Automatic reverse invoicing method based on scrap steel online transaction system
By applying automation and intelligent technologies in scrap steel transactions, reverse invoice is realized in scrap steel transactions, the problem of inefficiency of traditional manual invoice is solved, the invoice efficiency and accuracy are improved, and data consistency and compliance are ensured.
Patent Information
- Application Number
- CN202411698464.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-26
- Publication Date
- 2025-03-04
AI Technical Summary
The traditional manual invoice is inefficient in scrap steel transactions, and the existing automated invoice system still requires a large amount of manual information to be entered in the reverse invoice process, resulting in insufficient efficiency and accuracy.
Through automated means and intelligent technology, reverse invoice is realized in scrap steel transactions, including data collection and preprocessing, qualification verification and matching, automated invoice issuance and optimization, push to the electric ticket platform and generation of reverse invoices. Using OCR, NLP, machine learning models and other technologies, we automatically identify and verify qualification files, match tax registration information, automatically generate electronic invoices, and connect with the national gold tax system.
It significantly improves the efficiency and accuracy of invoices, simplifies the qualification verification process, ensures data consistency and compliance, reduces manual operations and errors, and improves the automation of the entire reverse invoice process.
Smart Images

Figure CN119559000A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of tax management, and in particular to an automatic reverse invoicing method based on an online scrap steel trading system. Background Art
[0002] In scrap steel transactions, the traditional manual invoicing method is inefficient and prone to errors. Although some existing automated invoicing systems have improved efficiency, they still require the input of more business information, especially in the reverse invoicing process (i.e., the seller issues an invoice to the buyer), the buyer still needs to provide a lot of information to the seller offline, such as: buyer information, buyer's invoiced quantity, buyer's tax payment information, etc., for the seller to check and determine whether they are qualified for reverse invoicing. Therefore, a method that can automatically complete reverse invoicing is needed, and intelligent technology is introduced to improve accuracy and efficiency. Summary of the invention
[0003] The purpose of the present invention is to provide an automated reverse invoicing method based on an online scrap steel trading system, which realizes reverse invoicing in scrap steel trading through automated means and intelligent technology, improves invoicing efficiency and accuracy, simplifies the qualification verification process, ensures data consistency and compliance, and solves the problems raised in the above-mentioned background technology.
[0004] To achieve the above object, the present invention provides the following technical solutions:
[0005] An automated reverse invoicing method based on an online scrap steel trading system comprises the following steps:
[0006] S01. Data collection and preprocessing: Collect basic user information and business data of both parties to the transaction, clean and format the collected data, extract key features from the original data, and mark and prompt the data that meets the requirements of reverse invoicing;
[0007] S02. Qualification verification and matching: Identify and verify qualification documents and parse transaction terms, match the tax registration information of both parties to the transaction, check the historical transaction records of both parties to the transaction, automatically generate a qualification verification report, and provide it to relevant parties for review;
[0008] S03. Automated invoicing and optimization: The system automatically generates and reviews invoicing applications based on the user qualifications of suppliers and purchasers, clarifies the invoicing amount and invoicing account information, and automatically calculates the taxable amount and tax amount based on transaction information and qualification verification results, generating electronic invoices that meet national standards;
[0009] S04. Push to the electronic invoice platform: The approved invoice information is sent to the electronic invoice platform. The electronic invoice platform uses RPA robots and single sign-on services to complete the connection with the national golden tax system;
[0010] S05. Generate reverse invoice: The State Administration of Taxation receives the invoice information, executes the invoice instruction, and transmits the reverse invoice information back to the electronic invoice platform after the invoice is completed. The electronic invoice is pushed to the platform users. The users file tax returns through the platform based on the reverse invoice information.
[0011] Preferably, with respect to S01:
[0012] The collected basic user information includes but is not limited to mobile phone number, name, ID number, address, real-name authentication status, and contract certificate information applied for through facial collection;
[0013] The collected business data includes but is not limited to business process data, business flow information, logistics information, payment information, order information, warehousing information and settlement order information;
[0014] Among them, business flow information includes but is not limited to the contracting qualifications of the buyer and seller, the reverse invoicing agreement and the electronically signed contract; logistics information includes but is not limited to delivery appointment information, driver departure information with bills, on-site photo information, logistics track, purchaser's entry photo information, heavy vehicle weighing photos and gross weight information, quality inspection photos, empty vehicle weighing photos and tare weight information, estimated dry basis information and exit photo information; payment information includes but is not limited to payment flow information and bank receipts;
[0015] The key features extracted include but are not limited to transaction amount, transaction time and transaction frequency.
[0016] Preferably, the implementation method for the qualification verification described in S02 is specifically as follows:
[0017] Use OCR optical character recognition technology to automatically identify and verify the qualification documents provided by the seller;
[0018] For users who meet the reverse invoicing qualifications, a business registration portal is provided on the platform, through which platform users can quickly complete qualification certification;
[0019] Connect with the industrial and commercial and taxation administration systems, check the user's reverse invoicing quota through the platform, and promptly indicate the business scale that can be carried out;
[0020] Connect with the industrial and commercial and State Administration of Taxation systems to obtain withholding information of recycling companies through the platform.
[0021] Preferably, the implementation method for the qualification matching described in S02 is specifically as follows:
[0022] Use NLP technology to analyze text information in qualification documents, extract key information, and clarify the responsibilities and obligations of both parties to the transaction;
[0023] Compare the extracted information with the backend database to verify the authenticity of the qualification information;
[0024] Use the rule engine to determine whether the seller meets the reverse invoicing conditions based on qualification information;
[0025] Use machine learning models to predict the effectiveness of seller qualifications;
[0026] Identify potentially abnormal qualification information through anomaly detection algorithms.
[0027] Preferably, the automated invoicing and optimization described in S03 are specifically as follows:
[0028] Automatically generate invoice information including invoice number, amount and tax number using template filling technology;
[0029] Automatically generate invoices based on settlement information and ensure the consistency of invoice data;
[0030] Use predictive models to predict future billing needs and prepare invoices in advance;
[0031] Distribute invoicing tasks through load balancing algorithms;
[0032] Use priority scheduling algorithms to handle urgent or important invoicing tasks;
[0033] Use machine learning models to optimize data processing logic in the invoice generation process.
[0034] Preferably, the push to the electronic ticket platform described in S04 is specifically as follows:
[0035] Synchronize the generated electronic invoice information to the electronic invoice system of the State Taxation Bureau in real time;
[0036] Use API interface to connect with electronic ticket platform;
[0037] Monitor abnormal situations during data transmission through anomaly detection algorithms and handle transmission failures and other issues in a timely manner;
[0038] Supports electronic management and storage of invoices, including but not limited to invoice query, printing and downloading functions, supports backup and recovery of invoice data, and provides invoice status tracking function.
[0039] Preferably, the generation of reverse invoicing described in S05 is specifically as follows:
[0040] Generate reverse invoicing requests based on feedback and needs from both parties of the transaction;
[0041] The State Administration of Taxation automatically processes the reverse invoicing request and generates the corresponding red-letter invoice or adjustment invoice, which is then sent to the buyer via the electronic invoice platform;
[0042] The electronic invoice platform provides detailed records and reports of reverse invoicing;
[0043] Use consistency checking algorithms to ensure consistency between invoice data and settlement data.
[0044] Preferably, the step of extracting key features from the original data in S01 is as follows:
[0045] The image texture features are described by calculating the frequency of the grayscale value combination of two pixels at a certain distance and direction in the image. For a given displacement vector (△x, △y), the element P(i,jAx, △y) of GLCM indicates that the feature extraction is performed when the pixel with grayscale value i and the pixel with grayscale value j at a distance of (△x, △y) appear at the same time in the image. The formula is as follows:
[0046]
[0047] For a binary support vector machine (SVM), assuming that the training sample set is {(1,y1), (2,y2), ..., (n,yn)}, where i is the feature vector and 1 / 4€{-1,1} is the category label, the formula is as follows:
[0048] subject to you i (w·x i +b)≥1, i=1,2,…,n.
[0049] Assuming C categories, for the i-th category data, the number of samples is ni, and the sample set is X; = {i1,"i2, ..., in;}, the formula is as follows:
[0050] in
[0051] Compared with the prior art, the present invention has the following beneficial effects:
[0052] 1. The present invention uses automated means to complete the entire reverse invoicing process from receiving transaction information to generating electronic invoices, reducing the time and errors of manual operations and significantly improving the efficiency and accuracy of invoicing. By utilizing OCR technology and natural language processing technology, key data in transaction documents can be automatically identified and verified to ensure data accuracy and consistency, reducing human errors. By connecting to the industrial and commercial and State Administration of Taxation systems, the user's reverse invoicing amount and withholding status can be automatically checked, simplifying the qualification verification process and improving the accuracy and speed of verification. Machine learning models are used to optimize the data processing logic in the invoice generation process, improving processing efficiency and ensuring the accuracy and compliance of invoice information.
[0053] 2. The present invention synchronizes the generated electronic invoice information to the electronic invoice system of the State Taxation Bureau in real time to ensure the timeliness and legality of the invoice information. It supports the electronic management and storage of invoices, provides functions such as invoice query, printing, and downloading, and facilitates users to manage and use invoices; it is suitable for the characteristics of scrap steel transactions, optimizes all aspects of invoice generation and management, and improves the overall financial management level of the industry. BRIEF DESCRIPTION OF THE DRAWINGS
[0054] Figure 1 It is a flow chart of the reverse invoicing method of the present invention;
[0055] Figure 2 It is the work flow chart of the present invention. DETAILED DESCRIPTION
[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0057] To solve the problem of low efficiency of existing manual reverse invoicing, please refer to Figure 1-2 , this embodiment provides the following technical solutions:
[0058] An automated reverse invoicing method based on an online scrap steel trading system comprises the following steps:
[0059] S01. Data collection and preprocessing: Collect basic user information and business data of both parties to the transaction, clean and format the collected data to ensure data accuracy and consistency, extract key features from the original data, and mark and prompt the data that meets the requirements of reverse invoicing;
[0060] S02. Qualification verification and matching: Identify and verify qualification documents and parse transaction terms, match the tax registration information of both parties to the transaction, ensure the correctness of the invoicing entity, check the historical transaction records of both parties to the transaction, assess credit risks, and automatically generate qualification verification reports for review by relevant parties;
[0061] S03. Automated invoicing and optimization: The system automatically generates and reviews invoicing applications based on the user qualifications of suppliers and purchasers, clarifies the invoicing amount and invoicing account information, and automatically calculates the taxable amount and tax amount based on transaction information and qualification verification results, generating electronic invoices that meet national standards;
[0062] S04. Push to the electronic invoice platform: The approved invoice information is sent to the electronic invoice platform. The electronic invoice platform uses RPA robots and single sign-on services to complete the connection with the national golden tax system;
[0063] S05. Generate reverse invoice: The State Administration of Taxation receives the invoice information, executes the invoice instruction, and transmits the reverse invoice information back to the electronic invoice platform after the invoice is completed. The electronic invoice is pushed to the platform users. The users file tax returns through the platform based on the reverse invoice information.
[0064] The collected basic user information includes but is not limited to mobile phone number, name, ID number, address, real-name authentication status, and contract certificate information applied for through facial collection;
[0065] The collected business data includes but is not limited to business process data, business flow information, logistics information, payment information, order information, warehousing information and settlement order information;
[0066] Among them, business flow information includes but is not limited to the contracting qualifications of the buyer and seller, the reverse invoicing agreement and the electronically signed contract; logistics information includes but is not limited to delivery appointment information, driver departure information with bills, on-site photo information, logistics track, purchaser's entry photo information, heavy vehicle weighing photos and gross weight information, quality inspection photos, empty vehicle weighing photos and tare weight information, estimated dry basis information and exit photo information; payment information includes but is not limited to payment flow information and bank receipts;
[0067] The key features extracted include but are not limited to transaction amount, transaction time and transaction frequency.
[0068] The specific implementation methods of qualification verification are as follows:
[0069] Use OCR optical character recognition technology to automatically identify and verify the qualification documents provided by the seller, such as business licenses and tax registration certificates, to ensure the legitimacy and validity of the qualifications;
[0070] For users who meet the reverse invoicing qualifications, a business registration portal is provided on the platform, through which platform users can quickly complete qualification certification;
[0071] Connect with the industrial and commercial and taxation administration systems, check the user's reverse invoicing quota through the platform, and promptly indicate the business scale that can be carried out;
[0072] Connect with the industrial and commercial and State Administration of Taxation systems to obtain withholding information of recycling companies through the platform, and prevent tax risks caused by recycling companies’ failure to withhold taxes.
[0073] The implementation method of qualification matching is as follows:
[0074] Use NLP technology to analyze text information in qualification documents, extract key information, and clarify the responsibilities and obligations of both parties to the transaction;
[0075] Compare the extracted information with the backend database to verify the authenticity of the qualification information;
[0076] Use the rule engine to determine whether the seller meets the reverse invoicing conditions based on qualification information;
[0077] Use decision trees to predict the effectiveness of seller qualifications;
[0078] Identify potential abnormal qualification information through the isolation forest algorithm.
[0079] Automated invoicing and optimization include:
[0080] Automatically generate invoice information including invoice number, amount and tax number using template filling technology;
[0081] Automatically generate invoices based on settlement information and ensure the consistency of invoice data;
[0082] Use time series analysis to predict future billing needs and prepare invoices in advance;
[0083] Distribute billing tasks through minimal connections to ensure system stability and efficiency;
[0084] Use priority queues to handle urgent or important billing tasks;
[0085] Use machine learning models to optimize the data processing logic in the invoice generation process and improve processing efficiency.
[0086] The specific information pushed to the electronic ticket platform is as follows:
[0087] The generated electronic invoice information is synchronized to the electronic invoice system of the State Taxation Bureau in real time to ensure the timeliness and legality of the invoice information;
[0088] Use API interface to connect with electronic ticket platform to ensure the accuracy and timeliness of data transmission;
[0089] Monitor abnormal situations during data transmission through anomaly detection algorithms, handle transmission failures and other issues in a timely manner, and ensure data accuracy;
[0090] It supports electronic management and storage of invoices, including but not limited to invoice query, printing and downloading functions. It also supports the backup and recovery of invoice data and provides invoice status tracking function to ensure that the circulation and use of invoices can be traced.
[0091] Generate reverse invoice as follows:
[0092] Generate reverse invoicing requests based on feedback and needs from both parties of the transaction;
[0093] The State Administration of Taxation automatically processes reverse invoicing requests and generates corresponding red-letter invoices or adjustment invoices to ensure that the reverse invoicing process complies with national tax regulations and avoids tax risks, and sends them to the buyer through the electronic invoice platform;
[0094] The electronic invoice platform provides detailed records and reports of reverse invoicing, which is convenient for users to query and manage;
[0095] Use consistency checking algorithms to ensure consistency between invoice data and settlement data.
[0096] The algorithm design description is as follows:
[0097] 1. Algorithm logic
[0098] Application for invoicing qualification: Resource recycling enterprises need to submit the "Application Form for Reverse Invoicing of Resource Recycling Enterprises" to the competent tax authorities, and provide relevant qualification certificates, enterprise qualification certificates and the registration certificate of renewable resource recycling operators issued by the commerce department;
[0099] The image texture features are described by calculating the frequency of the combination of gray values of two pixels at a certain distance and direction in the image. For a given displacement vector (△x, △y), the element P(i,jAx, △y) of GLCM indicates that the feature extraction is performed when the pixel with gray value i and the pixel with gray value j at the distance (△x, △y) appear at the same time in the image.
[0100]
[0101] Character recognition: For a binary support vector machine (SVM), assume that the training sample set is {(1,y1), (2,y2), …, (n,yn)}, where i is the feature vector and 1 / 4€{-1,1} is the category label.
[0102] subject to you i (w·x i +b)≥1, i=1,2,…,n.
[0103] Online invoicing: The recycling company issues an invoice to the seller through the electronic invoice service platform, with the words "scrap product acquisition" marked on it, and selects the scrap product category code;
[0104] Invoice amount adjustment: Resource recycling enterprises can apply to the competent tax authorities to adjust the invoice amount or the maximum invoice limit and number of copies according to actual business needs;
[0105] Invoice type selection: Resource recycling enterprises can choose to issue ordinary invoices or special VAT invoices according to the VAT calculation method;
[0106] Tax declaration and payment: After the reverse invoicing is successful, the recycling company will handle the declaration of value-added tax, additional taxes and fees, and personal income tax on behalf of the seller, and submit the "Agency Tax and Fee Report Form" and "Agency Tax and Fee Detail Report Form" to the competent tax authority during the declaration period of the following month, and pay the agency taxes and fees in accordance with regulations. The data in each link adopts the blockchain encryption algorithm, cannot be tampered with, and the data is authentic and valid.
[0107] Within-class scatter matrix
[0108] Assuming C categories, for the i-th category data, the number of samples is ni, and the sample set is X; = {i1,"i2,…,in;}
[0109] in
[0110] 2. The data table is as follows:
[0111]
[0112]
[0113]
[0114] Working principle: The reverse invoicing method of the present invention is as follows: collect basic user information and business data of both parties to the transaction, clean and format the collected data, extract key features from the original data, and mark and prompt the data that meets the requirements of reverse invoicing; identify and verify qualification documents and parse transaction terms, match the tax registration information of both parties to the transaction, check the historical transaction records of both parties to the transaction, automatically generate a qualification verification report, and provide it to relevant parties for review; the system automatically generates an audited invoicing application based on the user qualifications of the supplier and the purchaser, and clarifies the invoicing amount and invoicing subject information, and automatically calculates the taxable amount and tax amount based on the transaction information and qualification verification results, and generates an electronic invoice that meets national standards; the invoicing information that has passed the review is sent to the electronic invoice platform, and the electronic invoice platform uses RPA robots and single sign-on services to complete the connection with the national golden tax system; the State Administration of Taxation receives the invoicing information, executes the invoicing instructions, and after completing the invoicing, the reverse invoicing information is transmitted back to the electronic invoice platform to form an electronic invoice and push it to the platform users, and the users make tax returns through the platform based on the invoice information of the reverse invoice.
[0115] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.
[0116] While the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that many changes, modifications, substitutions and variations can be made to the embodiments without departing from the principles and spirit of the invention.
Claims
1. An automated reverse invoicing method based on an online scrap steel trading system, characterized in that: The following steps are involved: S01. Data collection and preprocessing: Collect basic user information and business data of both parties to the transaction, clean and format the collected data, extract key features from the original data, and mark and prompt the data that meets the requirements of reverse invoicing; S02. Qualification verification and matching: Identify and verify qualification documents and parse transaction terms, match the tax registration information of both parties to the transaction, check the historical transaction records of both parties to the transaction, automatically generate a qualification verification report, and provide it to relevant parties for review; S03. Automated invoicing and optimization: The system automatically generates and reviews invoicing applications based on the user qualifications of suppliers and purchasers, clarifies the invoicing amount and invoicing account information, and automatically calculates the taxable amount and tax amount based on transaction information and qualification verification results, generating electronic invoices that meet national standards; S04. Push to the electronic invoice platform: The approved invoice information is sent to the electronic invoice platform. The electronic invoice platform uses RPA robots and single sign-on services to complete the connection with the national golden tax system; S05. Generate reverse invoice: The State Administration of Taxation receives the invoice information, executes the invoice instruction, and transmits the reverse invoice information back to the electronic invoice platform after the invoice is completed. The electronic invoice is pushed to the platform users. The users file tax returns through the platform based on the reverse invoice information.
2. The automated reverse invoicing method based on the scrap steel online trading system according to claim 1, characterized in that: Regarding S01: The collected basic user information includes but is not limited to mobile phone number, name, ID number, address, real-name authentication status, and contract certificate information applied for through facial collection; The collected business data includes but is not limited to business process data, business flow information, logistics information, payment information, order information, warehousing information and settlement order information; Among them, business flow information includes but is not limited to the contracting qualifications of the buyer and seller, the reverse invoicing agreement and the electronically signed contract; logistics information includes but is not limited to delivery appointment information, driver departure information with bills, on-site photo information, logistics track, purchaser's entry photo information, heavy vehicle weighing photos and gross weight information, quality inspection photos, empty vehicle weighing photos and tare weight information, estimated dry basis information and exit photo information; payment information includes but is not limited to payment flow information and bank receipts; The key features extracted include but are not limited to transaction amount, transaction time and transaction frequency.
3. The automated reverse invoicing method based on the scrap steel online trading system according to claim 2, characterized in that: The specific implementation method for the qualification verification described in S02 is as follows: Use OCR optical character recognition technology to automatically identify and verify the qualification documents provided by the seller; For users who meet the reverse invoicing qualifications, a business registration portal is provided on the platform, through which platform users can quickly complete qualification certification; Connect with the industrial and commercial and taxation administration systems, check the user's reverse invoicing quota through the platform, and promptly indicate the business scale that can be carried out; Connect with the industrial and commercial and State Administration of Taxation systems to obtain withholding information of recycling companies through the platform.
4. The automated reverse invoicing method based on the scrap steel online trading system according to claim 3 is characterized in that: The implementation method for the qualification matching described in S02 is as follows: Use NLP technology to analyze text information in qualification documents, extract key information, and clarify the responsibilities and obligations of both parties to the transaction; Compare the extracted information with the backend database to verify the authenticity of the qualification information; Use the rule engine to determine whether the seller meets the reverse invoicing conditions based on qualification information; Use machine learning models to predict the effectiveness of seller qualifications; Identify potentially abnormal qualification information through anomaly detection algorithms.
5. The method for automatic reverse invoicing based on the online scrap steel trading system according to claim 4, characterized in that: The specific details of automated invoicing and optimization described in S03 are as follows: Automatically generate invoice information including invoice number, amount and tax number using template filling technology; Automatically generate invoices based on settlement information and ensure the consistency of invoice data; Use predictive models to predict future billing needs and prepare invoices in advance; Distribute invoicing tasks through load balancing algorithms; Use priority scheduling algorithms to handle urgent or important invoicing tasks; Use machine learning models to optimize data processing logic in the invoice generation process.
6. The automated reverse invoicing method based on the scrap steel online trading system according to claim 5, characterized in that: The specific steps for pushing to the electronic ticket platform described in S04 are as follows: Synchronize the generated electronic invoice information to the electronic invoice system of the State Taxation Bureau in real time; Use API interface to connect with electronic ticket platform; Monitor abnormal situations during data transmission through anomaly detection algorithms and handle transmission failures and other issues in a timely manner; Supports electronic management and storage of invoices, including but not limited to invoice query, printing and downloading functions, supports backup and recovery of invoice data, and provides invoice status tracking function.
7. The method for automatic reverse invoicing based on the online scrap steel trading system according to claim 6, characterized in that: The specific steps for generating reverse invoices in S05 are as follows: Generate reverse invoicing requests based on feedback and needs from both parties of the transaction; The State Administration of Taxation automatically processes the reverse invoicing request and generates the corresponding red-letter invoice or adjustment invoice, which is then sent to the buyer via the electronic invoice platform; The electronic invoice platform provides detailed records and reports of reverse invoicing; Use consistency checking algorithms to ensure consistency between invoice data and settlement data.
8. The method for automatic reverse invoicing based on the online scrap steel trading system according to claim 7, characterized in that: The key features extracted from the original data described in S01 are as follows: The image texture features are described by calculating the frequency of the grayscale value combination of two pixels at a certain distance and direction in the image. For a given displacement vector (△x, △y), the element P(i,jAx, △y) of GLCM indicates that the feature extraction is performed when the pixel with grayscale value i and the pixel with grayscale value j at a distance of (△x, △y) appear at the same time in the image. The formula is as follows: For a binary support vector machine (SVM), assume that the training sample set is {(1,y1),(2,y2),…,(n,yn)}, where i is a feature vector, is the category label, and the formula is as follows: Assuming C categories, for the i-th category data, the number of samples is ni, and the sample set is X; = {i1,"i2, ..., in;}, the formula is as follows: in