During the summer campaign of 1673, Turenne had the thankless task of trying to contain Leopold's troops under the command of Raimondo Montecuccoli. Montecuccoli finally joined with the Dutch troops of William III to besiege and take the city of Bonn from the French. In August 1673, The Habsburg monarchies of Spain and the Holy Roman Empire signed a formal alliance with the Republic that required that France be returned to her boundaries of 1659. This alliance was strengthened in October by Charles IV of Lorraine. Imperial and Dutch troops conquered the town of Naarden from the French on 13 September. The Spanish, who had yet to formally enter the war, declared war on the French on 16 October. At about the same time Frederick William re-entered the war against France. The position of Louis at this stage was bad enough, but it worsened when England made a separate peace, the Treaty of Westminster, with all of the nations arrayed against France on 19 February 1674. Charles II had been forced into making peace with the Republic by the Parliament which returned to session in October 1673.
Question: How many months after the Hapsburg monarchies signed the alliance was Naarden conquered?
Answer: 1