CN111639240B - Cross-modal Hash retrieval method and system based on attention awareness mechanism - Google Patents

Abstract

The invention discloses a cross-modal hash retrieval method and system based on an attention perception mechanism. Modal features; input the cross-modal features of the cross-modal data pair into the hash learning model, and optimize the hash learning model with the goal of minimizing the loss function according to the output cross-modal hash code; The hash code of the data to be tested obtained by the hash learning model, among the hash codes of the modal data that is different from that of the data to be tested, screen the modal data that meets the retrieval requirements. The attention mechanism is applied to the cross-modal hash retrieval task, and a new attention method based on the attention-aware mechanism is proposed, which can suppress the noise and redundancy in the original data while enhancing the key attention areas and improve the hash rate. code generation quality.

Description

A cross-modal hash retrieval method and system based on attention-aware mechanism

technical field

The invention relates to the technical field of cross-modal hash retrieval, in particular to a cross-modal hash retrieval method and system based on an attention-aware mechanism.

Background technique

The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

With the explosive growth of network multimedia data, it is necessary to use existing images to retrieve related texts or videos, or to retrieve images or videos based on texts, that is, to use data from one modality to retrieve similar samples from another modality. At the same time, the efficient storage and fast query of data has also become a difficult problem. Based on this, in recent years, some scholars have proposed the use of hash learning to solve this problem, because the hash learning method can use the original high-dimensional sample data in a simple and compact manner. It can be represented by the binary hash code, which can greatly compress the data size, which is convenient for data storage and mutual retrieval.

Cross-modal retrieval technology aims at retrieving data of different modalities that match the existing data, such as searching for a set of pictures that match the text description in a database through text information. Existing technologies can be divided into deep models and non-deep models according to whether they are combined with deep learning technology. The traditional deep cross-modal hash retrieval model is usually divided into three steps. First, the deep network is used to extract the features of different modalities. The obtained features use a fully connected network to learn a hash function under the supervision of cross entropy loss and sample similarity matrix, and finally convert the sample into a hash code and save it in the database through the hash function.

At this stage, many cross-modal hash retrieval methods have been proposed. However, the inventor found that the prior art has at least the following problems: For retrieval tasks, real data often have some noise and redundancy, and when feature extraction , it is necessary to extract the most useful visual information, while ignoring the background information, because the background information will interfere with the retrieval; but in the actual data, the information of the valuable category only covers a small part, most of the areas are background, and the current large Most cross-modal retrieval methods ignore this problem and learn features directly from raw data, so they may be misled by invalid or redundant information, resulting in low-quality hash codes; In order to improve the retrieval effect of the modal hash retrieval model, a network model with more parameters and better effect is often introduced, such as GAN (generative adversarial network), etc., but it will greatly increase the training and retrieval time.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention proposes a cross-modal hash retrieval method and system based on an attention-aware mechanism, applies the attention mechanism to the cross-modal hash retrieval task, and proposes a new type of attention-aware mechanism. Force method, the cross-modal data set containing multiple modal data realizes feature learning and hash coding learning at the same time, and finally the attention-weighted feature representation is fed back to the hash learning model to guide the generation of hash codes , to suppress the noise and redundancy in the original data and enhance the key areas of interest, so as to improve the generation quality of the hash code.

In order to achieve the above object, the present invention adopts the following technical solutions:

In a first aspect, the present invention provides a cross-modal hash retrieval method based on an attention-aware mechanism, including:

Perform feature extraction and attention feature extraction on the training set in the cross-modal dataset to obtain cross-modal features weighted by attention features;

Input the cross-modal features of the cross-modal data pairs in the training set into the hash learning model, and optimize the hash learning model with the goal of minimizing the loss function according to the output cross-modal hash code;

According to the hash codes of the data to be tested obtained from the optimized hash learning model, the modal data that meet the retrieval requirements are screened from the hash codes of the modal data in the cross-modal data set that are different from the modalities of the data to be tested. .

In a second aspect, the present invention provides a cross-modal hash retrieval system based on an attention-aware mechanism, including:

The feature extraction module is used to perform feature extraction and attention feature extraction on the training set in the cross-modal data set, and obtain the cross-modal feature weighted by the attention feature;

The hash learning module is used to input the cross-modal features of the cross-modal data pairs in the training set into the hash learning model, and optimize the hash learning model with the goal of minimizing the loss function according to the output cross-modal hash code;

The retrieval module is used to filter the hash codes of the modal data that are different from the modalities of the data to be tested in the cross-modal data set according to the hash codes of the data to be tested obtained by the optimized hash learning model. Modal data requested.

In a third aspect, the present invention provides an electronic device, comprising a memory, a processor, and computer instructions stored in the memory and executed on the processor, and when the computer instructions are executed by the processor, the method described in the first aspect is completed .

In a fourth aspect, the present invention provides a computer-readable storage medium for storing computer instructions, and when the computer instructions are executed by a processor, the method described in the first aspect is completed.

Compared with the prior art, the beneficial effects of the present invention are:

In the present invention, the cross-modal data set includes multiple modal data, and the multiple modal data realizes feature learning and hash coding learning at the same time, thereby improving the efficiency of hash code generation.

The present invention proposes a new attention method of the attention perception mechanism, and applies the attention mechanism to the cross-modal hash retrieval task. Two different modal weights can not only highlight the key parts of the cross-modal data, such as in the picture The area where the object exists or a word in the text input can also suppress the influence of redundant or invalid parts on the retrieval effect, such as picture background or text noise words, etc., which can effectively improve the quality of hash code generation, and can be applied Cross-modal retrieval tasks in various multimodal data scenarios

Description of drawings

The accompanying drawings forming a part of the present invention are used to provide further understanding of the present invention, and the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, and do not constitute an improper limitation of the present invention.

Figure 1(a)-(b) is the picture modal data;

Figure 1(c) shows the top 10 words in the public dataset MIRFlicker-25K in terms of text annotation frequency;

Fig. 1(d) is the text annotation data of Fig. 1(a);

2 is a flowchart of a cross-modal hash retrieval method based on an attention-aware mechanism provided in Embodiment 1 of the present invention;

3 is a flowchart of image attention feature extraction provided by Embodiment 1 of the present invention;

4 is a flowchart of text attention feature extraction provided by Embodiment 1 of the present invention;

FIG. 5 is a structural diagram of a cross-modal hash retrieval system based on an attention-aware mechanism according to Embodiment 1 of the present invention.

Detailed ways:

The present invention will be further described below with reference to the accompanying drawings and embodiments.

It should be noted that the following detailed description is exemplary and intended to provide further explanation of the invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that the terms "including" and "having" and any conjugations thereof are intended to cover the non-exclusive A process, method, system, product or device comprising, for example, a series of steps or units is not necessarily limited to those steps or units expressly listed, but may include those steps or units not expressly listed or for such processes, methods, Other steps or units inherent to the product or equipment.

Embodiments of the invention and features of the embodiments may be combined with each other without conflict.

Example 1

At present, a variety of cross-modal hash retrieval methods have been proposed, but due to the noise and redundancy in real data, the current retrieval methods directly learn features from the original data, which will be misled by invalid or redundant information, resulting in the generation of Low quality hash codes. Taking the two modes of picture and text as an example, as shown in Figure 1(a)-1(b), for the picture in Figure 1(a), it is necessary to highlight the area where bees and flowers are located and ignore the background part behind, because it will interferes with retrieval; similarly, for the picture in Figure 1(b), where the labels, i.e., the supervision information, are “animal”, “flower”, and “plant life”, the most useful visual information may be the butterfly hovering over the flower. However, the information of these valuable categories covers only a small part of the whole image, and most of the areas in this image are the background;

As shown in Figure 1(c), which contains the top 10 words in the public dataset MIRFlicker-25K, the word frequency of text annotations, you can see that there are half of the words: "explore", "canon", "bw", "nikon" ” and “2007” are both invalid words that are not directly related to the image content; Figure 1(d) is the text annotation of Figure 1(a), and only the word “bees” is relevant to the retrieval task.

It can be seen from this that if the noise and redundancy in the original data are not suppressed, it is easy to generate low-quality hash codes and affect the retrieval results.

The Attention mechanism has been widely used in the field of computer vision in recent years, such as natural language processing, object detection, image recognition, and speech recognition, but it is rarely used in cross-modal retrieval. The traditional Attention mechanism is used in image recognition, which can spontaneously find the part of the picture that needs to be focused on, that is, by learning to generate a Mask with the same size as the picture representation (this picture representation can be the original picture, or a feature map, etc.); For the region of interest, the corresponding position of the Mask has a higher activation value. According to the area of action, the Attention model can usually be divided into a spatial attention model and a channel attention model; the spatial attention model generates corresponding attention values for different positions in the feature map, and when restored to the original picture, the different positions in the picture are for Tasks have different degrees of influence; the channel attention mechanism generates corresponding attention values for different channels in the feature map, which is more abstract.

This embodiment integrates the spatial attention mechanism, applies the attention mechanism to the cross-modal hash retrieval task, and proposes a new attention method based on the traditional attention mechanism, which is called the attention-aware mechanism. for two different modal weights;

That is, the cross-modal hash retrieval method based on the attention perception mechanism in this embodiment suppresses the noise and redundancy in the original data while enhancing the key attention area, and then extracts the attention matrix. The quality of the code has a good improvement effect, and can be used for cross-modal information retrieval in various multi-modal data scenarios, as shown in Figure 2, which includes the following steps:

S1: Perform feature extraction and attention feature extraction on the training set in the cross-modal dataset to obtain cross-modal features weighted by attention features;

S2: Input the cross-modal features of the cross-modal data pairs in the training set into the hash learning model, and optimize the hash learning model with the goal of minimizing the loss function according to the output cross-modal hash code;

S3: According to the hash code of the data to be tested obtained by the optimized hash learning model, among the hash codes of the modal data in the cross-modal data set with different modalities from the data to be tested, filter the models that meet the retrieval requirements. state data.

In the step S1, the cross-modal data set includes multiple modal data. In this embodiment, taking image modal data and text modal data as examples, it can be understood that this modal type can extend other modalities. , such as video, voice, etc.

Divide the cross-modal data set into a training set and a test set, and use two parallel convolutional neural networks to simultaneously perform feature extraction and attention feature extraction on the cross-modal data pairs of images and texts in the training set; specifically: obtaining The initial attention matrix is used to train the convolutional neural network by minimizing the loss function, and the improved attention matrix is output; the attention matrix and the feature matrix output by the convolutional neural network are dot-multiplied to obtain the weighted attention feature. cross-modal features.

Among them, image feature extraction and image attention feature extraction are performed on the images in the training set, including:

S1-1: The image feature extraction process uses the convolutional neural network CNN_F as the basic network structure, and outputs the image feature matrix in the fifth convolutional layer Conv5;

S1-2: The image attention feature extraction process includes: (1) An attention layer is introduced between the fifth convolutional layer and the fully connected layer, and the residual network Resnet-50 is improved, as shown in Figure 3, using a new The convolutional layer Conv6 and the maximum pooling layer Max pooling replace the fully connected layer. The purpose of introducing the Conv6 layer is to ensure that the size of the final attention map is consistent with the image feature matrix output by the Conv5 layer during the image feature extraction process; using the improved Resnet- 50 The network extracts the initial attention matrix O and uses the cross-entropy function as the loss function to pre-train this network.

(2) Further improve the initial attention matrix:

O′ _ir = sigmoid(max _k (O _ijk )),

Among them, _O'ir is the attention weight corresponding to the rth region of the image I _i , and _Oijk is the value of the kth category (a total of Nc categories) in the same position in the output O of the pre-training network.

是最终获得的注意力矩阵，μ_i是可计算的阈值，具体计算方式如下：in,

is the final attention matrix obtained, and μ _i is the computable threshold, the specific calculation method is as follows:

个激活值，其中Nr＝n×n表示区域数量。Sort the attention values of different areas of the image in ascending order, and assume that about p% (0<p<100) of the areas in an image belong to redundant areas, while the rest (about 1-p%) is the key area; then the value of μ _i is set to the _th

activation values, where Nr=n×n represents the number of regions.

在通道层面上进行延展，得到新的权重矩阵

然后和Conv5层输出的图像特征矩阵做点乘操作，得到经图像注意力特征加权的图像特征。(3) will

Extend at the channel level to get a new weight matrix

Then, do a dot product with the image feature matrix output by the Conv5 layer to obtain image features weighted by image attention features.

Perform text feature extraction and text attention feature extraction on the images in the training set, including:

S1-3: In the process of text feature extraction, two fully connected layers are used to obtain text features;

S1-4: The text attention feature extraction process includes: (1) Introducing an attention layer before the first fully connected layer Fc1, using a neural network without hidden layers, that is, a two-layer nonlinear classification network, to obtain the input text representation The mapping relationship W between each annotation and its corresponding classification is shown in Figure 4, and using W as the initial attention matrix, the least square error loss is used to guide the training of the classification network.

(2) Further improve the initial attention matrix:

Use the SoftMax function to standardize Wi _ij , and assume that the contribution of text _yi to different categories obeys the distribution F _i ( ),

F _i (l _j )=W′ _ij ,

Among them, l _j is the label information corresponding to the jth sample,

Solve the information entropy corresponding to each label:

W″ _i =-E _i ,

Solve the final attention matrix

Among them, v is a computable threshold, and the specific calculation method is:

个位置对应的值，其中Nt表示文本标注集合中不同标签的数量。Arrange the attention matrix W″ _i in ascending order, and set v as the first

The value corresponding to each position, where Nt represents the number of distinct labels in the text annotation set.

相乘得到经文本注意力特征加权的文本特征；其中，原始文本特征使用BoW表示，也可以是其他形式如Word2Vec。(3) Combine the original text features with the text attention map

Multiply to obtain text features weighted by text attention features; wherein, the original text features are represented by BoW, and can also be in other forms such as Word2Vec.

In the step S2, the image features and text features are input into the hash learning network model, the sign function is used to obtain a binary hash code, and the global objective function is constructed with the goal of minimizing the loss function:

γ和η均为超参数；相似度矩阵S为：对于两个不同的样本i，j，若两个样本标签至少有一个类都存在，那么将S_ij设置为1，否则置为0。Among them, n is the number of samples in the sample set, B ^x is the binary hash code corresponding to the picture mode, By is the binary hash code corresponding to the text mode, set B ⁼ B ^{x =} By = sign(γ( F+G)), W _x , W _y are the initial attention matrices corresponding to the image modal data and the text modal data, F _* = f ^x (x _i , θ ^x ), θ ^x is the image network parameter, F is The output of the image network; G _* = f ^y (y _i , θ ^y ), θ ^y is the text network parameter, G is the output of the text network; let

Both γ and η are hyperparameters; the similarity matrix S is: for two different samples i, j, if at least one class of the two sample labels exists, then S _ij is set to 1, otherwise it is set to 0.

In this embodiment, the first term of the global objective function is the negative log-likelihood loss function, and the second term is the quantization loss function. Using the sample supervision information, this embodiment proposes a third loss, that is, a semantic preservation loss function.

In the step S2, the hash learning model is optimized with the goal of minimizing the loss function, and the variables to be optimized are B, F, G, W _x , and W _y respectively. In this embodiment, an iterative optimization method is used to minimize the loss function, That is, only one variable is optimized at a time, and the other variables remain unchanged. The specific optimization strategy is as follows:

S2-1: Fix variables B, G, W _x , W _y , update variable F:

For sample points x _i , use stochastic gradient descent to optimize F _* , ie:

即

经反向传播更新图像网络的参数θ^x。Calculated using the chain rule

which is

The parameters θ ^x of the image network are updated via backpropagation.

S2-2: Fix variables B, F, G, W _y , update variable W _x :

Update this variable using stochastic gradient descent,

S2-3: Fix variables B, F, W _x , W _y , update variable G:

Similar to the process of updating the variable F, for the sample point y _j , the gradient of the variable G is first calculated, namely:

并更新参数θ^y。Calculate using the chain rule

and update the parameter θ ^y .

S2-4: Fix variables B, F, G, W _x , update variable W _y , namely:

S2-5: Fix variables F, G, W _x , W _y , update variable B, namely:

where V=γ(F+G).

In the step S3, after the optimization of the hash learning model is completed, according to the optimized hash learning model, the corresponding hash codes are calculated for all samples in the cross-modal data set;

When the retrieval task is performed, the obtained data is input into the model to obtain the corresponding hash code, and in the hash code of the modal data in the cross-modal data set with different modalities from the data to be tested, the N nearest Hamming distance is retrieved. A hash code is used to filter out cross-modal data that meets the retrieval requirements.

Example 2

As shown in FIG. 5 , this embodiment provides a cross-modal hash retrieval system based on an attention-aware mechanism, including:

The feature extraction module is used to perform feature extraction and attention feature extraction on the training set in the cross-modal data set, and obtain the cross-modal feature weighted by the attention feature;

The hash learning module is used to input the cross-modal features of the cross-modal data pairs in the training set into the hash learning model, and optimize the hash learning model with the goal of minimizing the loss function according to the output cross-modal hash code;

The retrieval module is used to filter the hash codes of the modal data that are different from the modalities of the data to be tested in the cross-modal data set according to the hash codes of the data to be tested obtained by the optimized hash learning model. Modal data requested.

It should be noted here that the above modules correspond to steps S1 to S3 in Embodiment 1, and the examples and application scenarios implemented by the above modules and corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1 above. It should be noted that the above modules may be executed in a computer system such as a set of computer-executable instructions as part of the system.

In this embodiment, the feature extraction module receives pictures and texts, and the image data and text data perform feature learning and hash coding learning at the same time. The image feature extraction network includes an image attention feature extraction module, and the text feature extraction network includes an image attention feature extraction module. Including the text attention feature extraction module, and finally input the attention-weighted features into the hash learning module to guide the generation of hash codes and improve the quality of hash code generation, which is suitable for various multi-modal data scenarios cross-modal retrieval task.

In further embodiments, there is also provided:

An electronic device includes a memory, a processor, and computer instructions stored on the memory and executed on the processor, and when the computer instructions are executed by the processor, the method described in Embodiment 1 is completed. For brevity, details are not repeated here.

It should be understood that, in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate array FPGA or other programmable logic devices , discrete gate or transistor logic devices, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.

The memory may include read-only memory and random access memory and provide instructions and data to the processor, and a portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

A computer-readable storage medium for storing computer instructions, when the computer instructions are executed by a processor, the method described in Embodiment 1 is completed.

The method in Embodiment 1 may be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor. The software modules may be located in random access memory, flash memory, read-only memory, programmable read-only memory or electrically erasable programmable memory, registers and other storage media mature in the art. The storage medium is located in the memory, and the processor reads the information in the memory, and completes the steps of the above method in combination with its hardware. To avoid repetition, detailed description is omitted here.

Those of ordinary skill in the art can realize that the unit, that is, the algorithm step of each example described in conjunction with this embodiment, can be implemented by electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may implement the described functionality using different methods for each particular application, but such implementations should not be considered beyond the scope of this application.

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, they do not limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solutions of the present invention, those skilled in the art do not need to pay creative efforts. Various modifications or deformations that can be made are still within the protection scope of the present invention.

Claims (9)

1. a cross-modal hash retrieval method based on attention perception mechanism, is characterized in that, comprises: Perform feature extraction and attention feature extraction on the training set in the cross-modal dataset to obtain cross-modal features weighted by attention features; The cross-modal features of the cross-modal data pairs in the training set are input into the hash learning model, and the hash learning model is optimized according to the output cross-modal hash code with the goal of minimizing the loss function; according to the output cross-modal hash code The Greek code builds a global objective function with the goal of minimizing the loss function; The global objective function is:

Among them, n is the number of samples in the sample set, B ^x and By are the hash codes corresponding to the x-modal data and the ^y -modal data in the cross-modal data pair, and θ ^x and θ ^y are the x-modal data and the y-modal data. The data corresponds to the network parameters of the network, W _x and W _y are the initial attention matrices corresponding to the x-modal data and the y-modal data, S _ij is the similarity matrix, γ and η are hyperparameters; F, G are the x-modal The modal data and the y modal data correspond to the output of the network, and L is the label information; According to the hash codes of the data to be tested obtained from the optimized hash learning model, the modal data that meet the retrieval requirements are screened from the hash codes of the modal data in the cross-modal data set that are different from the modalities of the data to be tested. . 2. A cross-modal hash retrieval method based on an attention-aware mechanism according to claim 1, wherein the cross-modal data set comprises multiple modal data, and the training set comprises a plurality of A cross-modal data pair that uses two parallel convolutional neural networks to perform feature extraction and attention feature extraction at the same time. 3. A cross-modal hash retrieval method based on an attention-aware mechanism as claimed in claim 1, wherein the attention feature extraction comprises: Obtain the initial attention feature matrix, train the convolutional neural network to minimize the loss function, and output the improved attention feature matrix; The attention feature matrix is dot-multiplied with the feature matrix output by the convolutional neural network, and the cross-modal feature weighted by the attention feature is obtained. 4. A cross-modal hash retrieval method based on an attention-aware mechanism as claimed in claim 1, wherein the global objective function comprises a negative log-likelihood loss function, a quantization loss function and a semantic preservation loss function. 5. A cross-modal hash retrieval method based on an attention-aware mechanism as claimed in claim 1, wherein an iterative optimization method is adopted to optimize the hash learning model, and the optimized variables include cross-modal data pairs. The hash code of , the output of the corresponding network for the cross-modal data pair, and the initial attention matrix. 6. A cross-modal hash retrieval method based on an attention-aware mechanism as claimed in claim 1, characterized in that, in the cross-modal data set, the hash codes of the modal data modalities different from those of the data to be tested are , compare the Hamming distance between the above hash code and the hash code of the data to be tested, retrieve the N hash codes with the nearest Hamming distance, and filter out the cross-modal data that meets the retrieval requirements. 7. A cross-modal hash retrieval system based on an attention-aware mechanism, comprising: The feature extraction module is used to perform feature extraction and attention feature extraction on the training set in the cross-modal data set, and obtain the cross-modal feature weighted by the attention feature; The hash learning module is used to input the cross-modal features of the cross-modal data pairs in the training set into the hash learning model, and optimize the hash learning model with the goal of minimizing the loss function according to the output cross-modal hash code; Construct a global objective function with the goal of minimizing the loss function according to the output cross-modal hash code; The global objective function is:

Among them, n is the number of samples in the sample set, B ^x and By are the hash codes corresponding to the x-modal data and the ^y -modal data in the cross-modal data pair, and θ ^x and θ ^y are the x-modal data and the y-modal data. The data corresponds to the network parameters of the network, W _x and W _y are the initial attention matrices corresponding to the x-modal data and the y-modal data, S _ij is the similarity matrix, γ and η are hyperparameters; F, G are the x-modal The modal data and y modal data correspond to the output of the network, and L is the label information; The retrieval module is used to filter the hash codes of the modal data that are different from the modalities of the data to be tested in the cross-modal data set according to the hash codes of the data to be tested obtained by the optimized hash learning model. Modal data requested. 8. An electronic device, characterized in that, comprising a memory and a processor and a computer instruction stored on the memory and running on the processor, when the computer instruction is run by the processor, completes any one of claims 1-6 the method described. 9 . A computer-readable storage medium, characterized in that it is used for storing computer instructions, and when the computer instructions are executed by a processor, the method according to any one of claims 1-6 is completed. 10 .

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