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 = [list(map(int,input().split())) for _ in range(N)]

cand = []
for i in range(N):
    xa,ya = xy[i]
    for j in range(i+1,N):
        xb,yb = xy[j]
        cand.append([(xa+xb)/2,(ya+yb)/2])
        for k in range(j+1,N):
            xc,yc = xy[k]
            if (xa-xb)*(ya-yc)-(xa-xc)*(ya-yb)!=0:
                x = (ya-yc)*(xa**2+ya**2-xb**2-yb**2)-(ya-yb)*(xa**2+ya**2-xc**2-yc**2)
                y = -(xa-xc)*(xa**2+ya**2-xb**2-yb**2)+(xa-xb)*(xa**2+ya**2-xc**2-yc**2)
                x /= 2*((xa-xb)*(ya-yc)-(xa-xc)*(ya-yb))
                y /= 2*((xa-xb)*(ya-yc)-(xa-xc)*(ya-yb))
                cand.append([x,y])

ans = float('inf')
for x,y in cand:
    d = 0
    for i in range(N):
        d = max(d,((xy[i][0]-x)**2+(xy[i][1]-y)**2)**0.5)
    ans = min(ans,d)
print(ans)