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:
n = int(input())
XY = []
for i in range(n):
    x, y = map(int, input().split())
    XY.append((x, y))


# 外積、平行判定
def cross(a, b):
    return a.real * b.imag - b.real * a.imag


# 内積、直行判定
def dot(a, b):
    return a.real * b.real + a.imag * b.imag


# 外心の中心
def circumcenter(a, b, c):
    bunshi = (a - b) * dot(c, c) + (b - c) * dot(a, a) + (c - a) * dot(b, b)
    bunbo = (a - b) * c.conjugate() + (b - c) * a.conjugate() + (c - a) * b.conjugate()
    if bunbo == 0:
        return False, 0
    return True, bunshi / bunbo


kouho = []
for i in range(n - 1):
    a, b = XY[i]
    z1 = complex(a, b)
    for j in range(i + 1, n):
        c, d = XY[j]
        z2 = complex(c, d)
        kouho.append((z1 + z2) / 2)
if n >= 3:
    for i in range(n - 2):
        a, b = XY[i]
        z1 = complex(a, b)
        for j in range(i + 1, n - 1):
            c, d = XY[j]
            z2 = complex(c, d)
            for k in range(j + 1, n):
                e, f = XY[k]
                z3 = complex(e, f)
                flag, gaishin = circumcenter(z1, z2, z3)
                if flag:
                    kouho.append(gaishin)
ans = 10 ** 10
for z in kouho:
    temp = 0
    for i in range(n):
        x, y = XY[i]
        z1 = complex(x, y)
        temp = max(temp, abs(z - z1))
    ans = min(ans, temp)
print(ans)