The37thACM-ICPCAsiaHangzhouRegionalContest---OnlineContestProblemListThe37thACM/ICPCAsiaHangzhouRegionalContest---OnlineContestProblemA.BoomerangDescriptionAustraliaoriginalinhabitantsusedtohuntbyaweaponcalled"boomerang".Whenaboomerangisthrownout,itrotates,hitsthetarget,andthenreturntothethrower.ZXXisthebestboomerangthrowerinAustralia.Hisskillissowonderfulthathisboomerangcandoanyrotationhewantsintheair.Hetravelsaroundtoshowhisskillandmakemoney.Oneofhisclassicshowistothrowouttheboomerang,anditwillpassthroughbetweentwoveryclosepillars.Ofcoursetheboomerangmustflyparalleltotheground.Ifnotso,everybodycandoit.ZXXalwaysputsthetwopillarsascloseaspossibletoshowhisskill,buthewantsyoutofigureoutthesmallestdistancebetweentwopillarswhichallowshisboomerangtogothrough.Tosimplifytheproblem,youcanconsidertheboomerangasasimplepolygonina2Dplane,andeachofitsedgeisparalleltox-axisory-axis.Eachinteriorangleiseither90degreesor270degrees.Twopillarscanbeconsideredastwopoints.Thisillustrationsimplyshowshowaboomerangpassesthroughtwopillars:InputTheinputconsistsofseveraltestcases(lessthan500).Eachtestcasebeginswithanintegern(4<=n<=8),representingthenumberofverticesofapolygon.Nextnlinesgivecoordinatesofnverticesinorder.Eachlinecontainstwointegersxi,yi(|xi|,|yi|<=100000).Foreachtestcasetherearenotwoverticesisinthesameplace.Inputendswithn=0.OutputForeachtestcase,printasinglerealnumberw,representingtheminimumdistancetoensuretheboomerangcanpassthrough.Theanswershouldberoundedto2digitsafterthedecimalpoint.The37thACM/ICPCAsiaHangzhouRegionalContest---OnlineContestSampleInput600100010011111000100800300303020302010101010300300SampleOutput1.4114.14The37thACM/ICPCAsiaHangzhouRegionalContest---OnlineContestProblemB.ArrestDescriptionThereare(N+1)citiesonTATisland.City0iswherepoliceheadquarterlocated.Theeconomyofothercitiesnumberedfrom1toNruinedtheseyearsbecausetheyareallcontrolledbymafia.ThepoliceplantocatchallthemafiagangsintheseNcit