Convex Hull

In mathematics, we define a shape or set is convex if for any two points that are part of the shape,

the whole connecting line segment is also part of the shape.

And the convex hull is the smallest convex set that contains that subset.

Given a set of points S, then calculate the convex hull.

Notice: These points are not collinear.

Input

The input consists of multiple tests. For each test:

The first line will give a number n, indicating the number of points. (\(1 \leq n \leq 100\))

Then there is n lines containing the x-coordinate and y-coordinate of each point.(\(1 \leq x, y \leq 1000\))

Tests end when n=0.

Output

For each case, print out the sum of x-coordinate of the vertex of the convex hull and the sum of y-coordinate of the vertex of the convex hull

Each line contains one vertex.

Sample Input

5
1 1
2 2
2 1
3 1
2 0
3
0 0
2 0
1 1
0

Sample Output

8 4
3 1

Author

imcmy