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10 초 (추가 시간 없음) 512 MB 0 0 0 0.000%

문제

Consider a set of points P in the plane such that no 3 points are collinear. Construct a windmill as follows:

  • Choose a point pP and a starting direction such that the line through p in that direction does not intersect any other points in P. Draw that line (Note: line, NOT ray).
  • Rotate the line clockwise like a windmill about the point p as its pivot until the line intersects another point qP. Designate that point q to be the new pivot, and then continue the rotation. This is called promoting point q.
  • Continue this process until the line has rotated a full 360°, returning to its original direction (it can be shown that the line will also return to its original position after a 360° rotation).

During this process, a given point in P can be a pivot multiple times. Considering all possible starting pivots and orientations, find the maximum number of times that a single point can be promoted during a single 360° rotation of a windmill. Note that the first point is a pivot, but not promoted to be a pivot at the start.

입력

The first line of input contains a single integer n (2 ≤ n ≤ 2000), which is the number of points pP.

Each of the next n lines contains two space-separated integers x and y (−105 ≤ x, y ≤ 105). These are the points. Each point will be unique, and no three points will be collinear.

출력

Output a single integer, which is the maximum number of times any point pP can be promoted, considering a full 360° rotation and any arbitrary starting point.

예제 입력 1

3
-1 0
1 0
0 2

예제 출력 1

2

예제 입력 2

6
0 0
5 0
0 5
5 5
1 2
4 2

예제 출력 2

3