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).</p>

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.

입력 형식

• 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
</ul>

 

출력 형식

• Line 1: A single integer, the maximum possible number of fence posts that form a convex polygon.
</ul>

 

예제 입력

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

예제 출력

5

힌트

The largest convex polygon is the pentagon (2,3), (3,2), (5,1), (5,5), (1,5).</p>