JP3737471B2 - Image processing method and image processing system - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an image processing method and an image processing system.
[0002]
[Prior art]
In recent years, the resolution of a printer has been improved in order to obtain a high-definition output. Accordingly, the amount of image data transferred from a computer to the printer has increased. In order to reduce the amount of image data and obtain a high-speed output, low-resolution multivalued image data is transferred from the computer to the printer, and a pattern is assigned to each pixel of the image data by the printer, thereby reducing the high-resolution low-value ( For example, there is a technique for converting into binary) image data.
[0003]
For example, when it is desired to finally obtain an output image of 600 dpi binary, when an output image of 600 dpi binary is transferred as it is from a computer to a printer, the information amount per pixel is 1 bit. However, when the above technique is used, the computer performs pseudo halftone processing on a 300 dpi 256-value image to generate a 300 dpi 5-value image and transfers it to the printer. The printer, for each pixel of the 300 dpi 5-value image, When a 600 dpi binary output image is generated by assigning a binary 2 × 2 pixel pattern according to the gradation value, the transfer information amount per pixel of the final output image of 600 dpi binary is transferred at 300 dpi 5 values. Because
(Log (5) ÷ log (2)) ÷ (2 × 2 [pixel]) ≈0.58 [bit]
It becomes.
[0004]
In addition, in contrast to the above technique, especially when the printer is an inkjet system, there is not much difference in printing results between 3 pixels in 2 × 2 pixels of 600 dpi and 4 pixels, so the computer has an image with 300 dpi 256 values. A 300 dpi 4-value image is generated and transferred to the printer. The printer assigns a binary 2 × 2 pixel pattern to each pixel of the 300 dpi 4-value image according to the pixel value, and outputs a 600 dpi binary output image. A technique for generating is proposed (for example, see Patent Document 1).
[0005]
In this case, the transfer information amount per pixel of the final output image of 600 dpi binary value is transferred with 300 dpi 4 value,
(Log (4) ÷ log (2)) ÷ (2 × 2 [pixel]) = 0.5 [bit]
Thus, the amount of transfer information can be further reduced.
[0006]
[Patent Document 1]
Japanese Patent Application Laid-Open No. 9-46522
[Problems to be solved by the invention]
However, in the system based on the above-mentioned publication, the printer does not strike 3 pixels in 2 × 2 pixels of 600 dpi, and does not fully utilize the capabilities of the printer.
[0008]
The present invention has been made in view of the above problems,
An object of the present invention is to provide an image processing method and an image processing system that realize high-definition image output by making use of the capabilities of a printer while reducing the amount of transfer information.
[0009]
[Means for Solving the Problems]
According to the present invention, there is provided an image processing method for generating fourth image data having a number of gradations r, the number of pixels being n times horizontal and m times vertical with respect to the first image data having the number of gradations p, In the image processing method, a resolution conversion process is performed on the first image data to generate second image data having a number of pixels of n0 times horizontal and m0 times vertical; and the second image data is simulated. Performing halftone processing to generate third image data having the number of gradations q; and generating fourth image data having a pixel number n1 times horizontal and m1 times vertical to the third image data. And the step of generating the fourth image data includes each of the fourth image data of the horizontal n1 pixel and the vertical m1 pixel corresponding to the position according to the gradation value of the third image data at a certain pixel position. The gradation value of the pixel position is determined, and the third image data of the certain pixel position And tone value, a value obtained by adding the average tone value of the pattern of the fourth image data Te weighted by occurrence probability corresponding to the position generally coincides. However, p> q ≧ r ≧ 2. N, m, n0, m0, n1, and m1 are positive integers, n0 × n1 = n, m0 × m1 = m .
[0010]
Further, the method includes a step of determining the magnifications n0 and m0 according to the image processing mode .
[0011]
Further, the number of gradations q of the third image data is q < 1 + n1 × m1 × (r−1).
Is a power of 2.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be specifically described below with reference to the drawings.
Example 1
FIG. 1 shows a configuration example of an image processing system according to the present invention. In this embodiment, it is assumed that the printing unit 104 in the printer 112 has a resolution of 600 dpi in both vertical and horizontal directions and has a binary expression capability per pixel.
[0013]
In the computer 111, the application 101 sends a drawing command to the printer driver 102 according to an instruction from a user (not shown). At that time, the user designates the image processing mode and selects either the high-definition image processing mode or the high-speed image processing mode. The high-definition image processing mode is a mode in which it takes time to obtain an output result, but a high-definition output can be obtained. On the other hand, the high-speed image processing mode is a mode in which the output result can be obtained quickly although the output quality is inferior.
[0014]
When the image processing mode designated by the user is the high-definition image processing mode, the printer driver 102 interprets the drawing command received from the application and creates a 300 dpi page image.
[0015]
For example, when the printer driver 102 receives a 72 dpi 256-value monochrome image from the application 101 and receives a rendering command to process and output it, the printer driver 102 performs resolution conversion processing to a 300 dpi image, and then performs pseudo halftone processing. Processing is performed to convert a 256-value image per pixel into a 4-value image.
[0016]
Regarding resolution conversion processing, there are various processing methods such as the nearest pixel replacement method and cubic function convolution method, and any method may be used. Further, a configuration in which the resolution conversion process or the pseudo halftone process method is changed according to the image processing mode designated by the user may be used.
[0017]
On the other hand, when the image processing mode designated by the user is the high-speed image processing mode, the printer driver 102 interprets the drawing command received from the application and creates a 150 dpi page image.
[0018]
For example, when the printer driver 102 receives a 72 dpi 256-value black and white image from the application 101 and receives a rendering command to process and output it, the printer driver 102 performs resolution conversion processing to a 150 dpi image, and then performs pseudo halftone processing. Processing is performed to convert a 256-value image per pixel into a 16-value image.
[0019]
In the present embodiment, in the high-definition image processing mode, the printer driver 102 performs quaternization of 300 dpi, and the gradation values 0, 85, 170, and 255 for the quantized values 0, 1, 2, and 3, respectively. To correspond. Here, the gradation value 0 represents the state with the lowest density, and the gradation value 255 represents the state with the highest density.
[0020]
Further, in the case of the high-speed image processing mode, the printer driver 102 performs 16 dpi 16-value conversion, and the gradation values 0 to 255 are made to correspond uniformly to the quantization values 0 to 15 in 17 increments. Here, the gradation value 0 represents the state with the lowest density, and the gradation value 255 represents the state with the highest density.
[0021]
FIG. 2 shows a configuration example of pseudo halftone processing by error diffusion processing for converting a 256-value image per pixel into a 4-value image. The input unit 201 inputs 256 gradation values from a memory (not shown), and sends a corrected gradation value obtained by adding an output value from an error diffusion unit 204 described later to the comparison unit 202.
[0022]
The comparison unit 202 compares the corrected gradation value with the threshold value. As shown in FIG. 6, when the corrected gradation values are 0 to 42, 43 to 127, 128 to 212, 213 to 255, the output quantized values are 0, 1, 2, and 3, respectively, and the output quantized values are Send to output means 205. The output unit 205 sends the output quantized value to the printer controller 103.
[0023]
Further, the comparison unit 202 sends the difference between the output gradation value and the corrected gradation value to the error buffer 203 as an error. For example, when the corrected gradation value is 60 and the output gradation value is 85, +25 is sent to the error buffer 203. The error buffer 203 stores the error in the memory.
[0024]
When calculating the corrected gradation value of the target pixel, the error diffusion unit 204 inputs an error around the target pixel from the error buffer 203 and outputs a value obtained by a product-sum operation with an error diffusion matrix (not shown). The same can be done when a 256-value image per pixel is converted to a 16-value image.
[0025]
Thereafter, the printer driver 102 sends the 300 dpi 4-valued or 150 dpi 16-valued image to the printer controller 103 in the printer 112. The printer controller 103 creates an image to be output based on the image data received from the printer driver 102.
[0026]
FIG. 5 shows an example of a method in which the printer controller 103 creates an image to be output based on the image data received from the printer driver 102. The quantized value input unit 501 reads a quantized value, which is 300 dpi 4-value image data, from a memory (not shown). The appearance probability determining unit 502 determines which pattern in FIG. 3 is to appear at what probability based on the gradation value corresponding to the quantized value input from the quantized value input unit 501, The information is passed to the selection means 504.
[0027]
In FIG. 3, in each pattern, a pixel indicated by a black circle is output with a gradation value of 255, and a pixel other than that is output with a gradation value of 0. Here, the average gradation value of the pattern 00 is 0, the average gradation values of the patterns 10 to 13 are all 255 × 1/4 (= 63.75), and the average gradation values of the patterns 20 to 25 are all 255 × 2/4. (= 127.5), the average gradation values of the patterns 30 to 33 are all 255 × 3/4 (= 191.25), and the average gradation value of the pattern 40 is 255.
[0028]
Therefore, the appearance probability determining unit 502 determines the appearance probability of each pattern as follows, for example. That is, since the corresponding gradation value is 85 for the quantized value 1, the probability that any of the patterns 10 to 13 appears is 2/3, and the probability that any one of the patterns 20 to 25 appears is 1 / 3. As a result, the average gradation value of the appearing pattern is 85, which is equal to the gradation value 85 corresponding to the quantization value 1.
[0029]
Furthermore, regarding the patterns 10 to 13, the appearance probability of each pattern is set to 2/12 in order to set the sum of the appearance probabilities of the patterns to 2/3.
[0030]
Furthermore, for patterns 20 to 25, the appearance probability of each pattern is 1/18 in order to reduce the sum of the appearance probabilities of each pattern to 1/3.
[0031]
Similarly, the appearance probability of each pattern is determined for other quantized values, and the probability of each pattern appearing for the quantized values 0, 1, 2, 3 is shown by 401, 402, FIG. The values shown in 403 and 404 are transferred to the pattern selection unit 504.
[0032]
For example, when the quantized value, which is 300 dpi 4-valued image data that has been read, is 1, the relationship between the output pattern and the appearance probability shown in 402 is passed to the pattern selection means 504.
[0033]
The pseudo random number generation means 503 generates a pseudo random number and sends the value to the pattern selection means 504. The pattern selection unit 504 selects a pattern to be output from the appearance probability received from the appearance probability determination unit 502 and the pseudo random number value received from the pseudo random number generation unit 503 and writes the pattern to a memory (not shown).
[0034]
For example, when the appearance probability received from the appearance probability determining means 502 is the one shown in 402 of FIG. 4, the pseudo random number value is normalized to 0 or more and less than 1,
If the pseudo-random value is less than 6/36, select pattern 10, otherwise,
If the pseudo-random value is less than 12/36, select pattern 11;
If the pseudo-random value is less than 18/36, select pattern 12, otherwise,
If the pseudo-random value is less than 24/36, select pattern 13;
If the pseudo-random value is less than 26/36, select pattern 20;
If the pseudo-random value is less than 28/36, select pattern 21;
If the pseudorandom value is less than 30/36, select pattern 22, otherwise,
If the pseudo-random number is less than 32/36, select pattern 23, otherwise
If the pseudo-random value is less than 34/36, select pattern 24;
Otherwise, by selecting the pattern 25, the relationship between the output pattern and the appearance probability can be made as indicated by 402 in FIG.
[0035]
Therefore, when the pseudo random number value received from the pseudo random number generation means 503 is a value corresponding to 9/36 when the pseudo random number value is normalized to 0 or more and less than 1, the pattern 11 is selected.
[0036]
As described above, the printer controller 103 converts the 300 dpi 4-value image data received from the printer driver 102 into 600 dpi 2-value image data, and then sends the 600 dpi 2-value image data to the printing unit 104.
[0037]
Similarly, when receiving 150 dpi 16-value image data from the printer driver 102, the image data is converted into 600 dpi binary image data, and then sent to the printing unit 104 as 600 dpi binary image data. The printing unit 104 prints the image received from the printer controller on paper.
[0038]
In the present exemplary embodiment, the configuration in which the printing unit 104 has a binary representation capability per pixel has been described as an example. However, the present invention is not limited to this. For example, the printing unit 104 has an output resolution of 600 dpi, If the image has a ternary expression capability per pixel and an image having 72 pi 256 values in both vertical and horizontal directions is input from the application 101, the printer driver 102 creates a 300 dpi image by resolution conversion processing and then performs pseudo halftone processing. Alternatively, a 300 dpi 10-value image may be created and sent to the printer controller 103 in the printer 112, and the printer controller 103 may assign a ternary pattern per pixel for each 300 dpi 1 pixel in both vertical and horizontal directions.
[0039]
In this embodiment, the 72 dpi image is converted to 300 dpi by the resolution conversion process. However, the resolution conversion process may not be performed. For example, when the printing unit 104 has an output resolution of 600 dpi and has a binary expression capability per pixel, when the image input from the application 101 has 100 dpi 256 values, resolution conversion processing is not performed, and pseudo halftone processing is performed. A 100 dpi 256-valued image is converted into a 100 dpi 36-valued image and sent to the printer controller 103 in the printer 112. The printer controller 103 assigns a binary pattern per pixel for 6 pixels in the vertical and horizontal directions to 100 dpi 1 pixel. May be.
[0040]
In this embodiment, a black and white image is input from the application 101. However, the same operation can be performed when a color image is input. That is, in the printer driver 102, when an image input from the application 101 is expressed in RGB, and the printing unit 104 outputs using CMYK colors, color conversion processing is performed and the image is expressed in CMYK. After the conversion, processing can be performed in the same manner as when a monochrome image is input by performing resolution conversion processing and pseudo halftone processing independently for each color. The same processing can be performed even if the color conversion processing is performed after the resolution conversion processing.
[0041]
In this embodiment, pseudo halftone processing is performed using error diffusion processing in the printer driver. However, the present invention is not limited to this, and other methods such as an average error minimization method that can obtain almost the same processing results, dithering, and the like. A processing method may be used.
[0042]
In this embodiment, the gradation values corresponding to the quantized values are equally allocated in increments of 85, such as 0, 85, 170, 255 in the case of quaternization, and in increments of 17 in the case of 16-value. However, the present invention is not limited to this, and a configuration in which they are allocated unevenly may be used. For example, in the case of quaternarization, it is possible to increase the expressive power in an image region having a low density by finely taking gradation values such as 0, 64, 127, and 255 in a low density portion.
[0043]
In addition, this embodiment is configured to select only a pattern in which 2 pixels in 600 dpi 2 × 2 dots or 3 pixels are output with respect to the quantization value 1, but this is not limiting, and 0 pixel, 1 pixel in 600 dpi 2 × 2 dots, Or the structure which determines the pattern selected from various patterns, such as hitting 4 pixels, may be sufficient. By using more patterns using this configuration, it is possible to suppress the generation of texture, and to suppress the sense of incongruity caused by a large change in graininess from the surroundings when a gradation whose density gradually changes is processed. The essential point of the present invention is that the gradation value of the pattern at the position roughly matches the gradation value of a certain pixel in a probabilistic or average manner.
[0044]
(Example 2)
In the present embodiment, the difference from the first embodiment will be mainly described. The configuration example of the image processing system according to the present embodiment is the same as that of FIG. 1 described in the first embodiment.
[0045]
In this embodiment, it is assumed that the printing unit 104 in the printer 112 has a resolution of 600 dpi vertically and 1200 dpi horizontally, and has a binary representation capability per pixel.
[0046]
In the computer 111, the application 101 sends a drawing command to the printer driver 102 according to an instruction from a user (not shown). The printer driver 102 interprets the drawing command received from the application and creates a 300 dpi page image.
[0047]
For example, when the printer driver 102 receives a 72 dpi 256 monochrome image from the application 101 and receives a rendering command to process and output the image, it performs resolution conversion processing to a 300 dpi image.
[0048]
Thereafter, when the image processing mode designated by the user is the high-definition image processing mode, the printer driver 102 performs pseudo halftone processing and converts a 256-value image per pixel into an 8-value image.
[0049]
On the other hand, when the image processing mode designated by the user is the high-speed image processing mode, the printer driver 102 converts a 256-value image per pixel into a 4-value image by pseudo halftone processing.
[0050]
In this embodiment, in the high-definition image processing mode, the printer driver 102 performs octarization, and when 0 ≦ n <7, the quantization value n corresponds to a gradation value of 255 × n ÷ 7. .
[0051]
In the case of the high-speed image processing mode, the printer driver 102 performs quaternarization and associates the gradation values 0, 85, 170, and 255 with the quantized values 0, 1, 2, and 3, respectively. Here, the gradation value 0 represents the state with the lowest density, and the gradation value 255 represents the state with the highest density.
[0052]
Thereafter, the printer driver 102 sends the 300 dpi 8-valued or 300 dpi 4-valued image to the printer controller 103 in the printer 112. The printer controller 103 creates an image to be output based on the image data received from the printer driver 102.
[0053]
Similar to the first embodiment, FIG. 5 illustrates an example of a method in which the printer controller 103 creates an image to be output based on image data received from the printer driver 102. The quantized value input means 501 reads a quantized value, which is 300 dpi 8-value or 300 dpi 4-value image data, from a memory (not shown).
[0054]
The appearance probability determining unit 502 determines which pattern in FIG. 7 is to appear at what probability based on the gradation value corresponding to the quantized value input from the quantized value input unit 501, The information is passed to the selection means 504.
[0055]
In FIG. 7, in each pattern, a pixel indicated by a black circle is output with a gradation value of 255, and a pixel other than that is output with a gradation value of 0.
[0056]
here,
The average gradation value of pattern 00 is 0,
The average gradation values of the patterns 10 to 13 are all 255 × 1/8 (= 31.875),
The average gradation values of the patterns 20 to 25 are all 255 × 2/8 (= 63.75),
The average gradation values of the patterns 30 to 33 are all 255 × 3/8 (= 95.625),
The average gradation values of the patterns 40 to 41 are all 255 × 4/8 (= 127.5),
The average gradation values of the patterns 50 to 53 are all 255 × 5/8 (= 159.375),
The average gradation values of the patterns 60 to 61 are all 255 × 6/8 (= 191.25),
The average gradation values of the patterns 70 to 73 are all 255 × 7/8 (= 223.125),
The average gradation value of the pattern 80 is 255.
It is.
[0057]
Therefore, the appearance probability determining unit 502 determines the appearance probability of each pattern as follows, for example.
[0058]
When the high-speed image processing mode is designated, since the corresponding gradation value is 85 for the quantization value 1, the probability that any of the patterns 20 to 25 appears is 85/255, and the patterns 30 to 33 The probability that any of the above appears is 170/255. As a result, the average gradation value of the appearing pattern is 85, which is equal to the gradation value 85 corresponding to the quantization value 1.
[0059]
Furthermore, regarding the patterns 20 to 25, the appearance probability of each pattern is set to 85/1530 in order to set the sum of the appearance probability of each pattern to 85/255.
[0060]
For patterns 30 to 33, the appearance probability of each pattern is set to 170/1020 in order to set the sum of the appearance probability of each pattern to 170/255.
[0061]
Similarly, the appearance probability of each pattern is determined for other quantized values, and the probability that each pattern appears for the quantized values 0, 1, 2, and 3 in the high-speed image processing mode is shown in FIG. 1001, 1002, 1003, and 1004, and in the high-definition image processing mode, the probability of appearance of each pattern with respect to the quantized values 0 to 7 is shown in FIG. 9 and FIG. As the value, the appearance probability of each pattern is determined based on the selected image processing mode and the quantization value input to the quantization value input unit 501, and the appearance probability information is passed to the pattern selection unit 504.
[0062]
For example, when the quantized value, which is 300 dpi 4-value image data read in the high-speed image processing mode, is 1, the relationship between the output pattern 1002 and the appearance probability is passed to the pattern selection unit 504. The pseudo random number generation means 503 generates a pseudo random number and sends the value to the pattern selection means 504.
[0063]
The pattern selection unit 504 selects a pattern to be output from the appearance probability received from the appearance probability determination unit 502 and the pseudo random number value received from the pseudo random number generation unit 503 and writes the pattern to a memory (not shown).
[0064]
For example, when the appearance probability received from the appearance probability determining means 502 is the one shown in 1104 of FIG. 9, the pseudo random number value is normalized to 0 or more and less than 1,
If the pseudo-random value is less than 2/14, select pattern 30;
If the pseudo-random value is less than 4/14, select pattern 31;
If the pseudo-random value is less than 6/14, select pattern 32, otherwise
If the pseudo-random value is less than 8/14, select pattern 33, otherwise
If the pseudorandom value is less than 11/14, select the pattern 40, otherwise,
Otherwise, by selecting the pattern 41, the relationship between the output pattern and the appearance probability can be made as indicated by 1104 in FIG.
[0065]
Therefore, when the pseudo random number value received from the pseudo random number generation means 503 is a value corresponding to 3/14 when the pseudo random number value is normalized to 0 or more and less than 1, the pattern 31 is selected.
[0066]
As described above, the printer controller 103 converts the 300 dpi 8-value or 4-value image data received from the printer driver 102 into 600 dpi binary image data, and then sends the 600 dpi binary image data to the printing unit 104. The printing unit 104 prints the image received from the printer controller on paper.
[0067]
【The invention's effect】
As described above, according to the present invention, a high-speed and high-quality image can be obtained by reducing the amount of image data to be transferred.
[Brief description of the drawings]
FIG. 1 shows a configuration example of an image processing system according to Embodiments 1 and 2 of the present invention.
FIG. 2 shows a configuration example of pseudo halftone processing by error diffusion processing.
FIG. 3 shows a first pattern example assigned according to a gradation value.
4 shows an output pattern corresponding to a quantized value and its appearance probability in Example 1. FIG.
FIG. 5 illustrates a configuration example of a printer controller according to first and second embodiments.
6 shows a relationship between an output tone value and an output quantized value in the error diffusion process of FIG.
FIG. 7 shows a second pattern example assigned according to the gradation value.
8 shows an output pattern corresponding to a quantized value and its appearance probability in Example 2. FIG.
FIG. 9 shows another example of output patterns corresponding to quantized values and their appearance probabilities in the second embodiment.
FIG. 10 shows a continuation of FIG.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 101 Application 102 Printer driver 103 Printer controller 104 Printing part 111 Computer 112 Printer

Claims (6)

An image processing method for generating fourth image data having the number of pixels of n times the width and m times the height of the first image data of the number of gradations p and having the number of gradations r, and the image processing method includes: ,
Performing a resolution conversion process on the first image data to generate second image data having a number of pixels of n0 times horizontal and m0 times vertical;
Performing pseudo halftone processing on the second image data to generate third image data having the number of gradations q;
Generating fourth image data having a pixel count of n1 times horizontal and m1 times vertical to the third image data,
The step of generating the fourth image data is performed according to a gradation value of the third image data at a certain pixel position at each pixel position of the fourth image data of horizontal n1 pixels and vertical m1 pixels corresponding to the position. Determine the tone value,
The gradation value of the third image data at a certain pixel position substantially coincides with the value obtained by weighting and adding the average gradation value of the pattern of the fourth image data corresponding to the position according to the appearance probability. Image processing method.
However, p> q ≧ r ≧ 2.
N, m, n0, m0, n1, and m1 are positive integers, n0 × n1 = n, m0 × m1 = m . 2. The image processing method according to claim 1, further comprising a step of determining the magnifications n0 and m0 according to an image processing mode . The number of gradations q of the third image data is
q <1+ n1 × m1 × (r−1)
The image processing method according to claim 1, wherein the image processing method is a power of 2. An image processing system for generating fourth image data having a number of gradations r and a number of pixels that is n times wide and m times long with respect to the first image data having the number of gradations p, the image processing system comprising: ,
A second image data generating unit that performs resolution conversion processing on the first image data and generates second image data having a pixel number of n0 times horizontal and m0 times vertical;
Third image data generating means for performing pseudo halftone processing on the second image data to generate third image data having the number of gradations q;
Fourth image data generation means for generating fourth image data having a pixel number n1 times horizontal and m1 times vertical to the third image data;
The fourth image data generation means is configured to change the gradation of each pixel position of the fourth image data of the horizontal n1 pixel and the vertical m1 pixel corresponding to the position according to the gradation value of the third image data at a certain pixel position. Determine the value,
The gradation value of the third image data at a certain pixel position substantially coincides with the value obtained by weighting and adding the average gradation value of the pattern of the fourth image data corresponding to the position according to the appearance probability. Image processing system.
However, p> q ≧ r ≧ 2.
N, m, n0, m0, n1, and m1 are positive integers, n0 × n1 = n, m0 × m1 = m . 5. The image processing system according to claim 4, further comprising magnification determining means for determining the magnifications n0 and m0 according to an image processing mode . The number of gradations q of the third image data is
q <1+ n1 × m1 × (r−1)
The image processing system according to claim 4, wherein the image processing system is a power of 2.

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