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

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