Knights of the Round Table

It is the year 573 AD. King Arthur rules all of Britain. He is a just ruler, loved by the people. But governing such a big country is a daunting task and requires a lot of effort. Luckily, he is aided in this by the most noble Knights of the Round Table. Initially, this council was composed only of the most valiant heroes of the kingdom, such as Sir Gawain, Sir Lancelot, and Sir Galahad. However, recently, King Arthur found it politically necessary to admit additional members to this most holy round. The main reason for this is that, due to the prolonged peace under his reign, the guilds demanded more influence over the country’s governance. "After all, in times of peace you need bread more than swords, don't you?", said the head of the guild of bakers. Being an exceptionally just and noble ruler, Arthur agreed.

This led to an increase in the number of "knights" of the Round Table. Arthur found that he needed to order a much bigger table from the guild of carpenters (who, in turn, immediately demanded seats at it), and subsequently had to add a new wing to Castle Camelot to accommodate it (you can guess what the stonemasons asked for next).

As a result, the weekly meetings of the Round Table have now become quite crowded. In fact, there are so many people that it can be difficult to understand each other when sitting at opposite sides of the table. To determine how serious this problem is, Arthur wants you to compute how far apart the two farthest members of the Round Table are seated. The complication is that there is only a finite number of people sitting at the table, and they are not distributed equally around it—some sit close together (to discuss important matters), while others prefer to distance themselves from their neighbors (for example, the representative of the guild of healers and the head of the guild of assassins).

Your task is to write a program that computes the maximum distance between any pair of chairs around the table. For this, you are given a list of angles (sorted counter-clockwise) that indicate the placement of chairs around the table. The radius of the table is equal to the number of knights seated at it.