Triangles and Regular Polygons
By M.C. Pinto, UNILA 
Brazil
By M.C. Pinto, UNILA Brazil
Professor Rafael loves Computer Graphics. Its favourite activity is rendering objects, specially dolls. But he does not like to draw regular polygons using triangles. This task is done by composing a regular polygon using only triangles, in such a way that the triangles do not intercept each other and the minimum number of them are used in this composition. In the picture below you can see a square and a pentagon with its triangles.
Professor Rafael asked you to calculate the minimum number of triangles necessary to compose a N-sided regular polygon.
The input is a single number N (3 ≤ N ≤ 109), indicating the number of sides of a regular polygon.
The output is the minimum number of triangles necessary to compose an N-sided regular polygon.
| Input Samples | Output Samples |
|
3 |
1 |
|
4 |
2 |
|
5 |
3 |