Onion Core In every domain there is a strong urge to get a sense of the center of things. For instance when a set of numbers is under considered, commonly used notions of centralness are the mean, median, and mode. Likewise for geometric objects, there are numerous definitions of center. The one we will consider here is the center you get by "peeling the onion". To be specific, given a set of points in the real plane, first remove the points which lie on some line such that all the other points are strictly on one side of the line (vertices of the convex hull). Then recursively repeat this procedure until you arrive at a set of points each one of which lies on such a line, in other words as set for which one more layer removal would leave no remainint points. The core is considered to be the average of the points of this last layer. Here average means sum of points divided by number of points. Addition of points and division of a point by a scalar are well defined.

Input: Each data set has a header line giving a name to the data set, followed by a number of lines containing the points. Each line contains two real numbers, the x coordinate followed by the y coordinate.

Output: For each data set, print on one line the core point followed by a space and the data set name.

Sample input:
cube
0 0
0 1
1 0
1 1
cube with random interior point
0 0
0 1
1 0
1 1
.3 0.58

Sample output:
0.5 0.5 cube
0.3 0.58 cube with random interior point