Problem:
Score : 600 points

Problem Statement

Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

2 \leq N \leq 50

0 \leq x_i \leq 1000

0 \leq y_i \leq 1000

The given N points are all different.

The values in input are all integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in Rust (1.15.1) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;

fn main() {
    input! {
        n: usize,
        xy: [(f64, f64); n],
    }
    let decay = 0.999;
    let mut range = 1000.0;
    let mut cx = 0.0;
    let mut cy = 0.0;
    let dist = |x1: f64, y1: f64, x2: f64, y2: f64| -> f64 {
        ((x1 - x2).powi(2) + (y1 - y2).powi(2)).sqrt()
    };
    let mut ans = 0.0;
    for _ in 0..100000 {
        let mut far_dir = (0.0, 0.0);
        let mut far_dist = 0.0;
        for &(x, y) in xy.iter() {
            let d = dist(x, y, cx, cy);
            if d > far_dist {
                far_dist = d;
                far_dir = (x - cx, y - cy);
            }
        }
        let fd_norm = dist(far_dir.0, far_dir.1, 0.0, 0.0);
        far_dir.0 /= fd_norm;
        far_dir.1 /= fd_norm;
        cx += far_dir.0 * range;
        cy += far_dir.1 * range;
        ans = far_dist;
        range *= decay;
    }
    println!("{:.12}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin63D822AF";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";