Convex Hull

• Time limit: 1.00 s
• Memory limit: 512 MB

Given a set of $n$ points in the two-dimensional plane, your task is to determine the convex hull of the points.

Input

The first input line has an integer $n$: the number of points.

After this, there are $n$ lines that describe the points. Each line has two integers $x$ and $y$: the coordinates of a point.

You may assume that each point is distinct, and the area of the hull is positive.

Output

First print an integer $k$: the number of points in the convex hull.

After this, print $k$ lines that describe the points. You can print the points in any order. Print all points that lie on the convex hull.

Constraints

• $3 \le n \le 2 \cdot 10^5$
  
• $-10^9 \le x, y \le 10^9$
  

Example

Input:
6
2 1
2 5
3 3
4 3
4 4
6 3

Output:
4
2 1
2 5
4 4
6 3