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:
import sys
sys.setrecursionlimit(10**9)
input = lambda: sys.stdin.readline().rstrip()
inpl = lambda: list(map(int,input().split()))

N = int(input())
x = []
y = []
for i in range(N):
    xy = inpl()
    x.append(xy[0])
    y.append(xy[1])
ans2 = 10**12
for i in range(N-2):
    for j in range(i+1,N-1):
        for k in range(j+1,N):
            a = 2*(x[j]-x[i])
            c = 2*(x[k]-x[j])
            b = 2*(y[j]-y[i])
            d = 2*(y[k]-y[j])
            P = x[j]**2 - x[i]**2 + y[j]**2 - y[i]**2
            Q = x[k]**2 - x[j]**2 + y[k]**2 - y[j]**2

            det = a*d - b*c
            if det == 0:
                continue
            Cx = (d*P - b*Q)/det
            Cy = (a*Q - c*P)/det
            r2 = (Cx-x[i])**2 + (Cy-y[i])**2
            for p in range(N):
                if p in (i,j,k):
                    continue
                if (Cx-x[p])**2 + (Cy-y[p])**2 > r2:
                    break
            else:
                if r2 < ans2:
                    ans2 = r2

for i in range(N-1):
    for j in range(i+1,N):
        Cx = (x[i] + x[j])/2
        Cy = (y[i] + y[j])/2
        r2 = ((x[i]-x[j])**2 + (y[i]-y[j])**2)/4
        for p in range(N):
            if p in (i,j):
                continue
            if (Cx-x[p])**2 + (Cy-y[p])**2 > r2:
                break
        else:
            if r2 < ans2:
                ans2 = r2

print(ans2**0.5)