Crossing Points

 

            On his 6th anniversary, little Gigel has received a convex polygon with N vertices. Not knowing what to do with it, he started drawing lines between any two non-adjacent vertices. After he painted all the possible lines, he noticed that any 3 lines do not cross in the same point. Being a curious person, he would like to know the number of different crossing points which lie inside the polygon (the vertices of the polygon do not count as crossing points).

 

Input Data

            The input file POINTS.IN contains the number N of vertices of the polygon.

 

Output Data

            The output file POINTS.OUT will contaim the number of crossing points.

 

Limits

·                     3 <= N <= 65535

 

Examples:

POINTS.IN                  POINTS.OUT

3                          0

 

POINTS.IN                  POINTS.OUT

4                          1

 

POINTS.IN                  POINTS.OUT

5                          5

 

 

Time limit: 0.25 seconds/test case