A kind of industrial chain supply chain resilience index calculation method for engineering machinery field

Abstract

The application provides an engineering machinery field-oriented industry chain supply chain resilience index calculation method, and belongs to the technical field of supply chain resilience index evaluation, and comprises the following steps: based on historical demand and supply data, a continuous demand increase fluctuation period is identified through threshold analysis; for each fluctuation period, quantitative evaluation is carried out from two dimensions of delivery guarantee and capacity elasticity; on one hand, a delivery index is calculated by combining a total amount delivery ratio and a time coincidence degree to measure an instant response capability; on the other hand, a production increase resistance index is calculated by fitting an actual production growth curve and comparing it with a target growth rate based on total production to evaluate production capacity climbing potential. Finally, the supply chain resilience index is calculated by comprehensively considering the two indexes of all fluctuation periods, weighted and adjusted for stability. The index can effectively quantify the comprehensive adjustment and adaptation capability of the supply chain when facing demand shocks.

Description

Technical Field

[0001] This invention relates to the field of supply chain resilience index assessment technology, specifically to a method and system for calculating the supply chain resilience index for the engineering machinery industry. Background Technology

[0002] Supply chain resilience is defined as the ability of a system to recover to its original state or evolve towards a more ideal state after being disrupted; that is, whether it possesses inherent stability, dynamic adaptability, and the ability to guarantee basic functions under extreme conditions. Assessing supply chain resilience helps upstream and downstream enterprises in the supply chain to rationally optimize products based on the supply chain, and to adjust production volume and production lines in a timely manner, thereby improving supply chain stability while enhancing their own profitability and competitiveness.

[0003] In the construction machinery sector, changes in demand for construction machinery products within a certain number of years of production can disrupt and impact the supply chain. Demand shocks better demonstrate the dynamic adaptability of the supply chain system to smooth fluctuations and maintain efficiency by flexibly adjusting production capacity, inventory, and procurement rhythm. In this sector, there is a lack of assessment methods that can quantify the adaptability of the supply chain in the face of demand shocks. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a method for calculating the supply chain resilience index in the engineering machinery industry. This method proposes a novel assessment approach for the supply chain resilience index, which effectively reflects the supply chain's self-adjustment capability in the face of demand shocks.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for calculating the resilience index of the industrial chain and supply chain in the construction machinery industry includes the following steps: Obtain historical demand data for the target construction machinery products to be evaluated, as well as historical supply data for the target products from each supplier in the supply chain; Based on historical demand data and statistics of supply time periods corresponding to various supply demands, the demand in each supply time period is determined; based on the demand in multiple consecutive supply time periods and a preset demand change threshold, continuous time analysis is performed to extract multiple consecutive supply time periods of demand increase fluctuation, thus forming multiple demand increase fluctuation time periods. Total supply and demand are determined based on all supply and demand items within the period of increased demand fluctuations in historical demand data; daily production and total production are determined based on historical supply data within the period of increased demand fluctuations. Determine the delivery ratio and quantify delivery indicators based on the total production and total supply-demand during periods of increased demand fluctuations. The daily production growth curve is determined based on the daily production volume to obtain the daily production growth rate. The daily production target growth rate is determined based on the first day's production volume and the total production volume. The production increase and pressure resistance index is determined based on the daily production growth rate and the daily production target growth rate. The supply chain resilience index is determined by adding delivery metrics and production resilience metrics for periods of increased demand fluctuation.

[0006] Preferably, the extraction of demand increase fluctuations across multiple consecutive supply periods constitutes multiple demand increase fluctuation periods, including the following steps: Preset basic supply time period length T For each supply period, the quantities of all demanded items within that period are summed to obtain the demand for that period. : ; In the formula, The total number of time windows. For the required date, The quantity of demand corresponding to the demand date; Obtain the rate of change in demand over consecutive time periods Determine demand fluctuations: ; Set demand growth threshold ,when At that time, mark the first The +1 time window marks the starting point for potential demand growth fluctuations; Starting from each starting point, iterate backwards. If the subsequent m consecutive (e.g.) (Preset) Demand change rate over a time period All are greater than the sustained growth threshold If it is, then growth is considered to be continuous; when encountering At that time, the fluctuation period ends; The consecutive time periods that meet the conditions are merged to form a set of time periods with fluctuating demand increases, totaling M time periods: ; in, , For the start date of the demand, This is the last required date.

[0007] Preferably, determining the daily production volume and total production volume during periods of increased demand fluctuation based on historical supply data includes the following steps: Add a fluctuation period to each identified demand. By summing up the demand for all original demand items during this period, we can obtain the total supply and demand for this period of fluctuation: ; In the formula, The quantity of demand corresponding to the demand date; For the start date of the demand, The last required date; Obtain the daily production volume of suppliers for the corresponding time period. From the daily production volume, summarize the actual production quantity of each supplier for the target product during the period of increased demand fluctuation, and obtain the total production volume for that fluctuation period.

[0008] Preferably, the step of determining the delivery ratio and quantifying delivery indicators based on the total production and total supply demand during the demand fluctuation period includes the following steps: For each period of increased demand, calculate the ratio of total production to total supply demand, using this ratio as the baseline delivery ratio. ; The closer the value is to 1, the better the supply delivery capacity matches the demand growth; Considering the degree of matching between the temporal distribution of production and the urgency of demand, the daily production volume is calculated to meet the cumulative demand during periods of increased demand fluctuations, thus defining the time fit degree. : ; In the formula, For delivery efficiency.

[0009] Based on the basic delivery ratio and time fit, a comprehensive delivery index is obtained. : ; In the formula, These are the weight parameters.

[0010] Preferably, determining the production increase and stress resistance index based on the daily production growth rate and the daily production target growth rate includes the following steps: For the daily production volume sequence of each demand growth fluctuation period, an exponential growth model is used for fitting, and the result is obtained by solving the least squares method: ; In the formula, To fit the obtained daily production growth rate, This represents the actual growth rate. Set the target as the first day's output Initially, it grows at a constant rate, with a fluctuation period of [duration missing]. Total production reached within days: ; In the formula, The ultimate target growth rate; The final target growth rate is obtained by solving the formula for total production. ; By comparing the actual growth rate with the target growth rate, a production increase and stress resistance index is defined. for: ; Among them, a production increase and stress resistance index greater than 1 indicates that the actual production increase rate exceeds the target and the stress resistance is strong; less than 1 indicates that the production increase is weak and there is a risk of capacity bottleneck.

[0011] This invention also provides a system for calculating the resilience index of the industrial chain and supply chain in the field of construction machinery, the system comprising: The historical data analysis module is used to obtain historical demand data for the target engineering machinery products to be evaluated, as well as historical supply data for the target products from various suppliers in the supply chain. The fluctuation period analysis module is used to determine the demand in each supply period based on historical demand data and the supply period statistics corresponding to each supply demand; and to perform continuous time analysis based on the demand in multiple consecutive supply periods and a preset demand change threshold to extract multiple consecutive supply periods of demand increase fluctuation, thus forming multiple demand increase fluctuation periods. The demand and production analysis module is used to determine total supply and demand based on all supply and demand items during periods of increased demand fluctuations in historical demand data; and to determine daily production and total production during periods of increased demand fluctuations based on historical supply data. The delivery metrics analysis module is used to determine the delivery ratio and quantify delivery metrics based on the total production and total supply demand during periods of increased demand fluctuation. The production increase and stress resistance index analysis module is used to determine the daily production growth curve based on the daily production volume, obtain the daily production growth rate, determine the daily production target growth rate based on the first day's production volume and the total production volume, and determine the production increase and stress resistance index based on the daily production growth rate and the daily production target growth rate. The supply chain resilience index generation module is used to determine the supply chain resilience index by adding delivery indicators and production increase and stress resistance indicators for all demand fluctuation periods.

[0012] The present invention also proposes a computer-readable storage medium storing a data processing program, which, when executed by a processor, implements the aforementioned method for calculating the industrial chain and supply chain resilience index for the engineering machinery field.

[0013] The beneficial effects of this invention are: This invention proposes a method for calculating the resilience index of the industrial chain and supply chain in the engineering machinery field. This method, through the construction of a systematic data modeling and analysis process, aims to objectively quantify the complex response behavior of the supply chain in the face of surges in demand into a comprehensive resilience index, thereby providing accurate data-driven decision support for supply chain risk management. The method employs a continuous time window analysis algorithm based on threshold judgment to automatically identify typical periods of demand increase fluctuations from historical data. For each fluctuation period, the solution evaluates from two key dimensions: first, by combining the total delivery ratio and time fit as a comprehensive delivery indicator, the immediate response and delivery guarantee capabilities of the supply chain are quantified; second, by fitting the actual production growth curve and comparing it with the theoretical target rate, a production increase stress resistance indicator is calculated, quantifying the supply chain's capacity elasticity and ramp-up potential. This method calculates the final supply chain resilience index by normalizing, weighting, and synthesizing the above two indicators for all fluctuation periods, effectively quantifying the supply chain's self-adjustment ability in the face of demand shocks. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0015] Figure 2 This is a flowchart illustrating the process of obtaining the fluctuation time period required by an embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0017] Example 1 This embodiment proposes a method for calculating the resilience index of the industrial chain and supply chain in the construction machinery field. The specific steps are as follows: Figure 1 As shown, it includes: S1: Obtain historical demand data for the target construction machinery product to be evaluated, as well as historical supply data for the target product from each supplier in the supply chain.

[0018] S2: Based on historical demand data and statistics of supply time periods corresponding to various supply demands, determine the demand in each supply time period; based on the demand in multiple consecutive supply time periods and a preset demand change threshold, perform continuous time analysis to extract multiple consecutive supply time periods of demand increase fluctuation, thus forming multiple demand increase fluctuation time periods.

[0019] S3: Determine total supply and demand based on all supply and demand items within the period of increased demand fluctuation in historical demand data; determine daily production and total production within the period of increased demand fluctuation based on historical supply data.

[0020] S4: Determine the delivery ratio based on the total production and total supply-demand during the period of increased demand fluctuations, and quantify the delivery indicators.

[0021] S5: Determine the daily production growth curve based on the daily production volume to obtain the daily production growth rate; determine the daily production target growth rate based on the first day's production volume and the total production volume; determine the production increase and pressure resistance index based on the daily production growth rate and the daily production target growth rate.

[0022] S6: Determine the supply chain resilience index by adding delivery indicators and production increase and stress resistance indicators for all demand fluctuation periods.

[0023] In this embodiment, the historical demand data of the engineering machinery target product in S1 and the historical supply data of each supplier in the supply chain on the target product are provided by the suppliers in the supply chain. The purpose is to obtain a coherent structured data pool that can be used for time series analysis, so as to build a data foundation for subsequent fluctuation identification.

[0024] The demand for S2 increases the method for extracting fluctuation time periods, specifically as follows: Figure 2 As shown, the specific steps include: S2.1: Preset basic supply time period length T For each supply period, the quantities of all demanded items within that period are summed to obtain the demand for that period. : ; In the formula, The total number of time windows. For the required date, This refers to the quantity of demand generated corresponding to the demand date.

[0025] S2.2: Obtain the rate of change in demand over consecutive time periods Determine demand fluctuations: ; S2.3: Set a demand growth threshold (e.g., 20%), when At that time, mark the first The +1 time window marks the starting point for potential demand growth fluctuations.

[0026] S2.4: Starting from each initial point, traverse backwards. If the subsequent m consecutive (e.g.) (Preset) Demand change rate over a time period All are greater than the sustained growth threshold (e.g., 5%), then growth is considered sustained. When encountering At that time, the period of fluctuation ends.

[0027] S2.5: Merge consecutive time periods that meet the conditions to form a set of time periods with fluctuating demand increases, totaling M time periods: ; in, , For the start date of the demand, This is the last required date.

[0028] In the overall solution, identifying periods of increased demand fluctuations is not simply a matter of data segmentation. Instead, it involves proactively filtering out stress test windows from continuous time series using a pre-set threshold algorithm to pinpoint the actual pressure the supply chain can withstand. This step represents a crucial shift from a stable operational baseline to an abnormal shock scenario, ensuring that all subsequent quantitative assessments (delivery assurance and capacity resilience) are precisely focused on the most vulnerable moments in the supply chain. Therefore, it determines the representativeness and specificity of the assessment: calculating indicators only within these identified periods of fluctuation effectively filters out daily operational noise, directly revealing the supply chain's response weaknesses and resilience limits in the face of a surge in certain demand. This provides accurate, comparable, and high-value analytical scenarios for subsequent index synthesis and root cause analysis.

[0029] Furthermore, in S3: S3.1: Add a fluctuation period to each identified demand. By summing up the demand for all original demand items during this period, we can obtain the total supply and demand for this period of fluctuation: ; In the formula, The quantity of demand corresponding to the demand date; For the start date of the demand, This is the last required date.

[0030] S3.2: Obtain the daily production volume of suppliers for the corresponding time period. From the daily production volume, summarize the actual production quantity completed by each supplier for the target product during the period of increased demand fluctuation, and obtain the total production volume for that fluctuation period.

[0031] Furthermore, in S4: S4.1: For each period of increased demand, calculate the ratio of total production to total supply demand as the basic delivery ratio. . The closer the value is to 1, the better the supply delivery capacity matches the demand growth.

[0032] S4.2: Considering the degree of matching between the temporal distribution of production and the urgency of demand, calculate the daily production level's ability to meet cumulative demand during periods of increased demand fluctuation, and define the time fit degree. : ; In the formula, For delivery efficiency.

[0033] S4.3: Based on the basic delivery ratio and time fit, obtain the comprehensive delivery index. : ; In the formula, The weighting parameter (e.g., 0.7) can be adjusted according to business priorities (total volume vs. timeliness).

[0034] S4.4: According to The value can be further set into a grade range for quantitative evaluation. For example: Excellent (≥ 0.9), Good [0.75, 0.9), Pass [0.6, 0.75], Fail (<0.6).

[0035] The key focus of S4 in this invention is defining and calculating "time fit" to more precisely assess delivery performance. A simple total delivery ratio may mask the problem of "insufficient early delivery and concentrated late delivery," which can severely impact production continuity during periods of demand fluctuation. Implementation requires collaborating with the planning department to determine a reasonable "demand accumulation model," for example, distributing the total demand during the fluctuation period evenly across days, or determining daily demand weights based on the original demand dates. Then, the actual daily production volume is compared with the unmet "demand weights" from that day and previous days to calculate the proportion of "time-sensitive demand" actually met. This calculation process is slightly more complex but more accurately reflects the supply chain's responsiveness.

[0036] Furthermore, in S5: For the daily production volume sequence of each demand growth fluctuation period, an exponential growth model is used for fitting, and the result is obtained by solving the least squares method: ; In the formula, To fit the obtained daily production growth rate, This represents the actual growth rate. These are the fitted coefficients; This is the starting date for the demand.

[0037] Set the target as the first day's output Initially, it grows at a constant rate, with a fluctuation period of [duration missing]. Total production reached within days: ; In the formula, The ultimate target growth rate; The final target growth rate is obtained by solving the formula for total production. .

[0038] By comparing the actual growth rate with the target growth rate, a production increase and stress resistance index is defined. for: ; Among them, a production increase and stress resistance index greater than 1 indicates that the actual production increase rate exceeds the target and the stress resistance is strong; less than 1 indicates that the production increase is weak and there is a risk of capacity bottleneck.

[0039] In S6, the comprehensive delivery metrics will be... and production increase and stress resistance indicators Normalization and weighting are performed to obtain the final supply chain resilience index.

[0040] The weights are determined by referencing the proportion of financial losses caused by different failure modes (such as delivery shortages and inability to increase production capacity) in historical events. Normalization is used to eliminate the influence of absolute numerical differences between different periods and products, allowing the index to focus more on relative performance. The final calculated index is a relative, trend-based assessment tool.

[0041] This invention successfully transforms the complex dynamic response capabilities of the supply chain into a quantifiable and comparable resilience index by constructing a systematic data modeling process. Its core effects are: First, by automatically identifying historical periods of increased demand fluctuations through algorithms, the assessment accurately focuses on key scenarios where the supply chain is truly under pressure, rather than daily operations. Second, the solution innovatively quantifies the supply chain from two orthogonal dimensions: delivery assurance capability and capacity elasticity. The former measures immediate response efficiency through delivery ratio and timeliness, while the latter assesses medium- to long-term ramp-up potential by analyzing the growth rate of the production curve. Finally, by integrating performance under all stress scenarios and incorporating stability adjustments, the generated supply chain resilience index not only objectively evaluates the overall resilience of the supply chain but also accurately identifies specific weak links, such as delivery delays or capacity bottlenecks from particular suppliers. This provides direct and quantifiable decision-making basis for supply chain resilience building, supplier management, and strategic optimization, achieving an upgrade in risk management from passive response to proactive prevention.

[0042] The above is one embodiment of a method for calculating the resilience index of the industrial chain and supply chain in the field of construction machinery. Based on the same idea, this embodiment also provides a corresponding system for calculating the resilience index of the industrial chain and supply chain in the field of construction machinery. Each module of this system can be implemented entirely or partially through software, hardware, or a combination thereof. The above modules can be embedded in the processor of the computer device in hardware form or independent of the processor, or they can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above modules.

[0043] This embodiment also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 This paper presents a method for calculating the resilience index of the industrial chain and supply chain in the field of construction machinery.

[0044] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0045] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the resilience index of the industrial chain and supply chain in the construction machinery field, characterized in that, Includes the following steps: Obtain historical demand data for the target construction machinery products to be evaluated, as well as historical supply data for the target products from each supplier in the supply chain; Based on historical demand data and statistics of the supply time periods corresponding to various supply demands, the demand in each supply time period is determined. Based on the demand in multiple consecutive supply periods, continuous time analysis is performed using a preset demand change threshold to extract multiple consecutive supply periods with demand increase fluctuations, thus forming multiple demand increase fluctuation periods. Total supply and demand are determined based on all supply and demand items within the period of increased demand fluctuations in historical demand data. Determine daily and total production volumes during periods of increased demand fluctuations based on historical supply data. Determine the delivery ratio and quantify delivery indicators based on the total production and total supply-demand during periods of increased demand fluctuations. The daily production growth curve is determined based on the daily production volume to obtain the daily production growth rate. The daily production target growth rate is determined based on the first day's production volume and the total production volume. The production increase and pressure resistance index is determined based on the daily production growth rate and the daily production target growth rate. The supply chain resilience index is determined by adding delivery metrics and production resilience metrics for periods of increased demand fluctuation.

2. The method for calculating the resilience index of the industrial chain and supply chain in the field of construction machinery according to claim 1, characterized in that, The extraction of demand increases across multiple consecutive supply periods, constituting multiple periods of demand increase fluctuations, includes the following steps: Preset basic supply time period length T For each supply period, the quantities of all demanded items within that period are summed to obtain the demand for that period. : ； In the formula, The total number of time windows. For the required date, The quantity of demand corresponding to the demand date; Obtain the rate of change in demand over consecutive time periods Determine demand fluctuations: ； Set demand growth threshold ,when At that time, mark the first The +1 time window marks the starting point for potential demand growth fluctuations; Starting from each starting point, iterate backwards, and if subsequent steps are consecutive... m Demand change rate over a period of time All are greater than the sustained growth threshold If it is, then growth is considered to be continuous; when encountering At that time, the fluctuation period ends; Consecutive time periods that meet the criteria are merged to form a set of time periods with fluctuating demand increases. There are a total of M time periods: ； in, , For the start date of the demand, This is the last required date.

3. The method for calculating the resilience index of the industrial chain and supply chain in the field of construction machinery according to claim 1, characterized in that, Determining daily and total production volumes during periods of increased demand fluctuations based on historical supply data includes the following steps: Add a fluctuation period to each identified demand. By summing up the demand for all original demand items during this period, we can obtain the total supply and demand for this period of fluctuation: ； In the formula, The quantity of demand corresponding to the demand date; For the start date of the demand, The last required date; Obtain the daily production volume of the supplier for the corresponding time period; from the daily production volume, summarize the actual production quantity of each supplier for the target product during the period of increased demand fluctuation, and obtain the total production volume for that fluctuation period.

4. The method for calculating the resilience index of the industrial chain and supply chain in the field of engineering machinery according to claim 1, characterized in that, The process of determining the delivery ratio and quantifying delivery indicators based on the total production and total supply-demand during periods of increased demand fluctuations includes the following steps: For each period of increased demand, calculate the ratio of total production to total supply demand, using this ratio as the baseline delivery ratio. ; The closer the value is to 1, the better the supply delivery capacity matches the demand growth; Considering the degree of matching between the temporal distribution of production and the urgency of demand, the daily production volume meets the cumulative demand during periods of increased demand fluctuation, and the time fit is defined. : ； In the formula, For delivery efficiency; Based on the basic delivery ratio and time fit, a comprehensive delivery index is obtained. : ； In the formula, These are the weight parameters.

5. The method for calculating the resilience index of the industrial chain and supply chain in the field of engineering machinery according to claim 1, characterized in that, The process of determining the production increase and stress resistance index based on the daily production growth rate and the daily production target growth rate includes the following steps: For the daily production volume sequence of each demand growth fluctuation period, an exponential growth model is used for fitting, and the result is obtained by solving the least squares method: ； In the formula, To fit the obtained daily production growth rate, This represents the actual growth rate. These are the fitted coefficients; The start date of the demand; Set the target as the first day's output Initially, it grows at a constant rate, with a fluctuation period of [duration missing]. Total production reached within days: ； In the formula, The ultimate target growth rate; The final target growth rate is obtained by solving the formula for total production. ; By comparing the actual growth rate with the target growth rate, a production increase and stress resistance index is defined. for: ； Among them, a production increase and stress resistance index greater than 1 indicates that the actual production increase rate exceeds the target and the stress resistance is strong; less than 1 indicates that the production increase is weak and there is a risk of capacity bottleneck.

6. A system for calculating the resilience index of the industrial chain and supply chain in the construction machinery sector, characterized in that the system comprises: The historical data analysis module is used to obtain historical demand data for the target engineering machinery products to be evaluated, as well as historical supply data for the target products from various suppliers in the supply chain. The fluctuation period analysis module is used to determine the demand in each supply period based on historical demand data and the supply period statistics corresponding to each supply demand; and to perform continuous time analysis based on the demand in multiple consecutive supply periods and a preset demand change threshold to extract multiple consecutive supply periods of demand increase fluctuation, thus forming multiple demand increase fluctuation periods. The demand and production analysis module is used to determine total supply and demand based on all supply and demand items during periods of increased demand fluctuations in historical demand data; and to determine daily production and total production during periods of increased demand fluctuations based on historical supply data. The delivery metrics analysis module is used to determine the delivery ratio and quantify delivery metrics based on the total production and total supply demand during periods of increased demand fluctuation. The production increase and stress resistance index analysis module is used to determine the daily production growth curve based on the daily production volume, obtain the daily production growth rate, determine the daily production target growth rate based on the first day's production volume and the total production volume, and determine the production increase and stress resistance index based on the daily production growth rate and the daily production target growth rate. The supply chain resilience index generation module is used to determine the supply chain resilience index by adding delivery indicators and production increase and stress resistance indicators for all demand fluctuation periods.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a data processing program, which, when executed by a processor, implements a method for calculating the industrial chain and supply chain resilience index for the engineering machinery field as described in any one of claims 1 to 5.

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