Corners of the Hull

Statement

Given n points, some possibly repeated, count the corners of their convex hull: the smallest convex polygon that contains all the points. A point that lies in the middle of an edge, or strictly inside the hull, is not a corner. Repeated copies of one point count once.

Input

The first line has n. Each of the next n lines has the coordinates x y of one point.

Output

Print one integer: the number of corners of the convex hull.

Constraints

1 <= n <= 200000
|x|, |y| <= 10^9

Example 1

5
0 0
4 0
4 4
0 4
2 2

4

The square's four corners are the hull corners. (2,2) lies inside, so it is not a corner.

Example 2

4
0 0
1 1
2 2
3 3

2

All four points lie on one line. The hull is a segment, and only its two ends are corners.

Example 3

1
5 5

1

A single point is its own hull, with one corner.