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:
def main():
    n = int(input())
    xy = [list(map(int, input().split())) for _ in [0]*n]

    # 中心(x1,y1)・半径r1の円と中心(x2,y2)・半径r2の円の交点を出力する関数
    def circle_cross(x1, y1, r1, x2, y2, r2):
        dist_2 = (x1-x2)**2+(y1-y2)**2
        if dist_2 > (r1+r2)**2:
            return None, None, None, None
        a = (dist_2+r1**2-r2**2)/2
        r = (dist_2*(r1**2)-a**2)**0.5
        ans_x1 = ((a*(x1-x2))+(y1-y2)*r)/dist_2
        ans_x2 = ((a*(x1-x2))-(y1-y2)*r)/dist_2
        ans_y1 = ((a*(y1-y2))-(x1-x2)*r)/dist_2
        ans_y2 = ((a*(y1-y2))+(x1-x2)*r)/dist_2
        return ans_x1+x2, ans_y1+y2, ans_x2+x2, ans_y2+y2

    def check(r):
        flag = 0
        point_list = []
        for i in range(n):
            x1, y1 = xy[i]
            for j in range(i+1, n):
                x2, y2 = xy[j]
                if (x1-x2)**2+(y1-y2)**2 <= 4*(r**2)-10**-9:
                    temp = circle_cross(x1, y1, r, x2, y2, r)
                    point_list.append((temp[0], temp[1]))
                    point_list.append((temp[2], temp[3]))
        for i, j in point_list:
            for x, y in xy:
                if (i-x)**2+(j-y)**2 > r**2+10**-9:
                    break
            else:
                return True
        return False

    def b_search(a, b, value, delta):
        while True:
            med = (a+b)/2
            if abs(b-a) < delta:
                if value(a):
                    return a
                else:
                    return b
            elif value(med):
                b = med
            else:
                a = med

    print(b_search(0, 3000, check, 10**-7))


main()