Brand width prediction method and system for precise brand management
By applying linear regression algorithm and inverted pyramid theory in tobacco commercial companies, the problems of low efficiency of brand management and inaccurate prediction in the existing technology are solved, and more accurate and efficient brand width prediction is achieved.
Patent Information
- Application Number
- CN202411605220.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-12
- Publication Date
- 2025-02-28
AI Technical Summary
The prior art has problems such as inefficiency, untimely response and inaccurate prediction data in the precise brand management of tobacco commercial companies.
A brand width prediction method based on a linear regression algorithm is used to establish a linear regression equation through the logarithmic relationship between brand specification quantity and sales volume, and combined with the inverted pyramid theory and weighted average method, the number of brands in each category and industry is calculated.
It improves the accuracy and efficiency of brand width prediction, can respond to market changes in a timely manner, and provides more accurate brand management data.
Smart Images

Figure 00000000_0000_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of data processing and brand management, and in particular to a brand width prediction method and system for precise brand management. Background Art
[0002] At present, tobacco commercial companies do not have a theoretically complete set of precise brand management algorithms. Instead, marketers conduct empirical analysis based on historical data and historical experience. Precision brand management is an important part of precision marketing for tobacco commercial companies. The current empirical algorithms inevitably have the shortcomings of low efficiency, untimely response to changes, and inaccurate prediction data. Summary of the invention
[0003] The technical task of the present invention is to address the above shortcomings and provide a brand width prediction method and system for precise brand management, which is based on a large amount of historical data analysis and calculation to obtain results, and can effectively deal with the shortcomings of inaccurate prediction data; and convert the algorithm into actual software output, which can effectively deal with the problems of low efficiency and untimely response of precise brand prediction.
[0004] The technical solution adopted by the present invention to solve its technical problem is:
[0005] A brand width prediction method for precise brand management, which realizes brand width prediction based on linear regression algorithm, including the total number of brands, the number of brands in each category and the number of brands in each industry;
[0006] The total number of brands is calculated by setting the total number of specifications through the logarithmic relationship between the number of brand specifications and sales volume, forming a linear regression equation between the number of brand specifications and sales volume, and calculating the reasonable total number of specifications for a region throughout the year based on historical data;
[0007] The calculation of the number of brands in each category, combined with historical sales data, uses the inverted pyramid theory and weighted average method to calculate the reference value of the category width planning in each price range;
[0008] The number of each industrial brand is calculated by using a linear regression equation between the number of brand specifications and sales volume to calculate the number of each industrial sales brand in the region throughout the year.
[0009] Through the linear regression algorithm, we first fit the linear regression equation based on the historical sales and brand data, and determine the coupling coefficient. Then, we put the target sales volume of the forecast year into the equation to determine the total number of forecast sales brands in the city. Then, based on the brand data of the whole city, we use the inverted pyramid model to fit the forecast number of sales brands of each category in the city. Finally, we use the linear regression algorithm to fit the number of sales brands of each industry. The conclusion can be verified by comparing the actual sales brand data of each industry in the forecast year with the forecast number.
[0010] Furthermore, the logarithmic regression equation of the total number of brands, the number of brand specifications and sales volume is as follows:
[0011] Y=a×lnX+b
[0012] Among them: Y is the total sales volume of each year, X is the total number of specifications on sale in each year, and a and b are the correction amounts calculated by the system.
[0013] Furthermore, the process of calculating the total number of brands and the total number of reasonable specifications for a region throughout the year is as follows:
[0014] 1) Collect historical data of a city for a specified number of years, including historical sales volume and number of specifications on sale;
[0015] 2) drawing a scatter plot based on the historical data;
[0016] 3) Draw a trend line and fit a logarithmic function to obtain correction values a and b;
[0017] 4) Set the sales target and enter it into the formula to obtain the reasonable total number of specifications.
[0018] Furthermore, the calculation of the number of brands in each category specifically includes:
[0019] Category classification setting: classify cigarettes into categories according to their prices;
[0020] The inverted pyramid category coefficient is maintained, and the category distribution structure is an "inverted pyramid" shape in which the category width decreases as the price decreases;
[0021] Calculate the average sales share of each category;
[0022] Calculate the comprehensive coefficient of width of each category;
[0023] Calculate the reference value of width for each category.
[0024] Furthermore, the formula for calculating the comprehensive coefficient of width of each category is as follows:
[0025] The comprehensive coefficient of the width of each category = weight 1 × inverted pyramid theory category coefficient + weight 2 × average sales share.
[0026] Furthermore, the comprehensive coefficient of the width of each category is multiplied by the planned value of the total number of specifications in a specified year, and the result is rounded off to the nearest integer to obtain the reference value of the width planning of each category in that year.
[0027] Furthermore, the calculation of the number of industrial brands includes:
[0028] 1) Collect historical data of each industry in the region for a specified number of years, including historical sales volume and number of specifications on sale;
[0029] 2) Draw a trend line based on the historical data and fit a logarithmic function to obtain correction values a and b;
[0030] 3) Set the sales target and enter it into the formula to obtain a reasonable total number of specifications.
[0031] The present invention also claims a brand width prediction system for accurate brand management, comprising:
[0032] The module for calculating the total number of brands is used to set the total number of specifications through the logarithmic relationship between the number of brand specifications and sales volume, form a logarithmic regression equation between the number of brand specifications and sales volume, and calculate the reasonable total number of specifications planned for a region throughout the year based on historical data;
[0033] The module for calculating the number of brands in each category is used to combine historical sales data, apply the inverted pyramid theory and weighted average method to calculate the reference value for the planning of the category width in each price zone;
[0034] The module for calculating the number of brands in each industry is used to calculate the number of sales brands of each industry in the region throughout the year through the model;
[0035] The system specifically implements brand width prediction through the brand width prediction method of precise brand management mentioned above.
[0036] The present invention also claims a brand width prediction device for accurate brand management, comprising: at least one memory and at least one processor;
[0037] The at least one memory is used to store a machine-readable program;
[0038] The at least one processor is used to call the machine-readable program to implement the above method.
[0039] The present invention also claims protection for a computer-readable medium having computer instructions stored thereon, which can implement the above method when executed by a processor.
[0040] Compared with the prior art, the brand width prediction method and system for precise brand management of the present invention has the following beneficial effects:
[0041] The present invention uses a linear regression algorithm to first fit a linear regression equation based on historical sales and brand data, and determine the coupling coefficient, then bring the target sales in the forecast year into the equation to determine the total forecast sales brand number of the city. Then, based on the brand data of the city, an inverted pyramid model is used to fit the forecast number of sales brands of each category in the city. Finally, the linear regression algorithm is used to fit the sales brand number of each industry. The conclusion can be verified by comparing the actual sales brand data of each industry in the forecast year with the forecast number.
[0042] In response to the shortcomings of existing empirical algorithms, 1. The calculation results of this method are based on a large amount of historical data analysis and calculation, which can effectively deal with the shortcomings of inaccurate prediction data; 2. Converting the algorithm into actual software output can effectively deal with the problems of low efficiency and untimely response in accurate brand prediction. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] Figure 1 It is a flowchart of a brand width prediction method for precise brand management provided by an embodiment of the present invention;
[0044] Figure 2 This is an example diagram of a scatter plot diagram for calculating the total number of brands provided by an embodiment of the present invention;
[0045] Figure 3 This is an example diagram of calculating and drawing a trend line for the total number of brands provided by an embodiment of the present invention;
[0046] Figure 4 This is an example diagram of category division settings for calculating the number of brands in each category provided by an embodiment of the present invention;
[0047] Figure 5 This is an example diagram of calculating and drawing trend lines for the number of industrial brands provided by an embodiment of the present invention;
[0048] Figure 6 This is an example of calculating and drawing trend lines for the number of industrial brands provided by an embodiment of the present invention. Figure II ;
[0049] Figure 7 This is an example of calculating and drawing trend lines for the number of industrial brands provided by an embodiment of the present invention. Figure III ;
[0050] Figure 8 This is an example of calculating and drawing trend lines for the number of industrial brands provided by an embodiment of the present invention. Figure IV ;
[0051] Fig. 9 This is an example diagram of conclusion verification statistical data provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0052] The present invention will be further described below in conjunction with specific embodiments.
[0053] The embodiment of the present invention provides a brand width prediction method for precise brand management, which is applied to the precise brand management of the tobacco sales industry, and realizes brand width prediction based on a linear regression algorithm, including the calculation of the total number of brands, the calculation of the number of brands in each category, and the calculation of the number of brands in each industry, such as Figure 1 The following is the algorithm workflow diagram.
[0054] 1. Calculation of the total number of brands.
[0055] The total number of specifications for a certain city throughout the year is calculated through the model.
[0056] (1) Planning method for total number of specifications on sale:
[0057] The number of brand specifications and sales volume are in a logarithmic relationship. The total number of specifications is set based on the logarithmic relationship between the number of brand specifications and sales volume. When sales volume is low, increasing the number of brand specifications has a greater impact on sales volume; when sales volume reaches a certain level, increasing the number of brand specifications has a smaller impact on sales volume. Therefore, the formula between the number of specifications and sales volume is as follows:
[0058] Y=a×lnX+b
[0059] Among them: Y is the total sales volume of each year, X is the total number of specifications on sale in each year (excluding foreign cigarettes and cigars), and a and b are the correction amounts calculated by the system.
[0060] (2) The calculation steps are as follows:
[0061] a. Collect historical data of a city over the past few years,
[0062] The historical sales volume and the number of specifications on sale (excluding foreign cigarettes and cigars) of the city in the past five years are summarized as shown in Table 1-1 below:
[0063] Table 1-1
[0064] year Specifications (pcs) Total sales (boxes) 2015 160 255652 2016 143 241966 2017 147 247145 2018 160 250722 2019 166 250651 .
[0065] b. Select the data and draw a scatter plot, such as Figure 2 shown.
[0066] c. Draw a trend line and fit a logarithmic function, such as Figure 3 shown.
[0067] Depend on Figure 3 The logarithmic regression equation is y=63700ln(x)-72092, where y is the sales volume, x is the number of specifications, a=63700, and b=-72092.
[0068] d. Set the sales target and enter it into the formula to obtain the reasonable total number of specifications:
[0069] Substitute the sales target of 250,300 boxes for the city in 2020 into the formula y=63700ln(x)-72092, and round off to the nearest integer to obtain the planned total number of reasonable specifications for the city in 2020, x=158.
[0070] 2. Calculation of the number of brands in each category.
[0071] Combined with historical sales data, the inverted pyramid theory and weighted average method are used to calculate the reference value for category width planning in each price range.
[0072] (1) Category classification settings:
[0073] Cigarette categories are divided according to cigarette prices. From the perspective of consumer demand differences, the higher the consumption level, the more diverse the consumer demand for cigarettes. Conversely, the lower the consumption level, the less diverse the consumer demand for cigarettes. Figure 4 Example shown.
[0074] (2) “Inverted Pyramid” Category Coefficient Maintenance:
[0075] A reasonable category distribution structure should be an "inverted pyramid" shape in which the category width decreases as the price decreases. Based on the above "inverted pyramid" theory, the proportion of cigarette specifications in each category is shown in Table 2-1 below, and the coefficient supports flexible setting:
[0076] Table 2-1
[0077]
[0078] (3) Calculation steps:
[0079] a. Calculate the average sales share of each category,
[0080] Based on the data from the past five years, the average sales share of each category is calculated as shown in Table 2-2 below:
[0081] Table 2-2
[0082] Category Price range 2015 2016 2017 2018 2019 average First Category [600,1000) 1.25% 0.90% 1.03% 1.44% 0.91% 1.11% Second Category [400,600) 9.70% 7.41% 7.98% 8.46% 7.40% 8.19% The third category [290,400) 9.16% 4.43% 4.67% 4.64% 4.43% 5.47% The fourth category [210,290) 1.08% 1.52% 2.53% 3.71% 1.53% 2.07% Fifth Category [180,210) 17.01% 15.28% 15.98% 15.60% 17.21% 16.22% The sixth category [158,180) 0.55% 2.40% 0.58% 0.91% 0.47% 0.98% Seventh Category [135,158) 2.54% 3.17% 4.67% 5.63% 3.20% 3.84% Category 8 [110,135) 6.76% 6.53% 7.59% 8.46% 6.56% 7.18% Ninth category [80,110) 23.14% 27.49% 26.10% 25.66% 27.48% 25.97% Category 10 [55,80) 17.47% 20.86% 19.89% 18.34% 18.96% 19.10% Category 11 [0,55) 11.26% 10.01% 8.98% 7.16% 11.86% 9.87%
[0083] b. Calculate the comprehensive coefficient of width of each category,
[0084] According to the formula: Comprehensive coefficient of each category width = weight 1 × "inverted pyramid" theory category coefficient + weight 2 × average sales share, calculate the comprehensive coefficient of each category width. Take weight 1 set to 80% and weight 2 set to 20% as an example, see Table 2-3 below:
[0085] Table 2-3
[0086] Category Price range "Inverted Pyramid" Theory Category Coefficient Average sales share Category width comprehensive coefficient First Category [600,1000) 14% 1.11% 11.42% Second Category [400,600) 13% 8.19% 11.08% The third category [290,400) 12% 5.47% 9.39% The fourth category [210,290) 11% 2.07% 7.43% Fifth Category [180,210) 10% 16.22% 12.49% The sixth category [158,180) 9% 0.98% 5.79% Seventh Category [135,158) 8% 3.84% 6.34% Category 8 [110,135) 7% 7.18% 7.07% Ninth category [80,110) 6% 25.97% 13.99% Category 10 [55,80) 5% 19.10% 10.64% Category 11 [0,55) 2% 9.87% 5.15%
[0087] c. Calculate the reference value of width for each category,
[0088] Multiply the comprehensive coefficient of the width of each category by the planned total number of specifications in 2020, 159, and round it off to get the reference value of the width planning of each category in 2020 (excluding foreign cigarettes and cigars), as shown in Table 2-4:
[0089] Table 2-4
[0090]
[0091] 3. Calculation of the number of brands in each industry.
[0092] The model is used to calculate the number of industrial sales brands in a certain city throughout the year.
[0093] The calculation steps are as follows:
[0094] a. Collect historical data of various industries in a certain city over the past few years,
[0095] The historical sales volume and the number of specifications on sale (excluding foreign cigarettes and cigars) of a certain industry in this city over the past five years are summarized as shown in the following Table 3-1:
[0096] Table 3-1
[0097] year Specifications (pcs) Total sales (boxes) 2015 1 52.532 2016 2 133.784 2017 2 101.696 2018 3 246.044 2019 5 150 .
[0098] b. Draw a trend line and fit a logarithmic function, such as Figure 5 shown.
[0099] Depend on Figure 5 The logarithmic regression equation is y=163.03ln(x)+32.234, where y is the sales volume, x is the number of specifications, a=163.03, and b=32.234.
[0100] d. Set the sales target and enter it into the formula to obtain the reasonable total number of specifications.
[0101] Substitute the 2020 industrial sales target of 354 boxes for this city into the formula y=163.03ln(x)+32.234, and round it off to get the 2020 reasonable total planning value of specifications for this city x=7.
[0102] Through the linear regression algorithm, we first fit the linear regression equation based on the historical sales and brand data, and determine the coupling coefficient. Then, we put the target sales volume of the forecast year into the equation to determine the total forecast sales brand number of the city. Then, based on the brand data of the whole city, we use the inverted pyramid model to fit the forecast number of sales brands of each category in the city. Finally, we use the linear regression algorithm to fit the sales brand number of each industry. The conclusion can be verified by comparing the actual sales brand data of each industry in the forecast year with the forecast number. Fig. 9 Statistics shown: Accuracy = 1-error / measured value.
[0103] By integrating the linear regression algorithm described in the above method into the software system, it can help users predict sales brand data.
[0104] An embodiment of the present invention further provides a brand width prediction system for precise brand management, which specifically implements brand width prediction through the brand width prediction method for precise brand management described in the above embodiment.
[0105] The system includes:
[0106] 1. The module for calculating the total number of brands is used to set the total number of specifications through the logarithmic relationship between the number of brand specifications and sales volume, form a logarithmic regression equation between the number of brand specifications and sales volume, and calculate the reasonable total number of specifications planned for a region throughout the year based on historical data.
[0107] The logarithmic regression equation of brand specification quantity and sales volume is as follows:
[0108] Y=a×lnX+b
[0109] Among them: Y is the total sales volume of each year, X is the total number of specifications on sale in each year, and a and b are the correction amounts calculated by the system.
[0110] The process of calculating the total number of brands and the total number of reasonable specifications for a region throughout the year is as follows:
[0111] (1) Collect historical data of a city for a specified number of years, including historical sales volume and number of specifications on sale;
[0112] (2) drawing a scatter plot based on the historical data;
[0113] (3) Draw a trend line and fit a logarithmic function to obtain correction values a and b;
[0114] (4) Set the sales target and substitute it into the formula to obtain the reasonable total number of specifications.
[0115] 2. The module for calculating the number of brands in each category is used to combine historical sales data, apply the inverted pyramid theory and weighted average method to calculate the reference value for the planning of the category width in each price range. Including:
[0116] (1) Category classification: Cigarette categories are classified according to cigarette prices;
[0117] (2) Inverted pyramid category coefficient maintenance: the category distribution structure is an “inverted pyramid” shape where the category width decreases as the price decreases;
[0118] (3) Calculation:
[0119] a. Calculate the average sales share of each category;
[0120] b. Calculate the comprehensive coefficient of width of each category:
[0121] The comprehensive coefficient of the width of each category = weight 1 × inverted pyramid theory category coefficient + weight 2 × average sales share.
[0122] c. Calculate the reference value of width for each category:
[0123] Multiply the comprehensive coefficient of the width of each category by the planned value of the total number of specifications in a specified year, and round it off to the nearest integer to obtain the reference value of the width planning of each category in that year.
[0124] 3. The module for calculating the number of industrial brands is used to calculate the number of industrial sales brands in the region throughout the year through the model. It includes:
[0125] (1) Collect historical data of each industry in the region for a specified number of years, including historical sales volume and number of specifications on sale;
[0126] (2) drawing a trend line based on the historical data and fitting a logarithmic function to obtain correction values a and b;
[0127] (3) Set the sales target and substitute it into the formula to obtain the reasonable total number of specifications.
[0128] By collecting historical data of a city in the past five years in the forecast year and drawing scatter plots and linear fitting, we can derive the linear fitting formula for the sales volume and brand data of the city, such as Figure 2 and Figure 3 shown.
[0129] The linear fit can be obtained by statistically analyzing the historical data of multiple industrial companies in a certain city in the past five years, as follows Figure 5-Figure 8 Shown are the fitted data for four industries.
[0130] An embodiment of the present invention further provides a brand width prediction device for accurate brand management, comprising: at least one memory and at least one processor;
[0131] The at least one memory is used to store a machine-readable program;
[0132] The at least one processor is used to call the machine-readable program to implement the brand width prediction method for precise brand management described in the above embodiment.
[0133] The embodiment of the present invention further provides a computer-readable medium, on which computer instructions are stored, and when the computer instructions are executed by a processor, the processor executes the brand width prediction method for precise brand management described in the above embodiment. Specifically, a system or device equipped with a storage medium can be provided, on which software program codes for implementing the functions of any of the above embodiments are stored, and a computer (or CPU or MPU) of the system or device reads and executes the program code stored in the storage medium.
[0134] In this case, the program code itself read from the storage medium can realize the function of any one of the above-mentioned embodiments, and thus the program code and the storage medium storing the program code constitute a part of the present invention.
[0135] The storage medium embodiments for providing the program code include a floppy disk, a hard disk, a magneto-optical disk, an optical disk (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), a magnetic tape, a non-volatile memory card, and a ROM. Alternatively, the program code can be downloaded from a server computer by a communication network.
[0136] In addition, it should be clear that the functions of any of the above embodiments can be implemented not only by executing the program code read by the computer, but also by enabling an operating system operating on the computer to complete part or all of the actual operations based on instructions from the program code.
[0137] In addition, it can be understood that the program code read from the storage medium is written to a memory provided in an expansion board inserted into the computer or written to a memory provided in an expansion unit connected to the computer, and then based on the instructions of the program code, a CPU installed on the expansion board or the expansion unit is enabled to perform part or all of the actual operations, thereby realizing the functions of any of the above-mentioned embodiments.
[0138] The present invention is shown and described in detail above through the accompanying drawings and preferred embodiments. However, the present invention is not limited to these disclosed embodiments. Based on the above multiple embodiments, those skilled in the art can know that the code review methods in the above different embodiments can be combined to obtain more embodiments of the present invention, and these embodiments are also within the protection scope of the present invention.
Claims
1. A brand width prediction method for precise brand management, characterized in that: Brand breadth prediction is achieved based on linear regression algorithm, including the total number of brands, the number of brands in each category and the number of brands in each industry; The total number of brands is calculated by setting the total number of specifications through the logarithmic relationship between the number of brand specifications and sales volume, forming a linear regression equation between the number of brand specifications and sales volume, and calculating the reasonable total number of specifications for a region throughout the year based on historical data; The calculation of the number of brands in each category, combined with historical sales data, uses the inverted pyramid theory and weighted average method to calculate the reference value of the category width planning in each price range; The number of each industrial brand is calculated by using a linear regression equation between the number of brand specifications and sales volume to calculate the number of each industrial sales brand in the region throughout the year.
2. The brand width prediction method for precise brand management according to claim 1, characterized in that: The logarithmic regression equation for the total number of brands, brand specifications and sales volume is as follows: Y=a×lnX+b Among them: Y is the total sales volume of each year, X is the total number of specifications on sale in each year, and a and b are the correction amounts calculated by the system.
3. The brand width prediction method for accurate brand management according to claim 2, characterized in that: The process of calculating the total number of brands and the total number of reasonable specifications for a region throughout the year is as follows: 1) Collect historical data of a city for a specified number of years, including historical sales volume and number of specifications on sale; 2) drawing a scatter plot based on the historical data; 3) Draw a trend line and fit a logarithmic function to obtain correction values a and b; 4) Set the sales target and enter it into the formula to obtain the reasonable total number of specifications.
4. The brand width prediction method for precise brand management according to claim 1, characterized in that: The calculation of the number of brands in each category specifically includes: Category classification setting: classify cigarettes into categories according to their prices; Inverted pyramid category coefficient maintenance, the category distribution structure is an "inverted pyramid" type as the category width decreases with the price; Calculate the average sales share of each category; Calculate the comprehensive coefficient of width of each category; Calculate the reference value of width for each category.
5. The brand width prediction method for accurate brand management according to claim 4, characterized in that: The formula for calculating the comprehensive coefficient of width of each category is as follows: The comprehensive coefficient of the width of each category = weight 1 × inverted pyramid theory category coefficient + weight 2 × average sales share.
6. A brand width prediction method for precise brand management according to claim 4 or 5, characterized in that: Multiply the comprehensive coefficient of the width of each category by the planned value of the total number of specifications in a specified year, and round it off to the nearest integer to obtain the reference value of the width planning of each category in that year.
7. The brand width prediction method for accurate brand management according to claim 2, characterized in that: The calculation of the number of industrial brands includes: 1) Collect historical data of each industry in the region for a specified number of years, including historical sales volume and number of specifications on sale; 2) Draw a trend line based on the historical data and fit a logarithmic function to obtain correction values a and b; 3) Set the sales target and enter it into the formula to obtain a reasonable total number of specifications.
8. A brand width prediction system for precise brand management, characterized in that: include: The module for calculating the total number of brands is used to set the total number of specifications through the logarithmic relationship between the number of brand specifications and sales volume, form a logarithmic regression equation between the number of brand specifications and sales volume, and calculate the reasonable total number of specifications planned for a region throughout the year based on historical data; The module for calculating the number of brands in each category is used to combine historical sales data, apply the inverted pyramid theory and weighted average method to calculate the reference value for the planning of the category width in each price zone; The module for calculating the number of brands in each industry is used to calculate the number of sales brands of each industry in the region throughout the year through the model; The system specifically implements brand width prediction through the brand width prediction method for precise brand management as described in any one of claims 1 to 7.
9. A brand width prediction device for precise brand management, characterized in that: include: at least one memory and at least one processor; The at least one memory is used to store a machine-readable program; The at least one processor is used to call the machine-readable program to implement the method described in any one of claims 1 to 7.
10. A computer-readable medium, characterized in that The computer readable medium stores computer instructions, which, when executed by a processor, can implement the method described in any one of claims 1 to 7.