The Mongols' greatest triumph was when Kublai Khan established the Yuan dynasty in China in 1271. The Yuan dynasty created a "Han Army"  out of defected Jin troops and an army of defected Song troops called the "Newly Submitted Army" . The Mongol force which invaded southern China was far greater than the force they sent to invade the Middle East in 1256. The Yuan dynasty established the top-level government agency Bureau of Buddhist and Tibetan Affairs to govern Tibet, which was conquered by the Mongols and put under Yuan rule. The Mongols also invaded Sakhalin Island between 1264 and 1308. Likewise, Korea  became a semi-autonomous vassal state and compulsory ally of the Yuan dynasty for about 80 years. The Yuan dynasty was eventually overthrown during the Red Turban Rebellion in 1368 by the Han Chinese who gained independence and established the Ming dynasty.
Question: Which engaement did the Mongols take a larger force to, southern China or the Middle East?
Answer: southern China