Triangular Reform
King Triang IV of Polygonia is passionate about reforms. To leave a lasting legacy, he has decided to implement a territorial reform in his country. Polygonia is shaped like a simple polygon, meaning its boundary does not intersect or touch itself. In Polygonia, internal diagonals are crucial — these are segments connecting vertices of the polygon's boundary that lie entirely within the polygon, without touching the edges. Additionally, no two internal diagonals in Polygonia are collinear.
Instead of the conventional division into administrative units, King Triang IV plans to partition his country into administrative triangles using internal diagonals. To optimize the administrative structure, he has mandated a plan to divide the country into the fewest possible number of administrative triangles.
Your task is to write a program that divides Polygonia using internal diagonals into the minimum number of administrative triangles.
Input
The first line of the input contains the integer N (3 ≤ N ≤ 20) — the number of vertices of the polygon forming Polygonia's boundary. The following N lines each contain 2 integers, with absolute values not exceeding 10000 — the coordinates of the vertices listed in counterclockwise order. It is guaranteed that no three consecutive vertices of the polygon are collinear, and the polygon has no self-intersections or self-tangencies. Additionally, no two diagonals within the polygon are collinear.
Output
On the first line of the output, print the minimum number of administrative triangles into which Polygonia can be divided.
On the second line, print the number of different internal diagonals K used to achieve this division.
For each of the next K lines, print 4 integers — the coordinates of the start and end points of each diagonal used in the division, ensuring each lies entirely within the polygon and does not coincide with its boundary.
If there are multiple valid divisions, output any one of them.