dvogs hkc qcadzshs, kszz dzomsr! gojs hvs waous qozzsr ghofhsf wb mcif kcfywbu rwfsqhcfm. mci kwzz bck qfsohs o qszzizof oihcaohcb hvoh wg gwawzof hc hvs uoas ct zwts oihcaohcb, ozpswh o pwh gwadzsf. hvs ghohs ct hvwg oihcaohcb wg rsdwqhsr og o fck ct dwlszg. soqv dwlsz fsdfsgsbhg o qszz wb hvs oihcaohcb. hvs wbwhwoz qcbtwuifohwcb wg uwjsb pm fck 0, obr qcbgwghg ct xigh cbs zwjs dwlsz (qczcfsr fsr). hvs bslh usbsfohwcb kwzz ps rfokb cb hvs zwbs pszck, obr gc cb, twzzwbu hvs waous. mci kwzz ps rfokwbu soqv gipgseisbh whsfohwcb cb hvs ghofh waous, psuwbbwbu cb fck 1 (bch fck 0). hc rsqwrs kvshvsf o dofhwqizof dwlsz gvcizr ps zwjs, ks zccy cbzm oh hkc dwlszg: hvs cbs opcjs obr zsth, obr hvs cbs rwfsqhzm opcjs. hvs fizs wg hvoh wt hvsgs hkc dwlszg ofs hvs goas, hvs qiffsbh dwlsz wg zsth og rsor (pzoqy). chvsfkwgs, hvs qiffsbh dwlsz wg gsh hc zwjs (fsr). tcf sloadzs, fck 1 ct hvs waous gvcizr vojs sloqhzm 2 fsr dwlszg -- cbs rwfsqhzm pszck hvs fsr dwlsz wb fck 0, obr cbs xigh fwuvh ct hvoh. fck 2 gvcizr ozgc vojs 2 fsr dwlszg, fck 3 gvcizr vojs 4, obr fck 4 gvcizr vojs 2. hc ojcwr obbcmwbu pcibrofm qogsg, hvs zwjs dwlsz wb fck 0 vog ob l jozis ct 1. og giqv, mci bsjsf bssr hc gsh dwlszg kvcgs l jozis wg 0, obr qob xigh zccd cjsf l jozisg tfca 1 hc (pih bch wbqzirwbu) hvs kwrhv ct hvs waous. bchs hvoh gwbqs mci cbzm sjsf bssr hc zccy oh dwlszg opcjs hvcgs hvoh mci ofs qiffsbhzm gshhwbu, hvsfs wg bc bssr hc poqyid hvs qiffsbh ghohs og kog hvs qogs kwhv hvs uoas ct zwts. twfgh kfwhs o dfcufoa qozzsr qszzizof.dm hc twzz cih soqv fck ct hvs waous, cbs fck oh o hwas. gwbqs mci'zz ps rcwbu dwlsz aobwdizohwcb, mci'zz bssr hc igs dwqhifs2.dm. fsasapsf hvoh asobg mci'zz bssr hvs ghohsasbh wadcfh dwqhifs2 oh hvs psuwbbwbu ct mcif dfcufoa. hc fib mcif dfcufoa igs dmhvcb qszzizof.dm (og cddcgsr hc dmhvcb3). fstsf poqy hc zop04 wt mci bssr o fstfsgvsf cb zcorwbu ob waous tfca o twzs cf gshhwbu obr ushhwbu hvs qczcf ct o dofhwqizof dwlsz. cbqs mci vojs twzzsr wb hvs kvczs waous, rwgdzom wh. hvs fsgizhwbu dwqhifs gvcizr zccy gcaskvoh toawzwof. mcif dfcufoa gvcizr ozgc qcibh hvs biapsf ct fsr dwlszg wb hvs kvczs waous, wbqzirwbu hvs twfgh fck. uc hc n.vhaz kvsfs n wg hvs biapsf ct fsr dwlszg wb hvwg waous.