Enclose All

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

inputFormat

input are all integers.

Input

Input is given from Standard Input in the following format:

N x_1 y_1 : x_N y_N

outputFormat

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

样例

3
0 0
0 1
1 0

0.707106781186497524