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 dist2(a, b):
    # 2点a,bの距離の2乗
    ax, ay = a
    bx, by = b
    return (ax-bx)**2+(ay-by)**2

def circum(a, b, c):
    # 三角形ABCの外心
    ax, ay = a
    bx, by = b
    cx, cy = c
    s = dist2(b, c)*(dist2(c, a)+dist2(a, b)-dist2(b, c))
    t = dist2(c, a)*(dist2(a, b)+dist2(b, c)-dist2(c, a))
    u = dist2(a, b)*(dist2(b, c)+dist2(c, a)-dist2(a, b))
    ox = (s*ax+t*bx+u*cx)/(s+t+u)
    oy = (s*ay+t*by+u*cy)/(s+t+u)
    return ox, oy

n = int(input())
P = [tuple(map(int, input().split())) for i in range(n)]
eps = 10**(-7)
if n == 2:
    r = dist2(P[0], P[1])**0.5 / 2
    print(r)
    exit()
for i in range(n-2):
    for j in range(i+1, n-1):
        for k in range(j+1, n):
            a, b, c = P[i], P[j], P[k]
            ax, ay = a
            bx, by = b
            cx, cy = c
            if dist2(a, b) + dist2(b, c) <= dist2(c, a):
                p = (cx+ax)/2, (cy+ay)/2
                r2 = dist2(a, p)
            elif dist2(b, c) + dist2(c, a) <= dist2(a, b):
                p = (ax+bx)/2, (ay+by)/2
                r2 = dist2(b, p)
            elif dist2(c, a) + dist2(a, b) <= dist2(b, c):
                p = (bx+cx)/2, (by+cy)/2
                r2 = dist2(c, p)
            else:
                p = circum(a, b, c)
                r2 = dist2(a, p)
            if all([dist2(p, q) <= r2 + eps for q in P]):
                print(r2**0.5)
                exit()