The purpose of this work is to investigate the application of neural network technology in the preparation of Real Estate Appraisals.
Faced with the decline of multiple regression analyzes in the face of real estate market dynamics, mainly caused by the inability of statistical packages to consider more than rules and rigid mathematical models. The predictive ability of a neural network was compared with multiple regression models, obtaining as a result: In prediction tasks, neural networks and multiple regression models generate similar results; while for classification tasks neural networks perform better.
Keywords: artificial intelligence, neural network, multiple regression, statistics, prediction, classification, perceptron, backpropagation, back-propagation
neural-networks-applied-to-real estate-appraisal1.0 Introduction to Artificial Intelligence
- The Artificial Neural Network (ANN)
For years now, some researchers have been creating models that simulate brain activity in an effort to produce a form of artificial intelligence.
RNAs are composed of a large number of deeply interconnected processing elements (Neurons) working simultaneously to solve specific problems. ANNs, just like people, learn from experience.
In any case, it is a new form of computing that is capable of handling the inaccuracies and uncertainties that appear when it comes to solving problems related to the real world, offering precise and easy-to-implement solutions.
RNAs are composed of many simple elements that operate simultaneously, the design of the network is largely determined by the connections between its elements, thus simulating the connections of brain neurons.
1.2 Operation of an Artificial Neural Network:
1.2.1 Weights: ANNs can have fixed or adaptive weight factors. Those with adaptive weights use internal learning laws to adjust the value of the interconnection force with other neurons; in such a way that adaptive weights are essential if it is not previously known what the correct value of them should be.
For those software that use routines of variable weights, they will be automatically determined by the program from the description of the problem.
If the neurons use fixed weights, then their value or mathematical expression must be previously defined and will be independent of the type of data to be processed by the network.
1.2.2 The Laws of Learning: Are those that determine how the network will adjust its weights using a function of error or some other criterion. The appropriate learning or training law will be determined by ANN based on the nature of the problem it is trying to solve.
1.2.3 Types of Learning: There are two types of learning or training: Supervised and Unsupervised. The first occurs when both the input and output data are provided to the ANN; in such a way that the network adjusts its weights trying to minimize the calculated output error. Unsupervised learning or training occurs when the ANN is provided only the input Data, and the network adjusts its interconnections based solely on said data and the output of the network itself (this type of training will not be used for this monograph).
1.2.4 Phases of Operation of an ANN:
1.2.4.1 Network Training or Learning: The user provides the network with a precise number of input and output data; the network then adjusts its interconnect weights or synapses until the network output approaches the correct output.
1.2.4.2 Retrieval of what has been learned: The network is presented with a set of similar input and output data, and it simply recalculates the correct output. Therefore, the knowledge or ability to respond to an ANN is found in the Activation Function used and in the values of its Weights.
1.2.5 Characteristics of an ANN:
2.2.5.1 They are not algorithmic: The great difference in the use of neural networks in relation to other applications such as Multiple Regression; It lies in the fact that RNAs are not algorithmic, that is, they are not programmed by forcing them to follow a predefined sequence of instructions. ANNs generate their own "rules" themselves, to associate a response to their inputs. Learn from examples and from your own mistakes.
2.2.5.2 They associate and generalize without rules: Just like the human brain does
2.2.5.3 They require some type of pattern: RNAs are not capable of recognizing anything that does not have some type of pattern attached. This is why they cannot predict the lottery or horse races since by definition they are random processes.
2.2.5.4 The solution will depend on the way to make the connections: Just as there are several ways to connect biological neurons in our brain; the solution to a problem will vary according to the topology of an ANN.
2.3 Topologies of Artificial Neural Networks
There are several ways to make the connections in an ANN. Each type serves different processes; some of the most commonly used topologies are:
- Multilayer Perceptron Backpropagation Hopfield Kohonen
Of these, only the Multilayer Perceptron and Backpropagation Topologies will be developed in this monograph, which are the most commonly used in Artificial Intelligence software.
2.3.1 Perceptron
The figure below represents an "artificial" neuron, attempting to model the behavior of a biological neuron. Here the body of the neuron is represented as a linear adder of the external stimuli, followed by a non-linear function.
The function is called the Activation Function, and it uses the summation of external stimuli () to determine the output of the neuron.
This model is known as the "McCulloch-Pitts Perceptron", and it is the basis of most ANN architecture.
Artificial neurons use different activation functions depending on the application; sometimes these are linear functions and most of the time nonlinear. The synaptic efficiency is represented by the interconnection weight factors, from neuron i to neuron j.
The weights () can be positive (excitation) or negative (inhibition). The weights together with the Activation Functions dictate the operation of the neural network.
If the sum of the product of each input by the corresponding weight is greater than the value of the activation function, the perceptron will be activated.
The training or learning of a perceptron is carried out through a differential increase to each of the weights: For each weight an adjustment is made for each synapse.
The range of tasks that the Perceptron can handle is much greater than simple decisions and pattern recognition.
2.3.2 Backpropagation
The perceptron represents a single element of a neural network. If several perceptrons are combined in a "layer" and their corresponding input stimuli (); a neural network would be obtained.
In the network, several layered processing units are interconnected. The artificial neurons in each layer do not interconnect with each other; however: The output of each artificial neuron in one layer provides "an input" to each of the neurons in the next layer. That is to say: Each neuron will transmit its output signal to each neuron in the next layer. The following figure shows a schematic example of the architecture of this type of neural network.
The generalized learning or training algorithm for an intermediate or hidden layer is as follows: It begins by calculating the Activation Values (O) of each neuron, according to the following equation:
Where:
O represents the output (Activation Value) of each neuron of the previous layer
is the Fermi function
corresponds to the input value of each neuron in this layer
expresses the Weight assigned to the connection of the neuron of the previous layer with the neuron of this layer.
After all neurons have a trigger value associated with a pattern of input values (O), the algorithm continues to look for errors in each non-first layer or input neuron. The term "error" is defined as the difference between the output value estimated by the network and the input value, and it is a parameter that indicates the degree of training or learning of the ANN.
The errors found for the output neurons must be "Backpropagated" to the previous layer, so that they can be assigned to neurons of the intermediate or hidden layers, for this the error must be minimized throughout the network.
The function that minimizes the Activation or Output Value of each neuron is called "Signal Error" (); and is expressed as the First Derivative of said function:
This calculation is repeated for each intermediate or hidden layer of the network.
After the error associated with each group of neurons has been calculated, the weights must be updated, first finding the increment of value that each weight must be modified (), this is achieved by calculating:
Where: Increase in weight value
Activation value of the previous layer
Current layer signal error
C Constant called "Learning Ratio"
The new weight will be given by the relationship:
In summary, for each run the RNA calculates the error in the output layer; then it spreads it to the intermediate or hidden layers; immediately the network adjusts the weights of each neuron and recalculates the new Activation or Output Values of each neuron; repeating the procedure until the Sum of the Square of the Error (SCE) is very close to zero:
3.0 Artificial Neural Networks vs. Multiple Regression Techniques
3.1 Preliminaries
3.1.1 The Classic Market Method
For many years, the classical methodology of Approach to the Market (Marketing Approach) was the main tool of the professional real estate appraiser. This methodology contemplated the valuation principle: "Similar properties will be sold at similar prices" and was based on the search for benchmarks comparable or similar to the property being appraised in the real estate market.
So far there were no problems with the method; it was easily understood and perfectly valid. However, when due to the scarcity or insincerity of comparables, it was not possible to obtain a representative sample of similar properties, the process of correcting or standardizing said referentials was resorted to, using logical-mathematical expressions, sometimes empirical, in order to “force ”To the referential data, to artificially resemble the property object of the appraisal.
The problem consists of the presence of subjectivity factors in determining the value of a property, caused by the "criteria" used by the professional appraiser when applying one or more correction factors to a series of references, which obviously affect the accuracy of the calculation of the value of the good.
3.1.2 The Multiple Regression Techniques
With the popularization and accessibility of personal computers during the second half of the eighties and the release of statistical packages for them, professional appraisers had in their hands the possibility of using multiple regression techniques as a powerful and innovative tool for calculating the value of goods.
Multiple regression techniques were then considered as "the improvement of the market methodology", since the benchmarks themselves "self-correct" each other, without the need to use subjective criteria by the professional appraiser.
Although in theory, multiple regression techniques were the solution to the subjectivity problems suffered by the classical market method; For the multiple regression to converge on a real value, it was necessary for the reference series to fulfill a series of requirements, the main one being the insincerity of the values of the properties declared in the purchase-sale operations in the notaries and public registries..
However, there are other problems as important as the aforementioned, such as the inaccuracy of the multiple regression analyzes regarding the dynamics of the real estate market, caused mainly by the inability of statistical packages to consider something more than rules and rigid mathematical models and the inaccuracy in the processing of qualitative / categorical variables in linear multiple regression models.
- Purpose of this Monograph
The purpose of this work is to investigate the application of artificial neural network technology in the elaboration of Real Estate Appraisals in order to compare the predictive ability of an ANN with multiple regression models; In order to provide appraisers with an innovative tool based on Artificial Intelligence, to determine the value of goods and overcome the inconveniences posed by multiple regression models.
4.0 Theoretical Bases of this Monograph
4.1 Neural Networks vs. Regression models
4.1.1 Introduction
Doctors Alfonso Pitarque, Juan Francisco Roy and Juan Carlos Ruiz, professors at the Faculty of Psychology of the University of Valencia; investigated the comparison between Artificial Neural Network simulation techniques with statistical models on prediction and classification tasks.
As Prediction or Classification tools, ANNs have been conceptualized as "non-parametric" statistical techniques, since they are free from complying with the theoretical assumptions of parametric statistics, or they are also conceptualized as "non-linear regression techniques."
The problem arises when contradictory or dissimilar results are found when determining: Which models are more efficient in solving specific Prediction or Classification problems?
Although ANNs are capable of associating any input pattern with any output pattern, their performance will depend on the heuristic adjustment of numerous parameters (weights, activation value, signal error, activation function, error backpropagation, number of layers, learning coefficient, etc., previously explained). Settings that do not always guarantee the desired solution; in addition to its “black box” structure that characterizes this type of model.
4.1.2 Analysis and Conclusion of Results
- Favorable to Multiple Regression Techniques:
- a) Only for quantitative forecasting tasks and under ideal conditions of applicability; the multiple linear regression procedure obtained better results than the RNAs.
- For the rest of the cases in the quantitative prediction tasks, no differences were found between ANN and regression models.
4.1.2.2 Favorable to ANNs:
- The great advantage of using ANNs over statistical models is that ANNs can admit as input variables: Mixed sets of quantitative and qualitative variables.In Classification tasks, ANNs generate much more exact results than regression models. multiple logistics. In Prediction or Estimation tasks ANNs and multiple linear regression models generate similar results
4.1.2.3 Unfavorable to ANNs:
- Due to its “black box” nature, an ANN does not give explicit information on the relative importance of the various predictors. Training an ANN is a trial and error method; therefore the quality of the solutions given by an ANN cannot always be guaranteed.
4.2 Comparison between Neural Networks and Multiple Regression Approaches: An Application for Residential Appraisal in Finland
4.2.1 Introduction
Olga Karakozova, M.Sc., in her thesis for a Master's degree at the Swedish Academy of Economics and Business Administration dated October 2000; presented an investigation to determine the merits of applying RNA techniques to solve problems related to the Residential Real Estate Appraisal; in comparison with Multiple Regression models applied to the real estate market of the Helsinki metropolitan area for the year 1998.
4.2.2 Method Used
For this study, Karakozova used six (6) Artificial Neural Network Models and four (4) Multiple Regression models.
Said models were applied to three (3) data series: The first, using the complete data of houses in the Helsinki metropolitan area. For the second series, the data set was restricted to include only dwellings within the city of Helsinki and for the third Series, the data was further restricted, in order to include only homogeneous dwellings within the city of Helsinki.
4.2.3 Results
The study yielded the following result: The Artificial Neural Network Models outperformed the Multiple Regression Models, for each of the data series studied. However, only a very small difference between ANNs and multiple regression techniques was observed for the case of the homogeneous series of houses in Helsinki.
4.2.4 Conclusion of Results
- In prediction tasks, ANNs exceed Multiple Regression techniques by a small margin For heterogeneous data series, ANNs outperform Multiple Regression Techniques ANNs meet the necessary criteria for massive home appraisal techniques ANNs, more than a substitute to econometric analyzes, are a complement to the same
4.3 Analysis of the Effect of Age on the Value of Homes, through the Analysis of Artificial Neural Networks.
4.3.1 Introduction
Professor A. Quang Do of the Department of Finance at the San Diego State University School of Business Administration and Professor G. Grudnitski of the Accounting Department of the San Diego State University School of Business Administration at December 1992; presented a study where they demonstrated that the use of RNA allows to overcome the problems related to the use of multiple regression techniques, such as multicollinearity, heterosedasticity, etc.
4.3.2 Problem Description
The study by Professors Quang and Grudnitski, was based on examining the relationship that exists between the age of a property (home) and its market value.
Using multiple regression statistical techniques, it was determined that the age of a property is inversely proportional to its value throughout its useful life.
However, the method used (multiple regression) was also shown to generate significant errors. This inaccuracy was magnified by problems inherent in multiple regression techniques such as interaction between variables, non-linear behavior variables, multicollinearity problems between independent variables, heterosedasticity problems, etc.
ANNs have the particularity of adapting very well to solving problems related to the recognition of schemes, classification of qualitative or categorical variables; and they correspond to non-linear techniques. Therefore, RNAs have the ability to provide a very exact approximation to a wide class of non-linear functions.
The reason for the success of ANNs over regression techniques consists in the way in which their activation function is specified. Whereas in multiple regression techniques, its Activation Function is pre-specified regardless of the data; The ANNs self-determine their Activation Function by “fine-tuning” the parameters that allow the best fit to the data.
4.3.1 Method Used
A sample of 242 single-family dwellings (houses) was taken during the period January - September 1991, in the southwest of the city of San Diego (California, USA), taking care that said data belonged to similar neighborhoods. The following Independent Variables were selected:
- Age of the property of Bathrooms (1/4 bathroom = 1) Construction Area of Fire Station Parking Stations in the Neighborhood of flats Land area
4.3.2 Results and Conclusions
- It was concluded that the "Age" of a property is inversely proportional to its "Value", only during the first 16 to 20 years of its useful life. After this period of time, the variables "Age" and "Value" pass to be related in a directly proportional way. c) Demonstrating in this way that the use of RNA techniques corrected the heterosedasticity problem present in the linear regression model, which erroneously determined that the variables "Age" and "Value" were inversely proportional throughout the useful life of a home.
5.0 Comparative Example between Multiple Regression techniques and Artificial Neural Networks for the determination of the Unit Price of apartments in the city of Pampatar (Venezuela).
5.1 Data selection
The data used for this example of comparison between ANN techniques and multiple regression corresponds to a sample of Ninety-one (91) transactions for the purchase and sale of apartments in the city of Pampatar, protocolized during the Fourth Quarter of 2001..
Pampatar, is a city located on the Island of Margarita, currently Pampatar is physically linked to the city of Porlamar (Main city of the Island). The status of the "Free Port" of Margarita Island, together with the natural beauties of that portion of Caribbean land; It is the preferred tourist destination for both the inhabitants of Venezuela and foreign tourists.
Pampatar is biased into two main types of homes: Single-family, mainly intended for people who live on the Island, and Multi-family (Apartments and town-houses), mainly intended to serve as vacation homes or second homes.
5.2 Series Characteristics:
5.2.1 Description of the data for the application of Multiple Regression techniques
Explanatory Notes to Multiple Regression:
(1) The Independent Variable AGE is defined as the date of protocolization of the Condominium Document of the building where the reference is located.
(2) The Independent Variable SALE is defined as a set of dichotomous data in the form SALE = 0 corresponds to the sale of a used apartment. SALE = 1 corresponds to the sale of a new apartment.
(3) The Independent Variable VISTA, is defined as a dichotomous data set of the form VISTA = 0 corresponds to the sale of an apartment without ocean view. VIEW = 1 corresponds to the sale of an apartment with sea view.
(4) The Dependent Variable PU, is defined as the Reference Unit Price and is the result of the quotient between the Sale Price and its Area.
5.2.2 Description of the data for the application of Artificial Neural Networks (ANN) techniques
Explanatory Notes to the ANN:
(5) The Independent Variable PRIM, is defined as a dichotomous variable of the form PRIM = = 0 corresponds to the sale of a used apartment. PRIM = 1 corresponds to the sale of a new apartment.
(6) The Independent Variable SEC is defined as a dichotomous variable of the form SEC = 1 corresponds to the sale of a used apartment. SEC = 0 corresponds to the sale of a new apartment.
(7) The Independent Variable CON_VIS, is defined as a dichotomous variable of the form CON_VIS = 1 corresponds to the sale of an apartment with sea view. CON_VIS = 0 corresponds to the sale of an apartment without sea view.
(8) The Independent Variable SIN_VIS, is defined as a dichotomous variable of the form SIN_VIS = 1 corresponds to the sale of an apartment without sea view. SIN_VIS = 0 corresponds to the sale of an apartment with sea view.
5.3 Application of the Multiple Regression Technique
To calculate the linear model that best fits the data series (Apartments in Pampatar), the Microsoft Excel Spreadsheet was used.
5.3.1 Software output (Multiple Linear Correlation):
Coefficient of Determination: 0.754409
F-statistic: 36.422931
Degrees of Freedom: 83
Independent Variables: 7
Test F (Fo):> 2.36
Correlation Standard Error: 139,558.944842
SCR: 4.965789 E +12
SCE: 1.616566 E +12
5.3.2 Analysis of the Correlation Matrix:
Observations to the matrix:
- None of the Correlation Coefficients of the Independent Variables indicates a strong correlation (> 0.75). There are no Multicollinearity problems between the Independent Variables.
5.3.3 Waste Analysis:
5.3.4 Determination of the Unit Price of a Master Property
The Unit Price (PU) of a “Standard Property” was determined, representative of the series of 91 Referentials corresponding to apartments in the city of Pampatar:
Date of the “Appraisal” X1 = 11-Apr-2002
Apartment Area X2 = 80.97
Rooms X3 = 2
Bathrooms X4 = 2
Document Date
of Condominium X5 = 06-Oct-1996
Type of Sale X6 = 0 (Used Apartment)
Ocean View X7 = 0 (Without Ocean View)
Unit Price Y = 420,503.52
5.4 Application of the Artificial Neural Network (ANN) technique
5.4.1 Description of the software used
For the use of artificial intelligence techniques, the “Ainet” software was used. This program is based on Artificial Neural Networks with a Multilayer Perceptron Network topology with Error Back Propagation.
This application is one of the simplest tools for solving problems that require the use of Artificial Neural Networks (ANN) to achieve a result.
The algorithm used by "Ainet" does not require a training or learning phase of the RNA; and the result is generated immediately obtaining a great speed of solution to this type of problems.
The "Ainet" algorithm does not require specifying the initial "Weights" either; simply a coefficient called "Penalty Coefficient" controls the variability of the distribution of weights. Nor does it require the specification of the number of intermediate or hidden perceptron layers, or specification of the connections between neurons.
Additionally, the user interface is very simple to operate, the data enters and leaves with a simple "copy and paste", very similar to a spreadsheet.
However, the “Ainet” software suffers from commonly used statistical estimators such as the Coefficient of Determination. Due to its algorithm, more similar to an audio circuit; “Ainet” generates as the main indicator of the goodness of fit, the RMS statistic (Square Root of the Mean Error). Therefore, to be able to compare the ANN with the Multiple Linear Regression, the statistics Residue, Coefficient of Determination, SCE, SCR, SCT and F, were calculated manually through the "Prediction" (Y Calculated) of each referential, calculated by the program.
5.4.2 Characteristic of the Neural Network:
Type: MLBP
Input Variables (9): DATE
AREA
HAB
BATHROOMS
AGE
PRIM
SEC
CON_VIS
SIN_VIS
Output Variables (1): PU
5.4.2 Prediction of the Unit Price (PU) of a “Standard Property” through the RNA
The “Ainet” software, after running the series corresponding to 91 apartments in the city of Pampatar, using 9 input variables (5 Quantitative and 4 Dichotomous) and one (1) output variable (PU) in a Multilayer Perceptron Network with Backpropagation of the Error; predicted as a unit value of the “Standard Apartment”:
Date of the “Appraisal” DATE Entry # 1 = 11-Apr-2002 Quantitative
Apartment Area AREA Entry # 2 = 80.97 Quantitative
Rooms ROOM Entry # 3 = 2 Quantitative
Bathrooms BATHROOMS Entry # 4 = 2 Quantitative
Document Date
of Condominium AGE Entry # 5 = 06-Oct-1996 Quantitative
Sale Type PRIM Entry # 6 = 1 Dichotomous
SEC Entry # 7 = 0 Dichotomous
Ocean View CON_VIS Entry # 8 = 1 Dichotomous
SIN_VIS Entry # 9 = 0 Dichotomous
Unit Price PU Output # 1 = 492,849.94 Quantitative
5.4.3 Analysis of Control Statistics
SCR = 6.16633E + 12
SCE = 4.39901E + 11
SCT = 6.58236E + 12
Determination coefficient = 0.936797335
k = 9
n = 91
Degrees of freedom = 81
Fo = <2.24
F = 126.1578518
6.0 Conclusions and Recommendations
6.1 Comparison of Solutions between the Two (2) Techniques
When comparing the results of applying the techniques of Multiple Linear Regression and Artificial Neural Network (ANN), on the same data, the following result is obtained:
Where the fact that RNA techniques better explain the behavior of the phenomenon stands out: "Unit Value of Apartments in the city of Pampatar".
6.2 Conclusions
- The RNA techniques explain the behavior of statistical phenomena much better than the Multiple Regression techniques, in the case of Non-Linear behaviors of a series of data. The results of Drs. Alfonso Pitarque, Juan Francisco Roy and Juan Carlos are verified. Ruiz, professors at the Faculty of Psychology of the University of Valencia, regarding:
- The great advantage of using ANNs over statistical models is that ANNs can admit as input variables: Mixed sets of quantitative and qualitative variables.In Classification tasks, ANNs generate much more exact results than regression models. multiple logistics.
- Ainet (Turbajeva 42 SI-3000 Celje. Slovenia. Www.ainet-sp.si) BrainMaker Neural Networks (California Scientific Software 10024 Newtown Rd. Nevada City. California 95959. USA www.calsci.com)
- Phytia - The Neural Network Designer (Runtime Software, USA)
- Easy NN (S. Wolstenholme, Cheshire, UK www.easynn.com) Pathfinder: MS-Excel Add-in. Neural Network System (Z Solutions, Atlanta, USA www.zsolutions.com)
Although, they all differ in their interface, more or less they generate the same information. Some are more complicated than others in their handling, operation and interpretation of the results. But all agree on the fact that it is cumbersome to adapt them as a simple analysis tool to be used by appraisers without basic knowledge of Artificial Intelligence and ANN.
16-Apr-2002
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To obtain the Output (O) of the first layer of artificial neurons, it is replaced by the input stimuli (), leaving the equation of the form:
The Fermi Function is expressed as: and is graphically represented as a sigmoid in space (or hyperspace as the case may be).
Dichotomous variables (such as "With Ocean View" = 1 or "Without Ocean View" = 0) are an example of a qualitative / categorical variable, illustrating this problem. Because the qualitative and dichotomous variable "Sea View" is not linear, when combined with other quantitative variables (such as construction area, age of the property, etc.) in a multiple linear regression model, it will be very unlikely to estimate or correctly predict the variable "Unit Price" based on said mixed variables.
When quantitative (numerical) variables are used, it is defined as "Prediction or Estimation Techniques"; while when qualitative or categorical variables are used, it is defined as "Classification Techniques".
Microsoft Excel is part of the Microsoft Office 2000 package and corresponds to a general-purpose package, which has a complete statistical analysis as well as other functions.
When entering the data, the software automatically calculates and optimizes both the number of hidden layers and the connections between the "artificial neurons" needed to arrive at a result.
Multilayer Perceptron with Error Back Propagation.
Calculated manually through the MS-Excel spreadsheet
In the case of Multiple Regression, the Variables "Sale" and "View": They are considered "Categorical" but not "Dichotomous" (even when the input data of this variable is 0 and 1).
The difference between the Number of Independent Variables of Multiple Regression and ANN is due to the input format of the variables "Sale" and "View". RNA software treats each variable as an input "artificial neuron"; therefore they require the differentiation of the Dichotomous Variables "Sale" (in: PRIM - SEC) and "View" (in: CON_VIS - SIN_VIS) in order to be able to enter them into the system.91
The mere fact that there is a mixture of quantitative and dichotomous variables in a series of data, necessarily indicates a non-linear behavior of the model. Dichotomous variables are not linear since they are of the form:
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