Task: Question Understanding
Input (English): Passage: On 10 September 1580, 600 Papal troops  commanded by Sebastiano di San Giuseppe , landed in Smerwick, near the same point where Fitzmaurice had landed the previous year. They had been paid for and sent by Pope Gregory to aid the rebellion. Desmond, Baltinglass and John of Desmond made an effort to link up with the expeditionary force but English forces under Ormonde and Grey blocked them and prompt naval action by Richard Bingham blockaded the Papal force's ships into the bay at Smerwick. San Giuseppe had no choice but to fortify his men in the fort at Dún an Óir. In October 1580, Grey de Wilton with up to 4000 troops arrived at Smerwick and laid siege to the garrison. The invasion forces were geographically isolated on the tip of the narrow Dingle Peninsula, cut off by Mount Brandon on one side and the much larger English force on the other. They had no means of escape. In addition, the English had brought up heavy artillery by sea, which rapidly broke down the improvised defences of Dún an Óir. After a three-day siege, commander Di san Giuseppe surrendered on 10 October 1580. Grey de Wilton ordered the massacre of the invasion forces, sparing only the commanders. Italian and Spanish troops, and Irish men and women, were beheaded and their bodies thrown into the sea. Among the English soldiers present at the siege and massacre was the writer and explorer Walter Raleigh. This was brought against him as a criminal charge in one of his trials. Raleigh argued that he was "obliged to obey the commands of his superior officer" but he was unable to exonerate himself.
Question: On what day did the seige again the troops led by di San Giuseppe which would lead to his surrender begin?
Output (English): date