Largest Fence
Farmer John has purchased N (5 ≤ N ≤ 250) fence posts in order to build a very nice-looking fence. Everyone knows the best fences are convex polygons where fence posts form vertices of a polygon. The pasture is represented as a rectilinear grid; fencepost i is at integer coordinates (x_i, y_i) (1 ≤ x_i ≤ 1,000; 1 ≤ y_i ≤ 1000).
Given the locations of N fence posts (which, intriguingly, feature no set of three points which are collinear), what is the largest number of fence posts FJ can use to create a fence that is convex?
For test cases worth 45% of the points for this problem, N ≤ 65.
Input* Line 1: A single integer: N
* Lines 2..N+1: Line i+1 describes fence post i's location with two space-separated integers: x_i and y_i.
* Lines 2..N+1: Line i+1 describes fence post i's location with two space-separated integers: x_i and y_i.
Output* Line 1: A single integer, the maximum possible number of fence posts that form a convex polygon.
Input:
Output:
6
5 5
2 3
3 2
1 5
5 1
1 1Output:
5Hint:
A square with two points inside. The largest convex polygon is the pentagon (2,3), (3,2), (5,1), (5,5), (1,5).
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