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

**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