 Complete the following phrase:  In 1234, the Jin dynasty was conquered by the Mongols, who took control of northern China, maintaining uneasy relations with the Southern Song. Möngke Khan, the fourth Great Khan of the Mongol Empire, died in 1259 while besieging the mountain castle Diaoyucheng, Chongqing. His younger brother Kublai Khan was proclaimed the new Great Khan, though his claim was only partially recognized by the Mongols in the west. In 1271, Kublai Khan proclaimed himself Emperor of China and established the Yuan dynasty. After two decades of sporadic warfare, Kublai Khans armies 