Problem: 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}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

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


Output

6.726812023536805158

Solution (in PYTHON3):

Solution:
import math

def get_circle_center_and_radius(x1, y1, x2, y2, x3, y3):
    """
    3点を通る円の中心と半径を取得
    """
    d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
    x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
    y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
    r = math.sqrt((x - x1) ** 2 + (y - y1) ** 2)
    return x, y, r

n = int(input())
l = []
ans = float('inf')
for i in range(n):
    l.append([int(_) for _ in input().split()])

for i in range(0, n - 1):
    for j in range(i + 1, n):
        x = (l[i][0] + l[j][0]) / 2
        y = (l[i][1] + l[j][1]) / 2
        r = math.sqrt((l[i][0] - l[j][0])** 2 + (l[i][1] - l[j][1])**2) / 2
        flag = 1
        for k in range(n):
            if k != i and k != j:
                if (x - l[k][0]) ** 2 + (y - l[k][1]) ** 2 > r ** 2:
                    flag = 0
        if flag == 1:
            ans = min(r, ans)
        # print(x, y, r, ans)
for i in range(0, n - 2):
    for j in range(i + 1, n - 1):
        for k in range(i + 2, n):
            try:
                x, y, r = get_circle_center_and_radius(l[i][0],l[i][1],l[j][0],l[j][1],l[k][0],l[k][1])
                flag = 1
                for p in range(n):
                    if p != i and p != j and p != k:
                        if (x - l[p][0]) ** 2 + (y - l[p][1]) ** 2 > r ** 2:
                            flag = 0
                if flag == 1:
                    ans = min(r, ans)
                # print(x, y, r, ans)
            except:
                continue
print(ans)