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:
from math import sqrt
def dist(x1, y1, x2, y2):
    return sqrt((x1-x2)**2 + (y1-y2)**2) + 10**(-7)

def max_dist(p, x, y):
    res = 0
    for i in range(len(p)):
        dis = dist(p[i][0], p[i][1], x, y)
        if res < dis:
            res = dis
    return res

def calc(p, x):
    yL, yR = 0, 1000
    while yL + 10**-7 < yR:
        yl, yr = (2*yL + yR)/3, (yL + 2*yR)/3
        ql, qr = max_dist(p, x, yl), max_dist(p, x, yr)
        if ql < qr:
            yR = yr
        else:
            yL = yl
    return qr, yR

def main():
    n = int(input())
    p = [list(map(int, input().split())) for _ in range(n)]
    xL, xR = 0, 1000
    while xL + 10**-7 < xR:
        xl, xr = (2*xL + xR)/3, (xL + 2*xR)/3
        ql, yl = calc(p, xl)
        qr, yr = calc(p, xr)
        if ql < qr:
            xR = xr
        else:
            xL = xl
    print(max_dist(p, xR, yr))

if __name__ == "__main__":
    main()