Boundaries#229
The ancient state of NoRome had boundaries in the form of a convex polygon, defined by a fence. NoRome constantly expanded its territory by defeating enemies and annexing new lands.
Whenever a new boundary formed a convex polygon, the NoRomans would destroy the old fence and build a new one.
Modern historians decided to research the development of ancient NoRome. The only data they have are the coordinates of the holes from poles, which were previously placed at the vertices of the polygons.
Your program should help historians determine the number of fences built, using the coordinates of the holes, taking into account that each new fence was not contiguous with the previous one (shared no sides).
The input file contains several tests. The first line of each test gives the number of holes. Each of the following lines contains two integers and , separated by a comma, indicating the coordinates of a hole. The absolute values of the coordinates do not exceed . The coordinates are provided in a random order. There are no empty lines in the input file.
The program should print, on a separate line for each test, the number of fences built, or NO if at least one fence does not form a convex polygon.
Example 1