Description

Given $N$ points, find the smallest circle that contains all the points.

Input Format

The first line contains an integer $N$ representing the number of points. The next $N$ lines each contain two real numbers $x_i, y_i$ representing the coordinates of a point. Each value has at most two decimal places.

Output Format

The first line contains a real number representing the circle’s radius. The second line contains two real numbers representing the coordinates of the circle’s center. This problem uses an SPJ (special judge); your answer is considered correct if its absolute error from the standard answer does not exceed $10^{-9}$.

6
8.0 9.0
4.0 7.5
1.0 2.0
5.1 8.7
9.0 2.0
4.5 1.0

5.0000000000
5.0000000000 5.0000000000

Hint

For $100\%$ of the testdata, $1 \leq N \leq 10^5$, $|x_i|, |y_i| \leq 10^4$. SPJ added on 2022-02-26.

Translated by ChatGPT 5