Determine the convex hull of n points.
### Input
- The first lines contains an integer n.
- The next n lines, each line contains a point (x,y).
### Output
- Print p, the number of points in the convex hull on one line.
- The next p lines, print the points in the convex hull in any order.
### Constraints
- 1≤n≤105.
- −109≤x,y≤109.
### Example
Input:
871162151381195102875
Output:
7711621381195102815