시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB147787.500%

## 문제

There are N points in a plane whose coordinates are natural numbers. A convex polygon with maximal number of vertices is a convex polygon whose vertices are some of given points and the origin having maximal possible number of vertices. Origin, i.e. point with coordinates (0,0), must be one of vertices of a convex polygon with maximal number of vertices.

Write a program that will determine number of vertices in such polygon.

A polygon is convex if every line segment whose endpoints are inside that polygon is also completely inside it.

Consecutive edges of a polygon must not be parallel.

## 입력

The first line of input file contains a natural number N, 2 ≤ N ≤ 100, a number of given points.

Each of the following N lines contains two natural numbers X and Y, 1 ≤ X ≤ 100, 1 ≤ Y ≤ 100, separated by a space character, coordinates of one point. All points will be different.

## 출력

The first and only line of output file should contain number of vertices of convex polygon with maximal number of vertices.

Note: the result will always be at least 3.

## 예제 입력 1

5
4 2
2 2
2 3
3 2
3 1


## 예제 출력 1

4


## 예제 입력 2

8
10 8
3 9
2 8
2 3
9 2
9 10
10 3
8 10


## 예제 출력 2

8


## 예제 입력 3

10
9 6
1 7
2 2
3 9
8 7
3 2
9 4
3 1
9 7
6 9


## 예제 출력 3

7