How We Know Masks Work – An Informatics Explainer

Temple of the Sun, Teotihuacan, MX

Note — in this piece, when I use the term “mask” — I’m advocating for homemade masks. I absolutely believe that we should save surgical masks for our health care providers. I’ll make the point below that homemade masks are really good enough for any social distancing situations that Americans will encounter. And as our tech gets better, my bet is that our cloth masks will be almost as good as the disposable varieties. I’m on Rev. 4 of my own mask design, and it’s way better than Rev. 1. I am a design prof., after all.

One of the things I’ve been advocating recently, with the idea of getting back to a New Normal after the COVID-19 pandemic has passed, is the idea that all of us are going to have to wear masks in public — at least until we have some vaccine that works and is widespread. To me, this seems obvious. At the same time, I thought it might help to demonstrate how people “make sense” of things, so you can straighten out your own thoughts.

One of the ways that this debate has NOT been framed is understanding this from a scaling (in time/space) perspective. All our information is based on scales, that we more or less incorporate into our judgments. So let’s start at the bottom.

Back when the HIV/AIDS epidemic was a big deal, there was a large contingent on the Religious Right that was saying, among other things that AIDS was a divine punishment, and that the virus was so small, it could easily fit in the little spaces (interstices) in the rubber in a condom. So… because it fit their moral agenda, they went screaming around saying “condoms won’t protect you!” much in the way we now hear “masks won’t protect you!” Of course, condoms are waterproof, and the vehicle where the virus effectively floated, barring failure, couldn’t get through the impermeable barrier. The argument put forth by the “virus is too small” crowd was a canard.

So let’s slow down and understand this — the fundamental scale argument of virus transmission.

#1 principle of all virus transmission. Viruses live in stuff, and usually that stuff is wet. It may not all be water, but it will contain a good hunk of water. And water comes in lots of different forms. The smallest are called aerosols. Aerosols are typically sized at or under 1 micron (micro-meter). That’s really small, and when something is aerosolized (and viruses can be contained in aerosols) that’s super-fine. Viruses — the coronavirus is sized at something like 125 nano-meters. That means that the coronavirus, being somewhere between 10-100 times smaller can definitely fit in an aerosol particle.

But the fact that you can fit a bunch of viruses inside an aerosol particle doesn’t mean much. Because that particle that’s carrying the virus basically evaporates pretty quickly. And you can run this experiment yourself. Go pull out a can of aerosol-something out of your cupboard and spray it. The finer particles do fly — but they dissipate quickly. So no water. And no medium for viral transmission. Yeah, they can “Kinda” get spread around. But run the experiment with a can of air freshener. And another point –since they are aerosolized, they have less virus in them. That turns out to matter.

Super-small particles can indeed be breathed through something like a cloth facemask — that’s the reason behind the whole N95/N100 rating, which is really about how many particles under about .3 micron they’re guaranteed to remove (if the mask is fitted correctly.) You can see now why the rating exists — if aerosol particles are down there around 1 micron, you ideally would like to have a mask that blocks at about the third the diameter (.3 micron) to be perfectly safe.

But the particle has to also be floating around, or sprayed in your general direction. It’s prone to evaporation. And most of what people cough up ISN’T an aerosol.

It’s droplets. Droplets are more easily formed out of, well, snot, because of a lot of different reasons. Water has a certain “viscosity” (stickiness as a function of density) and snot is, well stickier. What this means is you’re likely to have bigger particles. And now another important factor comes into play.

That factor is called surface tension. Surface tension is the internal fluid static force that makes a drop round. Or kinda round when sticking to a surface. The minute a droplet comes flying across the atmosphere, headed toward your mouth, and hits the surface of your mask, it’s going to have a hard time. It’s not going to have a hard time going through the interstices of the fabric just because of droplet size — that’s part of it. The other part of it is that surface tension comes into play and starts slowing stuff down with the fabric itself. Just like when a droplet lands on a surface and turns into a little semi-bubble, the same physics happen with the snot-droplet that hits the cotton of a mask.

So let’s walk through this. A droplet of snot flies through the atmosphere, headed toward your mask. Viruses are in that droplet, and those little suckers are counting on using that droplet like their own little landing capsule. But it hits the cloth, and the droplet spreads out, and it may be kinda gross, but at least the droplet is not headed down into your respiratory tract, where the virus would like to get to.

What if your homemade mask is kind of open at the top? Well, it is absolutely true, once again, using a simplistic analysis, that the virus, and maybe even the snot droplet is smaller than that little gap in the top of the mask. Your mask will NOT be as effective as a fitted respirator. But the droplet has to hit in exactly the right place on your face to bounce down and get into your mouth. You’ve improved your odds with a facemask. A lot.

From This Paper — good stuff!

Since the volume of a droplet increases a WHOLE LOT as it gets bigger, (by a cubic power law, since a droplet is essentially a sphere) a droplet can contain a whole lot more viruses than an aerosolized particle. Regardless, if a droplet hits your mask, it may be gross. But it won’t go far. And yes — droplets are persistent, especially when compared to aerosols. But they’re not going to get thrown as far, as fast.

Now we come to what some may find a controversial part of my analysis. It may seem obvious, but how much of the virus gets in you, by my guess, is going to matter. Dose matters. If you get a lot of virus in you — if the dose is large, you’re far more likely to get sick than if you just get a little. This reasoning comes out of my observations of health care providers, who are getting far sicker than many people with exposure. Health care providers seem to be succumbing to the virus at some 2x – 4x the rate of the general population. No one really knows the answer to this question yet, but the short version is that DOSE MATTERS.

This isn’t true with all viruses, but it is with this one, and one that gives us an operative principle that we should follow. LIMIT THE DOSE.

Is there a situation where dose doesn’t matter? Some stuff is so bad-ass, that even if you get a little in you, you’re done. It’s easier seen with toxic substances. Plutonium is a great example. There is no amount of plutonium you can get in your lungs and not get cancer. Polonium seems to be close, and is used in spy vs. spy poison games.

But that’s not COVID-19. COVID-19 seems to be handled just fine by the vast majority of immune systems. Even if the death rate for the actually infected is only 1% (which is millions of victims — I’m not minimizing here!) the reality is that most folks’ immune systems can handle the virus just fine. Or rather, can handle a more standard DOSE of the virus just fine. How that all works is that your immune system can spin up faster than the virus can replicate.

Once again, masks help minimize the dose that someone might get walking around, practicing the 6′ distance recommended for social distancing.

The immediate physics are in the favor of masks. That’s the bottom line.


But humans are fallible creatures. They make mistakes. They pull their masks down. They fiddle. That’s what things with fingers do. How can we understand that?

For that, we have to draw a bigger circle — one that now contains the statistics of an entire population, and then decide if there’s something different between one population and another.

That’s this picture, which is making the rounds.

The data is from Johns Hopkins, the circles are from @jperla

The data plotted on this graph come from an official tabulation of data from Johns Hopkins, by a staff member of the Financial Times, John Burn-Murdoch. He’s their visualization person.

And who is @jperla? From his Twitter page, he’s a former founder and CTO, and an expert in launching and landing UAVs, and a software dude. He drew the circles.

The process that Joseph followed to draw his circles is somewhat unknowable — in my circle, we call this “sensemaking.” He has friends that are epidemiologists, he obviously knows something about the mitigation processes in the different countries. He took all that knowledge, along with past experience and drew those circles.

And unlocked a torrent of action. Some of that action was profound — the President of the Philippines saw that graph and decreed that the whole country should mask up. Other scientists saw that graph, and immediately started arguing for the various exceptions saying that we don’t know FOR SURE that masks were the cause of the success of the reduction in cases.

OK.

Since this is an explainer, I’m going to hold back on explaining why the various parties think the way they do. There’s much to learn from this particular example on that, how they lock into their various v-Memes and knowledge structures. But I digress.

Why do I believe the figure, and how did I come to the conclusion that we should start wearing masks about the same time as this picture? I honestly didn’t have access to this picture (it came out 10/15) before it went viral.

Here’s why — it is a classic example of a piece of evidence that’s SCAFFOLDED by information on a number of scales. Here we go:

  1. It “makes sense” for the smallest physics. That’s the lowest scale in play — in the context of interpersonal distance and the basic physics of how membranes/cloth/masks work. It reduces viral dose at that level.
  2. It makes sense for the physics of human interaction. At 6′, even a cloth mask is going to have a lot easier time cutting down on the mucus someone is spraying from their nose and mouth.
  3. It makes sense from what I know about societies that have successfully contained COVID-19. I first dialed into the cloth mask argument from my experience with my wife’s original Taiwanese culture, along with what is happening in Japan.
  4. It makes sense from what we don’t know. It is prudent. Though there are potential downsides from wearing a mask (let’s say you never wash it — it could become a virus sponge over time!) these can, in a public health arena be compensated for with education. We know that dosing matters, but honestly have no idea what specific dosing causes, with variation in immune systems, one to become afflicted. But it follows the Hippocratic Oath — do no harm.

One last thing. Any scientist, if they so desire, can tear apart empirical science like the Masks for All plot. Why? Because empirical, data driven science works best on closed systems, where one can run one system with the hypothesis to be tested, while another system can be run with what we call the “Null Hypothesis”. This is always NOT the case with open systems, like entire societies. And there are literally a bazillion examples where one can argue correlation (what we are doing with the mask plot — looking at two similar trends without experimentally confirming the link) vs. causation.

But scaffolding in causation can be present at smaller scales, and is a good start toward understanding larger, wicked problems — like the COVID-19 outbreak. And the primary thing I look for when deciding to believe any larger epidemiological study. Explain the mechanism, and the scaffolding physics.

And then finally, does it satisfy, in the case of public health, the Hippocratic Oath? I think the answer to that is also “yes”, with appropriate education. So I’m all in. I’m wearing my mask.

Finally — if I’ve made a mistake here — leave a comment, and I’ll fix it. I would love it if my multi-phase flow colleagues would give a more eloquent description of coughing than I do. Multi-phase flow is the engineering term for considering the droplets in air and how they move. My intuition tells me there’s some trade-off between body forces and aerodynamic drag linked to particle size that would actually create an inflection point on particle distance traveled dependent on that nominal size. I’m comfortable with the rest of it (surface tension as a dominant force in diffusion.)

7 thoughts on “How We Know Masks Work – An Informatics Explainer

  1. Why small particles can’t get through masks
    12h ago
    Corona Wikivoyage bannerMasks are in the news at the moment. The basic idea of a mask is simple, it filters out some of the nasty particles from the air. The hope then is that if a droplet containing virus particles gets sucked into or blown out through the mask, it will be trapped by the mask and go no further. How masks filter out the bigger droplets is easy to understand. Masks are basically made from meshes of fibres that are very roughly around ten micrometres or so thick. So when the user breathes in or out, the air is forced through holes in this mesh of fibres. Some of these holes may be only around a micrometre or a few micrometres across, and of course any droplet bigger than the hole will get trapped and so not get through.

    But naively I assumed that most droplets much smaller than the sizes of the holes in the mesh, would just zip through the mask. This is not so, in fact for small droplets, the smaller the droplet, the more likely it is to be caught in the mask. This looks a bit counter intuitive at first sight, but the reason is that small particles are very mobile, they diffuse rapidly. They do this even when they are in the air stream being sucked through the mask. And this mobility makes it likely that they will wander into one of the fibres and stick to it.

    Simply speaking, the argument is as follows. Small particles diffuse in air, with some diffusion constant D. This means that in addition to being carried by the flow it also pin balls around in the air such that it undergoes random-walk-like motion over a distance about x ~ (Dt)½ metres, in a time t seconds. Inside a mask, this particle is being carried by air flowing at u metres per second.

    Inside the mask there are holes of various size but let us consider a narrow gap about l across and l long between fibres. We want a rough estimate of the probability that the particle will diffuse into the surface of the fibres during the time it is carried through this gap, by the flow.

    The time for the particle to be carried through the gap is just l/u, or in other words the rate of this process of being carried through the gap is u/l. Roughly speaking the probability that it diffuses into the fibres should be roughly the rate of diffusion*, D/l2, divided by rate it goes through the pore, u/l. This ratio, which is our estimate of the probability of being trapped, is then D/ul**.

    This diffusion-and-capture probability is proportional to the diffusion constant D, so droplets with bigger diffusion constants are more likely to be filtered out. Now, the diffusion constant of a droplet is approximately inversely proportional to its size, so smaller droplets diffuse faster and are more likely to diffuse into a fibre and be filtered out.

    I guess this is why the fancy masks, called N95 in the USA and FFP2 in Europe, are specified in terms of their ability to filter our droplets 0.3 micrometres across. This size may be the tough ones to filter out as they diffuse more slowly than smaller droplets. And bigger ones are bigger than the gaps and so are easily caught. Note that you can’t just make the holes very small to filter out everything as the smaller the holes the harder it is to breath through them. If you halve the hole size you need to exert four times the force to breath through them.

    So there may be some basic physics behind the difficulty of filtering out droplets around a third of a micrometre across. I don’t know if droplets these size are good or bad at spreading the corona virus, hopefully not too good.

    * As I just want the scaling, a rate (dimensions of one over time) is just one over a timescale. The diffusive timescale is distance squared, divided by the diffusion constant.

    ** This is an inverse Péclet number, it compares flow and diffusion rates. Note that this argument is too simple, if you do the geometry better, the scaling is this inverse Péclet number to a power of two thirds. See Wang and Otani’s review of filtration.

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    GOD BLESS YOU BUT I HAVE TO PAY FOR REPORT CANT DO ,Snažne molitve presvetom Križu – izmoli ih u ovaj sveti i milosni dan! — ŽUPA ROKOVCI-ANDRIJAŠEVCI
    3h ago

    Oj, zdravo Križu, nado sva! MOLITVA SVETOM KRIŽU O, sveti Križu, na kojem je raspeta Ljubav srca mojega, premilosrdni moj Gospodin! Uzdižem pogled Tebi i vapijem: Spasi me! Neka čavli što probodoše ruke i noge moga Spasitelja, razapnu sve grijehe i zloće što ih učinih protiv Ljubavi i protiv svoga bližnjeg. Raskajana srca i lica […]

    Snažne molitve presvetom Križu – izmoli ih u ovaj sveti i milosni dan! — ŽUPA ROKOVCI-ANDRIJAŠEVCI
    AMEN
    Snažne molitve presvetom Križu – izmoli ih u ovaj sveti i milosni dan!
    6h ago

    Oj, zdravo Križu, nado sva!

    MOLITVA SVETOM KRIŽU
    O, sveti Križu, na kojem je raspeta Ljubav srca mojega, premilosrdni moj Gospodin! Uzdižem pogled Tebi i vapijem: Spasi me! Neka čavli što probodoše ruke i noge moga Spasitelja, razapnu sve grijehe i zloće što ih učinih protiv Ljubavi i protiv svoga bližnjeg. Raskajana srca i lica oblivena suzama, razapinjem svoju oholost da uskrsne na poniznost, svoju škrtost da uskrsne na sebedarje i dobrohotnost; razapinjem bludnost da uskrsne na čistoću srca, duše i tijela, neumjerenost da uskrsne na suzdržanost; razapinjem zavist i srditost da uskrsnu na ljubav, lijenost da uskrsne na gorljivost! O, sveti Križu, daj mi po Tebi zaslužiti Vječnost! Amen!

    MOLITVA POD KRIŽEM
    Isuse, ti si iz ljubavi preuzeo patnju
    I tako je pretvorio u patnju izbavljenja.
    Hvala Ti za križ,
    Hvala Ti za rane,
    I za tri sata smrtne agonije.
    Hvala Ti za tvoju riječ na križu
    Kojom si nam Mariju dao za Majku: »Evo ti majke» ( Iv 19,27 )
    Hvala ti za tvoju riječ na križu
    Kojom nam pokazuješ što je praštanje:
    «OČE, OPROSTI IM JER NE ZNAJU ŠTO ČINE.» (Lk 23,34 )
    U ovaj čas dolazimo pred tvoj križ
    I podastiremo ti sve naše patnje,
    Patnje u obiteljima, u Crkvi i u svijetu.
    Mi znamo: O Isuse, ti ćeš nas osloboditi.
    Marijo, majko puna ljubavi koja stojiš pred križem
    Moli sada s nama i za nas:
    Neka nas Svemogući Bog, pomoću križa, tog znaka ozdravljenja,
    oslobodi utjecaja zla.
    Uz pomoć križa, znaka pobjede,
    neka Svemogući Bog oslobodi sve one
    koji pate pod utjecajem zla.
    Pomoću tog svetog križa
    Neka nam Bog udijeli sve potrebne milosti,
    milost pomirenja, mira, ljubavi, vjere i ozdravljenja.
    Neka nas tim znakom križa, blagoslovi i zaštiti,
    Svemogući Bog, Otac, Sin i Duh Sveti. Amen.

    ISUSU NA KRIŽU…
    Uistinu, ovaj čovjek bijaše Sin Božji!
    (Mk 14,1-15,47)
    Nalazim se, Isuse, podno tvoga križa.
    Klanjam ti se!
    Klanjam se tvojoj ljubavi, klanjam se tvojoj boli.
    Klanjam se, Isuse, tvojoj odanosti volji Očevoj,
    tvojem hodu i pod križem dokraja.
    Klanjam se, Isuse, tvojoj ustrajnosti kojom si htio djelo spasenja
    dovesti dokraja i umrijeti na drvetu križa.
    Promatram, Isuse, tvoje izmučeno tijelo.
    Oprosti mi, kad ostajem hladan gledajući raspelo,
    ravnodušan na izvještaj o tvojoj muci i smrti.
    Kao da sam to već prečesto vidio, toliko puta čuo.
    A ipak, danas, “na dan uzvišenja tvoga križa”,
    želim po prvi puta zagledati se u tvoj križ,
    želim novom pozornošću i ljubavlju čuti izvještaj o tvojoj muci.
    Želim te vidjeti, Isuse!
    Vidjeti tvoje izmučeno tijelo, tvoju trnjem okrunjenu glavu,
    tvoje probodene ruke i noge, tvoje otvoreno srce.
    Želim vidjeti tvoje predano tijelo i prolivenu krv.
    Za mene, za nas, za sve ljude svijeta.
    Želim, Isuse, podno tvoga križa osjetiti snagu tvoje ljubavi
    i šaptati ti riječi sućuti i zahvalnosti.
    Oprosti, jer podno tvoga križa nisam bez krivnje,
    jer sam i sam utkan u grijeh svijeta što ga ti otkupljuješ svojom smrću.
    Oprosti što tako često zaboravljam na cijenu svoga otkupljenja,
    na ljubav koja želi biti ljubljena,
    što zaboravljam na poruku i poziv križa.
    Oprosti, Isuse, što te ne ljubim dovoljno!
    Hvala ti, Isuse, što si umro za mene.
    Hvala ti za sve ljude svijeta jer si za sve dao svoj život.
    Hvala ti što si ustrajao u žrtvi svoga križa.
    Hvala ti, Isuse, što me sa svoga križa želiš privući k sebi.
    Ne dopusti, Isuse, da se opirem tvojoj spasiteljskoj ljubavi.
    Daj mi, Isuse, milost da osjetim neizrecivu snagu križa
    kojom odgoniš od mene, i od svih nas, zle sile svijeta i đavla,
    te nam svima daješ novu snagu za život.
    Tvoj križ, Isuse, govori o ljubavi.
    U izvještaju o muci vidimo oko tebe toliko mržnje, toliko gorčine.
    U tebi, Isuse, toliko ljubavi i mira.
    Ispuni me, Isuse, svojom ljubavlju i mirom.

    Natuzza Evolo – gotovo je nemoguće opisati što je ova stigmatičarka proživljavala na Veliki petak

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    OVO JE VELIKO NEBISE ZAMISLI KAKO VELIKA JE PASHA ZIDOVSKA BILA

    DRUGO ČITANJE:
    Iz Drevne homilije na Veliku i svetu subotu
    (PG 43, 439. 451. 462-463)

    Gospodinov silazak u podzemlje

    Što je ovo danas? Velika tišina na zemlji, velika šutnja i samoća, velika smirenost, jer Kralj spava. Zemlja se prestrašila i zašutjela, jer je Bog u tijelu usnuo i probudio pomrle od početka svijeta. Bog je umro u tijelu i oživio podzemlje.
    Očito je najprije potražio praroditelja Adama kao izgubljenu ovcu. Svakako je htio posjetiti one koji su živjeli u tami i smrtnoj sjeni. Sigurno je Bog i njegov Sin htio osloboditi zarobljenog Adama i s njim zarobljenu Evu.
    Gospodin je ušao k njemu držeći pobjedni stijeg križa. Čim ga je ugledao praotac Adam, silno iznenađen udario se u prsi i uskliknuo svima: »Gospodin moj bio sa svima«. Krist je Adamu odgovorio: »I s duhom tvojim!« Uhvatio ga za ruku, podigao i rekao: »Probudi se ti što spavaš! Ustani od mrtvih, jer te Krist rasvjetljuje! Ja sam Bog tvoj, a radi tebe sam postao tvoj sin. Radi tebe i radi ovih koji su tvoji potomci sada govorim i zapovijedam svima što su okovani: Iziđite! A onima što su u tami: Nek vas Svjetlo obasja! A usnulima: Ustanite !
    A tebi zapovijedam: Probudi se ti što spavaš, jer te nisam za to stvorio da ležiš vezan u podzemlju. Ustani od mrtvih. Ja sam život mrtvima. Ustani, djelo ruku mojih! Ustani, sliko i priliko moja. Stvoren si sličan meni. Ustani, izidimo odavde! Ti si u meni a ja u tebi, jer smo jedna nedjeljiva osoba.
    Radi tebe sam ja, Bog tvoj, postao sin tvoj. Radi tebe sam ja, Gospodin, uzeo oblik sluge. Radi tebe sam ja koji prebivam nad nebom došao na zemlju i čak pod zemlju. Radi tebe, čovjeka, postao sam kao bespomoćan čovjek ubrojen među mrtvace. Radi tebe koji si iz vrta istjeran ja sam u vrtu predan Židovima i u vrtu razapet.
    Pogledaj kako mi je lice bilo radi tebe popljuvano zato da ti povratim onaj prvotni dar života. Pogledaj kako su mi obrazi bili zaušnicama bijeni. To sam podnio da tvoje nagrđeno lice obnovim prema mojoj slici. Pogledaj kako su mi leđa izbičevana. To sam podnio da zbacim teret tvojih grijeha što pritište tvoja leđa. Pogledaj kako su mi ruke čavlima bile pričvršćene za drvo križa. To sam podnio za tebe koji si pružio svoju ruku prema zabranjenom drvetu. Usnuo sam na križu i koplje je probolo bok moj radi tebe koji si u vrtu zaspao da od tvoga boka bude sazdana Eva. Moj je bok izliječio tvoj bok. To što sam na križu usnuo tebe će izvesti iz podzemnog sna. Moje je koplje zaustavilo oružje upereno protiv tebe. Ustani, idimo odavde! Neprijatelj te je istjerao iz raja zemaljskog. Ja te neću više povratiti u taj raj, nego ću te smjestiti na nebesko prijestolje. Udaljio te je od drva koje je slikovito predstavljalo život, a evo sada ja, koji sam Život, združujem se s tobom. Postavio sam kerubine da te poput slugu čuvaju, a evo sada će ti se kerubini klanjati slično kao Bogu. Pripravno je kerubinsko prijestolje, nosači spremni čekaju, odaje su uređene, jela pripremljena, urešeni su vječni šatori i prebivališta, otvorene su riznice dobara, a nebesko te kraljevstvo čeka još prije postanka svijeta.«

    Otpjev
    R. Otide naš Pastir, izvor žive vode, i o njegovu prijelazu sunce se pomrači; zatočen je onaj koji je držao zatočena prvog čovjeka. * Danas naš Spasitelj razvali vrata i zasune smrti.
    O. Razrušio je i zatvor Podzemlja i uništio moć đavla. * Danas.

    Molitva
    Svemogući vječni Bože, tvoj je Jedinac sišao u Podzemlje i odatle je slavan uzišao. Daj da tvoji vjernici koji su s njime u krštenju suukopani, s njime i uskrsnu te postignu vječni život. Koji s tobom.

    O. Amen.
    Blagoslivljajmo Gospodina.
    O. Bogu hvala.

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  2. The analysis of droplets, gaps in the cloth , aerosols etc miss the real life reality. It is almost impossible for a real life person to avoid touching the outside of the mask. Thereby putting all the carefully filtered blobs and drops of Covid onto their fingers and then onto their face.
    Reality vs academia.
    I wear a mask when near other people out of respect for their crazy idea that it will protect them. I am under no illusion that it’s doing them or me any good. And wearing it is flippin annoying.

    Like

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