1222 : radius
Time Limit: 1 Sec Memory Limit: 128 Mb Submitted: 7 Solved: 2 SpecialJudgeDescription
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 \(10^{-6}\).
Sample
1 0 0 -2 ##CASE## 3 3 -2 4 -1 -1 2 2 2 2
0.00000000 ##CASE## 1.41421356