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:
from decimal import Decimal
import sys
input = sys.stdin.readline


def dist(x1, x2, y1, y2):
    return (y1-y2)*(y1-y2)+(x1-x2)*(x1-x2)


def farthest(x, y):
    ret = 0
    point = (-1, -1)
    for u, v in X:
        d = dist(x, u, y, v)
        if d > ret:
            ret = d
            point = u, v
    return ret, point


N = int(input())
X = []
for _ in [0]*N:
    x, y = map(int, input().split())
    X.append((x, y))

x = (max(x for x, y in X) - min(x for x, y in X))/2
y = (max(y for x, y in X) - min(y for x, y in X))/2
x = Decimal(str(x))
y = Decimal(str(y))
step = Decimal('0.5')
o = 1
eps = Decimal('0.00000000000001')
while o > eps:
    _, (u, v) = farthest(x, y)
    x += (u-x)*step
    y += (v-y)*step
    step *= Decimal('0.999')
    o = (abs(u-x)+abs(x-y))*step

ans, _ = farthest(x, y)
ans **= Decimal('0.5')
print(ans)