Problem Description
If you are fond of ACM , you must have know the word “Convex Hall ” . which can forms a convex polygon .
Now we define the size of a convex hall as the number of edges it contains .
Give you several points , you can choose some points to form a Convex Hall .Can you tell me the biggest size of convex hall you may find?
What’s more , the convex hall must contains the point (0,0).
Input
Each test case will contains an integer n (2<= n<= 100 ), which stands for the number of points you are given besides (0,0).
Then n lines follow. Each line contains two integers x and y ( 0<=x, y <=100) , mean the coordinate of the point .
You may suppose you can at least find a convex hall with 3 edges.
Output
For each case, output the biggest size of convex hall in one line.
Sample Input
4
0 1
1 0
0 2
2 0
Sample Output
3
