using binary search r, and check for each segment,find the inner side part of other segment
that distance is smaller than 2*r,get the segment of these points in each line, check if union of them is the hole line segment.

for check two segments' distance we only need to check innerside adjctent two line segments

it can be done by O(n*log(n)) sweepline precalculate..

admin please set another version with n<=100000.