Elephants
In the Mendeleev Zoo, there are n elephants, each residing in its own cage. For the purposes of this problem, each cage can be considered as a point on a plane. Each elephant has a field of view of 180º, meaning it can see all objects located within and on the boundary of a specific angle at any given time.
When setting up the cages, the Mendeleev zoologists ensured that each elephant could orient itself in such a way that no other elephants were within its field of view. Before the arrival of schoolchildren from various countries, the zoo management decided to paint two cages green. The elephants in these two cages must be able to position themselves so that they can see only each other and no other elephants.
Your task is to determine how many ways two such cages can be selected.
Input
The first line of the input contains a natural number n (1 ≤ n ≤ 1000), representing the number of cages in the zoo. Each of the following n lines contains two integers x_i and y_i, which are the coordinates of each cage. All coordinates are integers and do not exceed 10^6 in absolute value. No two cages share the same location.
Output
Output the number of ways to select a pair of cages that meet the specified conditions.