Knowledge tracking method and device fusing learner ability, and storage medium

Abstract

The invention relates to a knowledge tracking method and device fusing the ability of a learner and a storage medium. The method comprises the steps that a learner set, an exercise set, a knowledge concept set and a learner answering interaction sequence are obtained, the knowledge concept set comprises at least one knowledge point, and the learner answering interaction sequence comprises learner answering results; aggregating by using a graph convolutional network to obtain exercise embedding; obtaining the ability embedding of the learner by using a logistic regression model and a clustering algorithm; and integrating exercise embedding, learner ability embedding and learner answering results, inputting the knowledge tracking model based on the long short-term memory network to obtain the knowledge state of the learner, and predicting the answering results of the learner. Compared with the prior art, the method has the advantages of improving the knowledge tracking accuracy and personalized recommendation effect and the like.

Description

Technical Field

[0001] The present invention relates to the field of knowledge tracking technology, and in particular to a knowledge tracking method, device and storage medium integrating learner capabilities. Background Art

[0002] With the development of big data and artificial intelligence technologies, online education platforms have risen rapidly, making personalized teaching possible. As a key component in the field of intelligent education, knowledge tracking technology monitors and predicts learners' learning progress and knowledge mastery by analyzing their interactive data on education platforms. With the rise of online education, personalized learning experience has become increasingly important, which has driven the demand for more accurate and dynamic knowledge tracking methods. However, traditional exercise recommendation technology fails to fully consider learners' knowledge mastery level and learning ability, and cannot meet the needs of personalized teaching. At the same time, existing knowledge tracking methods are mainly based on whether learners answer questions correctly or not, ignoring the difficulty of the knowledge points contained in the exercises and the learners' learning ability.

[0003] In the prior art, Chinese patent CN118095415A discloses a method for predicting the learning situation of learners based on meta-paths. After acquiring learner data, exercise data, and learner answer interaction sequence data, this method first constructs a learner behavior graph to extract the learning content preferences of each learner; secondly, calculates the learning ability of each learner; thirdly, integrates the characteristics of learning content preferences and learning ability to construct a learner heterogeneous information network based on meta-paths; then uses a hierarchical graph attention mechanism to embed learning into the learner heterogeneous information network and extract learner fusion features; finally, uses a GRU-based knowledge tracking model to predict the learning situation of each learner. However, this method only uses behavior graphs to analyze the interactive relationship between learners and exercises, and calculates learning ability by simply calculating the difference between the correct rate and the error rate. The analysis of learners' learning ability is not in-depth enough, and the influence of the difficulty of the knowledge points contained in the exercises is still not considered, which reduces the accuracy of learning situation prediction. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a knowledge tracking method that integrates learner capabilities. The method improves the accuracy of knowledge tracking and the effect of personalized recommendation by introducing learners' learning capabilities and exercise difficulty estimation.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] According to a first aspect of the present invention, there is provided a knowledge tracking method integrating learner capabilities, comprising the following steps: obtaining a learner set, an exercise set, a knowledge concept set and a learner answer interaction sequence, wherein the knowledge concept set includes at least one knowledge point, and the learner answer interaction sequence includes learner answer results; obtaining exercise embeddings by aggregating using a graph convolutional network; obtaining learner capability embeddings by using a logistic regression model and a clustering algorithm; integrating the exercise embeddings, the learner capability embeddings and the learner answer results, and inputting them into a knowledge tracking model based on a long short-term memory network to obtain the learner's knowledge state and predict the learner's answer results.

[0007] As a preferred technical solution, graph convolutional network aggregation is used to obtain exercise embedding, specifically including: calculating the difficulty of exercises and the difficulty of knowledge points based on the learner's answering interaction sequence; adding the difficulty of exercises and the difficulty of knowledge points to the nodes of the graph convolutional network to obtain the aggregated embedding of exercises and knowledge points; based on the aggregated embedding, using an activation function to calculate the final exercise embedding.

[0008] As a preferred technical solution, the final exercise embedding expression is:

[0009]

[0010] In the formula, ReLU is the activation function, W and b are the weight matrix and offset value respectively. Represents the aggregated embedding vector of the input exercises and knowledge points.

[0011] As a preferred technical solution, a logistic regression model and a clustering algorithm are used to obtain learner ability embedding, specifically including: dividing the learner's answering interaction sequence into time segments, and using a logistic regression model to calculate the first learner ability value in each time period; using a clustering algorithm to dynamically group the first learner ability to obtain the average ability value of each group, and using the average ability value as the learner ability embedding of the corresponding learner.

[0012] As a preferred technical solution, the first learner ability value is expressed as:

[0013]

[0014] In the formula, β n is the learner's own ability level, P ni is the probability that the learner answers one of the exercises correctly, D(q i ) is the difficulty of the exercise, q i represents the i-th exercise.

[0015] As a preferred technical solution, the knowledge state of the learner is obtained, and the calculation expression includes:

[0016]

[0017]

[0018] In the formula, h t represents the learner's knowledge state at time t, which is a hidden state, o t represents the output gate of the long short-term memory network, represents the memory state at time t, f t represents the forget gate of the long short-term memory network, represents the memory state at time t-1, i t represents the input gate of the long short-term memory network, is the intermediate variable, W c represents the weight of each gate, b c represents the bias of each gate, tanh represents the activation function, h t-1 represents the learner’s knowledge state at time t-1, A triple vector representing the concatenation of the exercise embedding, learner ability embedding, and learner answer result at time t.

[0019] As a preferred technical solution, predicting the learner's answer results specifically includes:

[0020]

[0021] In the formula, represents the probability that the learner correctly answers the exercise at time t+1, and W1 ... t and the current input features to the weight matrix of the hidden layer of the model, W2 represents the weight matrix from the hidden layer to the output layer, b1 and b2 represent the bias terms corresponding to the linear transformation and the output layer respectively, σ0 represents the activation function, Represents the triple vector at time t+1, t t+1 is the predicted probability.

[0022] As a preferred technical solution, the graph convolution network is a GCN network, the logistic regression model is a Rasch model, and the clustering algorithm is a K-means clustering algorithm.

[0023] According to a second aspect of the present invention, there is provided a knowledge tracking device integrating learner capabilities, comprising: a data acquisition module for acquiring a learner set, an exercise set, a knowledge concept set and a learner answer interaction sequence, wherein the knowledge concept set includes at least one knowledge point, and the learner answer interaction sequence includes learner answer results; a feature engineering module for obtaining exercise embeddings by using graph convolutional network aggregation, and obtaining learner capability embeddings by using a logistic regression model and a clustering algorithm; and a feature fusion and prediction module for fusing the exercise embeddings, the learner capability embeddings and the learner answer results, and inputting a knowledge tracking model based on a long short-term memory network to obtain the learner's knowledge state and predict the learner's answer results.

[0024] According to a third aspect of the present invention, there is provided a storage medium having a program stored thereon, wherein the program implements the method described above when executed.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. The present invention constructs a heterogeneous information network of learners, uses a graph convolutional network to add the difficulty information of questions and knowledge points to the embedding of exercises and knowledge points, forms high-quality exercise embedding, and constructs an exercise-knowledge point relationship graph to capture the complex relationship between exercises and knowledge points. At the same time, the logistic regression model and clustering algorithm are combined to dynamically evaluate the learner's learning ability and generate embedding. After grouping, the average ability value is used as the learner's ability embedding vector, which can refine the modeling of learners with different abilities, dynamically reflect the learner's learning ability that changes over time, and effectively improve the accuracy of learning situation prediction;

[0027] 2. The present invention also uses a long short-term memory network (LSTM) to process the time series characteristics of learners' answering behavior, which has advantages in capturing long time series dependencies. At the same time, it combines exercise embedding and learner ability embedding to support more complex dynamic modeling and model the dynamic changes of learners' answering behavior more carefully, thereby more accurately predicting learners' knowledge status. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A schematic flow chart of the method provided by the present invention;

[0029] Figure 2 A learner capability representation based on clustering in an embodiment of the present invention;

[0030] Figure 3 A schematic diagram of the framework structure of a method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0032] Example

[0033] like Figure 1 As shown, this embodiment provides a knowledge tracking method integrating learner capabilities, including the following steps:

[0034] Step S1, obtaining a learner set, an exercise set, a knowledge concept set and a learner answer interaction sequence, wherein the knowledge concept set includes at least one knowledge point, and the learner answer interaction sequence includes the learner's answer results.

[0035] Specifically, this step is used to obtain learner learning interaction data. Where: learner set S = {s1,s 2, …,s n}, exercise set Q = {q1,q2,...,q m}, knowledge concept set K = {k1, k2, …, k M}, learner answering interaction sequence X t ={(q1,r1),(q2,r2),…,(q t ,r t )}.

[0036] Among them, k i represents the i-th knowledge point vector. Each exercise contains one or more knowledge points, so the knowledge points represented in the data set may be one or more; the learner's answer interaction sequence X t ={(q1,r1),(q2,r2),…,(q t ,r t )}, a set consisting of t exercise vectors and learners’ answers, representing the order in which learners answer questions in the online learning system; q t is the exercise that the learner answers at time t, q t ∈Q, r in the sequence t is the answer result of the learner at time t, r t ∈{0,1}, if the learner answers correctly, then r t =1, if the learner answers incorrectly, then r t =0.

[0037] Step S2, use graph convolutional network aggregation to obtain exercise embedding.

[0038] Specifically, based on the learner's interactive sequence X t , calculate the difficulty of the exercise D(qi ) and knowledge point difficulty D(k i );The difficulty of the exercise D(q i ) and knowledge point difficulty D(k i ) is added to the nodes of the graph convolutional network (GCN) to obtain the aggregated embedding of exercises and knowledge points; based on the aggregated embedding, the final exercise embedding is calculated using the activation function.

[0039] The difficulty of an exercise refers to the interactive sequence X of the learner answering the question. t The correct rate of all learners answering the question in this data set; the difficulty of a knowledge point refers to the learner's interactive sequence of answering questions X t The correct rate of all learners answering a certain knowledge point in this data set. i ) represents exercise q i The difficulty, D(k i ) represents knowledge point k i The difficulty is calculated as follows:

[0040]

[0041] In the formula, correct(q i ) indicates a correct answer to question q i The number of learners, correct(k i ) indicates the correct answer to knowledge point k i The number of learners, M qi and M ki Respectively indicate that you have done exercises q i And done with knowledge point k i The total number of learners of the relevant exercises. The difficulty coefficient of each exercise finally obtained ranges from 0 to 1. The larger the difficulty coefficient of the exercise, the more difficult the question is, and the smaller the difficulty coefficient of the exercise, the simpler the question is.

[0042] Further, we obtain the embedding vector of the exercises. Each question corresponds to one or more knowledge points, and a knowledge point usually involves many questions. If a question is associated with a knowledge point, then the first-hop neighbor of the question should be the knowledge point it corresponds to, and the second-hop neighbor of the question should be other questions that share the same knowledge point. t ={(q1,r1),(q2,r2),…,(q t ,r t )}, construct a question-knowledge point relationship graph. This graph is an undirected graph, in which the nodes represent the question embeddings that appear in the answer sequence, and the edges represent the transfer between two questions. Then, the correct rate of all learners answering the question in the dataset is used to represent the difficulty of the question D(q i), and use the correct rate of all learners in the data set to answer a certain knowledge point to represent the difficulty D(k i ). GCN is used to transfer and aggregate the embedded representations of exercises and knowledge points to obtain the final embedded vector representation.

[0043] In this embodiment, GCN stacks multiple graph convolutional layers to encode high-order neighbor information. In each layer, the node representation is updated by embedding itself and neighbor nodes. The node representation obtained by GCN is x i , i.e. Exercise q i Embedded, the set of its neighbor nodes is represented as N i , the calculation formula of the lth GCN layer is as follows:

[0044]

[0045] In the formula, w l and b l is the total weight and bias to be learned by the lth GCN layer, and σ represents the nonlinear transformation. GCN transfers information between the embedded representations of exercises and knowledge points to obtain the aggregated embedding of questions and knowledge points. For each historical time t, the problem representation is projected into d dimensions through nonlinear transformation, is the final exercise embedding representation, and its calculation formula is as follows:

[0046]

[0047] In the formula, ReLU is the activation function, W and b are the weight matrix and offset value respectively. Represents the aggregate embedding vector of the input exercises and knowledge points.

[0048] Step S3, using logistic regression model and clustering algorithm to obtain learner ability embedding.

[0049] Specifically, the learners' answering interaction sequence is segmented by time, and the logistic regression model is used to calculate the first learner's ability value in each time period; the clustering algorithm is used to dynamically group the first learner's abilities to obtain the average ability value of each group, and the average ability value is embedded as the learner's ability of the corresponding learner, so as to dynamically reflect the learner's learning ability in different time periods.

[0050] Furthermore, the learner's learning ability is calculated. The learner's learning ability is a dynamic process that reflects the learner's ability to learn knowledge. Combined with the Rasch model of cognitive psychology theory, the relationship between the probability of a learner correctly answering a question, the difficulty of the question, and the learner's own ability level is described, and the relationship between the learner's own ability level, the difficulty of the question, and the probability of the learner correctly answering a question is obtained. The learner's answering interaction sequence is divided into multiple time periods, and the learner's learning performance is evaluated in each time period. The learning situation recorded in each time period reflects the learner's learning ability in that time period; learners are grouped according to their learning ability, and after K-means clustering, learners are dynamically assigned to groups with similar learning abilities. Learners are divided into different groups at each time interval. After grouping, the average ability of each group is taken as the learner ability embedding vector.

[0051] In this embodiment, a Rasch model, a logistic regression model with parameters, is used to describe the relationship between the probability of a learner correctly answering a question, the difficulty of the question, and the learner's own ability level.

[0052] Assume that the probability that a learner answers a question correctly is P ni , the learner's own ability level is β n , the difficulty of the exercise is D(q i ), the relationship between the three is as follows:

[0053]

[0054] In the formula, x ni is the answer of learner n to exercise i, x ni =1 means the answer is correct.

[0055] Completing the logit transformation of this formula, we can obtain the relationship between the learner's own ability level, the difficulty of the exercise, and the probability of the learner correctly answering a question, that is, the first learner's ability value is as follows:

[0056]

[0057] Based on this, since the learner's learning ability changes dynamically over time during the answering process, in this embodiment, the learner's interaction records over time are divided into 5 time steps as a unit length, and the learner's learning performance is evaluated in each time period. Figure 2As shown, K-means clustering is used to divide learners according to their learning abilities, that is, the first learner ability values, and dynamically assign learners to groups with similar learning abilities. In the clustering training phase, the center point of each learner group is found, and learners are divided into different groups at each time interval. After grouping, the average ability of each group is taken as the learner ability embedding vector of the corresponding learner, as shown below:

[0058] c t =mean(cluster(Stu)) (7)

[0059] In the formula, c t Represents the ability embedding of learners in a certain period of time. This embedding vector is based on the clustering results to which they belong, and takes the average of the ability levels of all learners in the cluster.

[0060] Step S4, integrating the exercise embedding, learner ability embedding and learner answer results, and inputting the knowledge tracking model based on the long short-term memory network to obtain the learner's knowledge state and predict the learner's answer results.

[0061] Specifically, a long short-term memory network (LSTM) is used to simulate the learner's knowledge state and capture the temporal dynamics and long-term dependencies in the process of answering questions. t 、f t and t They represent the three key parts of LSTM: input gate, forget gate and output gate. The calculation formula is as follows:

[0062]

[0063] Where W c is the weight of each gate, b c is the bias of each gate, subscript c = i, f, o. σ0 and tanh are activation functions, and their calculation formulas are as follows:

[0064]

[0065] In this embodiment, if Figure 3 As shown, the original data of the knowledge tracking model based on the long short-term memory network (LSTM) is concatenated: the exercise embedding vector The learner's answer result (vector) r t and the learner ability embedding vector c t , get the concatenated triple vector

[0066] The process of using the knowledge tracking model for prediction can be summarized as follows: embedding and splicing the exercises, answer results, and learner abilities into a triple input format; initializing the LSTM-based knowledge tracking model; inputting the triple into the knowledge tracking model for prediction, and obtaining the predicted label of the specified exercise. In this method, the input data is passed to the output layer through the calculation of the long short-term memory network (LSTM), simulating the learner's knowledge state, and predicting the learner's answer results on other questions, and outputting It is to predict the learner's answering performance at the next moment, that is, the probability that the learner will correctly answer the exercise at time t+1.

[0067] The entire practice process is modeled to capture the learner's state changes and understand the potential relationship between exercises. The learner's knowledge state formula in the input exercise representation is as follows:

[0068]

[0069] In the formula, h t represents the learner's knowledge state at time t, o t represents the output gate of the long short-term memory network, represents the memory state at time t, f t represents the forget gate of the long short-term memory network, represents the memory state at time t-1, i t represents the input gate of the long short-term memory network, is the intermediate variable, W c represents the weight of each gate, b c represents the bias of each gate, tanh represents the activation function, h t-1 represents the learner’s knowledge state at time t-1, A triple vector representing the concatenation of the exercise embedding, learner ability embedding, and learner answer result at time t.

[0070] Input Gate i t Input used to determine the current time What information should be stored in the memory state? In the forget gate f t Determine which information in the memory state of the previous moment should be forgotten, and the output gate o t Determine what information the hidden state should output at the current moment. Hidden state h t Through the output gate o t LSTM captures the dynamic changes of the learner's knowledge state through these calculations and updates its internal short-term memory and hidden state.

[0071] Get the hidden state H through LSTMt ={h1,h2,...,h t}, use this hidden state to represent the student's knowledge state, through the student's knowledge state and the student's answer interaction sequence X from 0 to t t ={x1,x2,…,x t} Calculate the interactive response of the students at time t+1. In this embodiment, after LSTM processing, the output of the model is the knowledge state representation h of each learner at the current time step t+1 t+1 Based on this knowledge state, the model further predicts the learner's answer to the next exercise (i.e., whether the answer is correct). Specifically, the knowledge state h t+1 The answer result of the current prediction is output as the predicted probability y through the fully connected layer t+1 , and then calculate the learner's interactive response at time t+1. The formula is as follows:

[0072]

[0073] In the formula, represents the probability that the learner correctly answers the exercise at time t+1, and W1 ... t and the current input features to the weight matrix of the hidden layer of the model, W2 represents the weight matrix from the hidden layer to the output layer, b1 and b2 represent the bias terms corresponding to the linear transformation and the output layer respectively, σ0 represents the activation function, Represents the triplet vector at time t+1.

[0074] According to the aforementioned prediction process, the knowledge tracking model integrating learner capabilities proposed in this application can extract exercise embedding vectors and learner capability embedding vectors from learner interaction data, and combine the learner's answer results to predict their performance in the next answer.

[0075] Furthermore, this embodiment also provides a knowledge tracking device that integrates learner capabilities, and the device includes one or more of a data acquisition module, a feature engineering module, and a feature fusion and prediction module, wherein: the data acquisition module is used to obtain a learner set, a problem set, a knowledge concept set, and a learner answer interaction sequence, wherein the knowledge concept set includes at least one knowledge point, and the learner answer interaction sequence includes the learner's answer results; the feature engineering module is used to obtain problem embedding by graph convolutional network aggregation, and obtain learner capability embedding by using a logistic regression model and a clustering algorithm; the feature fusion and prediction module is used to integrate problem embedding, learner capability embedding, and learner answer results, and input a knowledge tracking model based on a long short-term memory network to obtain the learner's knowledge state and predict the learner's answer results. The specific execution process of each module is the same as the aforementioned method, which will not be repeated here.

[0076] Furthermore, this embodiment also provides a storage medium on which a program is stored. When the program is executed, one or more steps of the aforementioned method are implemented, and the order in which the steps are executed is not limited, which will not be repeated here.

[0077] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A knowledge tracking method integrating learner capabilities, characterized in that: The following steps are involved: Acquire a learner set, an exercise set, a knowledge concept set, and a learner answer interaction sequence, wherein the knowledge concept set includes at least one knowledge point, and the learner answer interaction sequence includes learner answer results; Use graph convolutional network aggregation to get exercise embedding; Use logistic regression model and clustering algorithm to obtain learner ability embedding; The exercise embedding, the learner ability embedding and the learner's answer result are integrated and input into a knowledge tracking model based on a long short-term memory network to obtain the learner's knowledge state and predict the learner's answer result.

2. The knowledge tracking method integrating learner capabilities according to claim 1 is characterized in that: The exercise embedding is obtained by graph convolutional network aggregation, including: Based on the learner's interactive sequence of answering questions, calculating the difficulty of the exercises and the difficulty of the knowledge points; Adding the difficulty of the exercises and the difficulty of the knowledge points to the nodes of the graph convolutional network to obtain aggregate embedding of the exercises and the knowledge points; Based on the aggregated embedding, the final exercise embedding is calculated using an activation function.

3. The knowledge tracking method integrating learner capabilities according to claim 2 is characterized in that: The final exercise embedding expression is: In the formula, ReLU is the activation function, W and b are the weight matrix and offset value respectively. Represents the aggregated embedding vector of the input exercises and knowledge points.

4. The knowledge tracking method integrating learner capabilities according to claim 1, characterized in that: Use logistic regression model and clustering algorithm to obtain learner ability embedding, including: The learner's interactive sequence of answering questions is segmented by time, and the first learner's ability value is calculated using a logistic regression model in each time period; The first learner capabilities are dynamically grouped using a clustering algorithm to obtain an average capability value of each group, and the average capability value is embedded as the learner capability of the corresponding learner.

5. The knowledge tracking method integrating learner capabilities according to claim 4 is characterized in that: The first learner capability value is expressed as: In the formula, β n is the learner's own ability level, P ni is the probability that the learner answers one of the exercises correctly, D(q i ) is the difficulty of the exercise, q i represents the i-th exercise.

6. The knowledge tracking method integrating learner capabilities according to claim 1, characterized in that: The knowledge state of the learner is obtained, and the calculation expression includes: In the formula, h t represents the learner's knowledge state at time t, which is a hidden state, o t represents the output gate of the long short-term memory network, represents the memory state at time t, f t represents the forget gate of the long short-term memory network, represents the memory state at time t-1, i t represents the input gate of the long short-term memory network, is the intermediate variable, W c represents the weight of each gate, b c represents the bias of each gate, tanh represents the activation function, h t-1 represents the learner’s knowledge state at time t-1, A triple vector representing the concatenation of the exercise embedding, learner ability embedding, and learner answer result at time t.

7. The knowledge tracking method integrating learner capabilities according to claim 6, characterized in that: Predict the learner's answer results, including: In the formula, represents the probability that the learner correctly answers the exercise at time t+1, and W1 ... t and the current input features to the weight matrix of the hidden layer of the model, W2 represents the weight matrix from the hidden layer to the output layer, b1 and b2 represent the bias terms corresponding to the linear transformation and the output layer respectively, σ0 represents the activation function, Represents the triple vector at time t+1, y t+1 is the predicted probability.

8. The knowledge tracking method integrating learner capabilities according to any one of claims 1 to 7, characterized in that: The graph convolution network is a GCN network, the logistic regression model is a Rasch model, and the clustering algorithm is a K-means clustering algorithm.

9. A knowledge tracking device integrating learner capabilities, characterized in that: include: A data acquisition module, used to acquire a learner set, an exercise set, a knowledge concept set, and a learner answer interaction sequence, wherein the knowledge concept set includes at least one knowledge point, and the learner answer interaction sequence includes the learner's answer result; The feature engineering module is used to obtain exercise embeddings by using graph convolutional network aggregation, and to obtain learner ability embeddings by using logistic regression models and clustering algorithms; as well as The feature fusion and prediction module is used to fuse the exercise embedding, the learner ability embedding and the learner's answer result, and input the knowledge tracking model based on the long short-term memory network to obtain the learner's knowledge state and predict the learner's answer result.

10. A storage medium having a program stored thereon, characterized in that: When the program is executed, the method according to any one of claims 1 to 8 is implemented.

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