Super Star

During a voyage of the starship Hakodate-maru, researchers found strange synchronized movements of stars. Dr. Extreme heard about these observations and proposed a theory of super stars. The term has nothing to do with actors or singers. It is a theory in astronomy.

According to the theory, the stars we observe are not independent objects. Each one is a small part of a much larger object called a super star. A super star is filled with invisible transparent material, and only a few points inside it or on its surface shine. We observe those points as stars.

To test the theory, Dr. Extreme wants to write the equations of motion of a super star and compare their solutions with the observed movements of stars. As a first step he assumes that a super star is a sphere whose radius is the smallest one such that the sphere contains every given star inside it or on its surface. That assumption lets him estimate the volume of a super star, and the density of the invisible material is already known, so he also gets its mass.

Write a program that reads the positions of stars and finds the smallest sphere containing all of them inside it or on its surface. Ignore the size of a star and treat it as a point. Assume the universe is a Euclidean space.

The input consists of several data sets. Each data set has the following format.

n
x1 y1 z1
x2 y2 z2
...
xn yn zn

The first line of a data set holds the number of points $n$, where $1 \le n \le 29$.

The next $n$ lines give the positions of the points in three-dimensional orthogonal coordinates $(x_i, y_i, z_i)$. The three coordinates of one point appear on one line, separated by single spaces.

Each value is a decimal fraction between $0.0$ and $100.0$, both ends included. Any two points are at least $0.01$ apart.

A line containing a single $0$ marks the end of the input.

For each data set, print the radius of the smallest sphere containing all of the given points, one radius per line. Print the radius rounded to 5 digits after the decimal point. The answer of every data set stays far from a rounding boundary, so a computation with absolute error at most $10^{-7}$ prints the same digits.