Question: Kadava was the name of a Tamil ruling dynasty who ruled parts of the Tamil country during the thirteenth and the fourteenth century, it was at the height of their power briefly during the reigns of Kopperunchinga I and Kopperunchinga II, the two rulers were powerful enough to challenge the waning Chola dynasty, was one of the longest-ruling dynasties in the history of the southern region, of which country?

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Kadava dynasty: Kadava was the name of a Tamil ruling dynasty who ruled parts of the Tamil country during the thirteenth and the fourteenth century.  Kadavas were related to the Pallava dynasty and ruled from Kudalur near Cuddalore in Tamil Nadu.  The Kadava kingdom was at the height of their power briefly during the reigns of Kopperunchinga I and Kopperunchinga II.  These two rulers were powerful enough to challenge the waning Chola dynasty during the reign of Rajaraja Chola III and Rajendra Chola III.  The two Kopperunchingas have left a large number of inscriptions mostly in the North and South Arcot districts and in the Chingleput district.

Kopperunchinga II: Kopperunchinga II (reigned c. 1243-1279 CE) was a Kadava chieftain, who succeeded his father Kopperunchinga I and continued his successes against the Hoysalas.  Since the Chola power no longer constituted a threat, Kopperunchinga II acted as the "de facto" protector of the Chola king and helped him maintain his position on the throne.  As he expanded his territorial holdings, Kopperunchinga II assumed such titles as "Maharajasimha", "Khadgamalla", "Kadava Pallava", "Alappirandan", "Avaniyalappirandan", "Kanakasabhapathy", etc.  He has left numerous inscriptions mainly in the South Arcot and Chingleput districts and the northern portion of Thanjavur, and a few have also been found in the North Arcot and Chittoor districts.  Ultimately, however, the resurgence of the power of the Pandya kingdom of Madurai ended Kopperunchinga's reign and the Kadava dynasty.

Rajaraja Narendra: Rajaraja Narendra (1022–1061 CE) was the Eastern Chalukya king of the Vengi or Vengai Nadu (as recorded in inscriptions) kingdom in South India.  Rajaraja was related to the Cholas of Tanjavur by marital and political links.  Rajaraja Narendra established the city Rajahmahendravaram (Rajahmundry).  His period was famous for the Social and Cultural heritage.  During the time of Rajaraja Chola I, Rajahmundry got sacked.  The region witnessed war between Cholas and other neighbouring dynasties and Chalukya dynasty.  The solution to strengthen the feudatorial relationship with their overlord Cholas was marriage of state between the Rajaraja Narendra and the daughter of Rajendra Chola.  The feudatorial relationship with the powerful Cholas of Tamil Country continued for two centuries.

Kamboja Pala dynasty: The Kamboja-Pala dynasty ruled parts of Bengal in the 10th to 11th centuries CE, after invading during the reign of Gopala II, the Palas.  The last Kamboja ruler of the Kamboja-Pala Dynasty Dharmapala was defeated by the south Indian Emperor Rajendra Chola I of the Chola dynasty in the 11th century.

List of Chola temples in Bangalore: The Chola dynasty was one of the longest-ruling dynasties in the history of southern India.  In Bangalore the Cholas ruled nearly a century.  The heartland of the Cholas was the fertile valley of the Kaveri River, but they ruled a significantly larger area at the height of their power, including the present-day Bangalore.  During the reign of Rajaraja Chola I—around 1004 AD—the cholas captured Bangalore after defeating the Gangas.  During their rule, they built many temples in and around the Bangalore with the Chokkanathaswamy temple, Mukthi Natheshwara Temple, Choleswara temple and the Someshwara Temple being prominent ones.  The Chokkanathaswamy temple at Domlur, whose earliest inscriptions date back to the 10th century AD, is the oldest temple in the city.  Originally built by Raja Raja Chola I, the temple was later renovated by the Hoysalas and Vijayanagara rulers.  The temple's deity was Lord Shiva, but later a Vishnu temple was built for the local residents who were mainly Vaishnavas.

Kopperunchinga I: Kopperunchinga I (reigned c. 1216–1242 CE) was a Kadava chieftain who played a major role in the political affairs of the Tamil country.  At one time an official in the service of the Chola king Kulothunga Chola III (1178-1218), Kopperunchinga utilised the opportunity arising out of the Pandyan invasion of the Chola country to become an independent king.  Inscriptions of Kopperunchinga I are not many, since his kingdom was still in the making during the major part of his life, when he was actively engaged in conflict with other powers.

Vira Narasimha II: Vira Narasimha II (Kannada: ಇಮ್ಮಡಿ ವೀರ ನರಸಿಂಹ ) (r.1220–1234) was a king of the Hoysala Empire.  During his reign the Hoysalas gained much influence in the affairs of the Tamil country.  He defeated the Kadavas and Pandyas and levied a tribute.  He acted as a support to Chola king Rajaraja Chola III, who was possibly his son-in-law, against Pandya incursions.  During his rule, Vira Narasimha made Kannanur Kuppam near Srirangam his second capital, with an intent to maintain close watch and control over affairs in Tamil country.  Later he fought for the Chola cause again and marched all the way to Rameswaram.  The Kannada poet Sumanobana was the court poet of King Vira Narasimha II

Chola dynasty: The Chola dynasty was one of the longest-ruling dynasties in the history of southern India.  The earliest datable references to this Tamil dynasty are in inscriptions from the 3rd century BCE left by Ashoka, of the Maurya Empire.  As one of the Three Crowned Kings of Tamilakam, the dynasty continued to govern over varying territory until the 13th century CE.

Chola invasion of Srivijaya: In 1025, Rajendra Chola, the Chola king from Tamil Nadu in South India, launched naval raids on ports of Srivijaya in maritime Southeast Asia, and conquered Kadaram (modern Kedah) from Srivijaya and occupied it for some time.  Rajendra's overseas expedition against Srivijaya was a unique event in India's history and its otherwise peaceful relations with the states of Southeast Asia.  Several places in Malaysia and Indonesia were invaded by Rajendra Chola I of the Chola dynasty.  The Chola invasion furthered the expansion of Tamil merchant associations such as the Manigramam, Ayyavole and Ainnurruvar into Southeast Asia.  The Chola invasion led to the fall of the Sailendra Dynasty of Srivijaya and the Chola invasion also coincides with return voyage of the great Buddhist scholar Atiśa from Sumatra to India and Tibet in 1025.  The expedition of Rajendra Chola I is mentioned in the corrupted form as Raja Chulan in the medieval Malay chronicle "Sejarah Melaya", and Malay princes have names ending with Cholan or Chulan, such as Raja Chulan of Perak.

Flag of Chola: The Flag of Chola (Tamil: சோழர் கொடி ) or Tiger Flag (Tamil: புலி கொடி ) was used by the Tamil Chola dynasty.  The Tiger or Jumping Tiger was the royal emblem of the Cholas and was depicted on coins, seals and banners.  On the coins of Uttama Chola, the Chola Tiger was shown sitting between the twin fish of Pandya and the bow of Chera.  The flag of Chola is mentioned in Periya Puranam, which was compiled during the 12th century by Sekkizhar.

Supporting paragraphs: Kadava dynasty Chola dynasty
Answer: India