## MPOLY - Polygon

 English Vietnamese

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.

### Input

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.

### Output

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.

### Sample

```POLYGON.IN

5
4 2
2 2
2 3
3 2
3 1

POLYGON.OUT

4

POLYGON.IN

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

POLYGON.OUT

8

POLYGON.IN

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

POLYGON.OUT

7
Explanation for test data #2 (coordinates of polygon)

2 8
3 9
8 10
9 10
10 8
10 3
9 2
0 0

```