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 sys
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()
def resolve():
    n = int(input())
    C = [complex(*map(int, input().split())) for _ in range(n)]

    res = INF
    for k in range(n):
        p1 = C[k]
        for j in range(k):
            p2 = C[j]
            for i in range(j):
                p3 = C[i]
                a = abs(p2 - p3)
                b = abs(p3 - p1)
                c = abs(p1 - p2)
                numerator = a**2 * (b**2 + c**2 - a**2) * p1 + b**2 * (c**2 + a**2 - b**2) * p2 + c**2 * (a**2 + b**2 - c**2) * p3
                denominator = a**2 * (b**2 + c**2 - a**2) + b**2 * (c**2 + a**2 - b**2) + c**2 * (a**2 + b**2 - c**2)
                if denominator < 0.001:
                    continue
                center = numerator / denominator
                radius = -INF
                for p in C:
                    radius = max(radius, abs(center - p))
                res = min(radius, res)

    for j in range(n):
        for i in range(n):
            center = (C[i] + C[j]) / 2
            radius = -INF
            for p in C:
                radius = max(radius, abs(center - p))
            res = min(radius, res)

    print(res)
resolve()