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Description

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. Th

e 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, featu

re 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.

Farmer John

有n(5≤n≤250)个栅栏点，他需要围成一个栅栏圈，这个圈是一个凸包并且凸包上的点最多....

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

Output

• Line 1: A single integer, the maximum possible number of fence posts that form a convex polygon.

Samples

6
5 5
2 3
3 2
1 5
5 1
1 1
INPUT DETAILS:
A square with two points inside.

5
The largest convex polygon is the pentagon (2,3), (3,2), (5,1), (5,5), (1,5).