J. radius
time limit per test
1 second
memory limit per test
128 megabytes
input
standard input
output
standard output

There are $$$n$$$ distinct points in three-dimensional space，the coordinate of the i-th point is represented by $$$(x_i,y_i,z_i)$$$.

A compliant sphere is defined as having its center on the coordinate axis, and at least $$$ \lfloor n / 2 \rfloor $$$ points within or on its surface. What is the minimum radius of the compliant sphere.

Input

The first line contains an integer $$$n (1 \leq n \leq 10000)$$$.

Next n lines each contains three integers $$$ x_i , y_i, z_i.(\mid x_i\mid , \mid y_i \mid, \mid z_i \mid \leq 10000)$$$.

Output

The minimum radius.

Your answer will be considered correct if its absolute or relative error does not exceed $$$ 10^{-6} $$$.

Examples
Input
1
0 0 -2
Output
0.00000000
Input
3
3 -2 4
-1 -1 2
2 2 2
Output
1.41421356