CN106604290B - User perception evaluation wireless network performance method based on web browsing - Google Patents

Abstract

The invention provides a user perception evaluation wireless network performance method based on web browsing, which relates wireless performance indexes with web browsing services through a machine learning algorithm to obtain the influence of LTE wireless performance quality on the performance quality of the services; and quantifying objective webpage browsing services and performance indexes, and then correlating the objective webpage browsing services and the performance indexes into the perception of a user to generate a perception result. Further, the perception result of the user is reversely mapped back to the LTE wireless performance, a network performance short board causing the perception result to be low is obtained, and probability prediction is carried out on places with poor user perception; the method for evaluating the wireless network performance based on the webpage browsing user perception can not only find out key indexes influencing the webpage browsing service quality, but also predict the probability of places with poor user perception.

Description

User perception evaluation wireless network performance method based on web browsing

Technical Field

The invention relates to a user perception evaluation wireless network performance method based on web browsing.

Background

With the rapid development of TDD-LTE networks, the generation of 4G LTE network technology and smart phones have drawn closer interpersonal distance. In 2013, the global mobile data traffic is increased by 81% compared with 2012, and reaches 15 hundred million GB per month on average. Such rapidly increasing network traffic places a significant burden on LTE wireless networks. Meanwhile, the challenges faced by home and abroad operators in operating, maintaining and optimizing the LTE network are gradually revealed and exposed. The general idea of the evolution plan and 4G planning construction of an operator wireless target network is combined, and the whole network continuous coverage, the hot spot deep coverage and the indoor deep coverage of TD-LTE need to be realized as soon as possible; how to evaluate the coverage effect after completing each construction index.

The conventional LTE network coverage optimization problem is limited to the optimization of the wireless RF own parameters. Firstly, defining RF parameter optimization to reach a target, and then designing a physical method or a mathematical method to enable the RF parameter to reach the optimized target after being adjusted. The neglected problem is whether the user experience with the wireless network is improved when the RF parameters are optimized above the target values or the network coverage construction goal is achieved? Is the quality of service of various services used by the user in the network improved? To resolve a problem is that, as consumers of network traffic and users of wireless services, mobile users feel overall improvement of service quality and experience brought by RF index optimization of LTE network wireless coverage when using various services? Therefore, whether wide area coverage, indoor coverage, special (high-speed, etc.) coverage, a neutral and objective evaluation mechanism is needed from the perspective of mobile services and service audiences.

With the continuous maturity of network communication and computer technologies, the investment of operators on basic equipment such as networks, storage and computers follows the pace of the big data era, so that the operators can quickly become a gold mine with big data, have the full amount of RF indexes, telephone traffic statistical indexes, signaling indexes, service application performance index data and the like, accumulate a large amount of data resources, and provide an effective basis for discovering the knowledge hidden behind the network data through a big data mining technology.

The optimization of LTE wireless network coverage traditionally aims at enhancing coverage and reducing interference as two qualitative goals. From a quantitative point of view, passing threshold values and acceptance standards are strictly defined for all network indexes in the operator's TD-LTE network KPI assessment manual. From the operator's perspective, the quality of the wireless network is defined and judged, which is indicated by the wireless network index. From the perspective of wireless users, users themselves subjectively feel that services such as voice and data loaded on the network are used as standards for judging the quality of wireless networks of operators. It can be seen that the scale between the operator of the network and the user of the network traffic is not uniform and the standard is split. From the perspective of cognitive psychology, the reason for the fracture is that the objective index of the underlying network cannot accurately evaluate the subjective cognitive result generated after the upper layer service reaches the user.

This requires the operator to review the objective of network optimization, not only to optimize the network index to meet the criteria specified in the KPI assessment manual, but also to try to bridge the objective index at the network level and the subjective cognitive result of the user with a host-object mapping algorithm.

Objective 0 and 1 bit streams in an LTE wireless network undergo the following process to make a user cognizant, as shown in fig. 1: the RB in the Subframe in each TTS in the LTE physical layer contains 6-7 symbols in the time domain and 12 subcarriers in the space domain, and the RE in each RB is the carrier finally used for carrying and transmitting bits. These bitstreams, which contain signaling and user plane content, are encapsulated at the network layer into IP Packets, which encapsulate signaling and user plane data. And finally, transmitting the contents of each service after the service is encapsulated by the application layer to a terminal held by a user, and embodying the contents (Data Call or Voicecall) requested by the user. The user is only visible for the last presentation, or delivered content, so the quality of the content presented from network to terminal, the time consumption delivered, becomes the main criterion for the user to judge the LTE wireless network quality and terminal quality from the network audience's perspective. How the RF quality of an LTE wireless network maps to the service quality directly affecting the user perception is particularly critical.

For the web browsing service, after a user is linked from startup to a web page on a trigger terminal screen, the user will go through the steps of attach, RRC Connection Setup, PDN Connection Setup, ereba Setup, DNSLookup, TCPHandshaking, Get, Post, etc., and the sum of the time delays generated in each step will become a bottleneck that affects the quality of the web browsing service and also an index that causes the user to be directly perceived subjectively.

User perception, which is the organization, cognition and interpretation of sensory information by a user that may represent or understand a certain environment, comprises the ensemble of signals in the human nervous system that are generated by physical and chemical stimuli from which the sensory organs originate. The generation of awareness can be divided into two sub-processes. First, the processing and conversion of input sensory content by a person translates low-level information into high-level information. For example, shape interpretation of an object is used to recognize the object. Second, these interpreted information is associated with concepts, desires, concerns, that determine and generate human perception. When the user perception is reduced by the user, the user tends to be simply attributed to the fact that the webpage loading is unsuccessful or the speed is slow due to the reduction of the network quality, and the user does not have any obligation or driving force to recognize the reduction of the perception, and the service quality is reduced due to the reason.

Disclosure of Invention

The invention aims to provide a user perception evaluation wireless network performance method based on web browsing, which is based on a subject-object conversion algorithm of telecommunication psychology, designs a 'LTE cell network quality learning based on user perception', maps the network quality in LTE to the dimension which can be directly or indirectly perceived by a user in an application layer service, and finally maps the subjective perception of the user to a set of objective evaluation system, accurately quantifies how the network quality of LTE is mapped to the experience of the user service, and solves the problems in the prior art.

The technical solution of the invention is as follows:

a method for evaluating wireless network performance based on webpage browsing user perception comprises the following steps:

the wireless performance index is associated with the web browsing service through a machine learning algorithm, so that the influence of the LTE wireless performance quality on the performance quality of the service is obtained;

and quantifying objective webpage browsing services and performance indexes, and then correlating the objective webpage browsing services and the performance indexes into the perception of a user to generate a perception result.

Further, the perception result of the user is reversely mapped back to the LTE wireless performance, a network performance short board causing the perception result to be low is obtained, and probability prediction is carried out on the place with poor user perception.

Further, the mapping of the web browsing service to the quantifiable user awareness is specifically:

making the perception result of the user's perception MOS_wedThe service performance index i is SPI_iFor the web browsing service in the LTE network, the mapping equation between the two is

MOS_web＝f(SPI_i) Equation 1, 2, 3

Designing a webpage, setting a plurality of different parameters, namely different quality indexes, at the background, wherein the different quality indexes inevitably lead to different webpage browsing experience qualities, collecting background index data under different parameters in the process of opening the webpages with different parameter settings one by one at the same terminal, and only needing to perform one-out-of-two voting on every two webpages with different parameter settings by a user to obtain a user voting matrix;

establishing a user scoring matrix according to the following formula and performing continuous mapping association according to the following formula through a user voting matrix and a terminal background index:

wherein S is_ijValues, Π, representing rows and columns of the user voting matrix i_ijRepresenting a function associated with i, j, S_jiRepresenting the values of the rows j and columns i of the user voting matrix, Logit representing the log of the logarithm of the function, β_iRepresenting the functional form of a logarithmic function followed by an i-correlation, β_jRepresenting the functional form of a logarithmic function followed by a j-correlation,

a value of between 0 and 1, Norm_[0，5]The linear programming is performed on the former, so that the value range of the former is between 0 and 5; webqualityScore has the same meaning as MOS_webNamely the perception result of the perception of the webpage browsing user.

Further, the service performance index includes: RRC time delay, service request time delay, ERAB time delay, DNS searching time delay, TCP12 time handshake time delay, TCP23 time handshake time delay, page display time delay, page response time delay and page downloading speed.

Further, mapping LTE micro-area RF performance to service performance specifically includes: the wireless performance index is correlated with the webpage browsing service, RFI is an RF Indicators wireless performance index, Delay is Delay, and the following equation is defined:

Latency＝f(RFI_i) Equation 5, i ═ 1, 2, 3

Where Lantency represents the sum of the above delays, f represents the expression form of the function, and RFI_iRepresenting the ith wireless performance index;

because the user perception index exists in the signaling data, and the wireless RF index data exists in the MR data, the two data sets are integrated according to the cell, the user and the time dimension, then the user perception index is used as a dependent variable, and the wireless RF index is used as an independent variable to carry out regression; several regression models are computed on the training set, and a weight is assigned to each regression model to combine the regressions into one integrated regression model.

Further, the wireless performance index includes reference signal received power RSRP of the TD-LTE serving cell, reference signal received quality RSRQ of the TD-LTE serving cell, signal to noise ratio SINR of the TD-LTE serving cell, channel quality indicator CQI, and configuration of rate in LTE, which implements MCS through MCS index value, number of PRBs occupied by PDSCH channel on UE, i.e. PDSCH PRBs, and number of PRBs occupied by PUSCH channel on UE, i.e. PUSCH PRBs.

Further, the combination is an integrated regression model, specifically: for each regression model j, performing leave-one-out cross validation on each sample i in the training set to generate a predicted value

Then, using regression algorithm j on samples except i, obtaining the predicted value

Calculating the square of the errorThus, each regression model j, by ε_j：＝(ε_ij)′_iIs defined as a defined column vector, where ε_jRepresents the column vector formed by the square of the error of the ith sample on the regression algorithm j, representing the transpose;

the weights are derived by error, specifically: the weight w is calculated with the constraint of a minimum weighted two-multiplication and a sum of weights of one₁，w₂，…，w₈The true value of (d); these weights are derived from the optimization problem as defined by equation 1 below, plus the constraint defined by equation 2, | · | | survival₂Representing the euclidean norm.

Wherein, w_jRepresents the weight, ε, of the regression algorithm j_jRepresents the column vector formed by the square of the error of the ith sample on the regression algorithm j;

determining a predicted regression function after obtaining the weight value, finding out the weight value and determining which regression function is used for prediction aiming at each regression method; to achieve this, j regression is performed on all elements in the training set, resulting in a prediction function P for each regression method_jFinally, the ensemble regression is defined as P_jLinear weighted combination of (1).

The method calls a scoring equation of webqualityScore by obtaining data containing user perception indexes and wireless quality indexes; then, a regression model of the wireless indexes and the user perception indexes is established. The method for evaluating the wireless network performance based on the webpage browsing user perception can not only find out key indexes influencing the webpage browsing service quality, but also predict the probability of places with poor user perception. The mobile company can develop targeted network optimization service for areas with poor user perception, and further improve the webpage browsing service quality of corresponding cells/users.

The invention has the beneficial effects that: according to the method for evaluating the performance of the wireless network based on the user perception of the web browsing, the quality perception generated by the user perception aiming at the LTE wireless coverage quality as an evaluation target is quantized by butting wireless RF index data, telephone traffic statistical data, measurement report data, signaling data and the like, a set of big data algorithm is developed by utilizing big data, machine learning and data mining technologies, and a two-stage nonlinear correlation algorithm mapping model is designed according to three dimensions of the LTE wireless network quality, the LTE service quality which can be experienced by a user and the user perception. Through the development of the platform system, the user perception experience can be backtracked to be influenced by indexes finally, and a set of technical advanced systematized solution is provided for network optimization and market collaboration.

Drawings

Fig. 1 is an explanatory diagram of how network quality affects user-perceived quality of service.

Fig. 2 is a schematic diagram of a user voting matrix in the embodiment.

Fig. 3 is an explanatory diagram of the integrated learning of seven different regression algorithms in the embodiment.

FIG. 4 is a schematic flow chart of the regression algorithm training in the example.

Detailed Description

Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

The words in the examples are explained below: LTE (Long Term Evolution), rrc (Radio RESOURCE Control), era (Evolved Radio Access Bearer), DNS (Domain Name System), TCP (Transmission Control Protocol), RF (Radio frequency), MR (Measurement Report), which means that information is transmitted once per 480ms (signaling Channel, 470ms) on a traffic Channel, which may be used for network evaluation and optimization, TD-LTE (Time Division Long Term Evolution), MCS (Modulation and Coding Scheme), PDSCH (Physical Downlink Channel, Physical Downlink Shared Channel), Physical Downlink Shared Channel (Physical Uplink), PUSCH (Physical Uplink Shared Channel, PUSCH), TDD-lte (time Division duplex Long Term evolution), Long Term evolution, PDN (Public Data Network (PDN)).

Examples

A user perception evaluation wireless network performance method based on web browsing correlates wireless performance indexes with web browsing services through a machine learning algorithm to obtain the influence of LTE wireless performance quality on the performance quality of the services; and quantifying objective webpage browsing services and performance indexes, and then correlating the objective webpage browsing services and the performance indexes into the perception of a user to generate a perception result. Further, the perception result of the user is reversely mapped back to the LTE wireless performance, a network performance short board causing the perception result to be low is obtained, and probability prediction is carried out on the place with poor user perception.

The mapping of the webpage browsing service to the quantifiable user awareness comprises the following specific steps: in LTE or other mobile communication networks, the perception of the user and the signaling underlying the network are not directly related to traffic indicators. The user's perception is directly perceived on the service index, such as the web page download rate, the web page delay, etc. Making the perception result of the user's perception MOS_webThe service performance index i is SPI_i. For the web browsing service in the LTE network, the mapping equation between the two is

MOS_Web＝f(SPI_i) Equation 1, 2, 3

A standard webpage is designed, a plurality of different parameters, namely different quality indexes, are set in the background, and different webpage browsing experience qualities are inevitably caused by different quality indexes. For example, 4 webpages with different parameter settings are opened one by one at the same terminal, in the process, background index data under 4 different parameters are collected, and for each two webpages with different parameter settings, the user only needs to perform voting by 2-out-of-1 to obtain a user voting matrix, as shown in fig. 2, S1, S2, S3 and S4 in fig. 2 are the above SPI indexes.

Establishing a user scoring matrix according to the following formula and performing continuous mapping association according to the following formula through a user voting scoring matrix and a terminal background index:

wherein S is_ijValues, Π, representing rows and columns of the user voting matrix i_ijRepresenting a function associated with i, j, S_jiRepresenting the values of the rows j and columns i of the user voting matrix, Logit representing the log of the logarithm of the function, β_iRepresenting the functional form of a logarithmic function followed by an i-correlation, β_jRepresenting the functional form of a logarithmic function followed by a j-correlation,

a value of between 0 and 1, Norm_[0，5]The linear programming is performed on the former, so that the value range of the former is between 0 and 5; webqualityScore has the same meaning as MOS_webNamely the perception result of the perception of the webpage browsing user.

Among them, SPI indexes are: RRC delay, service request delay, ERAB delay, DNS search delay, TCP12 handshake delay, TCP23 handshake delay, page display delay, page response delay, page download rate, etc.

Mapping of the LTE micro-area RF performance to the service performance, the mapping at this stage aims to relate the radio performance of the LTE wireless network micro-area to the quantitative relation of the radio service in the area. According to the professional interpretation of the webpage browsing service by the service expert, the following wireless performance indexes are only required to be considered to participate in the mapping work of the webpage browsing service indexes. In the cell-level measurement report, the following RF indicators are considered as potential radio performance indicators to associate the web browsing service: the wireless performance indexes comprise Reference Signal Received Power (RSRP) of a TD-LTE service cell, Reference Signal Received Quality (RSRQ) of the TD-LTE service cell, signal to noise ratio (SINR) of the TD-LTE service cell, Channel Quality Indication (CQI), configuration of the rate in LTE, and the like, wherein MCS is realized through an MCS index value, the number of PRBs occupied by a PDSCH channel on UE (user equipment), namely PDSCH PRBs, the number of PRBs occupied by the PUSCH channel on the UE, namely PUSCH PRBs, and the like.

The following equations are defined. Let RFI be the RF Indicators radio performance index and Delay be Delay.

Latency＝f(RFI_i) Equation 5, i ═ 1, 2, 3

Where Lantency represents the sum of the above delays, f represents the expression form of the function, and RFI_iIndicating the ith wireless performance indicator.

Since the user perception index exists in the signaling data and the wireless RF index data exists in the MR data, it is necessary to integrate the two data sets in dimensions of cell, user, time, etc., and then perform regression using the user perception index as a dependent variable and the wireless RF index as an independent variable. The present invention has been described in detail using seven different regression methods. These regression algorithms cover a wide range of statistical approaches involving completely different statistical algorithms to ensure the robustness and flexibility of the integrated regression system. As shown in fig. 3, the seven regression methods are: linear regression, polynomial regression, ridge regression, Lasso regression, Elastic regression, Generalized Additive Model (GAM), multivariate adaptive regression spline Model (MARS).

As in fig. 4, calculations are performed on the training set for each regression model. The goal is to find the appropriate weights to combine these regressions into one integrated regression, as described below.

For each regression model j, performing leave-one-out cross validation on each sample i in the training set to generate a predicted valueThen, using regression algorithm j on samples except i, obtaining the predicted value

Thus, the square of the error can be calculatedCan be calculated. Thus, for each regression model j, the through ε_j：＝(ε_ij)′_iTo define a column vector, where ε_jRepresents the column vector formed by the square of the error of the ith sample on the regression algorithm j, representing the transpose;

weights are then derived from the errors. The weight w is calculated with the constraint of a minimum weighted two-multiplication and a sum of weights of one₁，w₂，…，w₈The true value of (d). Formally, these weights are obtained according to the optimization problem defined by equation 1 below, plus the constraints defined by equation 2. I₂Representing the euclidean norm.

Wherein, w_jRepresents the weight, ε, of the regression algorithm j_jRepresents the column vector formed by the square of the error of the ith sample on the regression algorithm j;

after the weight values are obtained, the predicted regression function can be determined, the weight values are found for each regression method, and which regression function is used for prediction is determined. To achieve this, j regression is performed on all elements in the training set. Thereby obtaining a prediction function P of each regression method_jFinally, the ensemble regression is defined as P_jLinear weighted combination of (1).

Once the integrated regression model is derived, testing is performed on the test set. For this step, known values of true user perception indices are compared to the predicted values obtained on the test set. The average error rate as defined in equation 3 is calculated to obtain the error rate ε_test. To ensure the robustness of the systemAnd accuracy, making different comparisons. First, the same error rate calculation is performed on the training set to obtain the error rate ε_train。ε_testAnd ε_trainSmall differences indicate the absence of overfitting, demonstrating the robustness of the calculation. Then, predictions are made on the test set for each regression method, each yielding an error rate. By comparing the error rates ε obtained in the ensemble regression_testThereby detecting the accuracy of the system.

Wherein n is_testRefers to the number of rows in the test data set.

And then, calculating the weight according to an analytical formula method and deducing an integrated regression model. Thus, the average error rate was calculated over both the training set and the test set. In this example, the added error from the training set to the test set is small, indicating that there is no overfitting. Moreover, compared with other regression methods, the integrated regression model has a good effect and can be effectively applied to practical application. Furthermore, unlike all other methods (even cubic polynomial regression), integrated regression is more stable and self-adjusting. Therefore, a better regression should be an integrated regression.

Based on the above, a bridge of user perception and wireless indexes can be connected. When the user perception is poor, the short board indexes influencing the user perception can be traced back, and then the network optimization personnel are recommended to carry out targeted optimization work on the indexes.

Claims (6)

1. A user perception evaluation wireless network performance method based on web browsing is characterized by comprising the following steps:

the wireless performance index is associated with the web browsing service through a machine learning algorithm, so that the influence of the LTE wireless performance quality on the performance quality of the service is obtained;

quantifying objective webpage browsing services and performance indexes, and then correlating the objective webpage browsing services and the performance indexes into the perception of a user to generate a perception result;

the mapping of the web browsing service to the quantifiable user awareness comprises the following specific steps:

the sensing result of the perception of the webpage browsing user is MOS_webThe service performance index i is SPI_iFor the web browsing service in the LTE network, the mapping equation between the two is

MOS_web＝f(SPI_i) (1)

Designing a webpage, setting a plurality of different parameters, namely different quality indexes, at the background, wherein the different quality indexes inevitably lead to different webpage browsing experience qualities, collecting background index data under different parameters in the process of opening the webpages with different parameter settings one by one at the same terminal, and only needing to perform one-out-of-two voting on every two webpages with different parameter settings by a user to obtain a user voting matrix;

establishing a user scoring matrix according to the following formula and performing continuous mapping association according to the following formula through a user voting matrix and a terminal background index:

wherein S is_ijRepresenting the values of rows and columns j of the user voting matrix i,. pi.j represents the function associated with i, j, S_jiRepresenting the values of the rows j and columns i of the user voting matrix, Logit representing the log of the logarithm of the function, β_iRepresenting the functional form of a logarithmic function followed by an i-correlation, β_jRepresenting the functional form of a logarithmic function followed by a j-correlation,

value of 0 to 1Normal, Norm_[0,5]The linear programming is performed on the former, so that the value range of the former is between 0 and 5; webqualityScore has the same meaning as MOS_webNamely the perception result of the perception of the webpage browsing user.

2. The method for evaluating wireless network performance based on user perception of web browsing of claim 1, wherein: and reversely mapping the perception result of the user back to the LTE wireless performance to obtain a network performance short board causing the perception result to be low, and performing probability prediction on a place with poor user perception.

3. The method for web browsing-based user-aware assessment of wireless network performance as claimed in claim 1, wherein the service performance indicators comprise: RRC time delay, service request time delay, ERAB time delay, DNS searching time delay, TCP12 time handshake time delay, TCP23 time handshake time delay, page display time delay, page response time delay and page downloading speed.

4. A method for web browsing based user perception assessment of wireless network performance as claimed in any of claims 1-3, characterized by: mapping of the LTE micro-area RF performance to the service performance specifically comprises the following steps: the wireless performance index is correlated with the webpage browsing service, RFI is an RF Indicators wireless performance index, Delay is Delay, and the following equation is defined:

Latency＝f(RFI_i)，i＝1，2，3，...(5)

where Lantency represents the sum of the above delays, f represents the expression form of the function, and RFI_iRepresenting the ith wireless performance index;

because the user perception index exists in the signaling data, and the wireless RF index data exists in the MR data, the two data sets are integrated according to the cell, the user and the time dimension, then the user perception index is used as a dependent variable, and the wireless RF index is used as an independent variable to carry out regression; several regression models are computed on the training set, and a weight is assigned to each regression model to combine the regressions into one integrated regression model.

5. The method for web browsing-based user-aware assessment of wireless network performance of claim 4, wherein: the wireless performance indexes comprise Reference Signal Received Power (RSRP) of a TD-LTE service cell, Reference Signal Received Quality (RSRQ) of the TD-LTE service cell, signal to noise ratio (SINR) of the TD-LTE service cell, Channel Quality Indicator (CQI), and the configuration of the rate in LTE realizes Modulation and Coding Scheme (MCS) through an MCS index value, the number of PRBs occupied by a Physical Downlink Shared Channel (PDSCH) on the UE, namely the number of PDSCH PRBs, and the number of PRBs occupied by the PUSCH on the UE, namely the number of PUSCH.

6. A method for web browsing based user perception assessment of wireless network performance as claimed in any of claims 1-3, characterized by: the combination is an integrated regression model, which specifically comprises the following steps: for each regression model j, performing leave-one-out cross validation on each sample i in the training set to generate a predicted value

Then, using regression algorithm j on samples except i, obtaining the predicted value

Calculating the square of the error

Thus, each regression model j, by ε_j：＝(ε_ij)′_iTo define a column vector, where ε_jRepresents the column vector formed by the square of the error of the ith sample on the regression algorithm j, representing the transpose;

the weights are derived by error, specifically: the weight w is calculated with the constraint of a minimum weighted two-multiplication and a sum of weights of one₁,w₂,…,w₈The true value of (d); these weights are obtained according to the optimization problem defined by equation 6 below, plus the constraint defined by equation 7, | |. |₂Representing the euclidean norm;

wherein, w_jRepresents the weight, ε, of the regression algorithm j_jRepresents the column vector formed by the square of the error of the ith sample on the regression algorithm j;

determining a predicted regression function after obtaining the weight value, finding out the weight value and determining which regression function is used for prediction aiming at each regression method; to achieve this, j regression is performed on all elements in the training set, resulting in a prediction function P for each regression method_jFinally, the ensemble regression is defined as P_jLinear weighted combination of (1).

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