Convex Hull of the Polygon 

Suppose that a polygon is represented by a set of integer coordinates, {(x0, y0), (x1, y1), (x2, y2), ..., (xn, yn), (x0, y0)}. Please find the convex hull of the polygon, where a convex hull is the minimum bounding convex polygon and "convex" means the angle between two consecutive edges is less than 180o.

Input file 

The input file contains a sequence of integer coordinates. The ith pair of numbers means the coordinatex (xi, yi).

Output 

The output should contain a sequence of integer coordinates, in which each coordinate is represented by a pair of integer numbers in a line.

Sample Input  

0, 0
2, 0
1, 1
2, 2
0, 2
0, 0

Sample Output  

0, 0
2, 0
2, 2
0, 2
0, 0