Question: Who did the Han Chinese want to the help the people who established the vice royalty of the Sakya regime fight?

full_context: Document 1: Yuan dynasty: When the Mongols placed the Uighurs of the Kingdom of Qocho over the Koreans at the court the Korean King objected, then the Mongol Emperor Kublai Khan rebuked the Korean King, saying that the Uighur King of Qocho was ranked higher than the Karluk Kara-Khanid ruler, who in turn was ranked higher than the Korean King, who was ranked last, because the Uighurs surrendered to the Mongols first, the Karluks surrendered after the Uighurs, and the Koreans surrendered last, and that the Uighurs surrendered peacefully without violently resisting.
Document 2: Sino-Tibetan relations during the Ming dynasty: Laird writes that Altan Khan abolished the native Mongol practices of shamanism and blood sacrifice, while the Mongol princes and subjects were coerced by Altan to convert to Gelug Buddhism—or face execution if they persisted in their shamanistic ways. Committed to their religious leader, Mongol princes began requesting the Dalai Lama to bestow titles on them, which demonstrated "the unique fusion of religious and political power" wielded by the Dalai Lama, as Laird writes. Kolmaš states that the spiritual and secular Mongol-Tibetan alliance of the 13th century was renewed by this alliance constructed by Altan Khan and Sönam Gyatso. Van Praag writes that this restored the original Mongol patronage of a Tibetan lama and "to this day, Mongolians are among the most devout followers of the Gelugpa and the Dalai Lama." Angela F. Howard writes that this unique relationship not only provided the Dalai Lama and Panchen Lama with religious and political authority in Tibet, but that Altan Khan gained "enormous power among the entire Mongol population."
Document 3: Sino-Tibetan relations during the Ming dynasty: With the example of the Ming court's relationship with the fifth Karmapa and other Tibetan leaders, Norbu states that Chinese Communist historians have failed to realize the significance of the religious aspect of the Ming-Tibetan relationship. He writes that the meetings of lamas with the Emperor of China were exchanges of tribute between "the patron and the priest" and were not merely instances of a political subordinate paying tribute to a superior. He also notes that the items of tribute were Buddhist artifacts which symbolized "the religious nature of the relationship." Josef Kolmaš writes that the Ming dynasty did not exercise any direct political control over Tibet, content with their tribute relations that were "almost entirely of a religious character." Patricia Ann Berger writes that the Yongle Emperor's courting and granting of titles to lamas was his attempt to "resurrect the relationship between China and Tibet established earlier by the Yuan dynastic founder Khubilai Khan and his guru Phagpa." She also writes that the later Qing emperors and their Mongol associates viewed the Yongle Emperor's relationship with Tibet as "part of a chain of reincarnation that saw this Han Chinese emperor as yet another emanation of Manjusri."
Document 4: Sino-Tibetan relations during the Ming dynasty: P. Christiaan Klieger, an anthropologist and scholar of the California Academy of Sciences in San Francisco, writes that the vice royalty of the Sakya regime installed by the Mongols established a patron and priest relationship between Tibetans and Mongol converts to Tibetan Buddhism. According to him, the Tibetan lamas and Mongol khans upheld a "mutual role of religious prelate and secular patron," respectively. He adds that "Although agreements were made between Tibetan leaders and Mongol khans, Ming and Qing emperors, it was the Republic of China and its Communist successors that assumed the former imperial tributaries and subject states as integral parts of the Chinese nation-state."
Document 5: Sino-Tibetan relations during the Ming dynasty: Nevertheless, the ethno-geographic caste hierarchy favoring the Mongols and other ethnicities were accorded higher status than the Han Chinese majority. Although Han Chinese who were recruited as advisers were often actually more influential than high officials, their status was not as well defined. Kublai also abolished the imperial examinations of China's civil service legacy, which was not reinstated until Ayurbarwada Buyantu Khan's reign (1311–1320). Rossabi writes that Kublai recognized that in order to rule China, "he had to employ Chinese advisors and officials, yet he could not rely totally on Chinese advisers because he had to maintain a delicate balancing act between ruling the sedentary civilization of China and preserving the cultural identity and values of the Mongols." And "in governing China, he was concerned with the interests of his Chinese subjects, but also with exploiting the resources of the empire for his own aggrandizement. His motivations and objectives alternated from one to the other throughout his reign," according to Rossabi. Van Praag writes in The Status of Tibet that the Tibetans and Mongols, on the other hand, upheld a dual system of rule and an interdependent relationship that legitimated the succession of Mongol khans as universal Buddhist rulers, or chakravartin. Van Praag writes that "Tibet remained a unique part of the Empire and was never fully integrated into it," citing examples such as a licensed border market that existed between China and Tibet during the Yuan.
Document 6: Sino-Tibetan relations during the Ming dynasty: Josef Kolmaš, a sinologist, Tibetologist, and Professor of Oriental Studies at the Academy of Sciences of the Czech Republic, writes that it was during the Qing dynasty "that developments took place on the basis of which Tibet came to be considered an organic part of China, both practically and theoretically subject to the Chinese central government." Yet he states that this was a radical change in regards to all previous eras of Sino-Tibetan relations.
Document 7: Yuan dynasty: The reason for the order of the classes and the reason why people were placed in a certain class was the date they surrendered to the Mongols, and had nothing to do with their ethnicity. The earlier they surrendered to the Mongols, the higher they were placed, the more the held out, the lower they were ranked. The Northern Chinese were ranked higher and Southern Chinese were ranked lower because southern China withstood and fought to the last before caving in. Major commerce during this era gave rise to favorable conditions for private southern Chinese manufacturers and merchants.
Document 8: Qing dynasty: There were too few ethnic Manchus to conquer China, so they gained strength by defeating and absorbing Mongols, but more importantly, adding Han Chinese to the Eight Banners. The Manchus had to create an entire "Jiu Han jun" (Old Han Army) due to the massive amount of Han Chinese soldiers which were absorbed into the Eight Banners by both capture and defection, Ming artillery was responsible for many victories against the Manchus, so the Manchus established an artillery corps made out of Han Chinese soldiers in 1641 and the swelling of Han Chinese numbers in the Eight Banners led in 1642 of all Eight Han Banners being created. It was defected Ming Han Chinese armies which conquered southern China for the Qing.
Document 9: Yuan dynasty: Many Han Chinese and Khitan defected to the Mongols to fight against the Jin. Two Han Chinese leaders, Shi Tianze, Liu Heima (劉黑馬, Liu Ni), and the Khitan Xiao Zhala (蕭札剌) defected and commanded the 3 Tumens in the Mongol army. Liu Heima and Shi Tianze served Ogödei Khan. Liu Heima and Shi Tianxiang led armies against Western Xia for the Mongols. There were 4 Han Tumens and 3 Khitan Tumens, with each Tumen consisting of 10,000 troops. The three Khitan Generals Shimobeidier (石抹孛迭兒), Tabuyir (塔不已兒) and Xiaozhacizhizizhongxi (蕭札刺之子重喜) commanded the three Khitan Tumens and the four Han Generals Zhang Rou, Yan Shi, Shi Tianze, and Liu Heima commanded the four Han tumens under Ogödei Khan.
Document 10: Samurai: In 1274, the Mongol-founded Yuan dynasty in China sent a force of some 40,000 men and 900 ships to invade Japan in northern Kyūshū. Japan mustered a mere 10,000 samurai to meet this threat. The invading army was harassed by major thunderstorms throughout the invasion, which aided the defenders by inflicting heavy casualties. The Yuan army was eventually recalled and the invasion was called off. The Mongol invaders used small bombs, which was likely the first appearance of bombs and gunpowder in Japan.
Document 11: Sino-Tibetan relations during the Ming dynasty: Starting in 1236, the Mongol prince Kublai, who later ruled as Khagan from 1260–1294, was granted a large appanage in North China by his superior, Ögedei Khan. Karma Pakshi, 2nd Karmapa Lama (1203–1283)—the head lama of the Karma Kagyu lineage of Tibetan Buddhism—rejected Kublai's invitation, so instead Kublai invited Drogön Chögyal Phagpa (1235–1280), successor and nephew of Sakya Pandita, who came to his court in 1253. Kublai instituted a unique relationship with the Phagpa lama, which recognized Kublai as a superior sovereign in political affairs and the Phagpa lama as the senior instructor to Kublai in religious affairs. Kublai also made Drogön Chögyal Phagpa the director of the government agency known as the Bureau of Buddhist and Tibetan Affairs and the ruling priest-king of Tibet, which comprised thirteen different states ruled by myriarchies.
Document 12: Sino-Tibetan relations during the Ming dynasty: Dawa Norbu argues that modern Chinese Communist historians tend to be in favor of the view that the Ming simply reappointed old Yuan dynasty officials in Tibet and perpetuated their rule of Tibet in this manner. Norbu writes that, although this would have been true for the eastern Tibetan regions of Amdo and Kham's "tribute-cum-trade" relations with the Ming, it was untrue if applied to the western Tibetan regions of Ü-Tsang and Ngari. After the Phagmodrupa Changchub Gyaltsen, these were ruled by "three successive nationalistic regimes," which Norbu writes "Communist historians prefer to ignore."
Document 13: Sino-Tibetan relations during the Ming dynasty: Historians Luciano Petech and Sato Hisashi argue that the Ming upheld a "divide-and-rule" policy towards a weak and politically fragmented Tibet after the Sakya regime had fallen. Chan writes that this was perhaps the calculated strategy of the Yongle Emperor, as exclusive patronage to one Tibetan sect would have given it too much regional power. Sperling finds no textual evidence in either Chinese or Tibetan sources to support this thesis of Petech and Hisashi. Norbu asserts that their thesis is largely based on the list of Ming titles conferred on Tibetan lamas rather than "comparative analysis of developments in China and Tibet." Rossabi states that this theory "attributes too much influence to the Chinese," pointing out that Tibet was already politically divided when the Ming dynasty began. Rossabi also discounts the "divide-and-rule" theory on the grounds of the Yongle Emperor's failed attempt to build a strong relationship with the fifth Karmapa—one which he hoped would parallel Kublai Khan's earlier relationship with the Sakya Phagpa lama. Instead, the Yongle Emperor followed the Karmapa's advice of giving patronage to many different Tibetan lamas.
Document 14: Yuan dynasty: Shi Tianze was a Han Chinese who lived in the Jin dynasty. Interethnic marriage between Han and Jurchen became common at this time. His father was Shi Bingzhi (史秉直, Shih Ping-chih). Shi Bingzhi was married to a Jurchen woman (surname Na-ho) and a Han Chinese woman (surname Chang); it is unknown which of them was Shi Tianze's mother. Shi Tianze was married to two Jurchen women, a Han Chinese woman, and a Korean woman, and his son Shi Gang was born to one of his Jurchen wives. The surnames of his Jurchen wives were Mo-nien and Na-ho; the surname of his Korean wife was Li; and the surname of his Han Chinese wife was Shi. Shi Tianze defected to Mongol forces upon their invasion of the Jin dynasty. His son Shi Gang married a Kerait woman; the Kerait were Mongolified Turkic people and were considered part of the "Mongol nation". Shi Tianze (Shih T'ien-tse), Zhang Rou (Chang Jou, 張柔), and Yan Shi (Yen Shih, 嚴實) and other high ranking Chinese who served in the Jin dynasty and defected to the Mongols helped build the structure for the administration of the new state. Chagaan (Tsagaan) and Zhang Rou jointly launched an attack on the Song dynasty ordered by Töregene Khatun.
Document 15: Qing dynasty: The Qing showed that the Manchus valued military skills in propaganda targeted towards the Ming military to get them to defect to the Qing, since the Ming civilian political system discriminated against the military. The three Liaodong Han Bannermen officers who played a massive role in the conquest of southern China from the Ming were Shang Kexi, Geng Zhongming, and Kong Youde and they governed southern China autonomously as viceroys for the Qing after their conquests. Normally the Manchu Bannermen acted only as reserve forces or in the rear and were used predominantly for quick strikes with maximum impact, so as to minimize ethnic Manchu losses; instead, the Qing used defected Han Chinese troops to fight as the vanguard during the entire conquest of China.
ground_truth: the Jin
sub_queries: Who was the vice royalty of the Sakya regime established by? Answer: the Mongols
Who did the Han Chinese want to help the the Mongols fight? Answer: the Jin