Finding the Shortest Path in Transit Networks

Victor Chircu

Faculty of Computer Science, “AlexandruIoanCuza” University, Iasi, Romania victor.chircu@info.uaic.ro

Abstract.More and more governments provide Sparql endpoints to query over public data, which sometimes includes route configuration for transit agencies. Knowing the route configuration and geolocation for each route stop in a transit network, one can run an algorithm to find the (k-)shortest path(s) from point A to point B. Since the Romanian Government does not provide this kind of information, this article describes a way one can access this data, store it in a triple server, and expose it in Sparql endpoint.

Keywords: semantic web, rdf, sparql, triple store, virtuoso universal server, dotNetRdf, transit network, public transportation network, k-shortest path, A*

1 Introduction

The focus of this paper is to provide a way to acquire, store and expose transit data, if this data is not found open over the Web. In recent years, public transportation agen-cies have been providing transit data freely over the internet, data that can be used by developers to build useful applications. In some cases1, the agencies even encourage developers to do so, by organizing applications contests. This trend started in 2005, when TriMet2and Google developed the Google Transit Feed Specification (GTFS)3

format that will be used for finding routes using the Google Transit Trip Planner4. Over the years, more transit agencies incorporated trip planners in their websites, and provided data in GTFS format to be used with the Google Transit Trip Planner.

Unfortunately, this is not the case for Romania, where public transportation (linked) data is still closed. For example, the RATB5(the main bus transit agency in Bucharest) websitedoes not provide a trip planner, but does provide an HTML view of all the routes, and stops per routes. On the other hand, Metrorex6 (subway transit

1 http://mtaappquest.com/2 http://trimet.org/3 https://developers.google.com/transit/gtfs/reference4 http://www.google.com/intl/en/landing/transit/#mdy5 http://www.ratb.ro/6 http://www.metrorex.ro

agency in Bucharest) does provide a trip planner, but provides only a visual route map, which cannot be parsed using a computer. But Metorex’s route planner would need some improvement, since it provides routes only from station to station (the average user would prefer to enand does not connect with the RATB routes. Thus, there is a need for a city level trasit route planner that uses routes from all agencies in a city. This is the main purpose of my dissertation paper, buin a manner that fits my purpose and exposing it in a Sparql endpoint, so it can be used by other developers.

2 Getting the data

I have managed to get part of the data I need as an SQL database. Thtains most of the routes (name, geometry) and stops (name, location) in the Bucharest transit network. The routes are managed by the two biggest transit agencies in the city, RATB and Metrorex. This data is incomplete, because I need to knowstops in each route and their sequence. To get this information, I can use a technique calledweb scarping, because the RATB website does provide a way for human users to see what stops are in each route. software technique of extracting information from websitesPart of the page for one of the RATB routes on the RATB website is represented in Figure 1.

Fig.

does provide a trip planner, but provides only a visual route map, which cannot be parsed using a computer. But Metorex’s route planner would need some improvement, since it provides routes only from station to station (the average user would prefer to enter the origin and destination by clicking on a map) and does not connect with the RATB routes. Thus, there is a need for a city level trasit route planner that uses routes from all agencies in a city. This is the main purpose of my dissertation paper, but this paper focuses only on getting the data, organizing it in a manner that fits my purpose and exposing it in a Sparql endpoint, so it can be

Getting the data

I have managed to get part of the data I need as an SQL database. This database cotains most of the routes (name, geometry) and stops (name, location) in the Bucharest transit network. The routes are managed by the two biggest transit agencies in the city, RATB and Metrorex. This data is incomplete, because I need to know the route stops in each route and their sequence. To get this information, I can use a technique

, because the RATB website does provide a way for human users to see what stops are in each route. As defined in [1], web scraping is“is a computer software technique of extracting information from websites”.Part of the page for one of the RATB routes on the RATB website is represented in

Fig.1.Route page on the RATB website.

does provide a trip planner, but provides only a visual route map, which cannot be parsed using a computer. But Metorex’s route planner would need some improvement, since it provides routes only from station to station (the

ter the origin and destination by clicking on a map) and does not connect with the RATB routes. Thus, there is a need for a city level tran-sit route planner that uses routes from all agencies in a city. This is the main purpose

organizing it in a manner that fits my purpose and exposing it in a Sparql endpoint, so it can be

is database con-tains most of the routes (name, geometry) and stops (name, location) in the Bucharest transit network. The routes are managed by the two biggest transit agencies in the

the route stops in each route and their sequence. To get this information, I can use a technique

, because the RATB website does provide a way for human users omputer

Part of the page for one of the RATB routes on the RATB website is represented in

As you can see, you canrepresents a type of route: rail, trolley, bus). The selected route name must be sent as a parameter to the server. To find out how, we can use a Net monitoring tool, like Firebug7for Mozila’s Firefox browser.from the bus route drop down list (the third from the left). This selection automaticaly triggers a postback. The post parameters are shown in

Fig.2

As you can see, the route name is indeed sent as a post parameter, with the name tlin3. Knowing this, I can build a small (to http://www.ratb.ro/v_trasee.phpthat I am interested in (e.g.: the bus route list), and for each option value, HTTP Post requestwith the required post parameters (e.g.: if we choose the third down list, then thetlin1, tlin2, tlin4, tlin5option value). The POST returns the page in HTML format. Now, I have to parse the page, extract the information from the table and write it to disk. The nexwrite the route steps to the existing SQL database. This can be done manually, or automatically, by matching the stop name from the filetabase. Following these steps I have found the complete route itinerary for throutes.

7 http://getfirebug.com/

select the route from one of the drop down lists (each list represents a type of route: rail, trolley, bus). The selected route name must be sent as a parameter to the server. To find out how, we can use a Net monitoring tool, like

irefox browser. So, for example, let’s say we have chosen 106 from the bus route drop down list (the third from the left). This selection automaticaly triggers a postback. The post parameters are shown in Figure 2.

2.Using Firebug to detect post parameters.

As you can see, the route name is indeed sent as a post parameter, with the name I can build a small (PowerShell) script that makes a GET request

http://www.ratb.ro/v_trasee.php, gets all the options from the HTML select element that I am interested in (e.g.: the bus route list), and for each option value, makes

questwith the required post parameters (e.g.: if we choose the third drop tlin1, tlin2, tlin4, tlin5 parameters are set to 0, and tlin3 is set to the

The POST returns the page in HTML format. Now, I have to parse the page, extract the information from the table and write it to disk. The next step is to write the route steps to the existing SQL database. This can be done manually, or automatically, by matching the stop name from the file with the stop name in the d

Following these steps I have found the complete route itinerary for th

select the route from one of the drop down lists (each list represents a type of route: rail, trolley, bus). The selected route name must be sent as a parameter to the server. To find out how, we can use a Net monitoring tool, like

So, for example, let’s say we have chosen 106 from the bus route drop down list (the third from the left). This selection automatical-

As you can see, the route name is indeed sent as a post parameter, with the name makes a GET request

, gets all the options from the HTML select element makes an

drop is set to the

The POST returns the page in HTML format. Now, I have to parse the t step is to

write the route steps to the existing SQL database. This can be done manually, or with the stop name in the da-

Following these steps I have found the complete route itinerary for three

3 Modeling the data

3.1 General Information

Taking in account the classes of entities, and the relationships between these classes, the domain I want to model is shown in

Because I want the dataset that I am exposing to be extensible and interoperable with other datasets, I have chosen to model the data using RDF triples, store it in a Triple Store and expose it in a SPARQL endpoint.In the semantic Web, a knowledge base coFramework) [2] triples of the form <subject, predicate, object>. fied by a unique URI. Subjects and predicates are always resources, while objects can be either resources or literals (having an akind of domain can be represented.

Because in semantic web it is strongly advised to usecabularies, and not create needs. I have found the T

8 http://vocab.org/transit/terms/

Modeling the data

General Information

Taking in account the classes of entities, and the relationships between these classes, the domain I want to model is shown in Figure 3.

Fig.3.Transit Domain Model.

Because I want the dataset that I am exposing to be extensible and interoperable with other datasets, I have chosen to model the data using RDF triples, store it in a Triple Store and expose it in a SPARQL endpoint.In the semantic Web, a knowledge base contains a set ofRDF (Resource Description

triples of the form <subject, predicate, object>. Resources are identfied by a unique URI. Subjects and predicates are always resources, while objects can be either resources or literals (having an associated data type). Using this model,any

domain can be represented.Because in semantic web it is strongly advised to use, if possible, existing RDF v

cabularies, and not create a new one, I have searched for one that would suit my Transit8vocabulary, which models exactly the domain I am

http://vocab.org/transit/terms/

Taking in account the classes of entities, and the relationships between these classes,

Because I want the dataset that I am exposing to be extensible and interoperable with other datasets, I have chosen to model the data using RDF triples, store it in a Triple

RDF (Resource Description Resources are identi-

fied by a unique URI. Subjects and predicates are always resources, while objects can Using this model,any

existing RDF vo-, I have searched for one that would suit my

models exactly the domain I am

trying to describe. Transitand is based on the General Transit Feed Specification published by GoogleTransit vocabulary core classes are shown in

The Transit vocabulary is already used to expose MTA New York city transit dataand bus route data in SouthamptonRDF vocabulary.

Fig.

As you can see, the classes in this vocabulary map over the classes in my domain model. There is one class that I do not use in my domain module, the This is done because in most of the cities in Romania, public transportation does not run according to a fixed schedule. By eliminating this class,the amount of data I have to manipulate.

9 http://kasabi.com/dataset/mta10 http://data.southampton.ac.uk/bus

. Transit is “a vocabulary for describing transit systems and routess based on the General Transit Feed Specification published by Google. The

re classes are shown in Figure 4.The Transit vocabulary is already used to expose MTA New York city transit data

and bus route data in Southampton, UK10, so it definitely is the most known transit

Fig. 4.Transit Vocabulary Core Classes.

As you can see, the classes in this vocabulary map over the classes in my domain There is one class that I do not use in my domain module, the Schedule class.

This is done because in most of the cities in Romania, public transportation does not according to a fixed schedule. By eliminating this class, I have greatly minimized

the amount of data I have to manipulate.

aset/mta-new-york-city-transit

http://data.southampton.ac.uk/bus-routes.html

a vocabulary for describing transit systems and routes”. The

The Transit vocabulary is already used to expose MTA New York city transit data9

, so it definitely is the most known transit

As you can see, the classes in this vocabulary map over the classes in my domain class.

This is done because in most of the cities in Romania, public transportation does not I have greatly minimized

3.2 Transit Core Classes and Properties

In this section, I will go over the main Transit classes and properties that I am using anddefine them according tothe Transit vocabulary document11. You may notice that I use only a subset of the classes and properties defined in this document, because I use a model a little less general, by eliminating the Schedule and Service classes.

Note: Each resource’s URI is written in the page footnote section

Classes

Agency12 - an agency is an organization that oversees public transportation for a city or region (e.g. RATB, Metrorex).

Route13 - a public transportation route; some of its subclasses are:─ Bus Route14

─ Rail Route15

─ Subway Route16

Stop17 - a location where passengers board or disembark from a transit vehicle Route Stop18 - a location where passengers board or disembark from a transit ve-

hicle for a specific route.

Properties

agency19 - the agency that operates this public transportation route route20 - A route associated with the given resource routeStop21 - Links a route to a particular stop and the sequence of that stop in the

route stop22 - the physical stop associated with this route stop (Note: this property is not

used according to the Transit vocabulary, because having this property implied be-ing a ServiceStop. In my domain, having this property implies being a RouteStop, because I do not need to use the ServiceStop class.

11 http://vocab.org/transit/terms12 http://vocab.org/transit/terms/Agency13 http://vocab.org/transit/terms/Route14 http://vocab.org/transit/terms/BusRoute15 http://vocab.org/transit/terms/RailRoute16 http://vocab.org/transit/terms/SubwayRoute17 http://vocab.org/transit/terms/Stop18 http://vocab.org/transit/terms/RouteStop19 http://vocab.org/transit/terms/agency20 http://vocab.org/transit/terms/route21 http://vocab.org/transit/terms/routeStop22 http://vocab.org/transit/terms/stop

3.3 Other Vocabularies

Some of the other RDF vocabularies I am using are:

FOAF23, for the name and page properties RDF24, for the type property RDF Schema25, for the label property Geometry Ontology 26 , for describing the geometry of a route in Well-Known

Text27 (WKT) format. WGS84 Geo Positioning28, for representing latitude and longitude information in

the WGS84 geodetic reference datum

4 Technical Information

4.1 General Information

Because of my hands-on experience with the Microsoft development stack, I have chosen to develop the application using .Net/C#. This might be a challenge, because most of the semantic web tools focus on non-Windows client, as seen in the pie chart represented in Figure 5, taken from [3]. The same source[3] shows that this trend is constant, since in 2011 there were not developed any new semantic tools for the .Net platform. I have taken in consideration switching to the Java platform, which provides a set of powerful tools for working with RDF and OWL, most notably the Jena Framework29, developed by Apache, but after doing some research I have found a tool written for the .Net platform which suits my needs. This tool will be presented in detail in section 4.4 of this paper.

23 http://xmlns.com/foaf/0.1/24 http://www.w3.org/1999/02/22-rdf-syntax-ns#25 http://www.w3.org/2000/01/rdf-schema#26 http://data.ordnancesurvey.co.uk/ontology/geometry/27 http://edndoc.esri.com/arcsde/9.0/general_topics/wkt_representation.htm28 http://www.w3.org/2003/01/geo/wgs84_pos#29 http://incubator.apache.org/jena/

Fig.4. Semantic Web Tools by Programming Language

4.2 Knowledge base

One of the disadvantages of using 3source products. But because of the nature of my problem, I could not use an inmemory triple store, I needed an efficient one, with a powerful query engine. researching different optionServer30 as a Triple Store. My option was based on Virtuoso maturity, and its RDF Graph Model features31:

Backward Chaining OWL Reasoner covering: rdfs:subClassOf, rdfs:subPropertyOf, owl:sameAs, owl:equivalentClass, owl:equivalentProperty, owl:InverseFunctionalProperty, owl:inverseOf, owl:SymmetricalProperty, and owl:TransitiveProperty

SPARQL 1.1 Query Language, Protocol, and Results Serialization support SPARQL Create, Update, and Delete (SPARUL)

30 http://virtuoso.openlinksw.com/31 http://virtuoso.openlinksw.com/rdf

Semantic Web Tools by Programming Language

One of the disadvantages of using 3rd party triple stores is that there aren’t any opensource products. But because of the nature of my problem, I could not use an inmemory triple store, I needed an efficient one, with a powerful query engine. Upon researching different options, I have decided to use OpenLink’s Virtuoso Universal

as a Triple Store. My option was based on Virtuoso maturity, and its RDF

ackward Chaining OWL Reasoner covering: rdfs:subClassOf, bPropertyOf, owl:sameAs, owl:equivalentClass, owl:equivalentProperty,

owl:InverseFunctionalProperty, owl:inverseOf, owl:SymmetricalProperty, and owl:TransitivePropertySPARQL 1.1 Query Language, Protocol, and Results Serialization support

Update, and Delete (SPARUL)

http://virtuoso.openlinksw.com/http://virtuoso.openlinksw.com/rdf-quad-store/

party triple stores is that there aren’t any open-source products. But because of the nature of my problem, I could not use an in-

pon , I have decided to use OpenLink’s Virtuoso Universal

as a Triple Store. My option was based on Virtuoso maturity, and its RDF

ackward Chaining OWL Reasoner covering: rdfs:subClassOf, bPropertyOf, owl:sameAs, owl:equivalentClass, owl:equivalentProperty,

owl:InverseFunctionalProperty, owl:inverseOf, owl:SymmetricalProperty, and

Supports data broad range of RDF model data representation formats: HTML+RDFa, RDF-JSON, N3, Turtle, TriG, TriX, and RDF/XML

REST interfaces for Create, Read, Update, and Delete operations RDF Data is accessible also accessible via ODBC, JDBC, ADO.NET (Entity

Frameworks compatible), OLE DB, and XMLA data providers / drivers.

Because the application that I’m building is a non-commercial application, I am not interested in acquiring a Virtuoso commercial license at the moment. OpenLink does provide 2 X 15 days trial of the software. I have used the first one while configuring and testing the Virtuoso Server, and will use the second one on demos later on. While working on the application, I will use in-memory triple stores, loaded and saved to the file system.

4.3 .Net API for working with RDF

While looking for a .Net API for working with RDF I have found three possible can-didates:

Linq2RDF32, a LINQ query provider that converts queries into the SPARQL query language. Unfortunately, it is not a mature enough API and the last update for this project was in august 2008, so it is not under development anymore.

Jena .NET33, a flexible .NET port of the Jena semantic web toolkit. Unfortunately this project is abandoned too, while still a beta 0.3 release.

dotNetRDF34, an open-source semantic web/RDF library for C#/.Net. Even if this is just a beta 0.5 release, it is still under development, which is a big advantage over the other two options. This API will be described in the next section.

4.4 dotNetRDF

General InformationSome of the points of interest regarding the API are:

currently a beta release (version 0.5.1) works on .Net 3.5 (but according to the project’s Issue Tracker35, moving the li-

brary to .Net 4.0 is a top priority) "simple but powerful API for working with RDF" operates primarily with Triples, Graphs and Triple Stores has limited support for Inference no support for OWL

32 http://code.google.com/p/linqtordf/33 http://semanticweb.org/wiki/Jena_.NET34 http://www.dotnetrdf.org/35 http://www.dotnetrdf.org/tracker/Issues/IssueDetail.aspx?id=22

Known formatsThe library can read RDF fragments (including Graphs and Triple Stores) from strings, files and even URIs. It can also write RDF fragments to files and strings. Reading and writing can be done in all of the most used RDF formats: RDF/XML, RDF/JSON, NTriples, Turtle, Notation 3, XHTML + RDFa/

GraphsThe API has support for getting Nodes and Triples from a Graph by a given criteria (which is a combination of subject, predicate and object), merging graphs and compu-ting graph difference and equality.

Triple StoresThe library can work with both in-memory Triple Stores and native Triple Stores.It provides support for working with:

in-memory triple stores, loaded and saved from and to disk in two ways:─ a folder, where each files represents a single Graph, and there is an additional

index file─ a single file, using one the following formats: TriG, TriX and NQuads

simple SQL based stores with MySQL and Microsoft SQL Server databases native 3rd party Triple Store: AllegroGraph36, Dydra37, 4store38, Fuseki39, Joseki40,

Sesame 41 (any Sesame based store e.g. BigOWLIM 42 ), SPARQL Graph Store HTTP Protocol for compliant stores, Stardog43, the Talis Platform44 and Virtuoso.

By providing an easy way to work with Virtuoso based Triple Stores, dotNetRDF proves to be the right choice.

QueryingUsing dotNetRDF one can query easily over:

in-memory Graph using the library’s SPARQL implementation remote SPARQL endpoints 3rd party Triple Stores, using native query (this is very important, since we can

rely on the more powerful Virtuoso query engine and not on the weaker dot-NetRDF implementation.

36 http://www.franz.com/agraph/allegrograph/37 http://dydra.com/38 http://4store.org/39 http://incubator.apache.org/jena/documentation/serving_data/index.html40 http://www.joseki.org/41 http://www.openrdf.org/42 http://www.ontotext.com/owlim43 http://stardog.com/44 http://www.talis.com/platform/

The query mechanism is compatible with the current draft45 of the SPARQL 1.1 stan-dard.

Inference and ReasoningThe current version provided three types of reasoners:

RDFS Reasoner, which does not apply the full range of possible RDFS based infe-rencing but does do the following:─ asserts additional type triples for anything which has a type which is a sub-class

of another type─ asserts additional triples where the property (predicate) is a sub-property of

another property─ asserts additional type triples based on the domain and range of properties

SKOS Reasoner is a simple concept hierarchy reasoner which can infer additional triples where the subject has an object which is a skos:Concept in the taxonomy by following skos:narrower and skos:broader links as appropriate.

Simple N3 Rules Reasoneris a reasoner that is able to apply simple N3 Rule

Unfortunately, there is no API support for using inference with 3rd party Triple Stores. Because of this, the reasoner that comes with the Virtuoso Universal Server cannot be used.

ConfigurationThe library comes with a very useful Configuration API that can be used to load dy-namically commonly used objects (such as Graphs, connections to Triple Stores etc.), and a couple of tools for deploying RDF enabled ASP.NET Web Applications. Be-cause of these last two features, exposing a SPARQL endpoint is a trivial task.

5 Implementation Details

5.1 Populating the Virtuoso RDF Triple Store

As mentioned in section 2, I have the data in a MS SQL Server Database, and, as mentioned in section 3, I have the RDF vocabulary. What I have to do is migrate the data from the SQL database into the Virtuoso Triple Store. I have done this in two steps:

Write the data from the SQL database into a set of files. To do this in the simplest way, I have used the RAD features of the Visual Studio 2010 IDE together with Entity Framework: the Entity Framework46 has created a set of classes, based on

45 http://www.w3.org/TR/sparql11-query/46 http://msdn.microsoft.com/en-us/data/ee712906

the database’s tables. In code, I got the data from the DB, using these classes, and wrote the data to a set of files.

The second step was to write the data from the files to a Graph. This could not be done because EF 4.1 is not compatible with .NET 3.5, and the dotNetRDF library is built on .NET 3.5. After this step, I have written the data from the Graph to the Virtuoso Triple Store (dotNetRDF makes this task easier).

5.2 Exposing the data through a SPARQL Endpoint

To expose the data in the Virtuoso Triple Store through a SPARQL Endpoint, I created a new ASP.NET Web Application, and Added in the App_Data folder, a con-figuration file with the following content:

@prefix dnr: <http://www.dotnetrdf.org/configuration#> .

# Firstly note that our Handler must have a subject which is a specialdotNetRDF URI as discussed in Configuration API - HTTP Handlers<dotnetrdf:/sparql> a dnr:HttpHandler ;dnr:type "VDS.RDF.Web.QueryHandler" ; # States that we're using theQueryHandlerdnr:queryProcessor _:proc .

_:proc a dnr:SparqlQueryProcessor ;dnr:type "VDS.RDF.Query.SimpleQueryProcessor" ;dnr:usingStore _:store .

_:store a dnr:TripleStore ;dnr:type "VDS.RDF.NativeTripleStore" ;dnr:genericManager _:manager .

# Register the Virtuoso Ffactory_:virtuosoFactory a dnr:ObjectFactory ;dnr:type "VDS.RDF.Configuration.VirtuosoObjectFactory, dot-

NetRDF.Data.Virtuoso" .

# Now we define the initial dataset_:manager adnr:GenericIOManager ;dnr:type "VDS.RDF.Storage.VirtuosoManager, dot-NetRDF.Data.Virtuoso" ;dnr:server "myIp" ;dnr:port "1111" ;

dnr:database "DB" ;dnr:user "user" ;dnr:password<appSettings:VirtuosoPassword> .

As you can see, we register an Http Handler47 of type QueryHandler. To this handler, we associate a QueryProcessor. The QueryProcessor use a Native Triple Store, which is defined by a manager that points to the Virtuoso Universal Server instance.Now all I have to do is to register the handlers in the web application’s configuration fiel (web.config), which is done automatically by the rdfDeploy tool that comes with dotNetRDF.

6 Future Development

As described in [4], [5], any algorithm that aims to get the shortest path in a network transit system needs some sort of pre-processing. This is needed since web usage studies have shown that the path computation time should be less than 7 seconds [6], [7]. The pre-processed data needs to be stored in the knowledge base, and since it is algorithm dependent, I might have to extend the Transit vocabulary with a couple of new classes and properties in order to store the information.

47 http://msdn.microsoft.com/en-us/library/aa479332.aspx

7 Bibliography

1. ***, Web Scraping, http://en.wikipedia.org/wiki/Web_scraping2. Allemang, D., Hendler j., Semantic Web for the Working Ontologist, Morgan Kaufmann,

20083. ***, The State of Tooling for Semantic Technolo-

gies,http://www.mkbergman.com/991/the-state-of-tooling-for-semantic-technologies/4. J. Jariyasunant, D. Work, B. Kerkez, R. Sengupta, S. Glaser, A. Bayen., Mobile Transit

Trip Planning with Real–Time Data. Presented at the Transportation Research Board , 2010

5. Qiujin Wu, Joanna Hartley, Using K-Shortest Paths Algorithms To Accommodate User Preferences In The Optimization Of Public Transport Travel, Applications of Advanced Technologies in Transportation Engineering, Proceedings of the Eighth International Con-ference, pp. 181-186, 2004

6. R. Jain, T. Raleigh, C. Graff, and M. Bereschinsky, Mobile internet access and qos guaran-tees using mobile ip and rsvp with location registers, IEEE Int. Conf. Commun., vol. 3, pp. 1690–1695, 1998.

7. T. Erl, Ed., Service-oriented architecture (SOA): concepts, technology, and design. Pren-tice Hall, 2005.