Rollercoasters Are Triggering The IPhone’s Crash Detection System

Apple has been busy adding new features to its smartphone and smartwatch offerings. Its new iPhone 14 and Apple Watch 8 now feature a safety system that contacts emergency services in the event the user is in a automobile accident.

As with so many new technologies though, the feature has fallen afoul of the law of unintended consequences. Reports are that the “crash detection system” is falsely triggering on rollercoasters and in other strange circumstances. Let’s take a look at how these systems work, and why this might be happening.

Can You Sense Something?

Smartphones are so much more than just telecommunications devices or pocket computers these days. They’re sophisticated sensor packages that we carry with us wherever we go. Top-tier models now pack in everything from advanced navigation chipsets to satellite communications hardware and even 3D scanners.

Apple’s Crash Detection

Across the board, though, virtually all modern smartphones feature some kind of accelerometer inside. The most obvious use for this device is to detect the orientation of the phone relative to gravity, in order to rotate the display to suit portrait or landscape mode as needed. They’re also commonly used for controlling games or as the basis for those popular lightsaber and “digital beer” apps of a decade ago. These sensors have become more sophisticated over time, and modern phones often feature three-axis accelerometers along with gyroscopes and even magnetometers inside.

Apple has now decided to leverage the iPhone’s suite of sensors for a more noble purpose, detecting if the user has been in an automobile accident. It follows on from Google’s Pixel line of hardware that has had a similar feature for several years now. The accelerometers can be used to determine if the user has been subjected to high acceleration, such as when hitting another car and coming to a sudden stop. Similarly, the GPS can provide data on sudden speed changes, too. Additionally, the microphones can be used to detect loud noises such as shattering glass if the phone is aware it’s in a driving situation. The phone’s on-board barometer can even detect a pressure spike of airbags going off in a car with the window’s closed.

But they also try to figure out if you’re in a car in the first place. They claim to be monitoring whether it sounds like you’re in a car, passing WiFi stations, and bound to a car’s Bluetooth.

When a crash is detected, the phones typically sound an alarm and display a prompt telling the user a crash has been detected. If the user doesn’t cancel the prompt after a short period of time, the phone automatically dials emergency services and can even notify contacts that the user has been in an accident.

The Real World

Google’s crash detection system allows the user to provide feedback on what just happened after a detection event. Credit: Google Pixel

Overall, there’s a whole suite of features that can work together to detect accidents. However, as testing by the Wall Street Journal showed, the crash detection features in modern smartphones come with some caveats. In a series of test crashes executed in a junkyard environment, both iPhones and Pixel phones failed to trigger alerts. The problem was that without being paired to a car’s Bluetooth device, and without the GPS indicating the user was on a public road, the phones didn’t always register that they were in a driving environment. Thus, they weren’t in a mode where the crash detection system was enabled.

It’s obviously not great if a phone fails to detect a major crash. However, these features are new, and few of us are relying on them as critical safety devices. Even if they only work to detect some crashes, they’re still delivering a net good.

However, there’s also a problem with false positives, where a crash is detected where none has occurred. One iPhone owner reported his iPhone flying off the handlebars of his motorcycle on the highway. The rider was fine; it was just that the phone had detached itself from the bike. Unfortunately, this apparently triggered the phone’s crash detection system, which notified several contacts that the owner had been in a serious accident. Upon sourcing a replacement phone, the owner was greeted by panicked voicemails from family thinking he was severely injured.

Rollercoasters have also proven problematic. Emergency dispatchers are already dealing with repeat calls from such rides, with several incidents concerning the Kings Island amusement park in Ohio. The Dollywood theme park now has signs posted up warning that the severe accelerations experienced on the ride can trigger the emergency call function on Apple Watches and other smart devices.

The Phone That Cried “WOLF!”

It’s nice to think that our electronic devices are looking out for us.  With smart devices that can call emergency services when someone is incapacitated, there’s real scope to save lives with such technology.

Of course, that can all be compromised if the technology is not reliable. Humans instinctively tend to ignore the boy that cried wolf, and a smartphone that cries “car crash!” on a rollercoaster is not that far removed.

The fact is that Apple’s new hardware is the subject of most current reports. Google’s Pixel phones haven’t been similarly indicted with these false positive results. Thus, it seems likely that the technology is fundamentally sound and workable. It just may need a little more work on Apple’s part.

[Banner Photo: “Lewin doesn’t have crash detection yet” by Lewin Day]

68 thoughts on “Rollercoasters Are Triggering The IPhone’s Crash Detection System

    1. Or perhaps the rollercoasters really are exceeding known limits for human safety and are responding appropriately.

      It most certainly would not be the first time that carnival ride designers didn’t understand the physics of what they are doing to the human bodies in their rides. Expecting carnival rides to be designed by experts in their field? Think again, there are no standards, you can just weld together some old junk and call it a carnival ride and charge money for people to risk their lives on it with no permission or certification necessary. If you don’t believe me, just read the news about water slides.

      1. There’s a big difference between water slides and roller coasters (yes there have been recent horrific water slides accidents due to bad design, but it seems like those are far more rare on roller coasters, which tend to have actual engineering and safety margins so injuries tend to be unknown pre-existing condition, intentional user error (standing up), or maintenance failure (part flies off)). Also there are at least minimal safety inspections in many locations in the US at least, though I imagine their effectiveness varies widely.

        1. “seems to”, “more rare”, “at least minimal” “effectiveness varies widely” these are all weasel-word “marketing phrases” specifically designed to be misleading at best. Are you a salesman by chance?

          1. Nope, I’m a former academic, who doesn’t want to assert anything I don’t have evidence of. They’re only “weasel words” when used in an encyclopedia (hence the Wikipedia policy). In the rest of real life, they’re useful hedging of things I can infer but am not an expert on.

            Not all of life is Wikipedia

      2. Humanity actually has really great data sets on what rapid changes in acceleration and momentum do to humans. Decades of testing for fighter pilots, astronauts, paratroopers, etc have proven the forces experienced during roller coasters, even the most extreme are perfectly safe for most people. The exceptions are listed at the beginning of the rides, moreso from an abundance of caution(pregnancy) or risk of the adrenaline rush(pacemaker) experienced.

        There has been numerous thrill ride accidents when you look at all rides operating all over the world throughout history. In that case an alert would be valid. That doesn’t make rollercoasters inherently harmful to the body anymore than tripping over a branch makes walking harmful. I do think there should be stricter federal guidelines and inspections for theme parks, but most all are operated by large corporations with shareholders whom don’t like bad press and wrongful death payouts. That’s why Action Park was closed and regulations put in place wouldn’t allow one like that to open there today. Designing, testing, and construction of rollercoasters is done by a handful of firms and they do indeed have a decent grasp of physics.

        Accusing others of being shills while insisting Apple omnipotently knows what’s best for our health is neat. Apple isn’t just using an accelerometer to check a threshold of G forces and calling the cops on people. They didn’t half-ass copy something else 3 years later and not iron out the bugs first. No, my favorite corporation are the good guys and everyone else is shills for my corporations (therefore also my) enemies.

    2. People tend to go for no-action when unsure, or back off when they see signs of trouble ahead.

      Machines produce spurious actions and don’t stop once they’ve started some action, which causes more trouble and dangerous situations. The machines don’t think – they react.

    1. Because GPS and other location services can be hundreds of yards off the mark due to multi-path echoes and they have to average your location over seconds to minutes to get it down precisely enough to say you’re actually on the ride – except you’re moving constantly which adds noise to the measurement.

      Even your phone’s navigator app is mostly guessing which road and which lane you’re on when you’re driving, and it will “snap” you to the road on the map while the GPS data may be telling it that you’re driving along the bottom of the ditch right next to the road. That’s because the direct path to the satellite may be blocked by a hill and it’s hearing the echo from a building on the other side of the road, adding 50 yards to the signal path.

      The fact that it seems to be following you spot-on is because it’s making predictions from old data with the knowledge that you can’t magically teleport somewhere.

      1. A mere hundreds of yards from a roller coaster you get into a car accident… what are the odds?

        Not sure about the idea of tracking all the traveling carnivals though. I’m thinking this strategy would be limited to stationary parks.

        Now that I think about it… my daughter’s fastener came undone and she almost flew off a carnival ride once. So maybe registering accidents at those places is a feature…

      2. They could do what Google(and 3rd party apps prior) assumedly do and not rely on a single data point before initiating a call. I am skeptical that modern GPS regularly has hundreds of yards error range. Not to mention that iPhones(and every other semi-modern device) don’t just rely on a once in a while GPS ping but has location history of every other iPhone that’s been in the area, BT, WiFi, and Tower location is as accurate or moreso than GPS in populated areas, but used in combination with it easily handles error detection and correction. They also use spatial sensors to track movement over time so even intermittent location/GPS connection is not cause for errors of any magnitude.

        Apple has the data to prevent these false positives. They didn’t fully test, or think through, their implementation. Even if GPS was a million yards innacurate, a flag that recognizes a dozen iphones an hour, connected to this specific tower, experience this exact sequence of changes in acceleration and momentum and decline emergency help should be excluded from this routine. It’s not the end of the world. But, it’s a stupid problem that does place unneeded stress upon emergency services and unchecked will undermine all the good things Apple adopting this technology can do for those in actual emergencies.

        1. Under clear-sky conditions, GPS is accurate to about 5 meters for a single fix, but the phone’s receiver is not under clear-sky conditions. It’s in your pocket and you’re in an amusement park with all that stuff around you – maybe the last clear fix it had was from the parking lot.

          1. “It’s in your pocket and you’re in an amusement park with all that stuff around you”

            You’re on a roller coaster! You’ve got wonderful field-of-view. Plus they know how accurate they are: DOP falls right out of the calculation. Using GPS receivers and accelerometers for physics projects at amusement parks is pretty standard. They do great. Open frame construction’s fine.

            Go listen to the 911 call. Take the coordinates, plug them in. It’s spot-on in the middle of the park. With the error reported.

    2. Yes, I think this is the best option, even if it results in a few hundred meters of roads not being covered by that safety net of the auto call.

      Or better yet, they can implement fuzzy logic where the closer your GPS is to these false positives, the higher the triggering threshold (or longer time to cancel).

      Also, a sensor fusion approach. For example, if it detects a crash, and then the person keeps moving, like, walking around and such, they’re probably fine, maybe it shouldn’t call.

  1. “It’s nice to think that our electronic devices are looking out for us.”

    Speak for yourself

    Shall we have “Norman”, from the ST-TOS episode “I Mudd” ?
    A race of intelligent androids “protecting” disgusting humans from themselves.

    1. I just saw that episode for the first time last night. I’ve never watched any Star Trek before (except the one with the whales) but started a few weeks ago with the original series.

      1. Now you know where the common SciFi trope of trapping AI computers in logic loops came from.
        Kirk: “Everything Harry Mudd says is a lie.”
        Mudd: “I’m lying to you now.”

        1. I always wished for Mudd’s granddaughter to show up in NG.

          Fat ugly girl that goosed Riker whenever he turned his back and demanded Data be washed and sent to her room. Data could learn coyote ugly shame.

    1. The difference in g-forces betwwen hard braking and hard objects are quite significant.

      Of couse, the software has to make that determination.

      From a goofle search on hard braking:
      “Many safety experts use 15 ft/sec2 (0.47 g’s) as the maximum deceleration that is safe for the average driver to maintain control, good to excellent tires, dry surface. A reasonably skilled driver can stop at 20 ft/sec2 (0.62 g’s). Most production street vehicles have a maximum braking around 0.8 g’s”

      from an accident:
      “According to GSU’s HyperPhysics Project, a 160 lb person—wearing a seat belt and traveling at only 30 miles per hour—experiences around 30 g’s of force in a front-end collision with a fixed object. That’s 2.4 tons of force acting on the body!”

      1. The MEMS accelerometers used to top out at 2g in each direction. You might get 2.8g therefore as a vector.

        As for max braking, well 1.2g seems reasonable for me and my jalopy with warm tires.

        So there isn’t much difference.

      2. G-forces are one of the most misunderstood subject about physics – like “how can something dropped on the floor experience 50 G forces, it would fly up to the ceiling!”

        If I stand up on a high chair and step down, my body will accelerate to about 6 m/s before my feet touch the ground. If I then come to a stop in 0.2 seconds, my acceleration will be about 3 g which 260 kg of force. That’s like I was an Olympic level weightlifter – so why don’t my legs just break? Indeed, how can we run and jump around normally experiencing up to 12 g forces on our body parts without having them snap off?

        Because the impulse of the force is small and the energy is almost instantly dissipated. The peak force is reached for a tiny fraction of a second and then it goes away, unlike an actual 260 or 2.4 ton weight which doesn’t just go away and would crush you.

        1. Your math is way off, humans cannot tolerate accelerations of greater than about 6 gs. Blood stops flowing, etc Even at lesser levels, many humans pass out or become incoherent. Even momentarily it will cause vertigo, vomiting, etc. You can’t really accelerate a limb separate from the body unless you detach it or …

          If you hit the desk with your hand, hard enough to break fingers, you are only talking 8 or 9 gs at the most. The flesh of your hand will absorb a lot of the impact but bones will still break. At 12 gs your arm will snap right off.

          You can break a finger from catching a baseball. Your arm and hand are very compliant and there is really not that much energy in a thrown baseball so your fingers are breaking at much less than 12 gs .

          1. Human extremities can take pretty extreme-seeming accelerations, actually, and it’s fairly easy to confirm the math:
            Consider someone moving both hands together to clap. A fairly gentle arm motion might be, say, 2m/s – pretty easy enough to wave your hand through 2 meters in a second, even reversing at each end. Now consider that your hands do not decelerate until they impact each other, and that the fingers are something on the order of 1cm thick; this means that at absolute most, they could only squish by 1cm while decelerating, assuming that they do not pass through each other. 1/2 * (2m/s)^2 / 1cm gives us the average acceleration assuming they do – 200m/s^2. That’s 20g. 2m/s is walking speed.

            Humans routinely throw things at 50 miles/hour, ten times that 2m/s mark. Double that for professional pitchers. Clapping at that speed certainly can sting a bit, but it’s not particularly damaging.

            Acceleration on it’s own doesn’t really tell you very much about how damaging impacts are; they’re too quick for comparisons to steady-state acceleration to be useful.

          2. Acceleration is a rate of change, while work (which does the damage) is accumulated by acceleration over time and distance. The actual impact depends on how much energy is available in the system and how it is distributed, so even great accelerations with little energy and little momentum behind them are nothing but a brief slap on the wrist – it may sting a bit but no damage done.

            This is basic physics.


            “Stapp proved that people can often survive high G forces for very brief periods. We’re all familiar with this to a certain degree. According to a 1994 article in the journal Spine, the average sneeze creates G forces of 2.9, a slap on the back 4.1, and a plop down into a chair 10.1. If you jump from three feet up and land stiff-legged, write the authors of the book Physics of the Body, you’ll feel about 100 G’s momentarily.”

  2. How long before mandatory always-on audio for gunshot detection and triangulation? Monitoring to see if you said a bad word. Detection of excessive speed and automatic call to the ‘authorities’?

    1. Why did you make the leap to mandatory? As a thought experiment, let’s continue with your idea. They would have to make it mandatory to own a cell phone, they would have to make it mandatory to carry it with you. It would be mandatory to fix it when it breaks. It would be illegal to get an MRI. What about all the places that prohibit cell phone usage? Its really nothing more
      than a big gift to the tech companies that everyone hates. Who exactly is going to go along with this? Just curious about what you are thinking.

        1. I read plenty of books and I like to keep my nice things. To preserve the value of your antique watch you should only let a real watchsmith touch it. Certainly you might be able to fix it but the next buyer will insist on receipts for all repairs. What you gain from fixing it yourself, you lose in resale value.

          Life is way too short for cheap modern “mechanical” watches, it’s either a classic antique mechanical for dress wear, or a dollar store special for everything else. Watches are a fashion statement whether you accept it or not.

          With the crypto crash, fancy modern mechanical watches are going for super cheap on ebay, and are certainly not in high style any more, more of a poseur thing.

          1. Certainly if I cared about the resale value I’d not do it myself, even though I know I can, as really its not difficult and the books and online resources for such things (along with the more specialist tools you may need) are so cheap and easy to get.

            But when good but not exceptionally old or stupid fashion statement bling with the big name label ones, are so cheap really who cares – If we haven’t all purchased in excess or ruined a enough parts and materials to buy a good mechanical many many many times over in the last few years we probably stand out quite badly in the HAD crowd. Where breaking stuff and impulse buying that interesting part is an inevitable part of making stuff…

            That said I don’t generally bother with watches at all – either the body clock and daylight are accurate enough or one of the millions of time keeping devices around us can supply the required precision.

      1. There are many examples of why this reasoning doesn’t work for me and probably other people.
        Do I also need a bare bones cheapo car, or am I allowed to have one nicer than strictly necessary simply because I like it?
        Can I get a digital torque wrench because i like it and it’s easier to use or do I need to use the old clicky kind?
        My 15 year old computer performs all necessary functions but I still like using my cellphone for, say, replying on this website while I’m on the go.
        A valuable (depends on who you ask) antique (is made in this century) on my wrist is because I like it. Should be justification enough. But also. Needs no batteries and has functioned to within 2 seconds a month for last 20 years. Never had band fail, is analog and easy for me to read, and highly subjective but isn’t ugly. Is stainless stew and easy to keep clean in my health care profession. And so on.

          1. They’ve skipped KISS in automotive engineering schools for the last 20+ years. I think they’ve let software UI ‘designers’ write the specs lately.

            Seriously, they’re basically all terrible, unmaintainable and designed to steadily drain your accounts. Media blast your intake valves lately?

            The best car ever made was a Civic with a B engine and a clutch. But that won’t pull many birds, but the ones it pulls make it worth it.

            If you put half a new car payment into an old car every month, it will last forever. Unless you live in car cancer country.

          2. Or at least as long as somebody keeps making parts for it.

            I was already quoted over $1000 for a new steering pump, for a car which isn’t worth that much. There’s always one part which breaks with every car at about the same mileage/age, so you can’t find a working one in the scrapyard either.

          3. $1000 for a power steering pump is about fair to cheap. (assuming healthy V8).

            It helps to only buy cars that had a lot of copies made. Parts available for long time. Never buy money pits (water cooled German, anything frogish including Nissan, Jatco CVTs in any brand). Mustangs interchange some parts for _decades_.

            Hydraulic pumps can usually be rebuilt, but nobody does locally. Why they want the core. Truck service places still fix old all metal radiators.

            This is hackaday, tear the pump open, fix it and post pictures. Bet it’s just o-rings and seals, light honing. If car is not too heavy you can drive without power steering for a week. If plastic then don’t bother.

            Best bet is have more than one car though. I need a 4×4 logging road truck with solid axles, an econo intentionally ugly ‘city car’ (looks uninsured, people get out of my way), a half race (tries to kill you when RPM goes over 3k) and a classic or two, but that’s me. Insurance is cheap for second and later cars.

            At some point, you do have to spend more than on parts than it’s open market value. For nice cars value bottoms out at about 25 years old. After that, you usually want to limit miles though.

            My 1960 has been the best investment I’ve ever made (worth 20x what I paid for it).
            My 1964.5 is only worth about 3x, but I’ve only owned that for six years. Too late buying and is Mustang, so obvious, also some work.

            Except art, where I got lucky/mom has great eye (one piece inherited ‘tax free’ worth 100x easy, neener IRS).

          4. >tear the pump open, fix it and post pictures. Bet it’s just o-rings and seals

            It’s a rotary vane compressor and it was simply worn out to the point that it was screeching and grinding. Nothing to do but buy a new one. There’s no seal kit sold for this pump because it’s basically a consumable item – that’s what the guy at the garage was wondering too, then checked the listings, and found out that there’s just no original or direct replacement parts to be found anywhere in the whole country. Only scrappers have them.

            Since it’s a belt driven pump that’s just sitting by the engine, you could fit in something else that’s similar enough, but I ain’t gonna pay the hours for somebody to figure it out – and the garages don’t do that anymore anyways.

          5. Vane based pumps can be rebuilt too. Not even hard. Usually just the vanes and springs are bad.
            Doable at home depending on how bad it is and how well equipped your shop is. Gaskets can be laser or hand cut (or Permatex), o rings are common parts.

            Also if you know someone from deep in the junkyard business, they have a universal parts interchange list. You’d be surprised how many things like that are common across brands, even national origins (e.g. Bosch parts in Italian trash for pennies on the dollar). Look at the replacement model from same brand, odds are it’s the same pump.

            Check the local heavy equipment hydraulics shop. Won’t be cheap for them to do it, but they’ve got the tools. Still less than 4 new car payments plus full coverage.

            IMHO Getting a ‘close enough’ one is best bet if you choose to save the car.
            Worst case, you have to fab a bracket or get one water cut, maybe use a different belt. You’re reading HackaDay. Use one from a common as dirt donor.

            If it’s a small car, just swap in a manual rack from junkyard. You’ll get much better steering feel. It’s the last step to get my Mustang GT to full Cobra R spec (or better in case of motor).

            You could go full hacker and get an electrically driven one for variable steering assist. Then you get to build a computer that speaks CAN bus for speed data. Fun!

            You have choices, because parts on old cars aren’t cryptographically signed. That’s the thing you want to avoid at all costs.

  3. Dumb question: but, shouldn’t the phone start making a loud noise to alert the driver of the potential automatic emergency call? Like, if I’ve been in a fender bender, there’s still a good chance the phone bounced somewhere unknown/unreachable if it wasn’t in my pocket. Then the auto call shouldn’t cause too much issue as long as the phone isn’t too hasty about making the emergency call (time is of the essence, but, too many false positives will negate it’s whole purpose), if someone’s phone is screeching when they get off the ride, they’ll probably look at it to turn the noise off.

    Is there possibly a way to integrate with emergency services in a way that it can contact them quickly without wasting emergency resources. Something like prepping by sending GPS and basic identification information, but not dispatching anyone until it’s confirmed.

    They could also identify if the areas are very crowded at the time it happens, as such, a human is likely to also report the accident, making the phones GPS valuable, but the phones report not.

    There isn’t really any solution the false positives from a dropped phone unless it can tell when the crash is too dramatic (and likely from just the phone itself) but, that seems like a hard problem to solve without false negatives).

    P.S. I mentioned in another comment that there are lots of things they can check to see if it was a false alarm, such as the user still moving around a lot or walking. And identifying locations where the system should be disabled or toned down even if it creates a tiny blindspot.

  4. This sounds nice when viewed superficially, but it’s completely bonkers once you start thinking about it a bit more. It’s unlikely to be reliable enough to trust upon, and it’s likely to have lots of false positives, or at least be another battery drain. And how does that sound analysis work? Is that uploading sound to some mist service?

    Some time ago I read that here in the EU, some system like this is going to mandatory in new cars within a few years time. At least the car has hard data about acceleration parameters and whether it triggered it’s own airbag. Battery life is also not a problem.

    1. A little off topic, but before seizures robbed me of my driving priviledges, I took my crappy 2012 Chevy sonic and in HAD fashion wired up my OBD and ECU to an old android phone for data parsing which was ultimately connected to a “dash projector” to put raw data on my windshield. Was ridiculous but cool as hell and the yokels would practically freeze in shock I “sci-fi”ed my crappy car.

  5. So, would a smart-watch (an oxymoron if I ever heard one) call the authorities every time I bumped my arm against the wall, which is a common occurrence for those of us with poor balance.

  6. I bet that automotive companies would love to know how to get reliable crash detection from one sensor…

    Airbag systems nowadays have multiple sensors in many places of a car and quite a number of people tuning algorithms behind them. Emergency dispatch is also often there, in a form of eCall system.

    I’m quite sceptic of detecting crash reliably in a cellphone. It’s like a 1st generation of airbag, carried on you (sans explosives).

  7. Fun fact from inside the industry: about 10% of coaster riders ignore the warnings to leave loose objects behind. Of those, about 5% lose a phone while riding. The typical loss rate is about 0.2% to 0.5% of all riders, or 5-10 phones per day.

    That leads to a strong mismatch between riders and operators. For the person who lost a phone, it’s a unique and unexpected event. For the operator who repeats the same warnings every three minutes, and deals with lost phones every few hours, it’s neither.

      1. I went to a quick mart the other day paid for gas and happened to hear something about surrendering backpacks in front. I didn’t have mine at the time. I told him about the big grocery store near by requesting such and reminded him that policy stopped, the signs came down. I asked him if he would personally sign a document claiming his responsibility for said item whilst it is in the store, women’s purses too. No answer. Next a pat down in the line? Like hell.

  8. Since Apple innovation in watches is to clone what Garmin did 5 years ago (badly) there is a simple solution.clone what Garmin did well. Stop pretending they had an original idea and donking it up. You have a loud vibrating alert that contacts your chosen contact not emergency services.

    With underserved 911 call centers all we need is hundreds of automated devices using news reporting as feedback for years ruining out emergency services until they can tweak the algorithm.

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