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())
L = [[int(l) for l in input().split()] for _ in range(N)]

def dist(x, y, x0, y0):
    return ((x-x0)**2 + (y-y0)**2)**0.5

def f(x, y):
    res = 0
    for i in range(N):
        res = max(res, dist(L[i][0], L[i][1], x, y))
    return res

lx = -10**4
rx = 10**4
for _ in range(100):
    cx1 = (lx*2 + rx) / 3
    ly = -10**4
    ry = 10**4
    for _ in range(100):
        cy1 = (ly*2 + ry) / 3
        cy2 = (ly + ry*2) / 3
        if f(cx1, cy1) < f(cx1, cy2):
            ry = cy2
        else:
            ly = cy1
    y = (ly + ry) / 2
    
    cx2 = (lx + rx*2) / 3
    ly = -10**4
    ry = 10**4
    for _ in range(100):
        cy1 = (ly*2 + ry) / 3
        cy2 = (ly + ry*2) / 3
        if f(cx2, cy1) < f(cx2, cy2):
            ry = cy2
        else:
            ly = cy1

    if f(cx1, y) < f(cx2, ly):
        rx = cx2
        ans = f(cx1, y)
    else:
        lx = cx1
        ans = f(cx2, ly)

print(ans)