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This year, Walter’s workplace resolved to try something radically different: they’re going to change the weekly order of biscuits for the break room to a whole other brand.
Biscuits come in many shapes and sizes, but the particular brand they settled on has two special qualities:
However, disaster struck immediately: the available mugs in the break room are too narrow for Walter to be able to dunk these new biscuits into, no matter what combination of rotations along the three axes he tries.
There is only one thing for it: Walter will need to order another mug.
Before taking this drastic step, it is vital to know how wide the diameter of this mug will need to be in order to succesfully accommodate a (possibly rotated) biscuit of the new brand.
Vertices are always given in anti-clockwise order. Also, as anyone can tell you, biscuits never self-intersect and always have positive area.
Output the minimum possible diameter of the new mug, in order that it can fit the new kind of biscuit fully inside in at least one orientation. The output must be accurate to an absolute or relative error of at most 10−6.
4 0 0 5 0 5 2 0 2
6 81444 14017 80944 13517 81127 12834 81810 12651 82310 13151 82127 13834
8 197 239 208 246 221 241 250 254 220 265 211 258 198 268 163 256