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 \leq n \leq 2 \cdot 10^5~
• ~-10^9 \leq x, y \leq 10^9~

Example

Sample input

6
2 1
2 5
3 3
4 3
4 4
6 3

Sample output

4
2 1
2 5
4 4
6 3