County-level drainage basin treatment unit division method and system

Abstract

The invention discloses a county-level drainage basin treatment unit division method. The method comprises the steps of obtaining county-level drainage basin treatment unit division basic data; determining a catchment relationship according to the obtained division basic data, dividing a natural drainage basin unit and an artificial drainage basin unit, and merging and optimizing the natural drainage basin unit and the artificial drainage basin unit to obtain a preliminary county-level drainage basin treatment unit result; and checking the integrity and rationality of the preliminary result of the county-level drainage basin treatment unit, and outputting and displaying the result of the county-level drainage basin treatment unit after the checking is passed. According to the method, the problem that drainage basin treatment units are difficult to divide in a county-level research area is solved to a certain extent in a mode of judging the combination of a natural watershed and an artificial watershed; according to the method, the drainage basin treatment units are corrected by utilizing the administrative boundary, a set of technical method for dividing the county-level drainage basin treatment units is formed, and the completeness and scientificity of the county-level drainage basin treatment units are enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated watershed management, and in particular to a method and system for dividing county-level watershed management units. Background Art

[0002] In hydrology, a watershed refers to a closed topographic unit. A watershed unit is a catchment area consisting of rivers or lakes surrounded by a watershed line. Traditional watershed unit division is mainly based on digital elevation model (DEM) or topographic map data, using hydrological analysis tools, combined with hydrological data and water resource zoning data to determine the natural watershed to generate hydrological units; secondly, based on the hydrological unit, superimposed control sections, water system maps and other data, and identified the watershed unit through watershed analysis; then the generated watershed units are checked, adjusted and merged to form the final watershed unit.

[0003] Different from the traditional watershed unit, the watershed governance unit is a spatial governance unit defined on the basis of watershed unit identification and administrative governance authority. It is a county-level secondary spatial control area between the county area and the small watershed area. It coordinates the protection and utilization of resources and urban and rural construction and development within the watershed to achieve the unity of high-level protection and high-quality development. In combination with the "Small Watershed Division and Coding Specifications", a small watershed is generally an area of ​​no more than 50km 2 The watershed management unit at the county level is composed of at least two small watershed units, so the minimum area of ​​the county-level watershed management unit is set at 100km. 2 .

[0004] In terms of the method of dividing watershed management units, most existing technologies are based on software that uses DEM or topographic map data to perform hydrological analysis and then automatically extract watershed units. They mainly focus on the impact of natural watersheds such as natural catchment relationships and terrain slopes on the division of watershed units. However, there is no unified standard method for the division of watershed management units, especially for plain areas that lack natural watersheds. The division effect of watershed management units is not good, and it is impossible to better achieve coordinated development and protection within the watershed units. Summary of the invention

[0005] In view of the above problems, the present invention is proposed to provide a method and system for dividing county-level watershed management units to overcome the above problems or at least partially solve the above problems.

[0006] In order to solve the above technical problems, the embodiments of the present application disclose the following technical solutions:

[0007] In a first aspect, an embodiment of the present invention discloses a method for dividing county-level watershed management units, including:

[0008] S100. Obtain basic data on the division of county-level watershed management units;

[0009] S200. According to the obtained basic data of division, clarify the watershed relationship, divide the natural watershed unit and the artificial watershed unit respectively, merge and optimize the natural watershed unit and the artificial watershed unit, and obtain the preliminary county-level watershed management unit result;

[0010] S300. Check the integrity and rationality of the preliminary county-level watershed management unit results, and output and display the county-level watershed management unit results that have passed the inspection.

[0011] Furthermore, in S200, the watershed relationship is clarified based on the obtained division basic data, and the specific method includes: obtaining the confluence direction and watershed direction of the water system based on the obtained water system related data, and obtaining the watershed relationship based on the confluence direction and watershed direction.

[0012] Furthermore, in S200, the natural watershed units are divided according to the obtained basic data for division, and the specific method includes: using topographic data to perform hydrological analysis, extracting natural watersheds, and using the natural watersheds to divide the natural watershed units.

[0013] Furthermore, in S200, the artificial watershed units are divided according to the obtained basic data for division, and the specific method includes: according to the obtained vector data of the county transportation road network, embankments, irrigation areas, and flood storage areas, the main transportation arteries with physical roadbeds such as highways, national roads, provincial roads, and railways, as well as embankments, irrigation areas, and flood storage areas are converted into single-line layers, and each line layer is connected. The gap areas between the line layers are divided and connected according to the actual terrain to divide the artificial watershed units.

[0014] Furthermore, in S200, the natural watershed units and artificial watershed units are merged and optimized to obtain a preliminary county-level watershed management unit result. The specific method includes: according to the divided natural watershed units and natural watershed units, the natural watershed units in the hilly and mountainous terrain area and the artificial watershed units in the plain terrain area are extracted and merged. For the units whose area is smaller than the preset area, they are merged into the watershed units within the preset range according to the watershed relationship to obtain a preliminary county-level watershed management unit result.

[0015] Furthermore, in S300, the integrity and rationality of the preliminary county-level watershed management unit results are checked, and the specific methods include: checking the integrity of the watershed management unit results, conducting a topological check, and ensuring that the preliminary county-level watershed management unit division results cover the entire administrative area; checking the rationality of the watershed management unit results, and revising them in combination with township boundaries. If a township contains multiple watershed management units, the township as a whole will be included in the watershed management unit with the largest area to obtain the final watershed management unit.

[0016] In a second aspect, an embodiment of the present invention discloses a system for dividing county-level watershed governance units, including: a basic data acquisition unit, a preliminary county-level watershed governance unit result acquisition unit, and a county-level watershed governance unit result inspection unit; wherein:

[0017] Basic data acquisition unit, used to obtain basic data on the division of county-level watershed management units;

[0018] A preliminary county-level watershed management unit result acquisition unit is used to clarify the watershed relationship according to the obtained basic division data, divide the natural watershed unit and the artificial watershed unit respectively, merge and optimize the natural watershed unit and the artificial watershed unit, and obtain the preliminary county-level watershed management unit result;

[0019] The county-level watershed management unit result inspection unit is used to inspect the integrity and rationality of the preliminary county-level watershed management unit results, and output and display the county-level watershed management unit results that have passed the inspection.

[0020] In a third aspect, an embodiment of the present invention discloses an electronic device, including:

[0021] one or more processors;

[0022] A memory for storing one or more programs;

[0023] When the one or more programs are executed by the one or more processors, the one or more processors implement the method of dividing county-level watershed management units.

[0024] The beneficial effects of the above technical solution provided by the embodiment of the present invention include at least:

[0025] The present invention discloses a method for dividing county-level watershed management units, including: obtaining basic data for dividing county-level watershed management units; clarifying the watershed relationship based on the obtained basic data for division, dividing natural watershed units and artificial watershed units respectively, merging and optimizing the natural watershed units and artificial watershed units, and obtaining preliminary county-level watershed management unit results; checking the integrity and rationality of the preliminary county-level watershed management unit results, and outputting and displaying the county-level watershed management unit results that pass the inspection. The present invention solves the problem that it is difficult to divide watershed management units in county-level study areas to a certain extent by combining the judgment of natural watersheds and artificial watersheds; the present invention uses administrative boundaries to correct watershed management units, forming a set of technical methods for dividing county-level watershed management units, and enhancing the integrity and scientificity of county-level watershed management units.

[0026] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0028] Figure 1 This is a flow chart of a method for dividing county-level watershed management units in Embodiment 1 of the present invention;

[0029] Figure 2 This is a schematic diagram of determining the flow direction of a water system in Example 1 of the present invention;

[0030] Figure 3 A schematic diagram of extracting a natural watershed in Example 1 of the present invention;

[0031] Figure 4 A schematic diagram of extracting an artificial watershed in Example 1 of the present invention;

[0032] Figure 5 This is a schematic diagram of the optimization of a natural artificial watershed in Example 1 of the present invention;

[0033] Figure 6 This is a schematic diagram of the division of county-level watershed management units in Example 1 of the present invention;

[0034] Figure 7 This is a schematic diagram of the structure of an electronic device in Example 3 of the present invention. DETAILED DESCRIPTION

[0035] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0036] In order to solve the problems existing in the prior art, an embodiment of the present invention provides a method and system for dividing county-level watershed management units.

[0037] Example 1

[0038] The present invention discloses a method for dividing county-level watershed management units, such as Figure 1 ,include:

[0039] S100. Obtain the basic data for the division of county-level watershed management units; in S100 of this embodiment, the basic data for the division of county-level watershed management units includes at least the administrative boundary data of the city, county, and township levels, the water system-related data within the county, the topographic data, the traffic network data, and the vector data of embankments, irrigation areas, and flood storage areas. After obtaining these data, data integration, cleaning, and verification are required to ensure the accuracy and consistency of the data. In addition, according to the specific needs of watershed management, further processing and analysis of the data may be required.

[0040] Specifically, based on the data in the land change survey database, the administrative boundaries of the city, county, and township levels within a certain county are clarified, and the data on important topographical features, important transportation arteries, and important water conservancy projects such as the terrain, water systems, transportation networks, embankments, irrigation areas, and flood storage areas within the study area are sorted out to carry out the division of county-level watershed management units.

[0041] S200. According to the obtained basic data of division, clarify the watershed relationship, divide the natural watershed unit and the artificial watershed unit respectively, merge and optimize the natural watershed unit and the artificial watershed unit, and obtain the preliminary county-level watershed management unit result;

[0042] In S200 of this embodiment, the watershed relationship is clarified based on the obtained division basic data. The specific method includes: obtaining the watershed direction and watershed direction of the water system based on the obtained water system related data, and obtaining the watershed relationship based on the watershed direction and watershed direction. Figure 2 shown.

[0043] Specifically, the method for determining the direction of confluence and water collection includes: using the hydrological analysis module of GIS software (such as ArcGIS) to process the water system data. Determine the confluence direction of the water system through operations such as filling depressions, flow direction analysis, and flow analysis. Adopt the eight-direction (D8) flow direction modeling method, create a flow direction grid based on the flow direction from each pixel to its steepest downslope adjacent point, and each pixel in the flow direction grid has a value indicating the direction of the water flow. Based on the flow direction grid, the water collection direction of each water body (such as rivers and lakes) can be determined.

[0044] After determining the direction of confluence and watershed, the watershed is divided, and the basin analysis tool is used to divide different watershed basins according to the flow direction grid data. The watershed relationship is established, and the watershed relationship between different water bodies can be determined based on the watershed division results. The watershed relationship shown refers to the path and relationship between the upstream water body and the downstream water body.

[0045] In S200 of this embodiment, the natural watershed units are divided according to the obtained basic division data. The specific method includes: using topographic data to perform hydrological analysis, extracting natural watersheds, and using the natural watersheds to divide the natural watershed units. Figure 3 shown.

[0046] Specifically, the topographic data is used for hydrological analysis, natural watersheds are extracted, and the natural watersheds are used to divide the natural watershed units; first, the slope is calculated, and the slope value is calculated by finite difference or other algorithms based on the elevation difference of adjacent pixels of the DEM. Then the flow direction is analyzed, and the flow direction of each pixel is calculated using the DEM data to determine the path and confluence point of the water flow. Finally, the watershed line is extracted, and the flow direction information is used to gradually advance upstream to determine the boundary of each watershed. The algorithm is used to find the topographic peak, which is used as a candidate point for the watershed line, and the watershed is derived in combination with the flow direction information.

[0047] After obtaining the watershed line, the natural watershed units are divided. First, the watershed is divided. Once the natural watershed is extracted, the process of watershed division is to define the boundaries according to the watershed line of each catchment area. This can be done through the rasterization method. Using raster data, through flow analysis and watershed extraction results, a unique identifier is assigned to each watershed unit. The watershed attributes are calculated, and the divided watershed units can further calculate their related attributes, such as watershed area, watershed perimeter, average slope, water system density of the watershed, etc. These attributes are of great significance for the input of hydrological models and water resources management of watersheds. The hydrological model is applied, and the natural watershed units after division are used. Through the division of natural watershed units, the precipitation-runoff process in different regions can be simulated, and the water flow in different watersheds can be calculated. By analyzing the water resources situation in different watersheds, the water supply and demand of each watershed is evaluated, which helps to reasonably allocate water resources in the watershed.

[0048] In S200 of this embodiment, the artificial watershed units are divided according to the obtained basic division data. The specific method includes: according to the obtained county traffic road network, levee, irrigation area, flood storage area vector data, the main traffic arteries with physical roadbeds such as expressways, national roads, provincial roads, and railways, as well as levees, irrigation areas, and flood storage areas are converted into single line layers, and each line layer is connected. The gap areas between the line layers are divided and connected according to the actual terrain to divide the artificial watershed units. The schematic diagram of dividing the artificial watershed units is shown in FIG. Figure 4 shown.

[0049] In S200 of this embodiment, the natural watershed units and artificial watershed units are merged and optimized to obtain preliminary county-level watershed management unit results. The specific method includes: according to the divided natural watershed units and natural watershed units, the natural watershed units in the hilly and mountainous terrain area and the artificial watershed units in the plain terrain area are extracted and merged. For the units whose area is smaller than the preset area, they are merged into the watershed units within the preset range according to the watershed relationship, and the preliminary county-level watershed management unit results are obtained. The preset area in this embodiment is preferably 100km 2 The natural watershed units and artificial watershed units are merged and optimized as follows: Figure 5 shown.

[0050] S300. Check the integrity and rationality of the preliminary county-level watershed management unit results, and output and display the county-level watershed management unit results that have passed the inspection.

[0051] In S300 of this embodiment, the integrity and rationality of the preliminary county-level watershed management unit results are checked. The specific methods include: checking the integrity of the watershed management unit results, conducting a topological check, and ensuring that the preliminary county-level watershed management unit division results cover the entire administrative area; checking the rationality of the watershed management unit results, and revising them in combination with the boundaries of towns and villages. If a town contains multiple watershed management units, the town as a whole will be included in the watershed management unit with the largest area to obtain the final watershed management unit. The schematic diagram of the final watershed management unit is shown in FIG. Figure 6 shown.

[0052] The present embodiment discloses a method for dividing county-level watershed management units, including: obtaining basic data for dividing county-level watershed management units; clarifying the watershed relationship based on the obtained basic data for division, dividing natural watershed units and artificial watershed units respectively, merging and optimizing the natural watershed units and artificial watershed units, and obtaining preliminary county-level watershed management unit results; checking the integrity and rationality of the preliminary county-level watershed management unit results, and outputting and displaying the county-level watershed management unit results that pass the inspection. The present embodiment solves the problem that it is difficult to divide watershed management units in county-level study areas to a certain extent by combining the judgment of natural watersheds and artificial watersheds; the present invention uses administrative boundaries to correct watershed management units, forming a set of technical methods for dividing county-level watershed management units, and enhancing the integrity and scientificity of county-level watershed management units.

[0053] Example 2

[0054] Based on the same inventive concept, the embodiment of the present disclosure also provides a system for dividing county-level watershed governance units, including: a basic data acquisition unit, a preliminary county-level watershed governance unit result acquisition unit and a county-level watershed governance unit result inspection unit; wherein:

[0055] Basic data acquisition unit, used to obtain basic data on the division of county-level watershed management units;

[0056] A preliminary county-level watershed management unit result acquisition unit is used to clarify the watershed relationship according to the obtained basic division data, divide the natural watershed unit and the artificial watershed unit respectively, merge and optimize the natural watershed unit and the artificial watershed unit, and obtain the preliminary county-level watershed management unit result;

[0057] The county-level watershed management unit result inspection unit is used to inspect the integrity and rationality of the preliminary county-level watershed management unit results, and output and display the county-level watershed management unit results that have passed the inspection.

[0058] Among them, the specific working methods of the basic data acquisition unit, the preliminary county-level watershed management unit result acquisition unit and the county-level watershed management unit result inspection unit have been recorded in detail in Example 1, and will not be repeated in this embodiment.

[0059] Example 3

[0060] Based on the same inventive concept, an embodiment of the present disclosure also provides an electronic device. Figure 2 FIG. 1 is a schematic diagram of the structure of an electronic device according to an embodiment of the present disclosure. Figure 2 As shown, an embodiment of the present disclosure provides an electronic device including: one or more processors 101, a memory 102, and one or more I / O interfaces 103. The memory 102 stores one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors implement any optimization method in the above embodiments; the one or more I / O interfaces 103 are connected between the processor and the memory, and are configured to implement information interaction between the processor and the memory.

[0061] Among them, the processor 101 is a device with data processing capabilities, including but not limited to a central processing unit (CPU), etc.; the memory 102 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory (FLASH); the I / O interface (read-write interface) 103 is connected between the processor 101 and the memory 102, and can realize information interaction between the processor 101 and the memory 102, including but not limited to a data bus (Bus), etc.

[0062] In some embodiments, the processor 101 , the memory 102 , and the I / O interface 103 are connected to each other via a bus 104 , and further connected to other components of the computing device.

[0063] In some embodiments, the one or more processors 101 include a field programmable gate array.

[0064] According to an embodiment of the present disclosure, a computer-readable medium is further provided, wherein a computer program is stored on the computer-readable medium, wherein when the program is executed by a processor, the steps in any optimization method in the above-mentioned embodiment are implemented.

[0065] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of protection of the present disclosure. The attached method claims present the elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.

[0066] In the above detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that the embodiments of the claimed subject matter require more features than are clearly stated in each claim. On the contrary, as reflected in the appended claims, the invention is in a state of having less than all the features of the disclosed individual embodiments. Therefore, the appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0067] Those skilled in the art will also appreciate that the various illustrative logic blocks, modules, circuits, and algorithmic steps described in conjunction with the embodiments herein can all be implemented as electronic hardware, computer software, or a combination thereof. In order to clearly illustrate the interchangeability between hardware and software, various illustrative components, blocks, modules, circuits, and steps are generally described above around their functions. Whether such functions are implemented as hardware or software depends on specific applications and the design constraints imposed on the entire system. A skilled person can implement the described functions in an alternative manner for each specific application, but such implementation decisions should not be interpreted as departing from the scope of protection of the present disclosure.

[0068] The steps of the method or algorithm described in conjunction with the embodiments herein may be directly embodied as hardware, a software module executed by a processor, or a combination thereof. The software module may be located in a RAM memory, a flash memory, a ROM memory, an EPROM memory, an EEPROM memory, a register, a hard disk, a mobile disk, a CD-ROM, or any other form of storage medium well known in the art. An exemplary storage medium is connected to the processor so that the processor can read information from the storage medium and can write information to the storage medium. Of course, the storage medium may also be an integral part of the processor. The processor and the storage medium may be located in an ASIC. The ASIC may be located in a user terminal. Of course, the processor and the storage medium may also be present in a user terminal as discrete components.

[0069] For software implementation, the techniques described in this application can be implemented with modules (e.g., procedures, functions, etc.) that perform the functions described in this application. These software codes can be stored in a memory unit and executed by a processor. The memory unit can be implemented within the processor or outside the processor. In the latter case, it is coupled to the processor in a communication manner via various means, which are well known in the art.

[0070] The above description includes examples of one or more embodiments. Of course, it is impossible to describe all possible combinations of components or methods for the purpose of describing the above embodiments, but it should be recognized by those skilled in the art that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to cover all such changes, modifications and variations that fall within the scope of protection of the appended claims. In addition, with respect to the term "comprising" used in the specification or claims, the word is covered in a manner similar to the term "including", just as "including," is explained as a transitional word in the claims. In addition, any term "or" used in the specification of the claims is intended to mean "non-exclusive or".

Claims

1. A method for dividing county-level watershed management units, characterized in that: include: S100. Obtain basic data on the division of county-level watershed management units; S200. According to the obtained basic data of division, clarify the watershed relationship, divide the natural watershed unit and the artificial watershed unit respectively, merge and optimize the natural watershed unit and the artificial watershed unit, and obtain the preliminary county-level watershed management unit result; S300. Check the integrity and rationality of the preliminary county-level watershed management unit results, and output and display the county-level watershed management unit results that pass the inspection.

2. A method for dividing county-level watershed management units as claimed in claim 1, characterized in that: In S100, the basic data for the division of county-level watershed management units includes at least city, county, and township-level administrative boundary data, water system-related data within the county, topographic data, transportation network data, and vector data of embankments, irrigation areas, and flood storage areas.

3. A method for dividing county-level watershed management units as claimed in claim 1, characterized in that: In S200, the watershed relationship is clarified based on the obtained basic data of division, and the specific method includes: obtaining the confluence direction and watershed direction of the water system based on the obtained water system related data, and obtaining the watershed relationship based on the confluence direction and watershed direction.

4. The method for dividing county-level watershed management units according to claim 1, characterized in that: In S200, the natural watershed units are divided according to the obtained basic data for division, and the specific method includes: using topographic data to perform hydrological analysis, extracting natural watersheds, and using the natural watersheds to divide the natural watershed units.

5. The method for dividing county-level watershed management units according to claim 1, characterized in that: In S200, the artificial watershed units are divided according to the obtained basic division data. The specific method includes: according to the obtained vector data of the county transportation road network, levees, irrigation areas, and flood storage areas, the main transportation arteries with physical roadbeds such as highways, national roads, provincial roads, and railways, as well as levees, irrigation areas, and flood storage areas are converted into single-line layers, and each line layer is connected. The gap areas between the line layers are divided and connected according to the actual terrain to divide the artificial watershed units.

6. A method for dividing county-level watershed management units as claimed in claim 1, characterized in that: In S200, the natural watershed units and the artificial watershed units are merged and optimized to obtain a preliminary county-level watershed management unit result. The specific method includes: according to the divided natural watershed units and the natural watershed units, the natural watershed units in the hilly and mountainous terrain area and the artificial watershed units in the plain terrain area are extracted and merged, and for the units whose area is smaller than the preset area, they are merged into the watershed units within the preset range according to the watershed relationship to obtain a preliminary county-level watershed management unit result.

7. A method for dividing county-level watershed management units as claimed in claim 1, characterized in that: In S300, the integrity and rationality of the preliminary county-level watershed management unit results are checked. The specific methods include: checking the integrity of the watershed management unit results, conducting a topological check to ensure that the preliminary county-level watershed management unit division results cover the entire administrative area; checking the rationality of the watershed management unit results, and revising them in combination with township boundaries. If a township contains multiple watershed management units, the township as a whole will be included in the watershed management unit with the largest area to obtain the final watershed management unit.

8. A system for dividing county-level watershed management units, using any unit division method in claims 1-7, characterized in that: include: Basic data acquisition unit, preliminary county-level watershed management unit result acquisition unit and county-level watershed management unit result inspection unit; among them: Basic data acquisition unit, used to obtain basic data on the division of county-level watershed management units; A preliminary county-level watershed management unit result acquisition unit is used to clarify the watershed relationship according to the obtained basic division data, divide the natural watershed unit and the artificial watershed unit respectively, merge and optimize the natural watershed unit and the artificial watershed unit, and obtain the preliminary county-level watershed management unit result; The county-level watershed management unit result inspection unit is used to inspect the integrity and rationality of the preliminary county-level watershed management unit results, and output and display the county-level watershed management unit results that have passed the inspection.

9. An electronic device, characterized in that: include: one or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the unit division method in any one of claims 1 to 7.

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