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)]

def dist(x, y, u, v):
    return ((x - u)**2 + (y - v)**2)**0.5

def mxR(x, y):
    return max([dist(x, y, u, v) for u, v in XY])

ans = 10**18
for i, A in enumerate(XY):
    ans = min(ans, mxR(A[0], A[1]))
    for j, B in enumerate(XY[i + 1:]):
        ans = min(ans, mxR((A[0] + B[0]) / 2, (A[1] + B[1]) / 2))

        for C in XY[j + 1:]:
            Z = [0, 0]

            a, b, c = dist(*(B + C)), dist(*(C + A)), dist(*(A + B))

            S = a**2 * (b**2 + c**2 - a**2) + b**2 * (c**2 + a**2 - b**2) + c**2 * (a**2 + b**2 - c**2)
            if S == 0:
                continue

            x = (a**2 * (b**2 + c**2 - a**2) * A[0] + b**2 * (c**2 + a**2 - b**2) * B[0] + c**2 * (a**2 + b**2 - c**2) * C[0]) / S
            y = (a**2 * (b**2 + c**2 - a**2) * A[1] + b**2 * (c**2 + a**2 - b**2) * B[1] + c**2 * (a**2 + b**2 - c**2) * C[1]) / S

            ans = min(ans, mxR(x, y))

print(ans)