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())

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

c = []

for i in range(n-1):
    for j in range(i+1, n):
        c.append([(p[i][0] + p[j][0]) / 2, (p[i][1] + p[j][1]) / 2])

for i in range(n-2):
    x = p[i][0] + p[i][1] * 1j
    for j in range(i+1, n-1):
        y = p[j][0] + p[j][1] * 1j
        for k in range(j+1, n):
            z = p[k][0] + p[k][1] * 1j
            a = y - x
            b = z - x
            if a.real * b.imag == a.imag * b.real:
                continue
            C = a * b * (a.conjugate() - b.conjugate()) / (b * a.conjugate() - a * b.conjugate())
            C = C + x
            c.append([C.real, C.imag])

ans = float('inf')
for X, Y in c:
    temp = 0
    for x, y in p:
        temp = max(((X-x)**2 + (Y-y)**2) ** 0.5, temp)
    ans = min(ans, temp)

print(ans)