 Complete the following phrase:  Following Roman rule, Sicily, Corsica and Sardinia were conquered by the Vandals, then by the Ostrogoths, and finally by the Byzantines. At one point, Sardinia grew increasingly autonomous from the Byzantine rule to the point of organizing itself into four sovereign Kingdoms, known as Judicates, that would last until the Aragonese conquest in the 15th century. Corsica came under the influence of the Kingdom of the Lombards and later under the maritime Republics of Pisa and Genoa. In 687, Sicily became the Byzantine Theme of Sicily; during the course of the ArabByzantine wars, Sicily gradually became the Emirate of Sicily 8311072. Later, a series of conflicts with the 