题目描述

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.

Time limit: 1.2 seconds

POINTS: 400

Farmer John的农场里有N（5<=N<=250）个篱笆桩，每个都有独一无二的坐标(xi,yi)（1<=xi,yi<=1000）。他想选择尽量多的篱笆桩来构建他的围栏。这个围栏要美观，所以必须是凸多边形的。那他最多能选多少个呢？

所有的篱笆桩中不存在三点共线。

输入格式

* 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

输出格式

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

6 
5 5 
2 3 
3 2 
1 5 
5 1 
1 1 

5 

提示

A square with two points inside.

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