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 C (GCC 5.4.1) (judge verdict: Accepted)

// ABC 151-F
// 2020.1.12 bal4u

#include <stdio.h>
//#include <stdlib.h>
#include <math.h>

#if 1
#define gc() getchar_unlocked()
#else
#define gc() getchar()
#endif

int in() {   // 非負整数の入力
	int n = 0, c = gc();
	do n = 10 * n + (c & 0xf); while ((c = gc()) >= '0');
	return n;
}

#define EPS 1e-10

typedef struct { double x, y; } PP;
PP p[55];

double dist(PP a, PP b)
{
	double x = a.x - b.x;
	double y = a.y - b.y;
	return sqrt(x*x + y*y);
}

double solve_by_movement(int n)
{
	int  k, i, t;
	PP a;
	double move, max, d;

    a.x = a.y = 500;
	move = 0.5;
	while (move > EPS) {
		for (t = 0; t < 100; t++) {
			max = 0;
			for (i = 0; i < n; i++) {
				if ((d = dist(a, p[i])) > max) max = d, k = i;
			}
			a.x += (p[k].x - a.x)*move;
			a.y += (p[k].y - a.y)*move;
		}
		move /= 2;
	}
	return max;
}

int main()
{
	int i, x, y, N;

	N = in();
	for (i = 0; i < N; ++i) {
		p[i].x = in(), p[i].y = in();
	}
	printf("%.10lf\n", solve_by_movement(N));
	return 0;
}