Minimizing Umbrella Radius

The Earth Defense Team plans to protect the Earth from the impact of sunspot eruptions by creating a special umbrella. The sun is modeled as a plane with its center at \( (0,0) \). In the year 2012, \( N \) sunspot regions appear on the sun's surface. Each sunspot is considered as a point. The umbrella is modeled as a large circular shield whose center must be placed at one of the sunspot points. Once placed, the umbrella will cover all the other sunspots. Since the material cost is extremely high, the aim is to minimize the area of the umbrella. In other words, if the umbrella's center is chosen at \( (x_i, y_i) \), then the radius \( R_i \) required to cover all points is given by:

[ R_i = \max_{1\leq j \leq N} \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2} ]

Your task is to choose the optimal sunspot as the umbrella's center so that the required radius is minimized. Output the minimum possible radius with 6 decimal places.

inputFormat

The first line contains an integer \( N \) representing the number of sunspots. Each of the following \( N \) lines contains two space-separated numbers representing the coordinates \( x \) and \( y \) of a sunspot.

outputFormat

Output the minimum required umbrella radius, formatted to 6 decimal places.

sample

1
0 0

0.000000