With the coming of the spring of 1577, the fighting began anew. The Danzig army, led by the German mercenary commander Johann Winkelbruch , was about 7,000-12,000 strong , but with less than 1,000 cavalry. Winckelburg decided to crush the small army of Zborowski , but the Danzig army was utterly defeated by Zborowski in the battle of Lubiszewo on 17 April 1577. After the battle, the Danzig forces retreated behind the walls, citizens pulled down trees and houses in front of fortifications and a siege began. Reinforcement with King Batory arrived only in July. During it King Stefan was using heated cannonballs and turned back the flow of the Radunia river. Bathory had about 11,000 men, and Danzig, about 10,000. A surprise attack by the Danzigers managed to destroy two-thirds of the Polish artillery, vastly slowing the progress of the siege. In September 1577 Danzig and Danish fleets started a blockade of Polish trade along Elbing and attacked its suburbs. Their troops that landed were soon pushed back by Bathory's Hungarian infantry under Kacper Bekiesza, and the city council send a note thanking the King. However, after a few months, Stephen's army was unable to take the city by force. On 16 December 1577, the siege ended and citizens swore loyalty to Stefan's representatives Eustachy Wołłowicz and Andrzej Firlej. .
Question: How many months after the Danzig army was utterly defeated by Zborowski did the siege end?
Answer: 8