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Comment by WalterBright | Hacker News Reader

Yesterday I was driving past midnight through the city. I'd frequently come to an intersection where 2 arterials crossed at 90 degrees. 3 of the roads had red lights and 2 or more cars backed up. The 4th had a green and no traffic coming at all. And ..... we'd sit there a while, and eventually the light would go yellow, again, for nobody, turn red, pause a second for the non-existent red light runners, then finally turn green for us.

The intersections had cameras mounted pointing all 4 ways, and sensor wires in the roads.

You'd think that if we could build self-driving cars, we could devise a traffic light that would not be monumentally inefficient and incompetent. How hard can it be? And think of all the gas, CO2 and time saved.

There's a heluva lot of low hanging fruit in traffic lights.

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The first time I heard of autonomous vehicles I imagined intersections where no cars stop, they simply make minor adjustments to their speed so that vehicles could be continually flowing through in both directions. It would be quite the sight, but would obviously require a prohibition on human drivers and in practice would probably never work out.

Something like this?

https://vimeo.com/106226560

Yes, but faster! Seriously though, that is wicked. I wonder how the creators pulled it off.

https://vimeo.com/37751380

This has actually already been rolled out in certain markets: https://youtu.be/08OpjYn1BlY?t=1m50s

Get rid of most traffic lights. Use well-designed roundabouts.

How much would that cost?

Depends on many factors, including how much you value human life. Quoting from http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_672.pdf :

> The initial design and construction cost of a roundabout can vary significantly depending on the roundabout size, right-of-way impacts, illumination requirements, and other design or aesthetic features that may be desired. A new single-lane roundabout intersection in an unbuilt environment can have construction costs comparable to a traffic signal. However, as the size of the roundabout increases, particularly in a fully built-out commercial or residential area, the cost of roundabout construction can be higher than that of a traffic signal, depending on the footprint of the roundabout relative to that needed for the signal. However, the ongoing operations and maintenance cost of a roundabout can be less than that for a signal, with the possible exception of increased illumination needs for a roundabout. Although the initial construction cost may be more, a roundabout can have less operating and maintenance costs than a traffic signal, and the service life of a roundabout is significantly longer, approximately 25 years, compared with 10 years for a typical signal (2). Roundabouts also provide substantial cost savings to society due to the reduction in crashes, particularly fatal and injury crashes, over their service life.

It also depends on how much you value people's time waiting for a light to change, as described in the parent scenario.

I guess I didn't phrase my question correctly, how much would it cost to replace all the traffic signals with roundabouts (per your original statement)? I am betting that would be cost prohibitive much less concerns for space.

I didn't say "all", I said "most". Even countries with roundabouts also have traffic signals.

My comment was not trying to establish what you are asking for. Instead, I was pointing out that there are many factors in addition to "cost to replace". There is also the yearly upkeep costs (power to the light, landscaping), signal timing maintenance every few years, and a shorter lifespan for signals vs. roundabout.

Plus, of course, the savings in human time and lives.

Then there's systemic issues which are harder to quantify. Roundabouts have higher throughput than signals, so switching to a roundabout might reduce the need to widen nearby parallel roads, which is an indirect cost savings. And roundabouts without signals work even when the power goes out.

Quoting from http://www.roundaboutresources.org/when-should-roundabouts-r... :

> Roundabouts give superior traffic and safety performance to signalized intersections and to cross intersections almost everywhere, but roundabouts cost more, and not every signalized intersection or cross intersection is in great need of correction. Therefore, a highway agency should start at the top of its high-crash list and its high-congestion list and work down, often converting the problem location into an offset intersection where crossing flows are not too high. ...

> The modern roundabout should be recommended not only as a retrofit where there are present safety and capacity problems, but also as an intersection in new construction where roads join or cross each other for the first time.

That seems eminently reasonable to me.

Recall too that the challenge was to "devise a traffic light that would not be monumentally inefficient and incompetent", so the question is, how much would that hypothetical system cost per intersection, vs. a known, good solution to the given problem?

> much would that hypothetical system cost per intersection, vs. a known, good solution to the given problem?

Since the lights already exist, as well as cameras, and network connections, the incremental cost would be a box with a computer in it. The development cost of the software would be amortized over tens of thousands of intersections.

Yes, we are programmers, and are philosophically inclined to solve things through clever centralization.

That doesn't mean it's the only, or the optimal solution. Roundabouts depend on decentralized control to achieve very similar goal. (Though without, by the way, the pretty nasty failure modes should that box, or the power, go down.)

It's all handwaving without experimental studies and economic analysis. The numbers for roundabout are much better established than the smart systems, which are still experimental in nature.

For that matter, how much is that cost? The proposal at http://readwrite.com/2014/01/22/ai-traffic-lights-intelligen... is "$20,000 to $40,000 per intersection" for 'a box with a computer in it'.

From http://safety.fhwa.dot.gov/intersection/innovative/roundabou... , "The average construction cost of roundabouts is estimated at approximately $250,000". That gets its numbers from http://www.fhwa.dot.gov/publications/research/safety/00067/0... which says:

> Recent roundabout projects in the United States have shown a wide range in reported construction costs. Assuming “1998 U.S. Dollars” in the following examples, costs ranged from $10,000 for a retrofit application of an existing traffic circle to $500,000 for a new roundabout at the junction of two State highways. National Cooperative Highway Research Program (NCHRP) Synthesis 264 (3) reports that the average construction cost of 14 U.S. roundabouts, none being part of an interchange, was approximately $250,000. This amount includes all construction elements, but does not include land acquisition.

Elsewhere I gave links to places which said the installation costs for a roundabout were more expensive than signals. I don't know if the extra 5-10% price of the "box with a computer" changes the balance.

I tried to get numbers for the cost of a intersection. from http://azdot.gov/business/engineering-and-construction/traff...:

> A modern signal can cost taxpayers between $80,000 and $100,000 to install, depending on the complexity of the intersection and the characteristics of the traffic using it. On top of this, there is the perpetual cost of the electrical power consumed in operating a signalized intersection 24 hours a day. This cost now averages about $1,400 per year.

However, that appears to be for the dumb light, and not one with 'cameras and network connections' or even magnetic sensors. From http://www.masslive.com/news/index.ssf/2009/02/450000_traffi... :

> A request to spend $450,000 to install a new traffic signal on Easthampton Road remains an option for the City Council.

> And while the price tag might seem high for one traffic light, city officials insist that's the going rate to design and install such an item.

> "They're smarter controllers than they ever were in the past," Department of Public Works Superintendent William D. Fuqua said yesterday.

It's definitely not clear to me that the high-tech, interconnected system you desire is cheaper or more effective than roundabouts. (Again, there are clearly place where signals are more effective. I am not saying to only use rounabouts.) I would be happy to read any evidence you have which says otherwise.

This also means I don't think you can call out "environmentalists" for not yet pushing for your high-tech dream to come to fruition. Mind you, some of those environmentalists are pushing for "complete streets", which is yet another way to achieve comparable goals of more effective use of public roads.

Since your own figures show it is cheaper, especially since the lights, cameras, and network connections are already installed and paid for, I don't understand what more evidence you need.

As for their efficacy, the anecdote I posted shows there's plenty of low hanging fruit that would substantially improve things, even without an AI.

Let me correct what appears to be a miscommunication.

The numbers I gave don't prove anything, other than show that there is a huge range in cost, depending on the intersection type. You say "the lights, cameras, and network connections are already installed and paid for", but how many intersections are that way?

More specifically, the numbers I showed are that a fully equipped signal, like what you want, costs $450,000, while a roundabout is cheaper. If all lights already have "lights, cameras, and network connections" then it's a sunken cost. If 1% of the signals are that way, then it's entirely different.

I certainly don't know how interconnected the lights are. But even with hard numbers - and you haven't made any claims to any numbers - that's only a part of the point. (FWIW, the best numbers I found are from http://readwrite.com/2014/01/22/ai-traffic-lights-intelligen... which says "According to el-Tantawy, many of today’s traffic lights at intersections operate based on pre-programmed repeated cycles that run with little or no input from fluctuations in traffic.". That's not really helpful, other than to show there are a lot of dumb signals in the US.)

Yes, construction is cheaper on average for signals, but bear in mind that signals with 'lights, cameras, and network connections' are definitely not average signals.

But construction is only part of the cost-benefit analysis. The signals need to be powered, and replaced about every 10 years according to one of the URLs I gave. Roundabouts have a 25 year lifetime. Roundabouts are also safer, so there the benefits to human life must be included. And as I pointed out, you also have to consider the failure modes.

Sure, yes, there's 'low hanging fruit' (which is a misnomer, as the really 'low hanging fruit', like traffic light coordination and in-pavement detectors, have long since been picked). But that's because you have a goal in mind, which is to "improve traffic signals", not "improve traffic systems" (which roundabouts do), or "improve quality of life" (which 'complete streets' and livable community advocates want to do).

Thus, if you think that '"The reductions of 40 percent in vehicle wait time, nearly 26 percent in travel time and 21 percent in projected vehicle emissions realized in this pilot are remarkable,"' is a good justification, then you have to compare it to other solutions which achieve or improve upon those same goals, and not just cherry-pick (again with the fruit metaphors!) the numbers that best support your goal.

As I also pointed out, the pathway to more roundabouts isn't to wholescale replace existing signals, but to use them for new intersections, and for those with high accident rates where it's most worthwhile to switch. The over time, as the old signals need replacing, switch many of them to roundabouts.

That too "would substantially improve things, even without an AI".

> You say "the lights, cameras, and network connections are already installed and paid for", but how many intersections are that way?

In the Seattle metro area, it's hard to find one on an arterial that doesn't have them. (This is just in the last handful of years.)

Why do you need to conjecture when the data is easily available? The list of every traffic light in Seattle is at https://data.seattle.gov/Transportation/Traffic-Signals/dr6d... . You can unzip it and open WGS84/TrafficSignals.dbf in LibreOffice as a spreadsheet. There are 1077 traffic lights in the city, according to those records.

Of them, 85 are "FULL", 271 are "PRE", and the remaining 721 are "SEMI". Based on http://ops.fhwa.dot.gov/publications/fhwahop08024/chapter5.h... these appear to mean respectively "Fully-Actuated", "Pre-timed", and "Semi-Actuated", so 271 or 25% of your cities traffic lights are on a timer and don't have vehicle detectors.

Your original example was of an intersection with "cameras mounted pointing all 4 ways", making it fully-actuated. There are only 85 of those signals in Seattle, or 8% of the signals.

To be fair to you, you said "on an arterial". However, your definition of "arterial" appears to be different than Seattle's, which subcategorizes them as 'Principal Arterials', 'Minor Arterials', 'Collector Arterials'. See http://www.seattle.gov/transportation/streetclassmaps.htm . More specifically, the map at http://www.seattle.gov/transportation/streetclassmaps/planwe... shows more than 85 intersections of an arterial with an arterial, so the pidgeonhole principal say it shouldn't be hard to find an intersection that isn't fully actuated.

To be fair to me, this is completely besides the point. There are many solutions to your original problem of being stuck at a light. One is to add another layer of technology (smarter signals). Another is to switch to a different type of technology (roundabouts). All you've been doing is cherry picking your observations to justify your initial beliefs. I further believe is because you, like many other programmers, are philosophically inclined towards complex, centralized control systems, because that's what we understand and work with all day.

But the observational evidence is that roundabouts are better than signals for many situations. Please stop ignoring the evidence because your mind is set on the first solution you came up with while your were stuck at that traffic light!

For examples drawn from Seattle, from these meeting notes in 2006 at http://www.seattle.gov/transportation/docs/setscctnov06%20mt... :

> The City Council did not vote to eliminate the roundabout proposed at 51st Ave S, Renton Ave S and S Roxbury ST from the Transportation Capital Improvement Program (CIP). SDOT has secured a grant for $1.7 million to design and build the roundabouts; unfortunately, based upon preliminary design and cost estimate, additional funding is necessary. If built, it would be the first roundabout in Seattle. The project was identified in the Rainier Beach Neighborhood Plan as the most problematic intersection in SE for all modes. The roundabout could be a very cost effective solution as unlike a traffic signal, it will have minimal on-going operating and maintenance costs. Environmentally, it's better than a traffic signal because vehicles would not be idling at the light. It is also far friendlier to pedestrians, which would have the right away and not have to find the pedestrian push buttons. CCT members reiterated that the area is routinely congested and difficult to negotiate.

and from http://www.seattle.gov/transportation/docs/nctipf_chapter%20...

> Modern roundabouts can provide safe and cost-effective traffic control at some intersections. A roundabout separates through and turning traffic into designated lanes with “splitter islands” to minimize traffic weaving. Well-designed and appropriately placed roundabouts also provide safer pe destrian crossings and can accommodate large turning radii required by trucks and emergency vehicles. Today’s roundabouts do not function like the large, high-speed traffic circles found in Washington, D.C., (Dupont Circle) and Paris (Arc de Triomphe). These large traffic circles have high crash rates, largely due to high volumes, high speeds, and a considerable amount of weaving between entries and exits. Roundabouts are not the small circles used primarily for neighborhood speed control. Studies of modern roundabouts show a reduction in serious crashes, as well as reduced delay and queue length compared to other forms of traffic control, such as four-way stops and traffic signals. However, engineering analysis will not always support a roundabout over a traffic signal or other traffic control measure. Consideration must be given to traffic volumes, capacity requirements, available right of way, and cost.

There's a newspaper article from 2002 which concerns a successful roundabout in Snohomish County, at http://community.seattletimes.nwsource.com/archive/?date=200... . A round-about replaced a stop sign, and reduced the number of accidents. While it cost $310,000 and "traffic signals at that location would cost only $200,000, the roundabout requires no mechanical maintenance or electricity, making long-term costs comparable, he said. Meanwhile, traffic flows much more smoothly without a signal or stop signs."

The article also says "DOT built its first state-highway roundabout in 1998 in Port Orchard, where a triangular intersection on Highway 160 had produced 39 crashes in three years. In the first 18 months after the roundabout opened, only two accidents occurred."

Continuing from the article, "National studies show that communities usually oppose the idea at first, DOT engineer Brian Walsh said. "Our experiences here in Washington have mirrored that; we have had a lot of people not very happy about the idea of roundabouts, but after they are constructed, those fears mostly go away."

which is why when SDOT brings it up over the years, there's pushback, like:

> The roundabout concept has generally received positive or neutral comments, but there is skepticism about the feasibility of building it and also some concern about the amount of land that would be required to build it, as well as the adjustment needed for motorists to learn how to drive this type of facility. - http://www.seattle.gov/dpd/cs/groups/pan/@pan/documents/web_...

I can accept an argument that people in Seattle won't use roundabouts because no one there has the political will to push for what is, really, a safer system. But your arguments so far haven't been anything better than "trust me, I know what I'm talking about". ... Which is exactly how the current system of "smart" (ie, actuated) but dangerous traffic signals were sold to us 20 years ago.

* Significantly more than $1.7m to build a roundabout, vs $40,000 for one that can be installed on existing infrastructure.

* Adding roundabouts requires more land, which is in tight supply in a built-up city like Seattle. I don't think shaving the corners off of buildings is going to go over very well.

* As I've noted, the buildup of the cameras is very recent. The traffic light data you cited is over a year old. They're creeping into the side streets now.

* Nobody needs a study to see the obvious improvements possible in cases I cited.

* Given the desire of the government to install cameras everywhere on the roads, the cost of them is going to be there with or without roundabouts.

* Far friendlier to pedestrians? How is that possible when cars don't stop? I've crossed roundabouts in England as a pedestrian. It involves pushing a button and a traffic light turns red so you can cross. I.e. the traffic lights are still there!

* In Romania the roundabouts also had traffic lights for the pedestrians, as well as pedestrian tunnels under the intersection. That can't be inexpensive.

* I can see a roundabout as cost effective in a rural area where land is cheap and there are few pedestrians. In a builtup city, not so much, as they'd be massive and expensive construction projects. A $40,000 box can be installed instead with no disruption and immediate improvements. Sounds like a winner to me.

   All modern roundabouts have median islands separating incoming and outgoing auto traffic.  Pedestrians don't have to find a gap in two directions of traffic, just one.  This is safer for pedestrians, especially for younger or older ones, because they only have to concentrate on one direction of traffic at a time.  This is what is meant by two-phase. Cross the first half, pause if you need to, then cross the second half.  On multi-lane crossings pedestrian beacons or signals are often added if the auto (or pedestrian) traffic is too numerous.  The signals can also be two phase, requiring the pedestrian to push a second button when they get to the median.  The median can also have a Z path to reorient the pedestrian to view oncoming traffic.  Also, the signals usually rest in off, so they are only activated if a pedestrian needs the help crossing. This way only motorists that need to stop are delayed.

"Significantly more than $1.7m to build a roundabout"

No. Look again. The quoted text says "$1.7 million to design and build the roundabouts". Plural. That was three roundabouts, not one, on "51st Ave S, Renton Ave S and S Roxbury ST". And some of the objections you just now raised have been addressed in links I gave earlier, including examples of SDOT proposals for roundabouts in urban Seattle.

I give up. You have decided on your answer and no real-world information will change your personal beliefs. You win.

It's still 10x the cost. Costs of the light system can be further reduced by instead of installing a computer at the light, have the computer centrally located to serve any number of lights. Since the cameras are already network connected, this is practical.

I've been in countries that are comfortable with roundabouts. They also still have traffic lights everywhere. Something is missing in your analysis that explains this choice.

     Modern roundabouts are the safest form of intersection in the world (much more so than comparable signals).  Visit http://tinyurl.com/iihsRAB for modern roundabout FAQs and safety facts.  Modern roundabouts, and the pedestrian refuge islands approaching them, are two of nine proven safety measures identified by the FHWA, http://tinyurl.com/7qvsaem
   The FHWA has a video about modern roundabouts on Youtube, or check out the IIHS video (iihs dot org).

http://priceonomics.com/the-case-for-more-traffic-roundabout... http://safety.fhwa.dot.gov/intersection/innovative/roundabou...

First cost is the wrong way to compare projects. It would be like buying a car without knowing the fuel economy or safety of the thing, just its price to buy. Present Value Life Cycle Cost Analysis (LCCA) is the best way to compare two or more choices. When comparing modern roundabouts to signals for a 20-year life cycle (the standard period), modern roundabouts usually cost less. Costs to compare include: first cost (design/land/construction), operation and maintenance (electricity, re-striping, upgrades, etc.), crash reduction (what’s your/your family’s safety worth?), daily delay (what’s your time worth?), daily fuel consumption (spend much on gas?), point source pollution (generated by stopped vehicles = health cost), area insurance rates (this costs more where it is less safe to drive). Each of these things, and others, can be estimated for any two choices and everyone near or using the project area will pay some portion of all of these costs.

Hmm, here in Australia, I can't recall a single time this has happened. I've actually tested how well the software for these lights work, for myself at night time when there's no traffic. Usually the lights on the main roads are green by default. In my case, it'd take 1-2 seconds after I approached the red light of the crossing road for the main one to turn yellow. Same when pressing the pedestrian crossing button.

The demand sensor wires are too close to the lights, so you wind up having to stop before it turns green. Also, if cars are coming from both directions, the demand system tends to get 180 degrees out of phase with the traffic and makes everyone stop.

A proper system is, well, like one on a self-driving car. Detect traffic from further back using the cameras rather than the sensor wires. Estimate the number of cars, speed, and position, then adjust for max flow.

Given the position/speed data that Google collects through Google play services (which assists then with determining traffic conditions for instance), I think Google could do much better at controlling the traffic lights (or at least provide one source of input for).

In Western Australia the prevailing culture within the Main Roads Department is "If people get used to having green lights they won't stop for a red light so we must try make people get as many red lights as we can" its moronic but true, a technician friend of mine resigned over the stupidity of it.

I'm not convinced that pedestrian crossing buttons are actually hooked up to anything.

Some aren't but the ones that are can mess up timings of lights and in some cases, those require manual readjustments.

You've obviously not tested them on a motorcycle in WA...

Grrr...I'm just waiting for the day I get picked off by some overzealous Judge Dredd cop because I ran a red arrow because I got tired of waiting for it to detect me.

Attach a largeish neodynium magnet (like a cow magnet, as a bonus they are coated in plastic so they don't corrode) to your bike frame. It will increase your magnetic signature massively and cause in wire-loop-in-road light controller to "see" you. (note, not all sensors are magnetic, some are weight based or IR based)

law in WA is you wait one full light cycle and you can run the light. So basically 30-45 seconds and if no one is going you go.

And how do you prove that you did after the red light camera catches you?

Same way they do, you ask for the full tape, which you can get. Or you know just go around the wrong way. Anecdotally red light covered cameras seem to be much better maintained as othewise they lose revenue.

Also this is why you have a dash cam.

The red light cameras I've seen trigger when someone approaches a red light without slowing down quickly enough. Sometimes, late at night, I make a game of setting them off on purpose, by waiting til the last minute to brake. They wouldn't fire if you stopped, waited, then continued after determining that the detector hadn't noticed you.

To give you an idea where the tech is at, the local news did a report for Plymouth MN about Bob who is the person that manually goes around and adjusts the timing on the street lights. It is sneaker net applied to traffic control.

The timing was done in the 70's, and it never worked. The city would argue that its traffic engineers were highly competent and had timed it perfectly, but all the drivers knew better.

It's like the TV sound engineers who'd argue that the commercials are not set to be louder. Yeah, I know, dynamic range compression, but I'd put VU meters on the sound and the loudest sound in the TV show was quite a bit lower than the average sound on the commercials.

(The traffic light problem is a small subset of the same problem a self driving car faces.)

http://www.cmu.edu/homepage/computing/2012/fall/smart-traffi...

That is what I'm talking about. Note that it is a 3 year old article. You'd think environmentalists would get all over "The reductions of 40 percent in vehicle wait time, nearly 26 percent in travel time and 21 percent in projected vehicle emissions realized in this pilot are remarkable," but nope.

Roundabouts - that's what I'm talking about.

http://www.iihs.org/iihs/topics/t/roundabouts/qanda and others cite "Retting, R.A.; Mandavilli, S.; Russell, E.R.; and McCartt, A.T. 2006. Roundabouts, traffic flow and public opinion. Traffic Engineering and Control 47(7):268-72". The above URL summarizes the paper as:

> A study of three locations in New Hampshire, New York and Washington state where roundabouts replaced traffic signals or stop signs found an 89 percent average reduction in vehicle delays and a 56 percent average reduction in vehicle stops.

That URL then goes on to say:

> Because roundabouts improve the efficiency of traffic flow, they also reduce vehicle emissions and fuel consumption. Installing roundabouts in place of traffic signals or stop signs has been found to reduce carbon monoxide emissions by 15-45 percent, nitrous oxide emissions by 21-44 percent, carbon dioxide emissions by 23-37 percent and hydrocarbon emissions by 0-42 percent. 6, 11, 12 Constructing roundabouts in place of traffic signals or stop signs reduced fuel consumption by an estimated 23-34 percent. 6, 11, 13

and

> A 2005 Institute study documented missed opportunities to improve traffic flow and safety at 10 urban intersections suitable for roundabouts where either traffic signals were installed or major modifications were made to 10 intersections with signals. 14 It was estimated that the use of roundabouts instead of traffic signals at these intersections would have reduced vehicle delays by 62-74 percent.

Sounds to me like existing roundabouts at least competitive to state-of-the-art experimental smart traffic signals ... and have the advantage of working even when the power goes out, and don't require more expertise in order to maintain.

I call bullshit on roundabouts improving the efficiency of traffic flow in New Hampshire.

The roundabouts on US 4 between Portsmouth and Concord will back up for miles, and the Portsmouth traffic circle is an enormous cluster, with more accidents than any signaled intersection I've ever seen (Doesn't help that one of the highest-volume liquor stores in New England is located right on the circle...).

Those are traffic circles or rotaries, not roundabouts.

Traffic circles are not roundabouts (nor are they 'traffic calming circles'). Eg, http://www.heraldtribune.com/article/20090621/columnist/9062... (warning: that's the "print" page, rather than having three differet pages):

> Often there is considerable confusion about roundabouts and traffic circles or rotaries. People often say that they don't work in the Northeast (especially in New York and New Jersey) and are being removed, so why build them here [in Florida]? ...

> A study done by Per Gardner at the University of Maine found that traffic circles have 3.5 to 6.5 times more crashes than roundabouts. ... Because of these growing concerns, the last design reference to traffic circles in the U.S. design standards was in 1965.

> Then came roundabouts. The first roundabout in America was built in 1992 at an intersection in Gainesville. Although traffic circles and roundabouts use a circular design, they operate very differently. Traffic circles are very large and are designed for high-speed vehicle operation. Roundabouts are designed as small as possible, 16 to 180 feet wide, and operate at 15 mph to 25 mph.

It isn't about designing an efficient intersection, it's about designing one that generates a lot of traffic revenue for the city.

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