Collinear Points#1654

Collinear Points

1 second
16 megabytes
Very easy

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.

Input

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.

Output

Print the maximum number of points that lie on a single straight line.

Examples

Example 1

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