Suppose you are given several distinct points on a plane, each specified by integer and coordinates. You want to determine the maximum number of points that lie exactly on the same straight line.
The first line contains the number of points (3 \leq n \leq 200). Each of the next lines contains the coordinates and (-2000 \leq x, y \leq 2000), separated by a space.
Print the maximum number of points that lie on a single straight line.
Example 1