Given N points on the cartesian plane, find the perimeter and area of the convex hull.

Input

The first line contains a single integer N. Next N lines contains the x and y coordinates of the points one per line. 

Output

Print two integers - perimeter and area of convex hull. Round up both to the nearest integer.

Example

Input:
4

2 3

6 9

5 5

2 3

Output:
14 10

Contraints:

3 <= N <= 106

0 <= x, y <= 104