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ICPC Finals

X Maratona de Programação IME-USP Brazil
Timelimit: 3

As we all know, it hasn't been decided the local of the next final of ICPC. This time, Prof. Poucher, tried to pick a place that, somehow, would be the closest for the various participants.

To solve that out, in a big map he pointed out the location of the many possible participants of the finals. In possession of this data, Prof. Poucher wishes to choose the closest place as possible, computing the center and the radius of the smallest circunference that involves all the cities pointed out in the map (a city is covered if it is in the region or on the border of the circuference).


This problem is composed by several instances. The first line is composed by one integer n(2 ≤ n ≤ 100), and indicates the numbers of the cities. The next n lines contain the description of the position of the cities from their coordinates x and y in the plan. the coordinates are real numbers. The problem must end the execution when 0 is the value of n given in the input.


For each integer, print a line saying integer k, where k is the number of the current instance. On the second line, print the coordinate x and the coordinate y of the center and of the radium of the circunference. After each instance, your program must print a blank line.

Sample Input Sample Output

0.00 0.00
3.00 0.00
0.00 0.00
0.00 1.00
1.00 0.00
1.00 1.00
2.00 2.00

Instancia 1
1.50 0.00 1.50

Instancia 2
1.00 1.00 1.41