Early in 1277, before the main royal army had been mustered, Edward deployed, in south and mid-Wales, a mixture of forces comprising paid troops, some of the marcher lords' retainers and knights of the royal household. They met with considerable success as many of the native Welsh rulers, resentful of Llywelyn's overlordship, surrendered and joined the English. In July 1277, Edward launched a punitive expedition into North Wales with his own army of 15,500 — of whom 9,000 were Welshmen from the south — raised through a traditional feudal summons. From Chester the army marched into Gwynedd, camping first at Flint and then Rhuddlan and Deganwy, most likely causing significant damage to the areas it advanced through. A fleet from the Cinque ports provided naval support. Llywelyn soon realised his position was hopeless and quickly surrendered. The campaign never came to a major battle. However, Edward decided to negotiate a settlement rather than attempt total conquest. It may be that he was running short of men and supplies by November 1277 and, in any case, complete conquest of Llywelyn's territories had not been his objective.
Question: How many months passed between Edward launching a punitive expedition into North Wales and negotiating a settlement with Llywelyn?
Answer: 4