# P2924 [USACO08DEC]大栅栏Largest Fence

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• 113提交
• 题目提供者 FarmerJohn2
• 评测方式 云端评测
• 标签 凸包 数论,数学 素数判断,质数,筛法 USACO 2008 高性能
• 难度 省选/NOI-
• 时空限制 1000ms / 128MB
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## 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。

## 输入输出格式

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.

## 输入输出样例

输入样例#1： 复制
6
5 5
2 3
3 2
1 5
5 1
1 1

输出样例#1： 复制
5


## 说明

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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