An Application Component Migration Method Applied to PaaS Cross-Platform Migration

Abstract

The present invention relates to the technical field of platform migration, and particularly to an application component migration method applied to PaaS cross-platform migration, including: obtaining the underlying hardware resource architecture information of the target PaaS platform; uploading the container image to the image repository of the target PaaS platform to complete image migration; performing adaptation conversion on the component feature parameters based on the migration rule library; migrating the application components and configuration files of the source PaaS platform to the target PaaS platform according to the migration priority; sequentially migrating the file data and object data, the database middleware, and the database data on which the application components depend to the target PaaS platform; performing business configuration adjustment and business verification, and switching the business traffic from the source PaaS platform to the target PaaS platform. The present invention realizes the improvement of migration accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of platform migration, and particularly relates to an application component migration method applied to PaaS cross-platform migration. Background Art

[0002] Currently, the demand for PaaS platform cross-platform migration has increased. The commonly used technical means at present are containerized encapsulation migration and snapshot migration, but they respectively have the problems of configuration redundancy and poor compatibility. In addition to the above existing technologies, there are also the following defects: insufficient detection of dependency cycles: static priority setting based on the startup order leads to resource contention and service oscillation; inefficient resolution of configuration conflicts: the manual intervention method of metadata merging has a high error rate.

[0003] Chinese Patent Publication No.: CN104468759A discloses a method and device for realizing application migration in a PaaS platform, including: determining a target hosting node for migrating an application; migrating the service function data of the migrating application in the source hosting node to the target hosting node. After the migration of the service function data of the migrating application is completed, the target hosting node receives a service request for the migrating application and forwards the service request to the source hosting node for processing; migrating the underlying service data of the migrating application in the source hosting node to the target hosting node. After the migration of the underlying service data of the migrating application is completed, the target hosting node receives a service request for the migrating application and processes the service request; deleting the underlying service data of the migrating application on the source hosting node. The present invention can complete the migration without downtime. It can be seen that the method and device for realizing application migration in the PaaS platform have problems in that during the process of application component migration, in the dependency analysis process, traditional topology analysis only identifies explicit dependencies and cannot handle implicitly generated dependency loops during runtime and inaccurate detection of dependency cycles. Summary of the Invention

[0004] Therefore, the present invention provides an application component migration method applied to PaaS cross-platform migration to overcome the problems in the prior art that in the process of application component migration, in the dependency analysis process, traditional topology analysis only identifies explicit dependencies and cannot handle implicitly generated dependency loops during runtime and inaccurate detection of dependency cycles.

[0005] To achieve the above object, the present invention provides an application component migration method applied to PaaS cross-platform migration, including:

[0006] Obtaining the underlying hardware resource architecture information of the target PaaS platform to create a new cluster and database middleware on the target PaaS platform;

[0007] Uploading the container image to the image repository of the target PaaS platform to complete the image migration;

[0008] Collect the metadata of the source PaaS platform and the target PaaS platform to perform reverse analysis on the application components of the source PaaS platform to extract component feature parameters;

[0009] Based on the migration rule library, adapt and transform the component feature parameters to generate a compatible configuration mapping for the target PaaS platform;

[0010] Determine the corresponding configuration file for each application component according to the compatible configuration mapping and the component feature parameters;

[0011] Scan the dependency relationships of the application components through a dependency analysis engine to determine the migration order, where the migration priority of the application components is determined according to the number of virtual dependency layers of the application components;

[0012] Determine the complexity of the dependency according to the number of nodes in the dependency cycle and the type of the dependency cycle in the dependency relationship to determine the complexity processing method, including re-determining the classification granularity of the metadata, or adjusting the data call method of the migration rule library according to the similarity of the compatible configuration mapping;

[0013] Migrate the application components and configuration files of the source PaaS platform to the target PaaS platform respectively according to the migration priority, and deploy the application components according to the migrated image and the configuration file;

[0014] Sequentially migrate the file data and object data, the database middleware, and the database data on which the application components depend to the target PaaS platform;

[0015] Perform business configuration adjustment and business verification, and switch the business traffic from the source PaaS platform to the target PaaS platform.

[0016] Further, determine the complexity of the dependency according to the number of nodes in the dependency cycle and the type of the dependency cycle in the dependency relationship, including:

[0017] Obtain the number of nodes in the dependency cycle in the dependency relationship;

[0018] Determine the type of each dependency cycle according to the number of nodes of each dependency cycle;

[0019] Calculate the complexity according to the number of nodes and the type.

[0020] Further, the complexity is the ratio of the number of nodes to the number of types of the dependency cycle.

[0021] Further, the migration priority of the application components is determined according to the number of virtual dependency layers of the application components, including:

[0022] Obtain the number of virtual dependency layers of the application component;

[0023] Traverse and compare the data of the virtual dependency layer with each application component respectively;

[0024] Obtain the traversal result, and determine the migration priority of the application component according to the order from large to small in the traversal comparison result.

[0025] Further, the virtual dependency layer of the application component means that there is the same running process between the application component and other application components or files, and this running process does not depend on the running of the current component and other application components or files.

[0026] Further, re - determine the classification granularity of the metadata, including:

[0027] Compare the complexity with a preset first complexity and a preset second complexity respectively;

[0028] If the complexity is greater than the preset second complexity, increase the classification granularity of the metadata.

[0029] Further, the increased classification granularity of the metadata is positively correlated with the complexity.

[0030] Further, adjust the data call mode of the migration rule library according to the similarity of the compatible configuration mapping, including:

[0031] Obtain the similarity between the compatible configuration mappings;

[0032] Compare the similarity with a preset similarity;

[0033] If the similarity is greater than the preset similarity, adjust the data call mode of the migration rule library from regular call to first conduct a similarity gradient sandbox test and then conduct mapping cross - elimination.

[0034] Further, the similarity between the compatible configuration mappings is the edit distance of each mapping result between the compatible configuration mapping and other compatible configuration mappings.

[0035] Further, the mapping cross - elimination is to calculate the similarity of the mappings after the sandbox test in the way of adjacent gradients. If the similarity is within the similarity limit range, eliminate this group of mappings.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows: by parsing metadata and dynamically converting configurations in the adaptation rule library, the platform compatibility problem is solved; the migration priority is dynamically determined based on the number of virtual dependency layers, and the migration order is optimized to reduce the risk of dependency conflicts; combined with the complexity analysis of dependency cycles, the classification granularity or calling method is dynamically adjusted to improve the migration robustness in complex scenarios; the incremental migration engine executes in stages, reducing the business interruption time and improving the migration efficiency.

[0037] Furthermore, by quantifying the node number and type characteristics of the dependency cycle, a structured index is provided for the calculation of complexity, making the analysis of dependency relationships more operable and accurate. The core conflict points of complex dependency structures can be accurately identified, providing data support for the dynamic adjustment of subsequent migration strategies.

[0038] Furthermore, the complexity is defined as the ratio of the number of nodes to the number of cycle types, realizing the quantitative evaluation of dependency relationships. The complexity judgment logic is simplified through numerical indexes, facilitating system automation processing; the ratio calculation can reflect the scale and diversity of dependency cycles, providing an intuitive basis for the dynamic optimization of migration rules.

[0039] Furthermore, based on the priority sorting mechanism of the number of virtual dependency layers, components with deep dependency levels and high coupling degrees are ensured to be migrated first. By traversing and comparing the virtual dependency layer data, potential dependency conflicts are exposed in advance, avoiding chain failures caused by improper migration order; at the same time, resource scheduling is optimized to reduce the cost of repeated migration operations.

[0040] Furthermore, the virtual dependency layer is clearly defined as a scenario of "sharing running processes but having no direct dependency relationship", solving the problem of mis-association caused by process sharing in traditional dependency analysis. The real dependencies and process sharing relationships are accurately distinguished, reducing redundant migration operations; the accuracy of the dependency relationship graph is improved, and the incompatibility risk of the runtime environment after migration is reduced.

[0041] Furthermore, by dynamically adjusting the metadata classification granularity through the complexity threshold, flexible resource allocation is achieved. Increasing the classification granularity in high-complexity scenarios can reduce the scale of metadata processing and improve the migration efficiency; refining the granularity in low-complexity scenarios ensures the accuracy of configuration mapping, balancing the requirements of efficiency and accuracy.

[0042] Furthermore, the design that the classification granularity is positively correlated with the complexity enables the metadata processing strategy to adapt to the actual scenario. Avoiding problems such as resource waste or insufficient accuracy caused by fixed classification granularity, the optimal utilization of resources in the migration process is achieved through dynamic adjustment.

[0043] Furthermore, a similarity gradient sandbox test and a mapping cross-elimination mechanism are introduced to solve the redundancy problem of high-similarity configuration mapping. The sandbox test verifies the feasibility of the configuration and reduces the risk of the production environment; the cross-elimination of redundant mappings reduces the invocation of invalid rules and improves the execution efficiency and accuracy of the migration rule library.

[0044] Furthermore, based on the edit distance, the similarity of compatible configuration mappings is calculated to provide a quantifiable difference evaluation criterion. The algorithm automatically identifies the subtle differences between configurations, avoiding omissions in manual comparison and ensuring the integrity and consistency of configuration conversion.

[0045] Furthermore, the mapping cross-elimination mechanism optimizes the configuration mapping set through gradient similarity comparison and threshold filtering: automatically eliminates duplicate or conflicting mapping rules, reducing configuration redundancy during migration; combines the sandbox test results to ensure the security of the elimination operation and prevent the accidental deletion of critical configurations. Description of the Drawings

[0046] Figure 1 It is the overall flowchart of the application component migration method for PaaS cross-platform migration in the embodiments of the present invention;

[0047] Figure 2 It is the specific flowchart of determining the complexity of dependencies according to the number of nodes in the dependency cycle and the type of dependency cycle in the application component migration method for PaaS cross-platform migration in the embodiments of the present invention;

[0048] Figure 3 It is the specific flowchart of determining the migration priority of application components according to the number of virtual dependency layers of application components in the application component migration method for PaaS cross-platform migration in the embodiments of the present invention. Detailed Embodiments

[0049] In order to make the objectives and advantages of the present invention clearer and more understandable, the present invention will be further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0050] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are only used to explain the technical principles of the present invention and do not limit the protection scope of the present invention.

[0051] Please refer to Figure 1 、 Figure 2 and Figure 3As shown, they are respectively the overall flowchart of the application component migration method of the embodiment of the present invention applied to PaaS cross-platform migration, the specific flowchart of determining the complexity of dependencies according to the number of nodes in the dependency cycle and the type of dependency cycle in the dependency relationship, and the specific flowchart of determining the migration priority of application components according to the number of virtual dependency layers of application components. An application component migration method applied to PaaS cross-platform migration of the present invention includes:

[0052] Obtain the underlying hardware resource architecture information of the target PaaS platform to create a new cluster and database middleware on the target PaaS platform;

[0053] Upload the container image to the image repository of the target PaaS platform to complete the image migration;

[0054] Collect the metadata of the source PaaS platform and the target PaaS platform to perform reverse analysis on the application components of the source PaaS platform to extract component feature parameters;

[0055] Based on the migration rule library, adapt and convert the component feature parameters to generate a target PaaS platform-compatible configuration mapping;

[0056] Determine the corresponding configuration file for each application component according to the compatible configuration mapping and the component feature parameters;

[0057] Scan the dependency relationship of the application components through the dependency analysis engine to determine the migration order, wherein the migration priority of the application components is determined according to the number of virtual dependency layers of the application components;

[0058] Determine the complexity of the dependencies according to the number of nodes in the dependency cycle and the type of dependency cycle in the dependency relationship to determine the complexity processing method, including re-determining the classification granularity of the metadata, or adjusting the data call method of the migration rule library according to the similarity of the compatible configuration mapping;

[0059] Migrate the application components and configuration files of the source PaaS platform to the target PaaS platform respectively according to the migration priority, and deploy the application components according to the migrated image and the configuration file;

[0060] Sequentially migrate the file data and object data on which the application components depend, the database middleware, and the database data to the target PaaS platform;

[0061] Perform business configuration adjustment and business verification, and switch the business traffic from the source PaaS platform to the target PaaS platform.

[0062] Specifically, the underlying hardware resource architecture information includes server type, CPU configuration, and network topology structure.

[0063] Specifically, the database middleware includes a database driver, connection pool management, and data caching.

[0064] Specifically, the metadata of the source PaaS platform and the target PaaS platform includes the name of the application component, the type of the application component, and the configuration parameters of the application component.

[0065] Specifically, the component characteristic parameters include the response time of the application component, the throughput of the application component, and the resource utilization rate of the application component.

[0066] Specifically, the compatible configuration is mapped to the computing resource mapping between the source PaaS platform and the target PaaS platform, the storage resource mapping between the source PaaS platform and the target PaaS platform, and the network resource mapping between the source PaaS platform and the target PaaS platform.

[0067] Specifically, the corresponding configuration files include resource configuration files, environment configuration files, and security configuration files.

[0068] Specifically, the dependency analysis engine includes SonarQube, Pinpoint, and Maven.

[0069] Specifically, the migration priority of the application component includes the migration complexity of the application component, the data sensitivity of the application component, and the dependency relationship of the application component.

[0070] Specifically, the virtual dependency layer of the application component is a logical layer located between the application component and the underlying PaaS platform. It abstracts and encapsulates the dependencies of the application component on the underlying platform, so that the application component does not need to directly depend on a specific PaaS platform, but interacts with the underlying platform through the virtual dependency layer.

[0071] Specifically, the types of dependency loops include direct dependency loops, indirect dependency loops, and transitive dependency loops.

[0072] Specifically, the file data depended on by the application component includes configuration files, code files, and data files.

[0073] Specifically, the object data depended on by the application component includes table data, common data dictionaries, and view data.

[0074] In implementation, the platform difference compatibility problem is solved by dynamically converting the configuration through the metadata parsing and adaptation rule library; the migration priority is dynamically determined based on the number of virtual dependency layers, and the migration order is optimized to reduce the risk of dependency conflicts; the classification granularity or call method is dynamically adjusted by combining the complexity analysis of the dependency loop to improve the migration robustness in complex scenarios; the incremental migration engine is executed in stages to reduce the business interruption time and improve the migration efficiency.

[0075] Specifically, the complexity of the dependency is determined according to the number of nodes in the dependency cycle and the type of the dependency cycle, including:

[0076] Obtain the number of nodes in the dependency cycle in the said dependency relationship;

[0077] Determine the type of each dependency cycle according to the number of nodes in each said dependency cycle;

[0078] Calculate the complexity according to the number of nodes and the type.

[0079] In implementation, by quantifying the number of nodes and type characteristics of the dependency cycle, a structured index is provided for the calculation of the complexity, making the analysis of the dependency relationship more operable and accurate. It can accurately identify the core contradiction points of complex dependency structures, providing data support for the dynamic adjustment of subsequent migration strategies.

[0080] Specifically, the complexity is the ratio of the number of nodes to the number of types of the dependency cycle.

[0081] In implementation, defining the complexity as the ratio of the number of nodes to the number of cycle types realizes the quantitative evaluation of the dependency relationship. Simplifying the complexity judgment logic through numerical indexes facilitates system automation processing; the ratio calculation can reflect the scale and diversity of the dependency cycle, providing an intuitive basis for the dynamic optimization of migration rules.

[0082] Specifically, the migration priority of the application component is determined according to the number of virtual dependency layers of the application component, including:

[0083] Obtain the number of virtual dependency layers of the application component;

[0084] Traverse and compare the data of the virtual dependency layer with each application component respectively;

[0085] Obtain the traversal result, and determine the migration priority of the application component in the order from large to small in the traversal comparison result.

[0086] In implementation, based on the priority sorting mechanism of the number of virtual dependency layers, it is ensured that components with deep dependency levels and high coupling degrees are migrated first. By traversing and comparing the data of the virtual dependency layer, potential dependency conflicts are exposed in advance, avoiding chain failures caused by improper migration order; at the same time, resource scheduling is optimized, reducing the cost of repeated migration operations.

[0087] Specifically, the virtual dependency layer of the application component is that there is the same running process between the application component and other application components or files, and the running process does not depend on the running of the current component and other application components or files.

[0088] In implementation, the virtual dependency layer is clearly defined as the scenario of "sharing running processes but having no direct dependency relationship", which solves the problem of false associations caused by process sharing in traditional dependency analysis. It accurately distinguishes the real dependency and the process sharing relationship, reduces redundant migration operations, improves the accuracy of the dependency relationship graph, and reduces the incompatibility risk of the runtime environment after migration.

[0089] Specifically, re-determining the classification granularity of the metadata includes:

[0090] Comparing the complexity with a preset first complexity and a preset second complexity respectively;

[0091] If the complexity is greater than the preset second complexity, increase the classification granularity of the metadata.

[0092] In implementation, the generally selected range of the preset first complexity is [45%, 55%], and the generally selected range of the preset second complexity is [60%, 70%].

[0093] Specifically, the preferred embodiment of the preset first complexity is 50%, and the preferred embodiment of the preset second complexity is 65%.

[0094] In implementation, dynamically adjust the metadata classification granularity through the complexity threshold to achieve flexible resource allocation. Increasing the classification granularity in high-complexity scenarios can reduce the scale of metadata processing and improve migration efficiency; refining the granularity in low-complexity scenarios ensures the accuracy of configuration mapping and balances the requirements of efficiency and accuracy.

[0095] Specifically, the increased classification granularity of the metadata is positively correlated with the complexity.

[0096] In implementation, the design of positive correlation between the classification granularity and the complexity makes the metadata processing strategy adapt to the actual scenario. It avoids the problems of resource waste or insufficient accuracy caused by a fixed classification granularity, and realizes the optimization of resource utilization in the migration process through dynamic adjustment.

[0097] Specifically, adjusting the data call method of the migration rule library according to the similarity of the compatible configuration mapping includes:

[0098] Obtain the similarity between the compatible configuration mappings;

[0099] Compare the similarity with a preset similarity;

[0100] If the similarity is greater than the preset similarity, change the data call method of the migration rule library from regular call to first performing a similarity gradient sandbox test and then performing mapping cross-exclusion.

[0101] In implementation, the generally selected range of the preset similarity is [80%, 90%].

[0102] Preferably, a preferred embodiment of the preset similarity is 85%.

[0103] In implementation, a similarity gradient sandbox test and a mapping cross-elimination mechanism are introduced to solve the redundancy problem of high-similarity configuration mapping. The sandbox test verifies the feasibility of the configuration and reduces the risk of the production environment; the cross-elimination of redundant mappings reduces the invocation of invalid rules and improves the execution efficiency and accuracy of the migration rule library.

[0104] Specifically, the similarity between the compatible configuration mappings is the edit distance of each mapping result between the compatible configuration mapping and other compatible configuration mappings.

[0105] In implementation, the similarity of the compatible configuration mappings is calculated based on the edit distance, providing a quantifiable difference evaluation criterion. The subtle differences between configurations are automatically identified by the algorithm, avoiding omissions in manual comparison and ensuring the integrity and consistency of the configuration conversion.

[0106] Specifically, the mapping cross-elimination is to calculate the similarity of the mappings after the sandbox test in the way of adjacent gradients. If the similarity is within the similarity limit range, this group of mappings will be eliminated.

[0107] In implementation, the mapping cross-elimination mechanism optimizes the configuration mapping set through gradient similarity comparison and threshold filtering: automatically eliminates duplicate or conflicting mapping rules, reducing configuration redundancy during migration; combines the sandbox test results to ensure the security of the elimination operation and prevent accidental deletion of key configurations.

[0108] Example 1: Virtual dependency layer identification: Deploy resource monitoring probes in the Kubernetes cluster, capture the process access patterns of shared storage volumes, and build a virtual dependency graph. Components accessed by the same PID establish virtual dependency edges;

[0109] Example 2: Gradient sandbox test, establishing a three-level test environment:

[0110] | Environment level | Test scope | Verification target |

[0111] | Level 1 | Single-component configuration mapping | Basic function verification |

[0112] | Level 2 | Component group interaction test | Dependency relationship verification |

[0113] | Level 3 | Full-link stress test | Performance baseline verification |

[0114] Gradient sandbox verification mechanism

[0115] - Develop a multi-dimensional similarity evaluation matrix:

[0116] | Dimension | Weight | Evaluation Method |

[0117] | Similarity of configuration structure | 0.4 | Abstract syntax tree comparison |

[0118] | Runtime characteristics | 0.3 | System call sequence matching |

[0119] | Resource pattern | 0.2 | DTW distance of memory / CPU usage curve |

[0120] | Exception pattern | 0.1 | Keyword matching degree of error logs |

[0121] So far, the technical solution of the present invention has been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. An application component migration method applied to PaaS cross-platform migration, characterized in that Including: Obtain the underlying hardware resource architecture information of the target PaaS platform to create a new cluster and database middleware on the target PaaS platform; Upload the container image to the image repository of the target PaaS platform to complete image migration; Collect the metadata of the source PaaS platform and the target PaaS platform to perform reverse analysis on the application components of the source PaaS platform to extract component feature parameters; Based on the migration rule library, adapt and transform the component feature parameters to generate a target PaaS platform-compatible configuration mapping; Determine the corresponding configuration file for each application component according to the compatible configuration mapping and the component feature parameters; Scan the dependency relationships of the application components through a dependency analysis engine to determine the migration order, where the migration priority of the application components is determined according to the number of virtual dependency layers of the application components; Determine the complexity of the dependency according to the number of nodes in the dependency cycle and the type of the dependency cycle in the dependency relationship to determine the complexity processing method, including re-determining the classification granularity of the metadata, or adjusting the data call method of the migration rule library according to the similarity of the compatible configuration mapping; Migrate the application components and configuration files of the source PaaS platform to the target PaaS platform respectively according to the migration priority, and deploy the application components according to the migrated image and the configuration file; Sequentially migrate the file data and object data on which the application components depend, the database middleware, and the database data to the target PaaS platform; Perform business configuration adjustment and business verification, and switch the business traffic from the source PaaS platform to the target PaaS platform; Determine the complexity of the dependency according to the number of nodes in the dependency cycle and the type of the dependency cycle in the dependency relationship, including: Obtain the number of nodes in the dependency cycle in the dependency relationship; Determine the type of each dependency cycle according to the number of nodes of each dependency cycle; Calculate the complexity according to the number of nodes and the type; The complexity is the ratio of the number of nodes to the number of types of the dependency cycle.

2. The application component migration method for PaaS cross-platform migration according to claim 1, characterized in that The migration priority of the application components is determined according to the number of virtual dependency layers of the application components, including: Obtain the number of virtual dependency layers of the application components; Traverse and compare the data of the virtual dependency layer with each application component respectively; Obtain the traversal result, and determine the migration priority of the application components in descending order according to the traversal comparison result.

3. The application component migration method applied to PaaS cross-platform migration according to claim 2, characterized in that, The virtual dependency layer of the application component means that there is the same running process between the application component and other application components or files, and the running process does not depend on the running of the current component and other application components or files.

4. The application component migration method applied to PaaS cross-platform migration according to claim 3, characterized in that Re-determine the classification granularity of the metadata, including: Compare the complexity with a preset first complexity and a preset second complexity respectively; If the complexity is greater than the preset second complexity, increase the classification granularity of the metadata.

5. The application component migration method applied to PaaS cross-platform migration according to claim 4, wherein, The increased classification granularity of the metadata is positively correlated with the complexity.

6. The application component migration method applied to PaaS cross-platform migration according to claim 5, wherein Adjust the data call method of the migration rule library according to the similarity of the compatible configuration mapping, including: Obtain the similarity between the compatible configuration mappings; Compare the similarity with a preset similarity; If the similarity is greater than the preset similarity, adjust the data call method of the migration rule library from regular call to first perform a similarity gradient sandbox test and then perform mapping cross-elimination.

7. The application component migration method for PaaS cross-platform migration according to claim 6, wherein The similarity between the compatible configuration mappings is the edit distance of each mapping result between the compatible configuration mapping and other compatible configuration mappings.

8. The application component migration method applied to PaaS cross-platform migration according to claim 7, wherein The mapping cross-elimination is to calculate the similarity of the mappings after the sandbox test in the way of adjacent gradients. If the similarity is within the similarity limit range, eliminate this group of mappings.

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