A Multi-Agent System for Obtaining Dynamic Origin/Destination Matrices on Intelligent Road Networks Rafael Tornero
Robotics and Information and Communication Technology Institute Universitat de València Catedrático José Beltrán 2 46980 Paterna, Spain
rafael.tornero@irtic.uv.es
Javier Martínez
Robotics and Information and Communication Technology Institute Universitat de València Catedrático José Beltrán 2 46980 Paterna, Spain
javier.martinezplume@irtic.uv.es
ABSTRACT Dynamic Origin/Destination matrices are one of the most important parameters for efficient and effective transportation system management. These matrices describe the vehicle flow between different points inside a region of interest for a given period of time. Usually, dynamic O/D matrices are estimated from link traffic counts, home interview and/or license plate surveys. Unfortunately, estimation methods take O/D flows as time invariant for a certain number of intervals of time, which cannot be suitable for some traffic applications. However, the advent of information and communication technologies (e.g., vehicle-to-infrastructure dedicated short range communications –V2I) to the transportation system domain has opened new data sources for computing O/D matrices. Taking the advantages of this technology, we propose in this paper a multi-agent system that computes the instantaneous and dynamic O/D matrix of any road network equipped with V2I technology for every time period and day in real-time. The implementation was done using JADE platform. The results show that the multi-agent system is able to obtain the instantaneous O/D matrix for any time period and day.
Categories and Subject Descriptors I.2.11 [Artificial Intelligence]: Distributed Artificial Intelligence - multiagent system
General Terms Application
Keywords Multi-Agent Systems, Intelligent Transport Systems, Distributed Problem Solving, Dynamic Origin/Destination Ma-
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Joaquín Castelló
Robotics and Information and Communication Technology Institute Universitat de València Catedrático José Beltrán 2 46980 Paterna, Spain
joaquin.castello@iritc.uv.es
trix, Traffic Parameter
1.
INTRODUCTION
Origin to destination (O/D) matrices are a vital artifact for effective and efficient transportation system safety, operation, design and planning. O/D matrices represent the network user’s demands given some network traffic conditions. They contain information about the spatial and temporal distribution of activities between different traffic zones in a determined study area. From a logistic standpoint, longterm average O/D trip demands are needed for transportation design and planning purposes (e.g., future network expansion or urban planning). On the other hand, short-term time-varying O/D demands are important inputs to intelligent transportation systems (ITS) such as advanced traffic information systems (ATIS) and advanced travel management systems (ATMS). For instance, with the information contained in time-varying O/D matrices, it is possible to forecast future traffic conditions and predict congestion so that appropriate control actions (e.g., ramp metering, rerouting) can be determined and effective traffic information can be provided to drivers; thus contribute to improve the safety of the transportation system [19]. O/D trip demands are traditionally obtained from homeinterview surveys and/or license plate surveys, which are highly expensive and time consuming. Another economical source of information to infer network O/D demands is automatically recorded link traffic counts. Since link traffic counts are measurements of various O/D flows using these links, the information contained in the measured link traffic counts can be used to estimate the unknown O/D demands. Furthermore, the advent of new information and communication technologies (ICT), as automatic vehicle identification (AVI) technology, in the transportation system domain offers new data sources for obtaining short-term timevarying O/D demands. The combination of different sources of information to determine time-dependent O/D demands has been investigated by several authors [28, 19, 24, 23, 9, 20]. However, the main problem of these methods is the assumption that O/D matrices are constant during some sub-sets of intervals in the period of study, which can be adequate for some traffic applications but not for others, as for instance re-routing. Several important innovations are coming up in the next
(a) V2I
(b) V2V
Figure 1: Dedicated Short Range Communication (DSRC) (a) Vehicle-to-Infrastructure and (b) Vehicle-toVehicle years; such as the use of ubiquitous and integral intelligent artificial vision or the development of new technologies, allowing direct communication from vehicles to infrastructure (V2I) and among vehicles (V2V) as well (see Figure 1) [1]. The goal of V2I and V2V integration is to provide a communication link between vehicles on the road (via On-Board Units, OBU) and between vehicles and the roadside infrastructure (via Roadside Units, RSU), in order to increase the safety, eďŹƒciency and convenience of the transportation system. They are based on widespread deployment of a dedicated short-range communications (DSRC) link, incorporating IEEE 802.11p [4]. These new innovations will be the base for providing more intelligence to current road networks. Using this technology, there will be a RSU every certain hundred meters, which will record data from every vehicle individually. Therefore, these technologies will not only generate such a huge amount of data that they will call for distributed processing and storing, but they will also provide additional data sources for computing accurate instantaneous and dynamic O/D matrices in real-time and without the need for an estimation method, since the path for every vehicle from an origin to a destination will be monitored. Also, in order to avoid an excessive growth of the RSU databases, the recorded data can be removed from the system as journeys are completed and processed by the multi-agent system. The V2I communication system could raise questions about the privacy of the drivers since it can monitor the path followed by a vehicle. However, working with MAC addresses would ensure privacy, as the MAC address is not associate to any other personal data. In addition, an asymmetric encryption algorithm could be applied to data, making it impossible to recover the original data [9]. Distributed problem solving involves the collective eort of multiple problems solvers to combine their knowledge, information, and capabilities so as to develop solutions to problems that each could not have solved as well (if at all) alone. It is the name applied to a subfield of distributed artificial intelligence (AI) in which the emphasis is on getting agents to work together well to solve problems that require collective eort, typically in a multi-agent system [32]. Due
to an inherent distribution of resources such as knowledge, capability, information, and expertise among the agents, an agent in a distributed problem-solving system is unable to accomplish its own tasks alone, or at least can accomplish its tasks better (more quickly, completely, precisely, or certainly) when working with others [16]. In this paper, we aim at obtaining the dynamic O/D matrix of any road network provided with V2I equipment. To achieve this goal, we propose a multi-agent system composed of two types of cooperating agents. In the system, agents cooperate hierarchically to compute the instantaneous and dynamic matrix in a distributed and real-time way for any time period and day. We validate our implementation by means of a simulator, which is based on a microscopic traffic model simulation and equipped with V2I communication technology [10]. The rest of the paper is structured as follows. In Section 2, we present the related work and our novel contribution. Section 3 defines the problem of obtaining dynamic O/D matrices. Section 4 describes the multi-agent system implemented to solve the problem. Section 5 explains the simulator used for running the experiments. Section 6 shows the results of the evaluation and the discussion. Finally, Section 7 presents the conclusions and put forward the future work.
2.
RELATED WORK
On the one hand, in Section 2.1 we review the literature on O/D matrix estimation models, including static and dynamic approaches. On the other hand, in Section 2.2 we review the literature on multi-agent systems for solving distributed problems. Finally, in Section 2.3 we pinpoint our novel contribution to the O/D matrix computation problem.
2.1
O/D Matrix Estimation Models
Since past decades, obtaining the O/D matrix of a road network or segment of has been under study by many researchers due to its importance for the transportation system management. Originally, O/D matrices were estimated using either direct estimation or model estimation. Direct estimation expands sample surveys using sampling theory, while demand model estimation applies synthetic travel de-
mand models to the present transportation system so as to obtain estimates of O/D flows. However, in the past two decades, there has been considerable interest in estimating of O/D flows using traffic counts [29, 26, 12, 18, 17, 34, 35, 13, 25, 14, 19, 28, 24, 37]. Nowadays, the new data sources provided by new ICT technologies (e.g. automatic vehicle location, bluetooth) contribute to improving the accuracy and reliability of the estimation processes [23, 9, 20]. The goal of the O/D estimation problem is to obtain an O/D matrix in such a way that when assigned to the network, it reproduces the observed traffic flows. This estimation problem presents two variants depending on the time dimension: static and dynamic estimation. Static approaches [29, 26, 12, 18, 35, 25, 14] do not take into account the time dimension and thus, the estimation method is applied to the whole data period. That is, the method is applied to all data recorded in the given period at once. However, dynamic approaches [13, 17, 34, 28, 19, 24, 37] do take into account the time dimension component, obtaining in that way timedependent O/D matrices. In these approaches, the given period of study is divided into several intervals of interest and then, these intervals are modeled and introduced in the formulation so as to obtain time-dependent O/D matrices.
2.1.1
Static O/D Matrix Estimation Models
Static estimation models have been developed mainly for transportation planning and designing purposes. In general, these models can be classified basically into two groups; namely, entropy maximization-based (EM) [29] and econometrics models [26, 12, 18, 35, 25]. In addition, there exist other approaches that cannot be included in the previous groups, such as multi-objective programming formulation and fixed point heuristic algorithms [14]. Since this paper does not provide an extended and detailed revision of the approaches, we refer the readers to Abrahamsson [5] and Barcel´ o [8] who present two literature reviews of approaches that address the static O/D matrix estimation problem by expanding and detailing the classification presented in this paper. The EM approach consists in applying the concept of entropy to quantitative methods so as to forecast spatial interaction [33]. The entropy of an O/D matrix is the number of different permutation trips. The hypothesis is therefore, that the matrix that maximizes the entropy subject to the constraints of link traffic measurements would be the most likely O/D matrix. Econometric-based approaches aim to build statistical models between O/D matrices and measured traffic counts. These approaches can be categorized into tree groups: maximum likelihood-based (ML) [18, 25], bayesian inference-based (BI) [26, 25] and generalized least square-based (GLS) methods [12, 35]. The ML approach maximizes the likelihood of observing the target O/D matrix and the observed traffic counts. In this approach, the elements of the target O/D matrix are obtained as observations of a set of random variables. Also, it is assumed that the target O/D matrix, the observed traffic counts and the O/D matrix to be estimated are usually considered to be statistically independent. The bayesian inference approach considers the target O/D matrix as a prior probability function of the estimated O/D matrix. The observed traffic counts are considered as another source of information with a given probability. Then, the Bayes theorem provides a method for combining the two
sources of information for obtaining a posteriori probability function which allows the determination of a confidence region for the true O/D matrix. Finally, the GLS approach (see equation 1) consists in minimizing the difference beˆ and the true O/D matrix, tween the O/D target matrix, G, G, plus the difference between the observed link volumes, Vˆ , and the link volumes obtained once the true O/D matrix is assigned to the network, A(G), which is weighted by the dispersion matrices of the O/D flows, Z, and the traffic counts, W , respectively. ˆ − G)T Z −1 (G ˆ − G) arg min{(G −1 +(Vˆ − A(G)) W −1 (Vˆ − A(G))}
2.1.2
(1)
Dynamic O/D Matrix Estimation Models
Dynamic O/D matrices are vital inputs for the success of the transportation system operation. As commented above, dynamic estimation models provide extensions of the static ones by incorporating the time dimension in the formulation. Normally, dynamic approaches are classified into two classes: dynamic traffic assignment (DTA)-based approaches [13, 28, 19, 23, 37, 9, 20] and non-DTA-based approaches [17, 34, 24]. Kattan and Abdulhai formulates the dynamic estimation problem for both families in general terms [22]. Usually, non-DTA-based approaches are used in situations where the route choice is unimportant and are often used to estimate O/D flows on small networks. On the other hand, the methods in the DTA-based approach rely on an appropriate assignment model so as to develop route-choice patterns for drivers. This type of methods are applicable to large urban or freeway networks, where drivers have the choice of more than one route to reach their destination. In general, dynamic DTA-based approaches are classified into two groups: GLS models [13, 28] and state-space-based models [19, 37]. Currently, ICT technologies offer additional data sources that can be combined with the traditional ones to achieve better estimation of O/D matrices [23, 9, 20].
2.2
Multi-agent Systems for Distributed Problem Solving
Multi-Agent systems have been proposed to solve distributed problems in a extensive number of application domains, such as strategic mission planning [21], multi-robot frontiers exploration [30] and production planning [27]. Vokˇr´ınek et al. present an abstract architecture of a multi-agent solver and its respective algorithm providing decomposition, task allocation, and task delegation for the domains mentioned [31]. In the traffic context, multi-agent systems have been applied for solving vehicle routing problems [36, 7] and urban traffic regulation [6, 11], among others.
2.3
Novel Contribution
To the authors’ knowledge there is no work in the literature that addresses the computation of the O/D matrix directly, that is, without using an estimation approach. Therefore, our research and developed work provides the following novel contributions: the development of a multi-agent system for obtaining long- and short-term time-dependent O/D matrices that are important for the transportation system management.
3.
PROBLEM DEFINITION
4.
Figure 2: A theoretical road network
In this section we define the problem of obtaining the dynamic O/D matrix corresponding to a set of different traffic zones on any road network equipped with V2I technology. We focus on the direct computation of this matrix. Here, direct computation means not to use an estimation method and this should be made possible because V2I technology allows us to record (through OBUs and RSUs communication) vehicle data (e.g., identification, detection time) from an origin to a destination. Therefore, the vehicle data is distributed along a set of RSUs, which can be queried in order to obtain the path travelled by each vehicle. In addition, we focus on the real-time or on-line computation problem, since the on-line or real-time problem involves the O/D computation with regard to real-time traffic management systems.
3.1
Network of Study
We compute the dynamic O/D matrix for the road network that is depicted in Figure 2. This network represents a segment of a theoretical freeway that is composed of 5 entry points and 4 exit points. Table 1 shows the distance between consecutive RSUs. RSU detectors are classified into three groups: input, exit and intermediate detectors, which are referred to as I, O and D, respectively in Figure 2. The mainline and the on/off ramps consist of three and one lanes, respectively. The vehicles flow from left to right in an oneway unique direction.
3.2
Problem Formulation
Time-dependent O/D matrices are obtained by using the data provided by all of the vehicles along a given period divided in a set of intervals of interest. Then an O/D matrix is obtained for each interval. To state the problem formally, the following variables are defined: Definition 1. The number of vehicles entering the network using on-ramp Ii during time interval k, qi (k). Definition 2. The number of vehicles entering the network using on-ramp Ii during time interval k that are destined to output Oj , gi,j (k) Definition 3. The proportion of vehicles entering on entry Ii during time interval k that are destined to Oj , bi,j (k) The cells of an O/D matrix can be specified directly as gi,j (k) or bi,j (k) among others. In this work, we focus on proportions; thus, each cell of the O/D proportion matrix is calculated according to equation 2 bi,j (k) = gi,j (k)/qi (k)
(2)
MULTI-AGENT SYSTEM
Next, we present a hierarchic cooperative multi-agent system solution for solving the distributed problem of obtaining dynamic O/D trip demands for any road network equipped with V2I technology. Figure 3 shows a diagram of the solution. As observed in Figure 3, our solution is composed of two types of agents mainly, namely RSUAgent and ODMatrixAgent. Although it is not shown in the figure, there is another type of agent, namely BrokerAgent. RSUAgents are simple agents and are usually located at RSU devices. The agents of this type communicate with agents of the ODMatrixAgent type. The cardinality of the relationship is one-to-many, i.e., each RSUAgent only communicates with one agent of the ODMatrixAgent type, but an ODMatrixAgent communicates with either several RSUAgents or several ODMatrixAgents. The main goal of RSUAgents is to send the V2I messages received at RSUs to the agent they communicate with. ODMatrixAgents are the most complex agents in the system. The main goal of these agents is to compute the partial dynamic O/D matrix. For that purpose, they receive V2I messages from RSUAgents or other ODMatrixAgents. With the data received, these agents fill a data structure that contains the partial journey carried out by each vehicle so far. This structure is used to update qi (k), gi,j (k) and bi,j (k) appropriately. BrokerAgent is again a simple type of agent. There only exists one agent of this type in the system. This agent is just in charge of getting the distributed partial dynamic O/D matrix that each ODMatrixAgent owns. It can act as a wrapper for storing the O/D matrix in a database or as a broker for an ITS system that requires this matrix as an input to carry out its normal operation. Taking into account the two lowest levels of the hierarchy, the road is divided into a set of logical segments composed of one ODMatrixAgent parent and several RSUAgents children. In this division, each ODMatrixAgent could communicate with a long number of RSUAgents but we restrict this number to a small number (10 at the most) in order not to overload the ODMatrixAgents with a large number of V2I messages, avoiding in that way possible memory overflows. Following the same approach as in the lowest level, the upper levels are composed of a ODMatrixAgent parent that communicates with up to ten ODMatrixAgents who act as children, repeating in this way the same structure until reaching the root node of the hierarchy. The O/D matrix of a road network is computed in a distributed way by means of cooperation among agents of the types described previously. For that purpose, each RSUAgent sends to its parent the V2I messages recorded by the corresponding RSU. Then, the parent checks all the V2I messages received from its children. The parent updates qi (k) when it finds V2I messages received from an input RSU. Next, the parent checks for ended journeys (i.e., journeys initiated at an input RSU i and ended at an output RSU j) among the V2I messages received. If it finds some of them, gi,j (k) and bi,j (k) are appropriately updated and the journeys are removed from the agent volatile memory. When journeys are initiated in one segment and ended in other segment, gi,j (k) and bi,j (k) cannot be computed in the second lowest level of the hierarchy. Therefore, the ODMatrixAgents containing this partial data have to send it up in the hierarchy until this data is received by the same parent
From To Distance
I1 D1 500
Table 1: I2 I3 D1 D4 50 50
Distances (in meters) between I4 I5 D1 D1 D2 D2 D6 D7 D2 O1 D3 O2 50 50 500 500 500 500
agent. Once the data arrives to this agent, it updates gi,j (k) and bi,j (k) accordingly. At the end of the process, the dynamic O/D matrix for interval k is distributed along all the ODMatrixAgents the hierarchy is composed of.
5.
SIMULATOR
In traffic research, four classes of traffic flow models are distinguished according to the level of detail of the simulation. In macroscopic models traffic flow is the basic entity. Microscopic models simulate the movement of every single vehicle on the street, mostly assuming that the behavior of the vehicle depends on both, the vehicle’s physical abilities to move and the driver’s controlling behaviors. Mesoscopic simulations are located at the boundary between microscopic and macroscopic simulations. Herein, vehicle movement is mostly simulated using queue approaches and single vehicles are moved between such queues. Submicroscopic models regard single vehicles like microscopic, but extend them by dividing them into further substructures, which describe the engine’s rotation speed in relation to the vehicle’s speed or the driver’s preferred gear switching actions, for instance. This allows more detailed computations compared to simple microscopic simulations. However, sub-microscopic models require longer computation times. This restrains the size of the networks to be simulated. Since our work require the simulation of each vehicle individually, a microscopic traffic model based simulator is required. SUMO [10] is a highly portable, microscopic road traffic simulation package designed to handle large road networks. It is mainly developed by employees of the Institute of Transportation Systems at the German Aerospace Center. It allows to simulate how a given traffic demand which consists of single vehicles moves through a given road network.
5.1
Network Modeling
In order to model the network that is depicted in Figure 2 two steps have to be carried out. In the first step, this network is modeled using josm tool [15]. Josm is an editor for OpenStreetMap (OSM) [3] written in Java 1.6. Currently it supports loading stand alone GPX tracks and GPX track data from the OSM database as well as loading and editing existing nodes, ways, metadata tags and relations from the OSM database. Therefore, this tool can be used to edit or generate road networks in OSM-data format. In the second step, these OSM-data files are converted to the SUMO network format. This is achieved by means of the netconvert tool. This tool, which is part of the SUMO package, imports digital road networks from different sources (e.g., OSM) and generates road networks that can be used by other tools from the SUMO package.
5.2
Demand Modeling
After having generated the network, one could take a look at it using SUMO graphic user interface (GUI), but no cars would be driving around. One still needs some kind of de-
road D3 D4 500
side D4 D5 500
units D4 D5 O3 D6 500 500
D6 D7 500
D7 O4 500
scription about the vehicles. From now on we will use the following nomenclature: A trip is a vehicle movement from one place to another defined by the starting edge (street), the destination edge, and the departure time. A route is an expanded trip, that means, that a route definition contains not only the first and the last edge, but all edges the vehicle will pass. SUMO needs routes as input for vehicle movements. There are several ways to generate routes for SUMO: • Using trip definitions. • Using flow definitions, this is mostly the same approach as using trip definitions, but one may join vehicles having the same departure and arrival edge using this method. • Using flow definitions and turning ratios, one may also leave out the destination edges for flows and use turning ratios at junctions instead. • Using O/D matrices, OD-matrices have to be converted to trips, first, then from trips to routes. • By hand, you can of course generate route files by hand. • Using random routes, this is fast way to fill the simulation with life, but nothing that has something to do with reality. • Describing the population in the net, this method is called activity-based demand modeling. • By importing available routes. In this work, we have selected O/D matrices option for generating SUMO routes. Then, the previous step to be done before generating any route is to use od2trips tool for computing trip tables from O/D matrices. These trip tables are converted to flow definitions by hand and these flows are provided as inputs for jtrrouter tool, which models traffic statistically using flows and returns the route that each vehicle follows in the network.
6.
RESULTS
In order to validate the multi-agent system proposed, we have developed a prototype using the Java Agent DEvelopment Framework (JADE). JADE provides a middleware which enables the developing and executing a peer-to-peer application based on agent paradigm [2]. The implementation of the multi-agent system for the network under study is shown in Figure 4. It consists of 16 RSUAgents (one agent for each RSU device) and three ODMatrixAgents. The agents in the system are organized into three levels and two logical segments. On the one hand, the root level, the intermediate level and the lowest level are composed of the 1 ODMatrixAgent, 2 ODMatrixAgents and 16 RSUAgents, respectively. On the other hand, the
Figure 3: General agent hierarchy for O/D matrix computation
Figure 4: Agent hierarchy for the theoretical road network two segments consist of 8 RSUAgents and 1 ODMatrixAgent, each one. In this way, the two ODMatrixAgents in the intermediate level compute the partial dynamic O/D matrix for each segment; meanwhile, the root ODMatrixAgent computes the O/D flows for the journeys initiated on one segment and ended on the other one. SUMO simulator has been used to simulate the road network under study. This simulator has been modified for storing V2I messages in a distributed database so as to emulate the real behavior of V2I technology. Each V2I message only consists of a vehicle identification but, when the message is stored in the database, a timestamp is also added. This allow us to sort these messages and recover the path that each vehicle followed on the road. We have verified and validated the system creating uncongested and congested traffic scenarios with SUMO simulator. Both scenarios consist of different O/D flows depending on the time of the day, generating more traffic in rush hours. However, due to space limitations, we only show here the results for the congested traffic scenario. Nevertheless, the results obtained for uncongested traffic conditions are similar to the ones presented here. Figure 5(a) shows the O/D proportion obtained by SUMO for pairs I1 − O1 , I1 − O2 and I3 − O3 . Concretely, this figure shows on the X-axis some intervals of 1 hour and on the Y-axis the proportion of vehicles that initiate the journey at I1 and end the journey at O1 or O2 in each interval. Also, the figure shows the
proportion of vehicles that initiate a journey at I3 and end the journey at O3 . Figures 5(b) and 5(c) show the O/D matrix obtained by the multi-agent system implementation for the intervals 8-9 and 11-12, respectively. These figures show on the X-axis the origin of the journeys, on the Z-axis the destination of the journeys and on the Y-axis the proportions of vehicles that initiate the journey at origin Ii and end the journey at Oj . As it can be seen in these figures, the OD patterns for pairs I1 − O1 , I1 − O2 and I3 − O3 in interval 8-9 are 12%, 19% and 60%, respectively. Looking at the interval 11-12, the OD patterns for the same pairs I1 − O1 , I1 − O2 and I3 − O3 are 7%, 43% and 75%, respectively. Therefore, these figures show us that the multi-agent system is able to obtain the dynamic O/D matrix in real-time.
7.
CONCLUSIONS AND FUTURE WORK
In this paper we have proposed a multi-agent system for obtaining dynamic O/D matrices on any road network equipped with V2I technology. Also, we have shown that when 100% of vehicles are equipped with the adequate technology, the proposed method obtains the exact dynamic O/D matrix for any time period and day. As future work, we want to extend the results presented in this paper. Specifically, we are planning to study the penetration rate, transmission errors and RSU/OBU failures with the accuracy of the O/D matrices obtained. We will
(a)
(b)
(c) Figure 5: (a) O/D flows for pairs I1 − O1 , I1 − O2 and I3 − O3 (b) instantaneous O/D matrix for interval 8-9 and (c) instantaneous O/D matrix for interval 11-12 also present the extension of the multi-agent system so as to obtain the dynamic O/D matrix of a general network of roads, where journeys can be initiated and ended on different roads.
8.
ACKNOWLEDGMENTS
The authors would like to thank Ra´ ul Mor´ an and Lorena Iba˜ nez for their collaboration with SUMO simulator. They were in charge of modeling the network, modifying the simulator accordingly to our requirements and running the needed simulations for obtaining all the raw data needed for computing dynamic O/D matrices. This work is part of the INTELVIA project, which is supported by the AVANZA I+D program of the Spanish MITYC, under grant TSI-020302-2009-90.
9. [1] [2] [3] [4]
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