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
import cmath
from itertools import combinations

inf = float('inf')

n, *xy = map(int, sys.stdin.read().split())
xy = zip(*[iter(xy)] * 2)
z = [x + y*1j for x, y in xy]

def circumcenter(z1, z2, z3):
    a = z2 - z1
    b = z3 - z1
    numerator = a * b * (b.conjugate() - a.conjugate())
    denominator = a * b.conjugate() - a.conjugate() * b
    o = numerator / denominator + z1
    return o

def center(z1, z2):
    return (z1 + z2) / 2

def main():
    cand = []
    for comb in combinations(z, 3):
        try: 
            cand.append(circumcenter(*comb))
        except:
            pass
    for comb in combinations(z, 2):
        cand.append(center(*comb))
    
    res = inf
    for o in cand:
        r = 0
        for i in z:
            r = max(r, abs(o - i))
        res = min(res, r)
    
    return res

if __name__ == '__main__':
    ans = main()
    print(ans)