#000009

prave

N different points with integer coordinates are given in a plane. You are to write a program that finds the maximum number of collinear points (they all belong to the same line).


InputThe first line of standard input gives a number N (1 <= N <= 600). In each of the next N lines there will be two integers X and Y (-32000 <= X,Y <= 32000) that will represent the coordinates of the given points.

OutputTo the standard output, output only one integer that yields the maximum number of points given in the input that are collinear.

Input:
4
1 1
2 2
2 1
3 1

Output:
3

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