French and Savoyard troops numbering over 50,000, under the command of Charles Emmanuel, entered Milanese territory as early as October 24, against minimal resistance, as the Austrian forces in the duchy numbered only about 12,000.  By  November 3, the city of Milan itself had surrendered, although the Austrian governor, Count Wirich Philipp von Daun, still held the fortress.  France's great general, the Duke de Villars, joined Charles Emmanuel in Milan on November 11.  While Villars wanted to move immediately against Mantua to secure the Alpine passes against Austrian reinforcements, Charles Emmanuel, mistrustful of his French allies and their dealings with Spain, sought to secure Milan.  The army spent the next three months eliminating Austrian opposition from the remaining fortified towns in the duchy.  Villars attempted to interest Don Carlos of Parma in joining the expedition against Mantua, but Carlos was focused on the campaign into Naples.  Villars began to move against Mantua, but Charles Emmanuel resisted, and the army made little progress.  In early May, an Austrian army of 40,000 under Count Claude Florimond de Mercy crossed the Alps and threatened to close in on the French army's rear by a flanking maneuver.  Villars responded by retreating from Mantua and attempted without success to interrupt the Austrian army's crossing of the Po River.  Villars, frustrated by Charles Emmanuel's delaying tactics, quit the army on May 27.  He fell ill on the way back to France and died in Turin on June 17.
Question: How many days passed after Milan surrendered and Duke de Villars arrived in Milan?
Answer: 8