpeterian economics to be minimal, is in fact massive in scale.  The fraction of citizens innovating for their own use ranges from 1.5% in China, to 5.2% in the US, to 9.6% in Russia. In aggregate across the 10 nations surveyed to date, 65 million citizen innovators - consumers - have been documented to be spending tens of billions of dollars per year to develop novel products for themselves.  A second major finding is that more than 90% of the innovation developments by citizens are "free" - freely revealed by their citizen-developers to both peer consumers and commercializing producers without any intellectual property protections. Free citizen innovators are willing to openly reveal their innovation designs because they justify their development costs in terms of direct "self-rewards" they gain from innovating rather than from sales of their innovations to others. These self-rewards importantly include benefits from personal use of their innovations, plus the learning and enjoyment they gained by engaging in the innovation development process. The remaining 10% of household sector innovators are consumer-entrepreneurs. These individuals do hope to commercialize their innovations and so generally do not freely reveal their developments.

Paragraph 19: When New York Law School reopened in 1919, it was located in another building at 215 West 23rd Street, in Midtown. However, George Chase contracted an illness that resulted in him running New York Law School for the last three years of his life from his bed; he died in 1924. New York Law School continued without Chase, seeing its enrollment peak in the mid-1920s, but it saw a steady decline after that. At the onset of the Great Depression, the law school began seeing a serious decline in enrollment, which forced the law school to accept a much lower quality of students than they had previously accepted. With much fewer and poorer performing students, the law school moved to smaller facilities at 253 Broadway, just opposite City Hall. In 1936, the law school moved to another location at 63 Park Row, on the opposite side of City Hall Park; it also became coeducational that same year. However, as enrollment was still declining, both because of the Great Depression and because of the military draft started in 1940, and the school closed in 1941. The remaining students that were still enrolled finished their studies at St. John's University School of Law, in Brooklyn.

Paragraph 20: Gunmajin (ガンマジン Ganmajin, 37, 38, 40, 41, 44, 48 & Ohranger vs. Kakuranger) is an ancient warrior known for his honor and courage. According to Riki, Gunmajin appeared once 600 million years ago. Imprisoned within the form of a tiny tiki, the only way to unlock his power is by placing a key into his forehead and reciting the magic words "Gunma Gunma Dondoko Gunma" (ガンマガンマ ドンドコガンマ Ganma Ganma Dondoko Ganma). For some reason, the key always ended up in the hands of a child and everyone knew the magic words after hearing them. When awakened, Gunmajin would grant a single wish to his discoverer as long as it didn't mean harm to anyone. There were times in which he simply didn't like the wish and refused to grant it or punished his awakener for lying to him. Gunmajin possessed the Mazin Saber (マジンサーベル Majin Sāberu) through which he focused his power into the Majin One Sword Style (マジン一刀流 Majin Ittō Ryū) of Majin One Sword Fencing (Fire, Lightning, Wind, and Light). His back can act as a shield to defend himself and others (even King Pyramider's beam). In the series finale, he took Acha, Kocha, and Buldont, Jr. to his care. In Ohranger vs. Kakuranger, he is revealed to be terrified of Youkai (monsters fought by the Kakurangers).

Paragraph 21: Gunmajin (ガンマジン Ganmajin, 37, 38, 40, 41, 44, 48 & Ohranger vs. Kakuranger) is an ancient warrior known for his honor and courage. According to Riki, Gunmajin appeared once 600 million years ago. Imprisoned within the form of a tiny tiki, the only way to unlock his power is by placing a key into his forehead and reciting the magic words "Gunma Gunma Dondoko Gunma" (ガンマガンマ ドンドコガンマ Ganma Ganma Dondoko Ganma). For some reason, the key always ended up in the hands of a child and everyone knew the magic words after hearing them. When awakened, Gunmajin would grant a single wish to his discoverer as long as it didn't mean harm to anyone. There were times in which he simply didn't like the wish and refused to grant it or punished his awakener for lying to him. Gunmajin possessed the Mazin Saber (マジンサーベル Majin Sāberu) through which he focused his power into the Majin One Sword Style (マジン一刀流 Majin Ittō Ryū) of Majin One Sword Fencing (Fire, Lightning, Wind, and Light). His back can act as a shield to defend himself and others (even King Pyramider's beam). In the series finale, he took Acha, Kocha, and Buldont, Jr. to his care. In Ohranger vs. Kakuranger, he is revealed to be terrified of Youkai (monsters fought by the Kakurangers).

Paragraph 22: Author James Riordan translated a tale from the Tatar people with the title Shaitan the Devil and His Forty Daughters, a man named Safa looks for adventure and rescues a swan in a lake from a black witch. In gratitude, the bird takes Safa to visit her sisters. He is given a little box and a warning not to open it until he reaches home. However, on his way, curiosity takes the better of him and he opens the box: a retinue of market sellers, wares, jades and money comes out of the box. At first, Safa is astonished by the wondrous contents of the box, but, after trying to shut them all back, regrets his decision. Suddenly, a mysterious gray-bearded man offers to help the man, in exchange for what Safa does not know he has at home. Safa closes the box and returns home, only to find his wife gave birth to a son, and immediately regrets his deal. Years later, Safa's son, a jigit, decides to fulfill his father's deal, and stops by a lakeside, waiting for the coming of Shaitan the Devil. He sees a flock of 40 swans coming to the lake and bathing in the water. The jigit creeps behind one of the birds and snatches it, while the other swans fly away. The bird in the jigit's hands shakes off her feathers and becomes a human maiden. She reveals that she is one of Shaitan's daughter, and her father plans to eat him, but he can delay this fate by asking to do chores for him. She flies back to the skies and Shaitan appears soon after to take the boy to his lair in the depths of the forest. the jigit offers to do chores for him, and Shaitan sets three tasks: first, to chop down the forest and sell the wood, then buy rye, plant it and harvest it, grind the corn and store hay - all in one night; secondly, to draw water from a lake to another with a sieve; thirdly, to bridle a wild stallion from Shaitan's stables (which is Shaitan metamorphosed). The jigit fulfills the tasks with the help of the swan girl. Shaitan agrees to marry the jigit to one of his daughters, after the youth passes more tests: to identify his daughter among 40 doves; then, to identify who is his daughter among her sisters, each playing a kurai. After succeeding twice more, Shaitan locks his youngest daughter and the jigit in the dungeons, but the swan girl takes the jigit with her and both escape in a "Magic Flight" sequence.

Paragraph 23: When New York Law School reopened in 1919, it was located in another building at 215 West 23rd Street, in Midtown. However, George Chase contracted an illness that resulted in him running New York Law School for the last three years of his life from his bed; he died in 1924. New York Law School continued without Chase, seeing its enrollment peak in the mid-1920s, but it saw a steady decline after that. At the onset of the Great Depression, the law school began seeing a serious decline in enrollment, which forced the law school to accept a much lower quality of students than they had previously accepted. With much fewer and poorer performing students, the law school moved to smaller facilities at 253 Broadway, just opposite City Hall. In 1936, the law school moved to another location at 63 Park Row, on the opposite side of City Hall Park; it also became coeducational that same year. However, as enrollment was still declining, both because of the Great Depression and because of the military draft started in 1940, and the school closed in 1941. The remaining students that were still enrolled finished their studies at St. John's University School of Law, in Brooklyn.

Paragraph 24: The Royal Scots Navy (or Old Scots Navy) was the navy of the Kingdom of Scotland from its origins in the Middle Ages until its merger with the Kingdom of England's Royal Navy per the Acts of Union 1707. There are mentions in Medieval records of fleets commanded by Scottish kings in the twelfth and thirteenth centuries. King Robert I (1274–1329, reigned 1306–1329), developed naval power to counter the English in the Wars of Independence (1296–1328), and after the establishment of Scottish independence continued to build up naval capacity. In the late fourteenth century naval warfare with England was conducted largely by hired Scots, Flemish and French merchantmen and privateers. King James I (1394–1437, reigned 1406–1437), took a greater interest in naval power establishing a shipbuilding yard at Leith and probably created the office of Lord High Admiral.

Paragraph 25: Eric von Hippel and his colleagues have conducted a series of national surveys to identify the amount and importance of innovation being developed by consumers for their own use.  These nationally-representative surveys have been conducted in ten nations to date. An important, top-level finding from these studies is that the level of household sector innovation development by consumers, thought in Schumpeterian economics to be minimal, is in fact massive in scale.  The fraction of citizens innovating for their own use ranges from 1.5% in China, to 5.2% in the US, to 9.6% in Russia. In aggregate across the 10 nations surveyed to date, 65 million citizen innovators - consumers - have been documented to be spending tens of billions of dollars per year to develop novel products for themselves.  A second major finding is that more than 90% of the innovation developments by citizens are "free" - freely revealed by their citizen-developers to both peer consumers and commercializing producers without any intellectual property protections. Free citizen innovators are willing to openly reveal their innovation designs because they justify their development costs in terms of direct "self-rewards" they gain from innovating rather than from sales of their innovations to others. These self-rewards importantly include benefits from personal use of their innovations, plus the learning and enjoyment they gained by engaging in the innovation development process. The remaining 10% of household sector innovators are consumer-entrepreneurs. These individuals do hope to commercialize their innovations and so generally do not freely reveal their developments.

Answer: 11