Subgraph partitioning method, device and medium based on heterogeneous GPU computing power perception

Abstract

The present invention discloses a subgraph partitioning method, device and medium based on heterogeneous GPU computing power perception, which belongs to the field of graph data processing technology. The method includes: obtaining the original graph data G and the target number of subgraph partitioning N, and calculating the overall computing burden according to the number of nodes and edges of the original graph; evaluating the computing power of each GPU, designing a computing power-aware heuristic function based on the evaluation results, and determining the target computing burden for each GPU; constructing a weighted graph G according to the degree of each node w ; Use the graph partitioning algorithm to partition the weighted graph G w The coarsened graph is divided into subgraphs; the sizes of different subgraphs are adjusted according to the heuristic function and the node weights to complete the division of all subgraphs. The present invention fully considers the computing power of different GPUs to refine and adjust the size of the subgraphs, which can significantly improve the execution efficiency of graph computing tasks on clusters containing GPUs with different computing powers to maximize the computing potential of each GPU.

Description

Technical Field

[0001] The present invention relates to the field of graph data processing technology, and in particular to a subgraph partitioning method, device and medium based on heterogeneous GPU computing power perception. Background Art

[0002] In recent years, deep learning has made remarkable achievements in computer vision, natural language processing, speech recognition and other fields, but it can only process data with regular structure in Euclidean space. Many problems in the real world involve non-Euclidean space, where the relationship between data is more complex, and graphs are particularly suitable for representing and analyzing data in non-Euclidean space. However, as the scale of data continues to increase, traditional graph processing has become increasingly inefficient. The rapid development of GPUs has provided a solution to this problem, and a large number of studies have begun to focus on multi-GPU acceleration methods. However, most of the current graph partitioning algorithms assume that the type of GPU is the same, so the size of the subgraph partitions is as similar as possible to achieve load balancing. However, now that GPUs are developing rapidly, it has become the norm to have GPUs with different computing power on one machine. In this case, the existing partitioning algorithms will lead to low computational efficiency and even memory overflow.

[0003] Terminology explanation:

[0004] GPU: Abbreviation of Graphics Processing Unit, graphics processor, also known as display core, visual processor, display chip, is a microprocessor specially used to perform image and graphics related calculations on personal computers, workstations, game consoles and some mobile devices (such as tablets, smart phones, etc.). Summary of the invention

[0005] In order to solve at least one of the technical problems existing in the prior art to a certain extent, the purpose of the present invention is to provide a subgraph partitioning method, device and medium based on heterogeneous GPU computing power perception.

[0006] The technical solution adopted by the present invention is:

[0007] A subgraph partitioning method based on heterogeneous GPU computing power perception includes the following steps:

[0008] Get the original graph data G and the target number of subgraph partitions N, and calculate the overall computational burden based on the number of nodes and edges in the original graph;

[0009] Evaluate the computing power of each GPU, design a computing power-aware heuristic function based on the evaluation results, and determine the target computing burden for each GPU;

[0010] Construct a weighted graph G based on the degree of each node w ;

[0011] Use the graph partitioning algorithm to partition the weighted graph G w Complete the division of the coarsened graph and obtain the subgraph;

[0012] According to the heuristic function and node weights, the sizes of different subgraphs are adjusted to complete the division of all subgraphs.

[0013] Furthermore, the obtaining of the original graph data G and the target number N of subgraph divisions, and the calculation of the overall computational burden according to the number of nodes and edges of the original graph, include:

[0014] Obtain the original graph data G and the subgraph division target number N input by the user;

[0015] According to the number of nodes and edges of the original graph, the overall computational burden is calculated using the following formula:

[0016] h(V,E)=α×|V|+β×|E|

[0017] Among them, α is the weight of the node; β is the weight of the edge; |V| represents the number of edges, |E| represents the number of nodes, and h(V,E) represents the overall computational burden.

[0018] Furthermore, the computing power of each GPU is evaluated, and a computing power-aware heuristic function is designed based on the evaluation result to determine a target computing burden for each GPU, including:

[0019] Use the GPU computing power evaluation tool to evaluate the computing power of each GPU and obtain the evaluation results of n GPUs: C = [c1, c2, ..., c n ];

[0020] Combine the evaluation results to design a heuristic function to guide subgraph allocation and calculate the score for each GPU;

[0021] Each GPU obtains the size of the subgraph it owns based on the obtained score, which serves as the target computing burden of the subgraph.

[0022] Furthermore, the calculation formula for the GPU score is as follows:

[0023]

[0024] Among them, Score i represents the score of the i-th GPU, Represents the sum of the computing power evaluation results of all GPUs, c i Represents the evaluation result of the i-th GPU.

[0025] Furthermore, the weighted graph G is constructed according to the degree of each node. w ,include:

[0026] Traverse each node in the original graph and calculate the degree of the node;

[0027] The calculated degree represents the weight of the node and is appended to the graph.

[0028] Furthermore, the weighted graph G is partitioned using a graph partitioning algorithm. w Complete the division of the coarsened graph and obtain subgraphs, including:

[0029] Use the graph partitioning algorithm to partition the weighted graph G w Partitioning is performed to obtain coarsened subgraphs of similar size.

[0030] Furthermore, adjusting the sizes of different partitions according to the heuristic function and the node weights includes:

[0031] A1. Randomly assign different subgraphs to different GPUs in advance;

[0032] A2. Select the subgraph corresponding to the GPU with the lowest computational burden and calculate the difference computational burden that needs to be allocated at least.

[0033] A3. Traverse the edge nodes of the subgraph and use the dynamic programming algorithm to select the nodes that need to be allocated in the end.

[0034] A4. Add the nodes to be allocated to their respective neighbor subgraphs and mark the current subgraph as completed.

[0035] A5. Traverse the remaining sub-graphs and repeat steps A1-A4 until all sub-graphs are adjusted.

[0036] Furthermore, the subgraph partitioning method further includes the following steps:

[0037] The adjusted subgraph is actually assigned to the corresponding GPU, and the graph computing task is executed.

[0038] Another technical solution adopted by the present invention is:

[0039] A subgraph partitioning device based on heterogeneous GPU computing power perception, comprising:

[0040] at least one processor;

[0041] at least one memory for storing at least one program;

[0042] When the at least one program is executed by the at least one processor, the at least one processor implements the method described above.

[0043] Another technical solution adopted by the present invention is:

[0044] A computer-readable storage medium stores a program executable by a processor, wherein the program executable by the processor is used to execute the method described above when executed by the processor.

[0045] The beneficial effects of the present invention are as follows: the present invention fully considers the computing power of different GPUs to refine and adjust the scale of the subgraph, which can significantly improve the execution efficiency of graph computing tasks on a cluster containing GPUs with different computing powers, maximize the computing potential of each GPU, and significantly improve the computing efficiency in a heterogeneous GPU environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the embodiments of the present invention or the drawings of related technical solutions in the prior art are introduced below. It should be understood that the drawings introduced below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 It is a flowchart of the steps of a subgraph partitioning method based on heterogeneous GPU computing power perception in an embodiment of the present invention;

[0048] Figure 2 is a diagram of the GPU topology structure on a single machine in an embodiment of the present invention;

[0049] Figure 3 It is a schematic diagram of the division of subgraphs in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limitations of the present invention. For the step numbers in the following embodiments, they are only provided for the convenience of explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0051] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., and orientations or positional relationships indicated are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0052] In the description of the present invention, "several" means one or more, "more" means more than two, "greater than", "less than", "exceed" etc. are understood as not including the number itself, and "above", "below", "within" etc. are understood as including the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0053] In addition, in the description of the present invention, unless otherwise specified, "plurality" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the associated objects before and after are in an "or" relationship.

[0054] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0055] In the existing partitioning technical solutions, a storage-optimized distributed graph processing method (CN 107122248 A) is evenly divided according to the total number of graph nodes; a graph retrieval method based on subgraph partitioning (CN 115080776 A) uses a separate graph convolutional network to generate a graph node allocation matrix, and uses the node feature matrix and the first-order adjacency matrix of the graph to divide the nodes into corresponding subgraphs; a graph data partitioning method for achieving load balancing (CN 115658975 A) averages the node degree to make the number of nodes between subgraphs as equal as possible. None of the above technical solutions consider that when there are differences in GPU computing power, such methods may not achieve true load balancing. Therefore, it is necessary to design an efficient subgraph partitioning method under single-machine multi-GPU, which allocates the best subgraph to each GPU node while fully considering the different GPU computing power. In order to fill the gap in the existing graph partitioning methods in heterogeneous GPU computing power perception, the present invention proposes a subgraph partitioning method based on heterogeneous GPU computing power perception, which can be conveniently applied to graph computing, graph neural network and other fields, and has very important practical significance for the development of graph data processing technology.

[0056] like Figure 1 As shown, this embodiment provides a subgraph partitioning method based on heterogeneous GPU computing power perception, which can allocate the best subgraph to each GPU node while fully considering the different GPU computing powers. The method specifically includes the following steps:

[0057] S1. Obtain the original graph data G and the target number of subgraph partitions N, and calculate the overall computational burden based on the number of nodes and edges of the original graph.

[0058] As an optional implementation, step S1 specifically includes the following steps:

[0059] S11. Obtain the original graph data G and the target number N of sub-graph divisions input by the user.

[0060] In this embodiment, it is assumed that there are 6 GPUs on a server, including 2 RTX3090, 2 A40 and 2 GTX1660Ti. Figure 2 As shown, therefore N=6.

[0061] S12. According to the number of nodes and edges of the original graph, the overall computational burden is calculated using the following formula:

[0062] h(V,E)=α×|V|+β×|E|

[0063] Among them, α is the weight of the node; β is the weight of the edge; |V| represents the number of edges, |E| represents the number of nodes, and h(V,E) represents the overall computational burden. When α=1 and β=1, it means that the number of nodes and the number of edges have the same computational burden weight. We take α=1 and β=0.5, indicating that the number of nodes has a greater impact on the amount of computation.

[0064] S2. Evaluate the computing power of each GPU, design a computing power-aware heuristic function based on the evaluation results, and determine the target computing burden for each GPU.

[0065] As an optional implementation, step S2 includes the following steps:

[0066] S21. Use the GPU computing power evaluation tool to evaluate the computing power of each GPU and obtain the evaluation results of n GPUs: C = [c1, c2, ..., c n ];

[0067] S22. Design a heuristic function for guiding subgraph allocation based on the evaluation results, and calculate the score of each GPU. In this embodiment, the score of the GPU is calculated by proportional allocation:

[0068]

[0069] Among them, Score i represents the score of the i-th GPU, Represents the sum of the computing power evaluation results of all GPUs, c i Represents the evaluation result of the i-th GPU.

[0070] S23. Each GPU obtains the size of the subgraph it owns according to the obtained score as the target computing burden of the subgraph.

[0071] S3. Construct a weighted graph G based on the degree of each node w .

[0072] As an optional implementation, step S3 includes the following steps:

[0073] S31, traverse each node in the original graph and calculate the degree of the node;

[0074] S32. The calculated degree represents the weight of the node and is added to the graph, thereby constructing a weighted graph.

[0075] S4. Use the graph partitioning algorithm to perform weighted graph G w Complete the division of the coarsened graph and obtain the subgraph.

[0076] The weighted graph is partitioned using a graph partitioning algorithm to obtain coarsened partition subgraphs of similar size. In an optional embodiment, the graph partitioning algorithm is implemented using a METIS algorithm, and in another optional embodiment, the graph partitioning algorithm is implemented using a Hash partitioning method.

[0077] S5. According to the heuristic function and the node weights, the sizes of different subgraphs are adjusted to complete the division of all subgraphs.

[0078] As an optional implementation, see Figure 3 , step S5 comprises the following steps:

[0079] S51, randomly assigning the divided different partition subgraphs to different GPUs in advance;

[0080] S52, first select the subgraph corresponding to the GPU with the lowest target computing burden, and calculate the difference computing burden that needs to be allocated at least;

[0081] S53, traversing the edge nodes of the subgraph, using a dynamic programming algorithm, selecting the subgraph nodes that need to be allocated in the end; the goal is to minimize the allocated subgraph nodes while achieving the highest computing burden on the current GPU;

[0082] S54, adding these allocated subgraph nodes to their respective neighbor partition subgraphs, and marking the current subgraph as completed;

[0083] S55 , traverse the remaining sub-graphs and repeat steps S51 - S54 until all sub-graphs are adjusted.

[0084] S6. Distribute graph partition data and start graph computing tasks.

[0085] As an optional implementation, step S6 includes the following steps:

[0086] S61, actually allocating the adjusted sub-image to the corresponding GPU;

[0087] S62, each GPU starts to execute graph computing tasks locally;

[0088] S63. Finally, the calculation results on each GPU are aggregated to form the output result of the graph computing task.

[0089] In summary, the method of this embodiment has at least the following advantages and beneficial effects compared with the prior art:

[0090] (1) The present invention first constructs a weighted graph according to the degree of each node, and then uses a graph partitioning method to partition the subgraph. The graph partitioning method can use existing methods, such as METIS, so it has universality and good compatibility.

[0091] (2) The present invention takes into full account the computing power of different GPUs to refine and adjust the size of the subgraph. It can significantly improve the execution efficiency of graph computing tasks on a cluster containing GPUs with different computing power, maximizing the computing potential of each GPU. It can also prevent the subgraph size from exceeding the GPU memory and causing memory overflow. The present invention provides an efficient and computing power-sensitive partitioning method for parallel processing of graph data, significantly improving the computing efficiency in a heterogeneous GPU environment.

[0092] This embodiment also provides a subgraph partitioning device based on heterogeneous GPU computing power perception, including:

[0093] at least one processor;

[0094] at least one memory for storing at least one program;

[0095] When the at least one program is executed by the at least one processor, the at least one processor implements the following Figure 1 The method shown.

[0096] A subgraph partitioning device based on heterogeneous GPU computing power perception in this embodiment can execute a subgraph partitioning method based on heterogeneous GPU computing power perception provided by the method embodiment of the present invention, can execute any combination of implementation steps of the method embodiment, and has the corresponding functions and beneficial effects of the method.

[0097] The present application also discloses a computer program product or a computer program, which includes a computer instruction stored in a computer-readable storage medium. A processor of a computer device can read the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes Figure 1 The method shown.

[0098] This embodiment also provides a storage medium storing instructions or programs that can execute a subgraph partitioning method based on heterogeneous GPU computing power perception provided by an embodiment of the method of the present invention. When the instructions or programs are run, any combination of implementation steps of the method embodiment can be executed, and the corresponding functions and beneficial effects of the method can be obtained.

[0099] In some selectable embodiments, the function / operation mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the function / operation involved, the two boxes shown in succession can actually be executed substantially simultaneously or the boxes can sometimes be executed in reverse order. In addition, the embodiment presented and described in the flow chart of the present invention is provided by way of example, for the purpose of providing a more comprehensive understanding of technology. The disclosed method is not limited to the operation and logic flow presented herein. Selectable embodiments are expected, wherein the order of various operations is changed and the sub-operation of a part for which is described as a larger operation is performed independently.

[0100] In addition, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise specified, one or more of the functions and / or features described may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in separate physical devices or software modules. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the present invention. More specifically, in view of the properties, functions, and internal relationships of the various functional modules in the device disclosed herein, the actual implementation of the module will be understood within the conventional skills of the engineer. Therefore, those skilled in the art can implement the present invention set forth in the claims without excessive experimentation using ordinary techniques. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0101] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program codes.

[0102] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0103] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0104] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0105] In the above description of this specification, the description with reference to the terms "one embodiment / example", "another embodiment / example" or "certain embodiments / examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0106] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

[0107] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the above embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A subgraph partitioning method based on heterogeneous GPU computing power perception, characterized in that: Constructing a single-machine multi-GPU topology structure, wherein the single-machine multi-GPU topology structure includes a CPU and N GPUs, the method comprising the following steps: Get the original graph data G and the target number of subgraph partitions N, and calculate the overall computational burden based on the number of nodes and edges in the original graph; Evaluate the computing power of each GPU, design a computing power-aware heuristic function based on the evaluation results, and determine the target computing burden for each GPU, which includes: Use the GPU computing power evaluation tool to evaluate the computing power of each GPU and obtain the evaluation results of n GPUs: C = [c1, c2, ..., c n ], Based on the evaluation results, a heuristic function is designed to guide subgraph allocation, and the score of each GPU is calculated. Each GPU obtains the size of the subgraph it owns based on the obtained score, which is used as the target computing burden of the subgraph. Construct a weighted graph G based on the degree of each node w , which includes: Traverse each node in the original graph and calculate the degree of the node. The calculated degree represents the weight of the node and is appended to the graph; Use the graph partitioning algorithm to partition the weighted graph G w Complete the division of the coarsened graph and obtain the subgraph; The subgraph partitioning method based on heterogeneous GPU computing power perception also includes steps A1-A5: A1. Randomly assign different subgraphs to different GPUs in advance; A2. Select the subgraph corresponding to the GPU with the lowest computational burden and calculate the difference computational burden that needs to be allocated at least. A3. Traverse the edge nodes of the subgraph and use the dynamic programming algorithm to select the nodes that need to be allocated in the end. A4. Add the nodes to be allocated to their respective neighbor subgraphs and mark the current subgraph as completed. A5, traverse the remaining sub-graphs and repeat steps A1-A4 until all sub-graphs are adjusted; Distribute graph partition data and start graph computing tasks, which include: S61, actually allocating the adjusted sub-image to the corresponding GPU; S62, each GPU starts to execute graph computing tasks locally; S63. Summarize the calculation results on each GPU to form the output result of the graph computing task.

2. According to the method of subgraph partitioning based on heterogeneous GPU computing power perception according to claim 1, it is characterized in that: The obtaining of the original graph data G and the target number N of subgraph divisions, and the calculation of the overall computational burden according to the number of nodes and edges of the original graph, include: Obtain the original graph data G and the subgraph division target number N input by the user; According to the number of nodes and edges of the original graph, the overall computational burden is calculated using the following formula: h(V, E)=α×|V|+β×|E| Among them, α is the weight of the node; β is the weight of the edge; |V| represents the number of edges, |E| represents the number of nodes, and h(V, E) represents the overall computational burden.

3. According to the method of subgraph partitioning based on heterogeneous GPU computing power perception according to claim 1, it is characterized in that: The calculation formula for the GPU score is as follows: Among them, Score i represents the score of the i-th GPU, Represents the sum of the computing power evaluation results of all GPUs, c i Represents the evaluation result of the i-th GPU.

4. According to the method of subgraph partitioning based on heterogeneous GPU computing power perception according to claim 1, it is characterized in that: The graph partitioning algorithm is used to partition the weighted graph Gw into a coarsened graph to obtain a subgraph, including: Use the graph partitioning algorithm to partition the weighted graph Gw to obtain coarsened subgraphs of similar size.

5. According to the method of subgraph partitioning based on heterogeneous GPU computing power perception according to claim 1, it is characterized in that: The subgraph partitioning method further comprises the following steps: The adjusted subgraph is actually assigned to the corresponding GPU, and the graph computing task is executed.

6. A subgraph partitioning device based on heterogeneous GPU computing power perception, characterized in that: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of claims 1 to 5.

7. A computer-readable storage medium storing a program executable by a processor, characterized in that: The processor-executable program is used to perform the method according to any one of claims 1 to 5 when executed by the processor.

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