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 math

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

ret = 100000000
def update(px, py):
    global ret
    r = 0
    for p in range(n):
        r = max(r, math.hypot(px - xy[p][0], py - xy[p][1]))
    ret = min(ret, r)

for i in range(n):
    x1 = xy[i][0]
    y1 = xy[i][1]
    for j in range(i + 1, n):
        x2 = xy[j][0]
        y2 = xy[j][1]
        update((x1 + x2) / 2, (y1 + y2) / 2)
        for k in range(j + 1, n):
            x3 = xy[k][0]
            y3 = xy[k][1]

            d = 2 * (y1 - y3) * (x1 - x2) - 2 * (y1 - y2) * (x1 - x3)
            if d != 0:
                px = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
                py = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
                update(px, py)

print(ret)