Describing a Circle, why is radix representation a ring isomorphism?

圈 Describing a Circle; 1305 Edmund Conf. 232 in Early Eng. Poems & Lives Saints (1862) 77  Þreo rounde cerclen heo wrot: in þe paume amidde., concentric; 1400 G. Chaucer Treat. Astrolabe (Cambr. Dd.3.53) (1872) i. §17. 10  The heued of capricorne turnyth euermo consentryk vp-on the same cercle.

Describing a Circle

x = sin( -5.009757041932 * y ) – cos( 5.0073237419122 * x );
y = sin( -5.006352424622 * x ) – cos( 5.0065770149236 * y );

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l’histoire secrète racontée entre les lignes sinueuses et le sens … Solvyn, supra in onbyyndyn

1384 Bible (Wycliffite, E.V.) (Douce 369(2)) (1850) Dan. ii. 5 Bot ȝe shuln shewe to me the sweuen, and the coniecturyng, or menyng, therof. 1400 Mandeville’s Trav. (Roxb.) viii. 29 By þe chaungeyng of þe coloures men..knawes and coniectures wheder it schall be derthe of corne. 1440 Promptorium Parvulorum 464/1 Solvyn, supra in onbyyndyn. 1450 Alphabet of Tales (1904) I. 254 And on þis maner þai war wunt..for to solve þer faste. 1450 J. Lydgate Secrees 1259 Afftir the sesouns Solve flewm brennyng or moysture. 1460 Promptorium Parvulorum (Winch.) 322 Onbyyndyn, or solvyn, soluo.

1513 R. Fabyan New Cronycles Eng. & Fraunce (1516) I. clxxxvi. f. cx Whiche thynge thus by the kynge desyred, the Lordes anone coniectured in their myndes that he desyred the kepynge of theyr yonge lorde, to ye ende that he myght the more easyerly optayne the possession of that Dukedome. 1528 S. Gardiner in N. Pocock Rec. Reformation (1870) I. l. 104 To the intent we might the better discipher the very lett and sticking. 1529 Bp. S. Gardiner Let. 7 Sept. (1933) 39 Bicause they [sc. letters from Rome] be moch in cifre, his Hignes desireth your Grace that they may be disciphred there and remitted hither again. 1529 T. More Supplyc. Soulys ii. f. xxxviv Yf he wold now..beleue those .iii. or .iiii. noughty persons, agaynst those .iii. or .iiii. C. good and honest men: he then shuld well decypher hym self, and well declare therby, [etc.]. 1530 J. Palsgrave Lesclarcissement 494/1 As I conjecture, it wyll be founde. 1550 J. Bale Image Both Churches (new ed.) ii. sig. h.iijv Wythout the blynd bussynges of a papyste, may no synne be solued. 1551 R. Robinson tr. T. More Vtopia sig. Nii They furthwyth verye wyttelye coniectured the thynge [sc. paper-making]. 1552 R. Ascham Let. July in H. Ellis Orig. Lett. Eminent Literary Men (1843) 12 Your Mrship is wel ware in seeing our lettres fittly dissiphered, lest..a clear other mynd may appeare in reading, than was ment in writing. 1555 R. Eden tr. Peter Martyr of Angleria Decades of Newe Worlde i. vi. f. 30v They coniectured that these thynges portended sum great matter. 1567 G. Fenton tr. M. Bandello Certaine Tragicall Disc. f. 253v He not liking to..heare the secrettes of his falte so plainely decipherede, replied accordynge to the discrecion of our wilfull youth now adaies. 1569 E. Fenton tr. P. Boaistuau Certaine Secrete Wonders Nature xli. f. 139v Ther was found sundry learned and holy men, which began not only to decipher the misery of this infant [Fr. a philosopher sur la misere de cest enfant], but also ye monstrous shape therof in this sort, saying, yt by the horne was signified pride & ambition, by the wings lightnesse & inconstancie. 1572 J. Knox Hist. Reformation Scotl. in Wks. (1846) I. 191 Thane begane he to dissipher the lyves of diverse Papes, and the lyves of all the scheavelynges for the most parte. 1573 G. Harvey Let.-bk. (1884) 40 Being not able to coniecture what purpose he should have in his hed. 1574 J. Dee Let. 3 Oct. in H. Ellis Orig. Lett. Eminent Literary Men (1843) 37 Yf by such a secret..Threasor hid may be decipherd in precise place. 1574 T. Newton in tr. G. Gratarolo Direct. Health Magistrates & Studentes Ep. sig. Aiiij In this litle Pamphlet, so clerkely and compendiously decyphered, I haue aduentured to deuest him of his Latine weede, and after a homely sorte forced into barbarous Englishe. 1576 A. Fleming tr. Erasmus in Panoplie Epist. 346 Occupying his pen (as by the course of his wordes, is to be conjectured) so unnecessarily. 1578 J. Banister Hist. Man i. f. 3 Those fewe decyffered names, which the aunncient Anathomistes haue giuen [to the Bones]. 1579 S. Gosson Schoole of Abuse f. 1 Whether he were better with his art to discifer the life of the Nimpe Melia, or Cadmus encounter with the Dragon, or [etc.]. 1580 C. Hollyband Treasurie French Tong Devinement, coniecturing, soothsaying. 1581 A. Fleming Diamond of Deuotion i. ix. 42 Of two differing waies deciphered by the letter Y. 1584 R. Scot Discouerie Witchcraft vii. xi. 145 Coniecture vnto me by thy familiar spirit. 1586 J. Stewart Poems (1913) 158 Thir verse disschyphre rycht..Or than ȝe sall no perfyt sentence find. 1586 Sir P. Sidney Apol. Poetrie (1595) sig. E1v A coniectured likelihood. 1587 D. Fenner Def. Godlie Ministers sig. Liv I coniecture..their meaning to be this. 1587 G. Turberville Tragicall Tales f. 68v Coniecture of her cares, imagine her distresse. 1594 J. Dickenson Arisbas sig. B 3 I haue a secret to disclose, a sorrowe to disciphre. 1599 S. Daniel Let. from Octavia xlix. sig. D2, in Poet. Ess. These secret figures, natures message beare Of coming woes, were they desciphered right.

1602 W. Watson tr. E. Pasquier Iesuites Catech. i. ii. f. 5 I beseech you decyfer [Fr. dechifrer] your doctrine that I may vnderstand it, for to say truth, this is high Dutch to me. 1605 F. Bacon Of Aduancem. Learning ii. sig. Qq1v The vertues of them [sc. ciphers]..are..that they be impossible to discypher . 1605 R. Bannatyne Memorials Trans. Scotl. (1836) 166 Sir Nicolas Throgmorton,..be frequent conferences,..had dischypheret ther wickit intentioune. 1605 T. Tymme in tr. J. Du Chesne Pract. Chymicall & Hermeticall Physicke Ep. Ded. sig. A3v Thus (right Honourable) you see a Paradox, no Paradox, & a Hieroglyphick plainly disciphered. 1607 E. Topsell Hist. Foure-footed Beastes 142 Those painters which could moste artificially decipher a Dog..were greatly reuerenced among the Egyptians. 1610 J. Healey tr. Cebes’ Table in tr. Epictetus Manuall (1636) 106 A table..the meaning whereof we could not possibly conjecture. 1616 J. Bullokar Eng. Expositor Decipher, to write after a strange fashion, that none shall reade it. 1616 J. Bullokar Eng. Expositor Solue, to vntie. 1619 E. M. Bolton tr. Florus Rom. Hist. ii. xv. 203 The furie of the rebels may be coniectured by this, that they pluckt downe house-tops. 1621 R. Burton Anat. Melancholy ii. ii. iii. 328 [H]e hath coyned 72 Homocentrickes, to solue all apparances. 1624 Bp. F. White Replie to Iesuit Fishers Answere 564 Summes of money..to be solued to the Publicans of the Ecclesiasticall Roman Tribute. 1624 T. Gataker Discuss. Transubstant. 69 Solving all objections gathered out of their obscurer sayings against Catholic doctrine. 1625 A. Garden Characters & Ess. 35 Yet time decyphers these Deceivers all, When they debosh, and play Bankrupt, with all. 1629 P. Massinger Roman Actor i. i. sig. Bv On the Stage Decipher to the life what honours waite On good, and glorious actions.

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A Ward of 2^30402457-1, Beowulf 319 Ic to sæ wille, wið wrað werod wearde healdan, eight hundred seventy one

680 Cædmon Hymn 1 Nu scylun hergan hefaen~ricaes uard. 971 Blickl. Hom. 11 Salomones reste wæs mid weardum ymbseted. OE Beowulf 229 Weard Scildinga, se þe holmclifu healdan scolde. 1377 W. Langland Piers Plowman B. xviii. 320 For any wye or warde wide opene the ȝatis. 1473 W. Caxton tr. R. Le Fèvre Recuyell Hist. Troye (1894) I. lf. 106 Thou hast slayn the wardes of the serpentes and the portyers of the lions [Fr. (1510) les soursers des serpens & les portiers des lyons] that kepte this contre Inhabitable.

Mersenne Prime Number ( 43 )

Three hundred fifteen tremilliamilliaquinquaginmilliasescendooctogintillion,
four hundred sixteen tremilliamilliaquinquaginmilliasescenunoctogintillion,
four hundred seventy five tremilliamilliaquinquaginmilliasescenoctogintillion,
six hundred eighteen tremilliamilliaquinquaginmilliasescennovemseptuagintillion,
eight hundred forty six tremilliamilliaquinquaginmilliasescenoctoseptuagintillion,
eighty tremilliamilliaquinquaginmilliasescenseptenseptuagintillion,

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Spellwaveringshard

Spellwaveringshard

Carefully questions unraveled in their answers
upon polite observation, dipping and drawing
untempered charms and it will not love me
any more if I thought your speech charming,
did I not know you till I will unsay
the spell that holds me there…
how odde soever your braines be
or your wisedomes make your heart
is filled with tears, and she said
“you must do exactly as I tell you.”

scratched across and walks away, with that she
carefully washed all darkly translucent in their
wavering shadows, clings and clinging,
neuer giues to truth and vertue
that which simpleness and merit purchaseth,
and lay ages drop unto it as were rain.

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Finnegans Triskaidekaphobia

732 thirteen letter words in Finnegans Wake

Recirculation, Camibalistics, Bidimetoloves, Habitacularly, Celescalating, Blackguardise, Hurtleturtled, Crunchbracken, Workingstacks, Consternation, Inimyskilling, Wounderworker, Verytableland, Wrothschields, Fleckflinging, Ladymaidesses, Scentbreeched, Bergincellies, Countrybossed, Harpsdischord, Antediluvious, Selfstretches, Jerrybuilding, Prapsposterus, Countlessness, Thanacestross, Anntisquattor, Mightmountain, Infrarational, Reversogassed, Starshootings, Paddyplanters, Doublejoynted, Sibsubstitute, Updipdripping, Authenticated, Leisureloving, Pouringrainia, Skertsiraizde, Magnificently, Vociferatings, Assbawlveldts, Conspicuously, Spontaneously, Circumstances, Reconstricted, Twitterlitter, Convertedness, Cobwebcrusted, Ecclectiastes, Phantomweight, Lodginghouses, Bakenbeggfuss, Correspondant, Appraisiation, Establishment, Particularist, Poulichinello, Norveegickers, Antilibellous, Nonactionable, Coulinclouted, Reamalgamerge, Quaintesttest, Objectionable, Semiprivately, Eventualising, Mighthavebeen, Peacebetothem, Fortitudinous, Sweatandswear, Storthingboys, Bottlebreaker, Heartskewerer, Cycloptically, Encirculingly, Ventriloquent, Beneficiaries, Unforgettable, Comparisoning, Sprangflowers, Sevenchurches, Alternatively, Parliamentary, Perpendicular, Vowelthreaded, Franchisables, Transparingly, Twelvechamber, Martiallawsey, Rejaneyjailey, Blanchessance, Analectralyse, Conscientious, Gentlewomanly, Lankyduckling, Apeegeequanee, Reconnoitring, Marmarazalles, Distinguished, Guestfriendly, Somnolulutent, Wastohavebeen, Ferroconcrete, Inhumationary, Plutorpopular, Becursekissed, Threescoreten, Dreariodreama, Reconcilement, Hatchettsbury, Unemancipated, Chickenestegg, Collidabanter, Portlifowlium, Schmallkalled, Sitisfactuary, Jugglemonkysh, Proofpositive, Thuddysickend, Umphrohibited, Wrathbereaved, Unaccountably, Impersonating, Paddlewicking, Angricultural, Observational, Significantly, Vercingetorix, Ajaciulations, Toastingforks, Solicitresses, Mollification, Manifestation, Complimenting, Whereoneafter, Twofromthirty, Chassetitties, Crackajolking, Dispillsation, Firstnighting, Forehearingly, Loughlinstown, Buikdanseuses, Envenomoloped, Gravitational, Loungelizards, Holenpolendom, Memorialising, Entomophilust, Chimerahunter, Personalities, Contrarieties, Carrageehouse, Ratiocination, Passionpallid, Psychological, Ethiquethical, Sequentiality, Kischabrigies, Uncouthrement, Dariaumaurius, Jiggerypokery, Antechristian, Semetomyplace, Prepossessing, Fundamentally, Sesquipedalia, Feueragusaria, Prepronominal, Jesuistically, Sinistrogyric, Floprightdown, Unfashionable, Paleographers, Exhibitionism, Bootherbrowth, Overcarefully, Droopadwindle, Imperfectible, Upandinsweeps, Forestallings, Billiardhalls, Buaboababbaun, Zoomorphology, Omnianimalism, Hookbackcrook, Booseworthies, Drinkthedregs, Plebmatically, Acknowledging, Hackleberries, Hockinbechers, Hickheckhocks, Unsightliness, Apostolopolos, Bubblingplace, Floodsupplier, Oldshouldered, Presumptively, Hearthsculdus, Uncustomarily, Livsadventure, Thoroughgoing, Contributting, Controversies, Justification, Comesilencers, Intempestuous, Assassiations, Dearstreaming, Skillmustered, Infustigation, Subtractional, Morbidisation, Obintentional, Paleoparisien, Pneumodipsics, Unconsciously, Poposterously, Honoriousness, Preprocession, Sarchnaktiers, Synerethetise, Constellatria, Adiaptotously, Heliogobbleus, Motamourfully, Baileycliaver, Inexhaustible, Laetification, Commontoryism, Reupprearance, Interlocative, Brutherscutch, Primomobilisk, Misunderstord, Unconditional, Helixtrolysis, Undistributed, Blanchemanged, Subordinating, Orchidectural, Needlesswoman, Morphological, Schoolteacher, Cleopatrician, Hyperchemical, Gropesarching, Singlebiassed, Avoirdupoider, Nearapoblican, Conversazione, Entertainment, Cuttlefishing, Extraordinary, Categorically, Hemiparalysed, Stonestepping, Bickerrstaffs, Impenetrablum, Occidentaccia, Shamelessness, Precipitation, Unwhisperably, Scoppialamina, Blasphematory, Moromelodious, Cyclewheeling, Consciousness, Missmisstress, Thoroughpaste, Monosyllables, Scissymaidies, Lightthrowers, Convulsionary, Rapidshooting, Hazelhatchery, Silvamoonlake, Forstfellfoss, Kissuahealing, Marcellewaved, Flushcaloured, Fishnetzeveil, Contemplation, Archdeaconess, Chattahoochee, Wickerpotluck, Nightmarching, Musquodoboits, Amphitheayter, Creakorheuman, Mangrovemazes, Sojestiveness, Diseasinesses, Hemustwhomust, Ringsoundinly, Vicereversing, Complementary, Imbretellated, Disconnection, Mademoisselle, Mightwhomight, Disconvulsing, Forforgetting, Inflammabilis, Inculmination, Nevertheleast, Smellsniffing, Parleyglutton, Lossassinated, Spectacularly, Lightingshaft, Ameltingmoult, Whiteliveried, Frockenhalted, Rhainodaisies, Poetographies, Aroundabrupth, Altfrumpishly, Whenceforward, Checkenbrooth, Streelwarkers, Dapplebellied, Troublebedded, Expectoration, Specification, Skirtaskortas, Thumbtonosery, Childergarten, Longsuffering, Thousandfirst, Gillyflowrets, Weatherbitten, Ivorbonegorer, Fortyshilling, Sherrigoldies, Singoutfeller, Rendningrocks, Moguphonoised, Antisipiences, Steppingstone, Beelyingplace, Trueprattight, Rifocillation, Maymeaminning, Tootpettypout, Vindicatively, Humphreystown, Bracelonettes, Sempereternal, Allwhichwhile, Olivehunkered, Castlecowards, Goldfashioned, Civilisations, Hyacinthinous, Caiuscounting, Dondderwedder, International, Bissyclitties, Antiquissimam, Wolsherwomens, Ventitillated, Steeplechange, Apostrophised, Medeoturanian, Lochlaunstown, Uteralterance, Toadhauntered, Approxemetely, Serpumstances, Goaneggbetter, Simperspreach, Blaablaablack, Triperforator, Countinghands, Sickenagiaour, Supershielded, Eclectrically, Circumcentric, Antidulibnium, Monofractured, Translatentic, Amplification, Arboriginally, Paradoxmutose, Shufflebotham, Breachesmaker, Secondsnipped, Annexandreian, Nosestorsioms, Donconfounder, Wholeabelongd, Drumadunderry, Salamagunnded, Ambilaterally, Illfollowable, Gielgaulgalls, Dressparading, Sleepytalking, Saksalaisance, Boomarpoorter, Louthmouthing, Passthecupper, Barneydansked, Myrioheartzed, Disgeneration, Begeylywayled, Synnbildising, Reformication, Caughtnapping, Witchbefooled, Paraguastical, Paramilintary, Intrepidation, Bulgeglarying, Psuckofumbers, Bulchrichudes, Satisfunction, Nupersaturals, Dustungwashed, Renewmurature, Herdsquatters, Stormtrooping, Bitteraccents, Hairmaierians, Barangaparang, Trosstpassers, Centelinnates, Foregotthened, Swishingsight, Heptahundread, Banjopeddlars, Rassociations, Aplompervious, Heliotropical, Cadderpollard, Hissindensity, Deboutcheries, Julianneswith, Assistershood, Projectilised, Keenheartened, Plinnyflowers, Wellnourished, Guiltshouters, Accampaigning, Boomarattling, Wellwillworth, Catatheristic, Contemplating, Murmurrandoms, Baskatchairch, Disassembling, Quazzyverzing, Sweecheeriode, Naytellmeknot, Parasollieras, Jangtherapper, Sixdigitarian, Dovesandraves, Valinnteerily, Avragetopeace, Mispeschyites, Ahquickyessed, Whallhoarding, Bottleholders, Thalassocrats, Whereinbourne, Incomputables, Uncomeoutable, Pedestarolies, Loovahgloovah, Receptionated, Gonlannludder, Clandoilskins, Dinnasdoolins, Rainydraining, Consideration, Inspiterebbed, Blennercassel, Greenislender, Motometusolum, Comicsongbook, Parthalonians, Allocutioning, Replenquished, Overopposides, Accomondation, Dissimulating, Fathomglasses, Cattleraiders, Gallowglasses, Sweepstakings, Manausteriums, Humbodumbones, Regnumrockery, Killeachother, Contradicting, Burrymecarott, Materfamilias, Brownesberrow, Andrewmartins, Nursetendered, Newhigherland, Wherebejubers, Perilwhitened, Pugnoplangent, Virilvigtoury, Goosegreasing, Krasnapoppsky, Crinklydoodle, Haggispatrick, Proprietoress, Soppositorily, Brozaozaozing, Thinkamuddles, Gratification, Chiefoverseer, Blindquarters, Fleshfettered, Genuflections, Pontoffbellek, Kisslemerched, Substantively, Poachmistress, Assauciations, Autobiography, Spondaneously, Pushpygyddyum, Fourmillierly, Besterfarther, Cantoridettes, Antitopically, Trestraversed, Blohablasting, Nissunitimost, Unshrinkables, Presumptuably, Pulladeftkiss, Longsephyring, Velktingeling, Prescriptions, Juxtaposition, Unmentionable, Fleischcurers, Intentionally, Asbestopoulos, Schisthematic, Disseminating, Allergrossest, Trampthickets, Comestabulish, Exsearfaceman, Slumbersomely, Equilebriated, Confarreating, Terrorgammons, Lostsomewhere, Fleshcoloured, Femorafamilla, Paynattention, Dallytaunties, Phyllisophies, Frecklessness, Interstipital, Clandestinely, Kellsfrieclub, Glorification, Redcolumnists, Companykeeper, Journalwriter, Allassundrian, Sleevemongrel, Constantineal, Brotherkeeper, Hebdomedaries, Filmacoulored, Unadulterated, Sallysfashion, Mortinatality, Wateringplatz, Wellbelavered, Grandnational, Disasperaguss, Commissioners, Shellyholders, Naughtingerls, Alltoolyrical, Ramescheckles, Wholeabuelish, Hummingsphere, Sidesplitting, Jollification, Littorananima, Personnalitey, Calvescatcher, Fullchantedly, Tightsqueezed, Catoninelives, Testymonicals, Moulsaybaysse, Agglutinative, Mirthprovoker, Dockandoilish, Neaheaheahear, Expressionism, Hammisandivis, Nikrokosmikon, Misunderstood, Concelebrated, Leafboughnoon, Phantastichal, Backscuttling, Droopleaflong, Irrepressible, Parapolylogic, Distressfully, Fourfettering, Tetrahedrally, Quadriliberal, Tortoiseshell, Encroachement, Theophrastius, Tripenniferry, Embarrassment, Administrants, Mudfacepacket, Dryfilthyheat, Turkeycockeys, Strawnummical, Pisciolinnies, Pebbledropper, Dispensations, Litterarumque, Archimandrite, Conciliabulum, Unbespokables, Factification, Tuttifrutties, Supernumerary, Trickspissers, Sinsinsinning, Windwhistling, Swatmenotting, Gladrolleries, Unmatchemable, Volimetangere, Pantoloogions, Thomistically, Puseyporcious, Northwhiggern, Caecodedition, Trippudiating, Mastersinging, Unnecessarily, Massacreedoed, Holyhagionous, Orangepeelers, Interferences, Interrogation, Concomitantly, Contravention, Regulationing, Disjunctively, Supernatently, Pickpuckparty, Superflowvius, Nircississies, Glenagearries, Pfuffpfaffing, Primapatriock, Macauscullpth, Allenglisches, Bestpreserved, Complimentary, Homesweetened, Teaspoonspill, Preprotestant, Disincarnated, Confoederated, Byusucapiture, Rivulverblott, Whencehislaws, Domestication, Drumcollogher, Mortification, Circumference, Wherewithouts, Freakandesias, Megalopolitan, Sunsmidnought, Unaccompanied, Companionship, Revolucanized, Lilienyounger, Peningsworths, Tallonkindles, Regimentation, Threadneedles, Attachatouchy, Muezzatinties, Lickybudmonth, Kinderwardens, Commandeering, Furrinfrowned, Silentsailing, Stiffstarched, Unpreoccupied, Salmonpapered, Daughterpearl, Thimblecasket, Godolphinglad, Caubeenhauben, Speechreading, Illuminatured, Litteringture, Skillmistress, Interrogarius, Blasphemously, Reprehensible, Chastisements, Interlocutory, Hedcosycasket, Luxuumburgher, Bluefunkfires, Photoflashing, Maypoleriding, Conningnesses, Christmastyde, Staggerhorned.

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Lessons of Darkness

Minnesota Declaration

Herzog
  1. By dint of declaration the so-called Cinéma Vérité is devoid of vérité. It reaches a merely superficial truth, the truth of accountants.
  2. One well-known representative of Cinéma Vérité declared publicly that truth can be easily found by taking a camera and trying to be honest. He resembles the night watchman at the Supreme Court who resents the amount of written law and legal procedures. ‘For me,’ he says, ‘there should be only one single law: the bad guys should go to jail.’ Unfortunately, he is part right, for most of the many, much of the time.
  3. Cinéma Vérité confounds fact and truth, and thus ploughs only stones. And yet, facts sometimes have a strange and bizarre power that makes their inherent truth seem unbelievable.
  4. Fact creates norms, and truth illumination.
  5. There are deeper strata of truth in cinema, and there is such a thing as poetic, ecstatic truth. It is mysterious and elusive, and can be reached only through fabrication and imagination and stylization.
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