Geometry Enjoyer

Altair was playing with the points on the plane, as usual. One day he found a new game and asked you to play it with him.

He drew a convex polygon with $k$ sides on the plane. No two sides of the polygon are parallel. Then he extended every side to a line and found the intersection point of every pair of lines.

He now gives you the points he got. Find the original polygon from these points.

The first line contains one integer $n$ ($1 \le n \le 200$), the number of points.

Each of the next $n$ lines contains four integers $p_x$, $q_x$, $p_y$, and $q_y$ ($-10^6 \le p_x, p_y \le 10^6$, $1 \le q_x, q_y \le 10^6$). The X coordinate of the $i$-th point is $p_x / q_x$, and the Y coordinate is $p_y / q_y$. $p_x$ and $q_x$ are coprime, and $p_y$ and $q_y$ are coprime.

It is guaranteed that the polygon is uniquely determined by the given points.

Print the number of vertices $k$ on the first line.

Each of the next $k$ lines contains the coordinates of one vertex in the form $p_x$, $q_x$, $p_y$, $q_y$. The vertices may be printed in any order. Each $p_x$ and $q_x$ must be coprime, and each $p_y$ and $q_y$ must be coprime.