1222 : radius

Description

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
 

Hint

Source