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

ans = 100000000

for i in range(N):
    ax, ay = XY[i]
    
    for j in range(i+1, N):
        bx, by = XY[j]

        dx = (ax+bx)/2
        dy = (ay+by)/2
        r2 = (ax-dx)**2 + (ay-dy)**2

        ok = True
        for x,y in XY:
            if (x-dx)**2 + (y-dy)**2 > r2 + 1e-5:
                ok = False
                break
        if ok:
            ans = min(ans, r2)

        
        for k in range(j+1, N):
            cx, cy = XY[k]

            a = (bx-cx)**2 + (by-cy)**2
            b = (cx-ax)**2 + (cy-ay)**2
            c = (ax-bx)**2 + (ay-by)**2

            aa = a*(b+c-a)
            bb = b*(c+a-b)
            cc = c*(a+b-c)
            delim = aa + bb + cc
            if delim<1e-10: continue
            dx = (ax*aa + bx*bb + cx*cc) / delim
            dy = (ay*aa + by*bb + cy*cc) / delim
            r2 = (ax-dx)**2 + (ay-dy)**2

            ok = True
            for x,y in XY:
                if (x-dx)**2 + (y-dy)**2 > r2 + 1e-5:
                    ok = False
                    break
            if ok:
                ans = min(ans, r2)

print(ans**0.5)