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
MOD = 10**9+7


def dist(a, b):
    dx = a[0]-b[0]
    dy = a[1]-b[1]
    return math.sqrt(dx * dx + dy * dy)


def max_dist(p, x, y):
    result = 0
    for i in range(len(p)):
        result = max(result, dist((x, y), p[i]))
    return result


def ternary_search2(p, x):
    l = 0
    r = 1000
    for i in range(100):
        c1 = (l*2+r)/3
        c2 = (l+r*2)/3
        if(max_dist(p, x, c1) > max_dist(p, x, c2)):
            l = c1
        else:
            r = c2
    return max_dist(p, x, l)


def ternary_search1(p):
    l = 0
    r = 1000
    for i in range(100):
        c1 = (l*2+r)/3
        c2 = (l+r*2)/3
        if(ternary_search2(p, c1) > ternary_search2(p, c2)):
            l = c1
        else:
            r = c2

    return ternary_search2(p, l)


def main():
    n = int(input())
    p = []
    for i in range(n):
        p.append(list(map(int, input().split())))

    print(ternary_search1(p))


main()