Performing at the Center of the World

A musician is preparing a performance for the fans. To make the performance feel shared with the audience, the concert hall is considered as a circle, and every fan must lie inside the circle or on its boundary.

The positions of N fans are given as plane coordinates (x, y). The musician wants to perform at the center of a circle with the smallest possible radius among all circles that contain every fan.

Write a program that finds the center coordinates and radius of such a smallest circle.

The first line contains N, the number of fans. (1 <= N <= 100)

Each of the next N lines contains the x-coordinate and y-coordinate of one fan. Each coordinate is given with at most six digits after the decimal point and satisfies -600000 <= x, y <= 600000.

Print three numbers on the first line: the x-coordinate of the circle's center, the y-coordinate of the center, and the radius. An absolute or relative error of at most $10^{-3}$ is accepted.