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
read = sys.stdin.buffer.read
readlines = sys.stdin.buffer.readlines
input = sys.stdin.buffer.readline
N = int(input())
X = [tuple(map(int, line.split())) for line in sys.stdin.buffer.readlines()]


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


def check(x, y):
    r = 0
    nx = ny = 0
    for u, v in X:
        z = d(x, y, u, v)
        if z > r:
            r = z
            nx, ny = u, v
    return nx, ny


eps = 10**-8
alpha = 1
x = 500
y = 500
while True:
    nx, ny = check(x, y)
    if d(nx, ny, x, y)**0.5 < eps:
        break
    x, y = x+(nx-x)*alpha, y+(ny-y)*alpha
    alpha *= 0.999
    if alpha < eps:
        break

print(d(*check(x, y), x, y)**0.5)