According to the Yuanshi, the Yuan fleet set out with an estimated 15,000 Mongol and Chinese soldiers and 1,600-8,000 Korean soldiers in 300 large vessels and 400-500 smaller craft along with several thousand sailors, although figures vary considerably depending on the source and many modern historians consider the numbers exaggerated. The primary port for the operation was Quanzhou in Fujian, then the center of China's maritime trade. They landed on Komodahama beach on Tsushima Island on October 5, 1274. Sō Sukekuni, governor of Tsushima, led a cavalry unit of 80 to defend the island, but he and his outnumbered unit were killed in the engagement. The Mongols and Koreans subsequently invaded Iki. Tairano Takakage, the Governor of Iki, fought the invaders with about 100 of his cavalrymen, but he killed himself after his unit was defeated. The Mongol forces landed on November 19 in Hakata Bay, a short distance from Dazaifu, the ancient administrative capital of Kyūshū. The following day brought the Battle of Bun'ei , also known as the "First Battle of Hakata Bay". The Japanese coalition force opposing them included 120 armed samurai each with a warband and likely numbered between 3,000 and 6,000 strong. Later accounts have both sides believing themselves to be drastically outnumbered by the enemy; the Yuanshi provides an estimate of 102,000 for the Japanese force, while the Japanese Hachiman Gudokun describes the invaders as outnumbering the Japanese 10 to 1. Conlan argues that the Yuanshi's account of the battle suggests that both the Japanese and Yuan forces were of similar size. Conlan estimated that both armies numbered around 3,000 each .

How many ships were there (at least) in the Yuan fleet in 1274?
700