Festival, holiday supply and demand prediction method and device based on region influence relationship

文档序号:191952 发布日期:2021-11-02 浏览:19次 中文

阅读说明:本技术 基于区域影响关系的节假日供需预测方法与装置 (Festival, holiday supply and demand prediction method and device based on region influence relationship ) 是由 胡文政 孙翊文 王建强 张长水 鲁睿 于 2021-07-26 设计创作,主要内容包括:本申请提出一种基于区域影响关系的节假日供需预测方法和装置,其中,方法包括:获取多个城市在预设时间段内产生的运营数据构成的时间序列数据,根据时间序列数据进行聚类,得到多个数据矩阵,将多个数据矩阵输入到预先训练的深度序列模型,得到预测阶段的预测矩阵,从预测矩阵中得到多个城市在预测时间段里的运营数据序列。本发明利用了其他城市(区域)的数据和城市(区域)之间的相似和抑制关系进行预测,实现了更高的预估准确性;保持了城市(区域)数据之间的关系,使得预估结果更稳定合理,利用深度模型对复杂信息的特征提取和处理,采用了可学习的时序分解对城市之间的关系进行了更深层次的挖掘,拓展了方法的计算空间,提高了计算效率。(The application provides a holiday supply and demand prediction method and device based on a region influence relationship, wherein the method comprises the following steps: the method comprises the steps of obtaining time sequence data formed by operation data generated by a plurality of cities in a preset time period, clustering according to the time sequence data to obtain a plurality of data matrixes, inputting the plurality of data matrixes to a pre-trained depth sequence model to obtain a prediction matrix of a prediction stage, and obtaining operation data sequences of the plurality of cities in the prediction time period from the prediction matrix. The method utilizes the similarity and inhibition relation between the data of other cities (regions) and the cities (regions) to predict, thereby realizing higher prediction accuracy; the method has the advantages that the relation between city (region) data is kept, the estimation result is more stable and reasonable, the characteristic extraction and processing of complex information are carried out by utilizing a depth model, the learnable time sequence decomposition is adopted to carry out deeper excavation on the relation between cities, the calculation space of the method is expanded, and the calculation efficiency is improved.)

1. A holiday supply and demand prediction method based on a regional influence relationship is characterized by comprising the following steps:

acquiring time sequence data formed by operation data generated in a plurality of cities within a preset time period;

clustering is carried out according to the time sequence data to obtain a plurality of data matrixes;

inputting the data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage;

and obtaining operation data sequences of the cities in a prediction time period from the prediction matrix.

2. The regional influence relationship-based holiday supply and demand prediction method according to claim 1, wherein the obtaining of time series data composed of operation data generated in a preset time period by a plurality of cities comprises:

and acquiring a time sequence p formed by the operation data generated by the cities in a preset time period and the operation data q of the corresponding date to be predicted in the preset time period.

3. The method for holiday supply and demand prediction based on regional influence relationship as claimed in claim 1,

each column of each matrix characterizes operation data generated by different cities in the same time unit, and each row characterizes serialized operation data generated by the same city in different time units.

4. The holiday supply and demand prediction method based on regional influence relationship according to claim 1, wherein before the data matrix is input to a depth sequence model trained in advance and a prediction matrix of a prediction stage is obtained, the method further comprises:

and training the depth sequence model.

5. The method according to claim 4, wherein the training of the depth sequence model comprises:

respectively disassembling the plurality of data matrixes based on a time sequence regularization matrix decomposition mode to obtain two matrixes, and splicing to obtain a new operation matrix to initialize the depth sequence model;

inputting training data into the initialized depth sequence model, training a loss function according to the model to obtain the depth sequence model trained in advance, and outputting training supervision label data.

6. The method for holiday supply and demand prediction based on regional influence relationship as claimed in claim 1,

the clustering mode comprises the following steps: pearson correlation coefficient, density clustering, k-means.

7. The regional impact relationship-based holiday supply and demand prediction method of claim 5, wherein the model training loss function is a predicted valueAnd true valueThe mean square error of (d).

8. The regional impact relationship-based holiday supply and demand prediction method of claim 5, wherein the depth sequence model comprises one of LSTM, GRU and transform.

9. The regional influence relationship-based holiday supply and demand prediction method according to claim 5, wherein the training data is a data matrix X formed by combining a time sequence p formed by operation data generated by the plurality of cities in a preset time period in a training period according to clusters1,…,Xa(ii) a The training supervision label data is a data matrix formed by combining operation data q of dates to be predicted corresponding to the cities in a preset time period according to clusters

10. A holiday supply and demand prediction device based on a regional influence relationship is characterized by comprising:

the system comprises an acquisition module, a processing module and a processing module, wherein the acquisition module is used for acquiring time sequence data formed by operation data generated by a plurality of cities in a preset time period;

the clustering module is used for clustering according to the time sequence data to obtain a plurality of data matrixes;

the training module is used for inputting the data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage;

and the prediction module is used for obtaining the operation data sequences of the cities in the prediction time period from the prediction matrix.

Technical Field

The invention relates to the technical field of supply and demand prediction, in particular to a holiday supply and demand prediction method and device based on a region influence relation.

Background

Holidays (including each legal holiday and each legal weekend) serve as a time window with large cross-regional population flow, have strong cultural and regional characteristics (for example, gathering custom is obvious in the traditional holidays in the Guangdong region), and show relatively strong similarity (similar supply and demand relations) or restriction (opposite supply and demand relations) of supply and demand relations among different cities. Similarly, there are differences between office and residential areas, and between residential residences of a regular population and rentable residences, for the same city. The flow of the holiday population directly brings about the difference change of supply and demand relations, such as: the travel service supply and demand relationship changes due to the cross-city flow of the population during holidays, the travel service supply and demand relationship changes in different areas of the city due to weekends, the distribution service supply and demand relationship (such as community shopping orders and delivery, take-out orders and distribution) changes, and the like. The accurate forecast of the supply and demand relationship is helpful for more reasonable resource and operation allocation, better customer experience and more supply and demand matching deals, such as: the phenomena that passengers are difficult to get a car and drivers run empty in travel supply and demand service are reduced, the phenomena that delivery personnel are insufficient and delivery time is too long in community shopping service are reduced, and the phenomenon of overtime waiting in take-out service is reduced.

In the first technical scheme, a method for predicting the demand of a taxi in a multi-view space-time mode based on deep learning is provided.

In order to simultaneously mine the space and time dependence relationship in complex traffic, a deep neural network is designed to predict the demand of a taxi. The author verifies the effectiveness of the method in a massive taxi demand data set, and in the testing stage, the MAPE value is 0.1616, and the RMSE value is 9.642.

The method contains three views for comprehensive analysis of complex patterns,

time view: the relationship between future demand and near point in time demand is modeled with LSTM.

Space view: and modeling the local spatial correlation based on the local convolutional neural network.

In the second technical scheme, a taxi demand prediction model is deeply learned by combining time sequence data and text data,

rodrigues et al emphasize that in addition to timing information, some contextual-interpreted textual information related to location also contributes to more accurate predictions in the task of taxi demand prediction. The model proposed by the authors makes use of word embedding techniques, convolutional layers and attention mechanisms to effectively fuse text information with time-series data. The authors verified the effectiveness of the proposed method on a published data set for taxis from new york, with MAE values, RMSE values, MAPE values of 93.2, 132.3 and 12.3, respectively.

Step 1. detrending of time series, authors have adopted a simple but effective method of detrending due to the apparent periodic tendency of time data that occurs with daily commutes and other recurring activities: constructing a historical average model;

and 2, preprocessing the text data. The method mainly comprises the steps of HTML mark deletion, lower case conversion, word formation and the like;

and 3, designing a deep neural network structure, wherein the text data is mainly processed through a word embedding layer, a 1-dimensional convolutional layer and an attention mechanism layer. The signal values of the time series, as well as weather and additional information, are mined primarily through the full connectivity layer. And finally, fusing the two paths of information through a prediction layer.

In the third prior art, a network appointment vehicle supply and demand prediction method based on deep learning is disclosed in patent No. CN 110458336 a.

The method carries out preprocessing operation on the network appointment vehicle travel data to convert the data into input characteristics, adopts a single-door Long Short-Term Memory network (MC-LSTM) to mine time correlation, and uses Nadam as an optimization algorithm to complete the prediction process of the supply and demand values of each region in a city in the future of 10 minutes. The method mainly comprises the following steps:

step 1, carrying out data preprocessing operation on information such as weather, congestion and the like in a data set;

step 2, selecting key attributes to construct features;

step 3, constructing a deep neural network, specifically MC-LSTM;

and 4, completing the difference value prediction of supply and demand.

The prior technical proposal has the following defects:

according to the technical scheme I, the deep neural network for predicting the demand of the taxi is designed, and the correlation between time and a spatial mode is considered. Although the method also considers the dependency relationship of the demand quantities of different region positions, the method has the defect that authors only consider the association between different regions in the same city and do not consider the similarity and restriction between different cities. During holidays, different cities have relatively strong similarity or restriction, so how to utilize the information is essential for more accurate prediction. Therefore, the invention proposes that the mutual dependency relationship among a plurality of target city patterns needs to be learned mainly by using clustering and matrix decomposition technologies.

The second technical scheme focuses on effectively fusing text information into a more formed time series prediction deep learning model. The main disadvantage of this technical solution is that the combination of the text information and the spatio-temporal information is not fine enough, that is, the text information is not very targeted for the assistance of the spatio-temporal information, such as text screening for holidays. In addition, in practical applications, text data matched with spatio-temporal data cannot be obtained effectively, which is also a main limitation of the method.

The third technical proposal mainly aims at exploring a specific deep learning model more suitable for supply and demand prediction, and authors recommend using MC-LSTM to perform temporal pattern analysis. The main disadvantage of this solution is the lack of a suitable, purposeful design for the spatial modeling of the area, in particular for the association of supply and demand values between different cities, which is not incorporated into the method framework.

Disclosure of Invention

The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.

Therefore, one objective of the present invention is to provide a method for predicting supply and demand of holidays based on regional influence relationship, and the problems to be solved are the prediction of supply and demand during holidays and the mutual influence of supply and demand changes among different regions. The invention realizes a more accurate supply and demand prediction scheme by utilizing the interrelation and the mutual influence among the areas. The redundancy elimination and relation extraction of the sequence are mainly implemented through a sequence clustering and parameter learnable time sequence matrix decomposition scheme, the redundancy elimination time sequence data is predicted through a depth time sequence prediction model, and finally the data is recovered through matrix decomposition inverse transformation.

Another object of the present invention is to provide a holiday supply and demand prediction device based on the regional influence relationship.

In order to achieve the above object, an embodiment of the invention provides a holiday supply and demand prediction method based on an area influence relationship, which includes the following steps:

acquiring time sequence data formed by operation data generated in a plurality of cities within a preset time period;

clustering is carried out according to the time sequence data to obtain a plurality of data matrixes;

inputting the data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage;

and obtaining operation data sequences of the cities in a prediction time period from the prediction matrix.

According to the holiday supply and demand prediction method based on the regional influence relationship, time sequence data formed by operation data generated by multiple cities in a preset time period are obtained, clustering is carried out according to the time sequence data to obtain multiple data matrixes, the multiple data matrixes are input into a depth sequence model trained in advance to obtain a prediction matrix in a prediction stage, and operation data sequences of the multiple cities in the prediction time period are obtained from the prediction matrix. The method utilizes the similarity and inhibition relation between the data of other cities (regions) and the cities (regions) to predict, thereby realizing higher prediction accuracy; the method has the advantages that the relation between city (region) data is kept, the estimation result is more stable and reasonable, the characteristic extraction and processing of complex information are carried out by utilizing a depth model, the learnable time sequence decomposition is adopted to carry out deeper excavation on the relation between cities, the calculation space of the method is expanded, and the calculation efficiency is improved.

In addition, the holiday supply and demand prediction method based on the regional influence relationship according to the above embodiment of the invention may further have the following additional technical features:

further, in an embodiment of the present invention, the acquiring time-series data composed of operation data generated in a preset time period by a plurality of cities includes:

and acquiring a time sequence p formed by the operation data generated by the cities in a preset time period and the operation data q of the corresponding date to be predicted in the preset time period.

Further, in one embodiment of the invention, each column of each matrix characterizes operation data generated by a different city in the same time unit, and each row characterizes serialized operation data generated by the same city in a different time unit.

Further, in an embodiment of the present invention, before the inputting the data matrix into the depth sequence model trained in advance to obtain the prediction matrix of the prediction stage, the method further includes:

and training the depth sequence model.

Further, in an embodiment of the present invention, the training the depth sequence model includes:

respectively disassembling the plurality of data matrixes based on a time sequence regularization matrix decomposition mode to obtain two matrixes, and splicing to obtain a new operation matrix to initialize the depth sequence model;

inputting training data into the initialized depth sequence model, training a loss function according to the model to obtain the depth sequence model trained in advance, and outputting training supervision label data.

Further, in an embodiment of the present invention, the clustering manner is: pearson correlation coefficient, density clustering, k-means.

Further, in one embodiment of the present invention, the model training loss function is a predicted valueAnd true valueThe mean square error of (d).

Further, in an embodiment of the present invention, the depth sequence model includes one of LSTM, GRU and transform.

Further, in an embodiment of the present invention, the training data is a data matrix X formed by combining, according to a cluster, a time sequence p formed by operation data generated by the plurality of cities within a preset time period in a training period1,...,Xa(ii) a The training supervision label data is a data matrix formed by combining operation data q of dates to be predicted corresponding to the cities in a preset time period according to clusters

The invention has the beneficial effects that:

1) the similarity and inhibition relation between the data of other cities (regions) and the cities (regions) is used for prediction, and higher prediction accuracy is realized;

2) the relation between city (region) data is kept, so that the estimation result is more stable and reasonable.

3) The feature extraction and processing of the complex information by using the depth model are not limited to a single formula, and the learnable time sequence decomposition is adopted to carry out deeper excavation on the relation between cities, so that the calculation space of the method is expanded, and the calculation efficiency is improved.

In order to achieve the above object, an embodiment of another aspect of the present invention provides a holiday supply and demand prediction apparatus based on a regional influence relationship, including:

the system comprises an acquisition module, a processing module and a processing module, wherein the acquisition module is used for acquiring time sequence data formed by operation data generated by a plurality of cities in a preset time period;

the clustering module is used for clustering according to the time sequence data to obtain a plurality of data matrixes;

the training module is used for inputting the data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage;

and the prediction module is used for obtaining the operation data sequences of the cities in the prediction time period from the prediction matrix.

The invention provides a holiday supply and demand prediction device based on a regional influence relationship, which is used for acquiring time sequence data formed by operation data generated by a plurality of cities in a preset time period through an acquisition module; the clustering module is used for clustering according to the time sequence data to obtain a plurality of data matrixes; the training module is used for inputting the data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage; and the prediction module is used for obtaining the operation data sequences of a plurality of cities in the prediction time period from the prediction matrix. The method utilizes the similarity and inhibition relation between the data of other cities (regions) and the cities (regions) to predict, thereby realizing higher prediction accuracy; the method has the advantages that the relation between city (region) data is kept, the estimation result is more stable and reasonable, the characteristic extraction and processing of complex information are carried out by utilizing a depth model, the learnable time sequence decomposition is adopted to carry out deeper excavation on the relation between cities, the calculation space of the method is expanded, and the calculation efficiency is improved.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a flow chart of a holiday supply and demand prediction method based on regional influence relationships according to an embodiment of the invention;

FIG. 2 is a schematic diagram of a matrix structure obtained based on a temporal regularization matrix decomposition according to an embodiment of the present invention;

FIG. 3 is a diagram illustrating a training structure of a depth prediction model according to an embodiment of the present invention.

Fig. 4 is a schematic structural diagram of a holiday supply and demand prediction device based on a regional influence relationship according to an embodiment of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.

The method and the device for predicting the supply and demand of holidays based on the regional influence relationship provided by the embodiment of the invention are described below with reference to the drawings, and firstly, the method for predicting the supply and demand of holidays based on the regional influence relationship provided by the embodiment of the invention is described with reference to the drawings.

Fig. 1 is a flowchart of a holiday supply and demand prediction method based on a regional influence relationship according to an embodiment of the present invention.

As shown in fig. 1, the method comprises the steps of:

in step S1, time series data composed of operation data generated in a preset time period in a plurality of cities is acquired.

Specifically, a time sequence formed by operation data generated in each historical time period in each city (or area) is acquired and recorded as a sequence p, and operation data of a to-be-predicted date corresponding to each historical time period is recorded as a label q. The operation data may be travel service data (such as times of calling a car by a passenger, and number of times of receiving a car by a driver), community distribution service data (such as number of times of receiving a car by a distributor), and the like generated in a certain supply and demand relationship.

And step S2, clustering is carried out according to the time sequence data to obtain a plurality of data matrixes.

Specifically, clustering is performed according to the time series of each city (or region), and a city (or region) group and a matrix (X) of operation data are determined1,...,Xa). Each column of the matrix is used to represent operation data generated by different cities (or areas) in the same time unit (such as the same day, the same hour, etc.), and each row is used to represent serialized operation data generated by the same city (or area) in different time units.

The clustering method can be any clustering method, such as Pearson correlation coefficient, Density clustering, k-means, and the like.

And step S3, inputting the multiple data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage.

It is understood that the sequence prediction model can be a common time sequence prediction model such as LSTM, GRU, Transformer, etc

Further, as shown in fig. 2, the matrix of each operation data is decomposed based on a Temporal regularized matrix decomposition (TRMF) mode, so as to obtain two matrix representations, which are matrix M and matrix N.

Where m is the number of cities, n is the length of the time series, and k is the given redundancy elimination dimension (typically k < n). M is a relation matrix between corresponding cities, each column represents a city combination mode, N represents time sequence data after redundancy elimination, and each row represents operation data generated in different time units (such as days, hours and the like) in a certain combination mode. For a operation matrixes, can obtain (M)1,N1),...,(Ma,Na).

For N1,...,NaSpliced into a new operation matrix N0∈Rak×nRepeating the decomposition method to obtain a matrixSum matrix For a given dimension.

FIG. 3 is a diagram illustrating a training structure of a depth prediction model according to an embodiment of the present invention. As shown in fig. 3, bySeparately initializing parameters P1,...,Pa(ii) a By usingThe parameters P are initialized.

Specifically, the training input data is a data matrix X formed by combining operation data sequences p of each region in a training period according to clusters1,...,Xa

Training supervision label data as a data matrix formed by combining operation data sequences q of all regions in a prediction period according to clustering

The model is trained in an end-to-end mode;

model training loss function as a predictorAnd true valueThe mean square error of (d).

And step S4, obtaining operation data sequences of a plurality of cities in the prediction time period from the prediction matrix.

Practical scenarios of the invention:

1) and adjusting supply and demand and strategy of the vehicles in holidays. For example, the network appointment platform predicts the relation of vehicle supply and demand in each city (or region) during the next holiday according to historical data, and adjusts subsidy force in different cities (or regions) according to supply and demand prediction to achieve the optimal supply and demand.

2) And (5) community distribution supply and demand and strategy adjustment. For example, the community shopping platform predicts the order quantity of different areas of a city during a holiday of a certain next festival according to historical data, and schedules and adjusts the optimal supply and demand by regulating and controlling means such as distribution price and subsidy according to the predicted order quantity.

3) And (4) predicting traffic flow of different areas.

In conclusion, the time sequence regularization matrix decomposition initialization model is adopted, and model convergence is improved; utilizing clustering and matrix decomposition technology to learn the mutual influence relationship among a plurality of targets end to end; and (3) utilizing a depth time sequence prediction method in combination with clustering, matrix decomposition and matrix restoration technologies to predict the time sequences of a plurality of targets.

According to the holiday supply and demand prediction method based on the regional influence relationship, time sequence data formed by operation data generated by a plurality of cities in a preset time period are obtained, clustering is carried out according to the time sequence data to obtain a plurality of data matrixes, the data matrixes are input into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage, and the operation data sequences of the cities in the prediction time period are obtained from the prediction matrix. The method utilizes the similarity and inhibition relation between the data of other cities (regions) and the cities (regions) to predict, thereby realizing higher prediction accuracy; the method has the advantages that the relation between city (region) data is kept, the estimation result is more stable and reasonable, the characteristic extraction and processing of complex information are carried out by utilizing a depth model, the learnable time sequence decomposition is adopted to carry out deeper excavation on the relation between cities, the calculation space of the method is expanded, and the calculation efficiency is improved.

Next, a holiday supply and demand prediction apparatus based on a regional influence relationship according to an embodiment of the present invention will be described with reference to the drawings.

Fig. 4 is a schematic structural diagram of a holiday supply and demand prediction device based on a regional influence relationship according to an embodiment of the present invention.

As shown in fig. 4, the prediction apparatus includes: an acquisition module 100, a clustering module 200, a training module 300, and a prediction module 400.

The system comprises an acquisition module 100, a processing module and a processing module, wherein the acquisition module is used for acquiring time series data formed by operation data generated by a plurality of cities in a preset time period;

the clustering module 200 is configured to perform clustering according to the time sequence data to obtain a plurality of data matrices;

the training module 300 is configured to input the multiple data matrices into a depth sequence model trained in advance, so as to obtain a prediction matrix in a prediction stage.

And the prediction module 400 is configured to obtain, from the prediction matrix, operation data sequences of multiple cities in the prediction time period.

It should be noted that the explanation of the embodiment of the holiday supply and demand prediction method based on the region influence relationship is also applicable to the holiday supply and demand prediction device based on the region influence relationship in this embodiment, and details are not repeated here.

According to the device for predicting the supply and demand of holidays based on the regional influence relationship, which is provided by the embodiment of the invention, the acquisition module is used for acquiring time series data formed by operation data generated by a plurality of cities in a preset time period; the clustering module is used for clustering according to the time sequence data to obtain a plurality of data matrixes; the training module is used for inputting the data matrixes into a depth sequence model trained in advance to obtain a prediction matrix of a prediction stage; and the prediction module is used for obtaining the operation data sequences of a plurality of cities in the prediction time period from the prediction matrix. The method utilizes the similarity and inhibition relation between the data of other cities (regions) and the cities (regions) to predict, thereby realizing higher prediction accuracy; the method has the advantages that the relation between city (region) data is kept, the estimation result is more stable and reasonable, the characteristic extraction and processing of complex information are carried out by utilizing a depth model, the learnable time sequence decomposition is adopted to carry out deeper excavation on the relation between cities, the calculation space of the method is expanded, and the calculation efficiency is improved.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

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