However when the results are returned they've changed these to addresses,. Ask Question Asked 6 years, 6 months ago. We need some advice about the map services provider. A low level access to route information offers our Matrix API. There are many offline, embedded and web-based routing services using OpenStreetMap data. The response shows the distance and duration between the. Trace attributes provide detailed information about what to expect on the route ahead, including speed limits, exit signs, tolls and so much more. It can use this open source routing engine or the GraphHopper Directions API , which provides the Routing API, a Route Optimization API (based on jsprit ), a fast Matrix API. The other packages implement a fair usage limit. 'GraphHopper' <GraphHopper is a fast and memory efficient open source routing library and server written in Java. maps. 1 Answer. Please let me know if there is any way to do it online or in programming languages like R or python. So the distance from 1 city A to another non-nearby city B, can be calculated by the distance of cityA -> hubX -> hubY -> cityB. Like Google Distance Matrix API. Here is the GPX data I am giving to GraphHopper Map matching library:. The resulting data are the initial (temporary) set used by theA developer-friendly API Even if you haven’t used other Bing Maps APIs before, it’s easy to jump in and make the most of the Distance Matrix API. 14); a. React JS Google Maps Distance Matrix Error: Uncaught TypeError: locations. ; depot: The index of the depot, the location where all vehicles start and end their routes. Distance matrices can be calculated. Microsoft have been busy, working hard on the Bing Maps v8 Web Control and adding rich new functionality. js:45) 0. The Time Filter – Advanced tool parameter window, completed. threshold positive int. See Libraries in the Maps JavaScript API. It can use this open source routing engine or the GraphHopper Directions API, which provides the Routing API, a Route Optimization API (based on jsprit), a fast Matrix API and an address search (based on photon). Peter | 22. route-, time- or distance-matrix should be calculated. All elements on the diagonal of A are zero (i. Specify at least 2 points. To get distances you'll have to call regular route service for each pair of coordinates (hours). ai provides a Distance Matrix AP. To install GraphHopper with this feature on your own server download the JDK, the routing server, the configuration file and the OpenStreetMap data: Now […] Make a distance matrix request. md#graphhopper-maps), read through our documentation and install. Geographical Coverage. The GraphHopper Directions API includes a Matrix API. rows is the object that has the multiple ZERO_RESULTS in the array. v: igraph object or numeric vector, the vertices from which each distance is calculated. 2. 9814292,-70. It supports several modes of. Distance matrices are sometimes called. I’m talking problems with more than 1000 points. . 162 Phoenix 2. Plan routes and get driving directions from GraphHopper Maps using open source and open data. We currently cache the Graphhopper response between two locations, so the next time we try to get the same costs we get the cached version. In this tutorial, you will learn how to calculate the distance between two points using the Distance Matrix API. A “leg” is a specific part of the route. for each vertex i: initialize an nxn matrix M run breadth-first search starting at i copy distances into row i of M return M. GraphHopper Maps is the face of the open source GraphHopper routing engine and a fully featured route planner in the browser. But then if I remove Inf, the length of the distance matrix and my clustering result won't match, and I can't replace Inf with zero in this case either. Map-matching is an approach to minimize the errors in GPS data. It calculates routes and alternatives very fast. . Often there are multiple ways to go from A to B and the question is how Google prioritizes different routes to find the one that is used for the distance calculation. A low level access to route information offers our Matrix API. 2. This article describes how we calculate and prepare travel time matrices to solve time dependent vehicle routing problems. Using publicly available map data from OpenStreetMap it can calculate the optimal route for a given source-target pair for many different vehicles and flexible. Also path details are now supported for the TomTom add-on. One Answer: active answers oldest answers newest answers popular answers. GraphDistanceMatrix returns a SparseArray object or an ordinary matrix. get distance using google maps distance matrix api JSON output. com> Description Provides a quick and easy access to the 'GraphHopper' Directions API. Fine-tuned controls to reduce latency The new Routes API introduces additional options for improving the performance of your app. Using publicly available map data from OpenStreetMap it can calculate the optimal route for a given source-target pair for many different vehicles and flexible optimization criteria. By definition, an object’s distance from itself, which is shown in the main diagonal of the table, is 0. 6 1 I will get a graph in which A are connected to C but not to B ,B are connected to C , and C are connected. With it you can calculate times and distances between dozens of locations very fast. Specify these by value, or. Querying the Distance Matrix API. The API mentions the “super fast” matrix calculator. Isochrone Calculation – provides you with the area that can be reached from a specific location in a given time frame, based on the method of travel (for example, how far you can travel on a bike in. I have gotten to. It can handle vehicle routing problems complicated by your business-specific side constraints. GraphHopper Maps is an open source user interface, which you can find here. Client (key='YOUR_API_KEY_HERE') Then declare an empty array where I will put my results: my_result= [] Then use a for loop for lst_store1 array and put a for loop inside it for lst_store2 array. g: igraph object, the graph on which to work. GraphHopper Maps is an open source user interface, which you can find here. 2 Likes. Made for easy generation of Routes and Directions on Maps, Isochrones, Time-Distance Matrix, Pelias Geocoding, POIs, Elevation and routing Optimizations using their amazing API. Like Google Distance Matrix API. For the following distance matrix: ∞, 1, 2 ∞, ∞, 1 ∞, ∞, ∞ I would need to visualise the following graph: That's how it should look like I tried with the following code: import networkx as nx importProperties. Get travel time between two addresses using The Google Maps Distance Matrix API. There is support for both the Standard License and Premium/Enterprise License types provided by Google. Or a delivery service in the need of often big NxN matrices to solve vehicle routing problems. Due to its Apache License it is a business friendly alternative to existing routing engines and. 1 to 5 or 4 to 4 like in the following example. The Bing Maps Distance Matrix API calculates distances and travel times between origins and destinations with an optional travel-time histogram. Basically, every city knows it's nearby cities and it's nearby hubs (= highway intersection). then import networkx and use it. java","path":"example/src/main. The _get_distance function does the same steps as the _get_chance_of_rain function. The order of the point parameter is important. We need some advice about the map services provider. The R packages I found so far seems can't deal with Inf in the distance matrix. , are in. It is defined in a similar way as the adjacency matrix. Map construction methods automatically produce and/or update street map datasets using vehicle tracking data. nodejs javascript map docker. If you check the Distance Matrix API, there are other optional parameters that can help you with this. 2 Date 2021-02-06 Maintainer Stefan Kuethe <crazycapivara@gmail. However, the coordinates you are using correspond to the following locations: Origin 42. 5 km) and in some cases as much as 3. A new version of the cartography package (v2. 0. I'm using Graphhopper core library to compute distance and best path between 2 points, i read about Graphhopper Routing. The Isochrone API calculates the reach of a location. i don't recommend anything, it depends on what you want. With the GraphHopper Directions API it is easy to calculate the route from A to B including multiple intermediate waypoints. The new API key is listed on the Credentials page under API keys. It is definitely larger compared to geodesic distance of 2. 9758161 End Point: 11. MaaS is the future of transportation. Directions API. See the updated blog post with several examples. easbar March 16, 2021, 11:51am 5. This is done by expanding the Add Data drop-down menu Add Data on the Map tab on the ribbon interface, and clicking “Data. On the rank of the distance matrix of graphs. We are a mobility app that just launched 5 months ago in Tunisia offering P2P carpooling. The following. As we already know, a distance matrix API computes distances and ETAs between any given set of origins and destinations. Times are based on predictive traffic information, depending on the start time specified in the request. origins=Fortis Medical Clinic, Sector 110, Noida, Uttar Pradesh 201304 destinations=Domino's Pizza, C 2/22, Sector 18, Noida, UP 201301 mode=driving. if you. The eccentricity matrix ϵ (G) of a connected graph G is obtained from the distance matrix of G by retaining the largest distance in each row and each column and setting the remaining entries as 0. Hi Guys, I just started using Graphhopper and this might be a noob question so forgive me for this. If less than 99. For example we have 10 records then we want travel time and distance between each point. 251953', '47. Besides the route calculations the GraphHopper engine offers a lot more features like the map matching (“snap to road”), the navigation and the isochrone calculation (for a point it finds all reachable roads within a specified time). how GraphHopper can be. Our classic route planning tool enables you to use most of the openrouteservice API with only a few clicks on a map. 8 Km. [1] Depending upon the application involved, the distance being used to define this matrix may or may not be a metric. 040182,5. My distance matrix is as follows, I used the classical Multidimensional scaling functionality (in R) and obtained a 2D plot that looks like: But What I am looking for is a graph with nodes. Step-4: Enable Distance Matrix API: To calculate distance and duration. public transit. This way the algorithm determines where to end the route according the overall optimization objective. for example: my input is start point 11. With it you can calculate times and distances between dozens of locations very fast. DistanceMatrix. Distance Matrix request and responses. In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. See the updated blog post with several examples. python distance geolocation geocoder distance-matrix-api travel-distances geocode-api. Make sure it is not a different problem and you use the POST request, very important for a matrix of this size also as the request could be gzipped. no turn cost support. Matrix Calculations – provides you with very fast time and distance matrices. google. DistanceMatrixService class. Let me first explain what a typical vehicle routing problem is: Given a vehicle fleet and a number of customers, find the optimal set of vehicle routes to serve all customers and to minimize total transportation costs, e. I try this sample url Sample URL This url displays the route on map with total time/distance of 1 hour 9 min 110. (i. For example our Route Optimization API needs all distances between 30 deliveries, so this Matrix API is requested and returns 870 distances (30*30-30) calculated within just milliseconds. SecurityError: Blocked a frame with origin from accessing a cross. Please note that currently only for car, small_truck, scooter, bike and foot the custom routing support is deployed. We provide free code samples, developer documentation, and even a lively forum to flatten the learning curve and speed up development cycles. [1] Depending upon the application involved, the distance being used to define this matrix may or may not be a metric. The API key created dialog displays your newly created API key. 6 C 0. " GitHub is where people build software. 1. The GraphHopper Directions API that we host falls under our usage terms and always requires an API key. @SRingne I'm not sure what you mean. Map Matching API; Isochrone API; Matrix API; Important to say that not all of the above mentioned APIs are available for free when you start GraphHopper from its sources. For each integer k ≥ 2 there exists an infinite family of graphs having rank k (see [3] ). y (N, K) array_like. If you set this value too small the. Nearest service; Route service — Similar to Directions API; Table service — Similar to Distance Matrix. Nevertheless, it has a low latency of the response. HERE). g. only one node is lifted, then the distance increases, in this specific case it increases to 0. We introduced it as a new, third option and called it “hybrid mode” as it combines the advantages of the flexible and the speed mode. 2. I'm building a routing service in Java with routing tools like graphhopper for generating routes between points, and jsprit for vehicle routing problems embedded in app through Maven. Designed for the server, desktop, as well as for mobile devices. The 2nd issue with the inability to properly calculate the distance on some berlin rails was solved by just using the entire German OSM file. Maybe there are APIs which can handle this? 1. Inspired by geopy and its great community of contributors, routingpy enables easy and consistent access to third-party spatial webservices to request route directions, isochrones or time-distance matrices. Ashwin February 5, 2019, 1:16pmPlan routes and get driving directions from GraphHopper Maps using open source and open dataOSRM matrix is very quick (seconds for 300 locations) but it provides driving times only. size() always give me 0. if you need to know how long a straight line between two locations is, you can easily calculate that without doing a request (use google. The diagonal entries d ii of the distance matrix are always zero. 092705, time: 744861, A diff of the two API responses show that they are exactly the same. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. Viewed 4k times 1 I am setting up a routine to get travel time between two locations using The Google Maps Distance Matrix API. With the Distance Matrix API, you can provide travel distance and time for a matrix of origins and destinations. It includes information such as the distance, estimated travel time, and the route to. To create a Cloud project with billing enabled: Console gcloud. draw (G) if you want to draw a weighted version of the graph, you have to specify the color of each edge (at least, I couldn't find a more automated way to do it):About External Resources. The Laplacian. Now calculate all travel times between all locations (A to B, A to C, B to A, B to C,. threshold positive int. A route planner user interface for the GraphHopper routing engine released under the Apache License 2. There are some more tools like cluster calculation, map matching, matrix calculations, and isochrone calculations. The rank of D ( G), denoted r a n k d ( G), is called the distance rank of G. 1. Demikian pembahasan mengenai Cara Menggunakan Google Maps Distance Matrix API. var params = { origins: [currentLocation], destinations: endPoints, travelMode: google. The tricky thing in the case above is that the elevation interpolation for ferries, tunnels and bridges rewrites the distances. Have a look into the Java API documentation for further details e. Just put a URL to it here and we'll apply it, in the order you have them, before the CSS in the Pen itself. Install the package using composer:I am looking to get an approximation of the travel distance and time between several locations. 7 B 0. Sincerely, HenningRouters. With the two newly created address tables, we can open ArcGIS Pro and create a new, empty project where we add both tables to the table of contents. , k-nearest neighbor, a machine learning algorithm which predicts the value of a given data point based on the weighted average value of its 'k' closest neighbors, distance-wise, where 'k' is. The default here is "min": "transport_time" (see “objectives” in our documentation). The GraphHopper Directions API is an offering of the GraphHopper GmbH and includes a Geocoding API, a Distance Matrix API, a Map Matching API, an Isochrone API and a Route Optimization. importLibrary ("routes"). Did you find it helpful? Yes. 79 cities in the UK. The first startup of GraphHopper can take quite long, because it loads and precomputes index files. Click the Select a project button, then select the same project you set up for the Maps JavaScript API and click Open. originlat = ; originlong = ; tolat = ; tolong = ; // Use graphhopper to return distances between the two points distance = pointToPointDistance(double originlat,double originlong,double tolat,double tolong); costMatrixBuilder. Google Maps Platform を使用して複数の場所をプロットすると、最寄りのマーカーを視覚的に確認することができます。さらに Distance Matrix API を使用することで一度に多くの距離を決定することができます。Using the Wasserstein distance as described in §2(a), we can take a collection of maps and form a distance matrix D ∈ R N × N, where D a b is the Wasserstein distance between normalized chlorophyll maps a and b. Google Distance Matrix API has a limit of elements set to 2500. Also do not want to use Azure maps. getPoints (); double. When you first set up an account you’ll get a free trial but when this expires you’ll have to enable billing. Based on OSM data and very fast. GraphHopper Maps - Open Source Route Planner UI. 1277583 = A4, London WC2N 5DU,. I want to draw route which generated by GraphHopper Routing Engine (actually in Java language). The aim of. Map data from OpenStreetMap. {"payload":{"allShortcutsEnabled":false,"fileTree":{"client-hc/src/test/java/com/graphhopper/api":{"items":[{"name":"model","path":"client-hc/src/test/java/com. 827. The API you need to get distances between points is the Google Distance Matrix API. From Theorem 3. The mean of all distances in a (connected) graph is known as the graph's mean distance. I found out that when R package"igraph" calculate closeness (sum of distances) of a disconnected graph, it. Path Details Updates. g. matrix. Here it shows the toll information (click the little triangle to show. Start development: Clone this repository. Using distance matrix to re-order route stops to minimize the total distance. The GraphHopper routing engine comes with the Dijkstra algorithm exploring a road network, where every junction is a node and roads connecting the junctions are the edges in the mathematical graph model. github","path":". Feel free to contact us via Email and send me the request or the time you sent it. I am from South Africa, and it refused to work for any local addresses until I changed the transport mode to driving (from walking, I mean. The code structure and data used in this example is also available in this GitHub repository. to avoid steps you can use this custom model and the route hint with the. You could calculate it, using (t x v) formula, because you specified that your vehicle moves at the average speed. 4. We were able to exclude a hardware problem and our first thoughts were that it had something to do with the type of the physical RAM but this was only an unlucky coincidence as we found other servers with a different RAM vendor that showed the. If there are N. I am planning to also use graphhopper's matrix API in optaplanner-webexamples, to generate the distance matrix for a number of locations in a VRP. 0 and of course make the request to Google Maps. Note: We do not want to use Bing maps Distance matrix because it is not in our bing maps license. js:45). As example , a route of 3,7 Km in the center of Milan city is : 10 Min - GoogleMaps 8 Min - Bing About 4 Min - my time matrix . You can specify several options, including mode of transportation, such as driving, biking, transit or walking, as well as transit modes, such as bus, subway, train, tram, or rail. Terralogiq sebagai satu-satunya Google Maps Premier Partner di Indonesia bertujuan membantu bisnis anda untuk meningkatkan efisiensi proses bisnis dengan mengintegrasikan Google Maps Platform dan menyederhanakan penerapan. In this article, using the well-known Ramsey's theorem, we prove that for each integer k ≥ 2, there is a finite amount of graphs whose distance matrices have. Geofabrik has updated osm. 1, the exponential distance matrix of block graph G = ( p 1, p 2, ⋯, p k) is invertible if and only if q ≠ 1 and q ≠ − 1 p i − 1 for each 1 ≤ i ≤ k. Use google-maps-react API on the front-end. . Connect and share knowledge within a single location that is structured and easy to search. To view your list of enabled APIs: Go to the Google Cloud Console . We need some advice about the map services provider. But saw nothing like this on my RSS feeds last couple of months. 0, you need to build the whole project and then invoke the /match endpoint. Long time is being hardly seen when matrix size goes beyond 2000x2000. maps. How we reduced the cost-distance calculation by 5 times. Which Minkowski p-norm to use. Our routing services come with elevation, road class and surface data which generate precise time and distance estimates. Nothing wrong with a mutli cloud strategy and in some cases even recommend in my opinion. g. 4 1 0. I enabled debug mode and found that may be i was hitting wrong endpoint , I changed to. Every routing service below has a separate module in routingpy. Great! response. DistanceMatrixRequest interface . ai provides a Distance Matrix AP. 02/07/2018) some deliveries get removed from the solution because the date to lays in the past. Note that, so far, we only offer turn restriction support for the. with a proper distance/time matrix calculated from the routing engine under the hood, with a simple JSON API and some advanced featured not in jsprit. add the time and distance of every instruction until you observe the sign==5 (VIA_REACHED) then you have the information of the first leg, then do it again and for the last leg do it again until sign==4 (FINISH) is observed. You can specify several options, including mode of transportation, such as driving, biking, transit or walking, as well as transit modes, such as bus, subway, train, tram, or rail. The distance matrix for graphs was introduced by Graham and Pollak (1971). {"payload":{"allShortcutsEnabled":false,"fileTree":{"jsprit-core/src/main/java/com/graphhopper/jsprit/core/util":{"items":[{"name":"ActivityTimeTracker. Graphhopper (github is an “open source routing engine”. If NULL, then each edge is assumed to have a distance of 1. We’ll assume you know the current position of each technician, such as from GPS. It can make use of different algorithms such as Dijkstra, A* and Contraction Hierarchies. The distance matrix of G has exactly one positive eigenvalue if and only if G is one of the following graphs: a cocktail party graph; the Gosset graph; the Schläfli graph; a halved cube; a Johnson graph; one of the three Chang graphs; a Hamming graph; a Doob graph; the icosahedron (see Fig. The Routing API is a powerful A-to-B routing service for many vehicle types: cars, trucks, bikes, walking, and more. maps. Also the solution includes no u-turns and you can simply keep going the same direction you came from at each location. here I think you should look at the full response to understand how Google API provides the requested query. The. This is called geocoding and is described here: Documentation - GraphHopper Directions API. Your "distance matrix" does not satisfy the triangle inequality. The following example demonstrates how to convert Distance Matrix service API to promises using jQuery:Hi @jie31best,. Any suggestions on how to achieve this or alternatives to Google Maps in India?Package ‘graphhopper’ October 13, 2022 Title An R Interface to the 'GraphHopper' Directions API Version 0. 946035 Result(KM): 30. The calculations can then be displayed as a list of. Regarding this, what is the fastest way to calculate the distance between two points? eg. Open source routes, driving directions and browser-based GPS navigation. GraphHopper Maps. Performs requests to the HERE Maps API services. Query POIs along your route, perform accessibility. rows[0]. When editing the custom model try out Ctrl+Space for auto complete e. maps. answered 26 Mar '15,. (commonly used in things like Google Maps) and order [lon,lat] for an array. It also offers several features enhancing the graphic presentation of maps like cartographic palettes, layout elements (scale, north. now () + N), // for the time N milliseconds from now. Karussell, I appreciate you trying to help but could you point me to a description of how to use this API offline? All I can see is a Java client which still hits the GraphHopper server to get the results. I am autofilling an input field with the below which gives me distance. See this guide on how to contribute. Google Maps Distance Matrix API; Google Places API Web Service; Google Places API for Android; Go to credentials and create a new Key. The parameter supports the following arguments: The Distance Matrix API is a service that provides travel distance and time for a matrix of origins and destinations. Other self hosted alternatives are GraphHopper (no matrix, repeated calls to route) and Valhalla (distance and time matrix). 1965 DISTANCE MATRIX OF A GRAPH 307 V: V4 Fig. The Bing Maps Distance Matrix API is a Microsoft-branded solution leveraging AI-powered search scenarios and accurate, high-quality geolocation features to help you build better geospatial applications. Thanks. Nearest service; Route service — Similar to Directions API; Table service — Similar to Distance Matrix API; Match. java -Xmx4g -jar graphhopper-web-[version]. distance. transit requests directions or distance via public transit routes (where available). It’s still not clear how you can run the map-matching functionality from the command line in the main graphhopper project without running the web module and POST ing to it. To set up the example and compute the. Using predicted traffic and support for various modes of transportation, the Distance Matrix API can optimize map routing performance in many-to-many scenarios, which can. A weighted graph and its distance matrix. easbar March 16, 2021, 11:51am 5. questions tags users badges unanswered ask a question. g. GraphHopper Maps. Path Details Updates. But we do not stop there, we also offer a time-, weight- and route-matrix. , a 2D matrix showing the distance between a point and every other point, are an intermediate output during kNN computation (i. Graph Distance for Complex Networks. GraphHopper Directions API. graphHopper = new GraphHopper (). Fortunately, even after the free trial expires, you. Then I read the file and remove the first line: graph = ReadList ["temp. Sample request and response. This is how I call the api:. We’ll assume you know the current position of each technician, such as from GPS. 1 km Questions: 1 - where can I find documentation for this url parameters (layer/point/profile etc. You can apply CSS to your Pen from any stylesheet on the web. TypeScript JavaScript CSS HTML. g. You can then access travel time and distance using response. M(S) = [ 2 −3 1 −2]. Google distance matrix api quota behaves unreliable. Bing Maps Distance Matrix API Bing Maps Distance Matrix APII know through google map API, we can find optimum route distance between 2 coordinates. the closest to the furthest). Plan routes and get driving directions from GraphHopper Maps using open source and open data Open Source Routing Engine. Modified 6 years, 6 months ago. MatrixApi () key = 'YOUR_KEY' # str | Get your key at graphhopper. For debugging you can use the custom model editor in GraphHopper. But we do not stop. GraphHopper Directions API. In this example, the algorithm finishes the route in Munich. However, such route calculations become considerably more […] The distance_influence property allows you to control the trade-off between a fast route (minimum time) and a short route (minimum distance). The initial algorithm was implemented fast but the implementation details got very tricky at the end and so this took several months before we could include. This way the algorithm determines where to end the route according the overall optimization objective. See full list on github. E. ”. The entries of the distance matrix d ij give the shortest distance from vertex v i to vertex v j. Thus, we received expensive bills from Google Cloud following the number of requests. The distance that we see as an output is 3246 metres which is around 3. If you constrain what GraphHopper can do by having a lot of jobs that are already "definite-status" assigned to particular techs; if you further constrain it by having a lot of jobs that already have a time or time-frame assigned. 9477546 = 130 Water St, Exeter, NH 03833, USA. If I put no restrictions in it, and a user gives me a list n locations,Distance Matrix API Function. See the example below and the first leg is from Schwarzkollm (start) to Bröthen (via point) and the second leg is from […] Hello, I would like to know which is the best option to use the matrix of time and distance. Thus it will definitely handle the load of your queries. A-to-B routing with turn-by-turn instructions. )Let G be a distance-regular graph. 011m but the ETA for this edge is 0. setGraphHopperLocation (workDir. DistanceMatrixService class. Fig. We use Graphhopper to get the routes between the jobs and workers to determine costs. GraphHopper Routing Engine 4. These salesorders contain timewindows. But, OSM (which builds the maps) is crowd-sourced data so it's not going to be as complete as one of the world's biggest tech. The project is the basis for managing services, credentials, billing, APIs, and SDKs. Powered by + – ⇧Open Source Routing Engine. value ; // Address where you need to. Once you have the output directory, configure ODL Studio to point towards this directory under the distance options as shown in the vehicle routing youtube video . importLibrary ("routes"). Price: Free (15,000 requests) – €304. 6.