JP2004336165A - Image processor - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image processor where reduction or enlargement with which a white stripe or a black stripe due to connection of white pixels or black pixels is prevented and the deterioration of the image quality is reduced is performed. <P>SOLUTION: An image processor 22 stores the number of pixels, which a control unit 10 calculates based on a magnification rate that is set and which is included in respective units that thin or interpolate one pixel in a first register 30. The control unit 10 calculates the number of the pixels showing an interval where a position of the thinned (or interpolated) pixel is shifted to a main scanning direction in the respective units adjacent to an auxiliary scanning direction based on the magnification rate, and stores the number of the pixels in a second register 31. An adder 32 suitably adds the number of the pixels stored in the first register 30 and the second register 31. A resolution converter 33 suitably thins or interpolates pixel data in image data which are sequentially obtained from CODEC 18 based on an added value. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an image processing apparatus that reduces or enlarges an image by thinning or interpolating pixels at a position based on a received scaling factor from an image in which a plurality of pixels are arranged in a matrix.
[0002]
[Prior art]
Generally, an image processing apparatus performs a reduction process by thinning out appropriate pixels on an image configured by arranging a plurality of pixels in a main scanning direction and a sub-scanning direction, and also appropriately performs image processing between adjacent pixels. The enlargement process is performed by inserting an interpolation pixel.
However, in particular, when the above-described reduction processing or enlargement processing is performed on a pseudo halftone image that forms a halftone with black and white alternation by performing dither processing or the like, the dither pattern is broken, and this is called moiré. White streaks or black streaks may occur and image quality may be degraded.
[0003]
Therefore, for example, when reducing an image, the position of the pixel to be thinned out is changed for each line in which a plurality of pixels are arranged in the main scanning direction or the sub-scanning direction, or the pixel to be thinned out is randomly selected. An image processing apparatus has been proposed in which the determination is made so that pixels continuous in the main scanning direction or the sub-scanning direction are not thinned out, thereby preventing deterioration in image quality.
By using such an image processing apparatus, it is possible to prevent not only continuous loss of white pixels or black pixels but also generation of white streaks or black streaks due to the connection of white pixels or black pixels.
An image processing apparatus that randomly determines the positions of pixels to be decimated is disclosed in Japanese Patent Application Laid-Open Publication No. H11-157421.
[0004]
[Patent Document 1]
JP 2001-285626 A
[Problems to be solved by the invention]
However, the image processing apparatus as disclosed in Patent Document 1 includes means for generating a random number in order to randomly determine the position of a pixel to be thinned or interpolated, and performs thinning or interpolation based on the generated random number. Since the configuration is such that the position of the pixel is determined, there is a problem that the circuit configuration becomes complicated.
[0006]
The present invention has been made in view of such circumstances, and performs thinning or interpolation in each unit adjacent to a plurality of pixels arranged in a straight line in a direction perpendicular to the arrangement direction of the plurality of pixels as one unit. By specifying the positions of the pixels so as not to be continuous in the vertical direction, the generation of white streaks and black streaks is prevented, and a reduction process or an enlargement process with reduced image quality deterioration can be performed, and thinning or interpolation is performed. An object of the present invention is to provide an image processing apparatus capable of simplifying circuit design as compared with a configuration in which pixel positions are determined at random.
[0007]
Another object of the present invention is to provide, for each unit adjacent in the direction perpendicular to the arrangement direction of a plurality of pixels arranged in a straight line, the positions of pixels at intervals of a predetermined number of pixels in the arrangement direction, And by thinning out or interpolating pixels at one of the positions near the position, a white or black vertical streak that may occur at intervals of a plurality of units in the vertical direction is obtained. It is an object of the present invention to provide an image processing apparatus capable of preventing the image processing.
[0008]
Still another object of the present invention is to set an interval for shifting the position of a pixel to be thinned out or interpolated in each unit based on the received scaling factor, thereby performing thinning in accordance with a reduction ratio or an enlargement ratio indicated by the scaling factor. Another object of the present invention is to provide an image processing apparatus capable of appropriately setting the position of a pixel to be interpolated and realizing a reduction process or an enlargement process with reduced image quality deterioration.
[0009]
[Means for Solving the Problems]
The image processing apparatus according to the first invention is configured such that, from an image in which a plurality of pixels are arranged in a matrix, a plurality of pixels arranged in a straight line are defined as one unit based on the received scaling factor, and one unit is used for each unit. In an image processing apparatus that thins or interpolates pixels and reduces or enlarges the image, for each unit adjacent in a direction perpendicular to the arrangement direction in which a plurality of pixels included in the unit are arranged, in the arrangement direction, It is characterized by comprising a specifying means for specifying the position of a pixel at intervals of a predetermined number of pixels, and a scaling means for thinning out or interpolating pixels at the position specified by the specifying means.
[0010]
In the case of the first invention, a plurality of pixels arranged linearly are defined as one unit, and each unit adjacent in a direction perpendicular to the arrangement direction of the plurality of pixels is a predetermined number of pixels in the arrangement direction. Identify the position of the pixel at intervals, at the specified position, thin out or interpolate the pixel, reduce or enlarge the image, the pixel to be thinned or interpolated in each unit, the direction perpendicular to the array direction , The generation of a vertical streak of black or white can be prevented, and a reduction process or an enlargement process with reduced image quality deterioration can be performed.
Further, the circuit design is performed by specifying the positions of the pixels to be thinned or interpolated by shifting the intervals of a predetermined number of pixels in the array direction, thereby comparing the positions of the pixels to be thinned or interpolated randomly. Can be simplified.
[0011]
An image processing apparatus according to a second aspect of the present invention is configured such that, based on a received scaling factor, a plurality of pixels arranged in a straight line form one unit from an image in which a plurality of pixels are arranged in a matrix. In an image processing apparatus that thins or interpolates pixels and reduces or enlarges the image, for each unit adjacent in a direction perpendicular to the arrangement direction in which a plurality of pixels included in the unit are arranged, in the arrangement direction, Specifying means for specifying the position of a pixel at intervals of a predetermined number of pixels; and a pixel to be thinned or interpolated from the position specified by the specifying means, and the position of the pixel at the position and the position of a pixel nearby in the arrangement direction. And a scaling unit for thinning out or interpolating pixels at the position selected by the selection unit.
[0012]
In the case of the second invention, for each unit adjacent in the direction perpendicular to the arrangement direction of the plurality of pixels arranged linearly, the position of the pixel is specified at intervals of a predetermined number of pixels in the arrangement direction. Then, by thinning out or interpolating pixels at the specified position and one of the positions near the position, it is possible to prevent the pixels to be thinned out or interpolated in each unit from continuing in the vertical direction. In addition, the pixels to be thinned or interpolated, which are positioned at intervals of a plurality of units in the vertical direction, can be appropriately shifted in the arrangement direction, and may be generated at intervals of the plurality of units. A white or black vertical streak can be prevented.
[0013]
An image processing apparatus according to a third aspect of the present invention includes a setting unit that sets the predetermined number of pixels based on the scaling factor, and the specifying unit sets a position of the pixel at an interval corresponding to the number of pixels set by the setting unit. Is configured to be specified.
[0014]
In the case of the third aspect, based on the received magnification, a predetermined number of pixels indicating an interval for shifting the position of the pixel to be thinned out or interpolated in each unit is set, so that the reduction ratio or the enlargement ratio indicated by the magnification is set. Accordingly, the positions of the pixels to be thinned out or interpolated can be appropriately set, and a reduction process or an enlargement process with reduced image quality deterioration can be realized.
[0015]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, an image processing apparatus according to the present invention will be described in detail with reference to the drawings showing an embodiment using a multifunction peripheral.
[0016]
(Embodiment 1)
FIG. 1 is a block diagram showing a configuration example of a multifunction peripheral according to the present invention. In the figure, reference numeral 1 denotes a multifunction peripheral.
The multifunction device 1 includes a control unit 10, a ROM 11, a RAM 12, an NCU (Network Control Unit) 13, a modem 14, a reading unit 15, a display unit 16, an operation unit 17, a CODEC 18, a code memory 19, an image memory 20, an image recording unit 21, , An image processing unit 22, etc., and are connected to each other via a bus 23.
[0017]
The control unit 10 is specifically configured by a CPU (Central Processing Unit) or an MPU (Micro Processor Unit), and controls the above-described hardware via the bus 23 and is stored in the ROM 11. Various software functions are realized according to the computer program.
The ROM 11 stores various computer programs and the like necessary for the operation of the multifunction peripheral 1 of the present invention in advance.
[0018]
The RAM 12 is configured by an SRAM, a flash memory, or the like, and temporarily stores data generated when the control unit 10 executes the computer program, and the obtained magnification. If a flash memory is used as the RAM 12, the stored contents will not be lost even if the power is cut off due to a power failure, movement of the MFP 1, or the like.
The modem 14 is constituted by a facsimile modem capable of performing facsimile communication, and is also directly connected to the NCU 13. The NCU 13 is connected to the public telephone network L, connects the modem 14 to the public telephone network L as necessary, and performs facsimile communication with another facsimile apparatus via the public telephone network L. It is possible.
[0019]
The display unit 16 is configured by a liquid crystal display (LCD) or the like, and displays an operation state of the multifunction device 1, data to be notified to a user, characters input from the operation unit 17, and the like.
The operation unit 17 includes various function keys necessary for operating the multifunction device 1, keys for a user to input a magnification, and the like. By using the touch panel type display unit 16, some or all of the various keys of the operation unit 17 can be substituted.
[0020]
The reading unit 15 reads an original using a scanner using a CCD (Charge Coupled Device), and inputs the read image data to the CODEC 18.
The CODEC 18 encodes the image data read by the reading unit 15 and stores the encoded image data in the code memory 19.
[0021]
The code memory 19 includes a DRAM or the like, and stores image data read by the reading unit 15 and encoded by the CODEC 18, and image data obtained from another facsimile apparatus via the NCU 13 and the modem 14.
In the present embodiment, the acquired image data is pseudo halftone image data in which each pixel is specified by binary data. Further, the scaling factor can be calculated not only by the user but also based on the size of the recording paper or the like specified by the user.
[0022]
The CODEC 18 is configured to decode the encoded image data stored in the code memory 19, decodes the image data read from the code memory 19, and performs image processing according to an instruction from the control unit 10. It is input to the unit 22 or the recording unit 21.
Here, the control unit 10 determines whether to perform the reduction processing or the enlargement processing on the image to be printed on the recording paper or the like based on the setting of the scaling ratio by the user or the setting of the recording paper size by the user. The instruction signal for instructing the execution of the reduction process or the enlargement process is input to the CODEC 18 and the image processing unit 22 based on the determination result.
[0023]
Therefore, when the instruction signal input from the control unit 10 instructs execution of the reduction process or the enlargement process, that is, when the set scaling ratio is not 100%, the CODEC 18 sends the decoded image data to the image processing unit 22. input. When the instruction signal input from the control unit 10 instructs not to perform the reduction process and the enlargement process, that is, when the set magnification is 100%, the CODEC 18 records the decoded image data in the recording unit. Input to 21.
The image processing unit 22 has a configuration as described below, and converts, from image data decoded by the CODEC 18, pixel data (pixels included in the pixel) constituting the image data at a position based on the scaling factor stored in the RAM 12. The pixel values are appropriately thinned out or interpolated, and the obtained image data is temporarily stored in the image memory 20.
[0024]
The image memory 20 includes a DRAM or the like, stores image data obtained from the image processing unit 22, and inputs the stored image data to the recording unit 21 under the control of the control unit 10.
The recording unit 21 is an electrophotographic printer, and converts the image data obtained from the CODEC 18 or the image based on the image data obtained from the image memory 20 into A3 portrait, B4 portrait, A4 portrait, B5 landscape, and hard copy. An optimum size is selected from recording paper of each size such as A5 width or an OHP (Over Head Projector) sheet and recorded.
[0025]
FIG. 2 is a block diagram illustrating a configuration example of the image processing unit 22 according to the first embodiment. The image processing unit 22 includes a first register 30, a second register 31, an adder 32, a resolution conversion unit 33, and the like. ing.
In the MFP 1 having the above-described configuration, the control unit 10 calculates the number of pixels included in one unit to be thinned out or interpolated, based on the scaling factor stored in the RAM 12. The number of pixels is input to the image processing unit 22, and the image processing unit 22 stores the acquired number of pixels in the first register 30.
[0026]
Specifically, for example, when performing a reduction process with a reduction ratio of 99%, the control unit 10 calculates 100 as the number of pixels included in the one unit so as to thin out one pixel from among 100 pixels. 100 is stored in the register 30.
Similarly, when performing the enlargement processing with the enlargement ratio of 101%, the control unit 10 calculates 100 as the number of pixels included in the one unit so as to interpolate one pixel for every 100 pixels, and 100 is stored in 30.
[0027]
In addition, the control unit 10 operates as a setting unit that sets a predetermined number of pixels based on the acquired magnification, and the set number of pixels is stored in the second register 31 of the image processing unit 22.
The image processing unit 22 determines, for each line formed by arranging a plurality of pixels in the main scanning direction, the position of a pixel to be thinned or interpolated in each adjacent line in the sub-scanning direction, by using the pixel stored in the second register 31. It operates as a specifying means for specifying at a time interval of several minutes.
The predetermined number of pixels may be set in advance and stored in the ROM 11.
[0028]
The adder 32 obtains the numerical values stored in the first register 30 and the second register 31 and performs an addition process as appropriate, thereby calculating the position of a pixel to be thinned out or interpolated for each unit and performing resolution conversion. The image processing unit 22 specifies the pixels to be thinned or interpolated based on the position calculated by the adder 32.
[0029]
Further, the image processing unit 22 acquires an instruction signal for instructing execution of a reduction process or an enlargement process from the control unit 10 and decoded image data from the CODEC 18, respectively. It is input to the resolution converter 33.
The resolution conversion unit 33 operates as a scaling unit that thins out or interpolates pixels at a position based on the added value calculated by the adder 32 of the image data input from the CODEC 18 according to an instruction signal input from the control unit 10. The image data obtained by thinning out or interpolating appropriate pixel data is stored in the image memory 20.
[0030]
FIG. 3 is a diagram for explaining a resolution conversion process by the image processing unit 22 according to the first embodiment. FIG. 3 shows a reduction process with a scaling factor of 99%. 3A shows an example in which the image processing unit 22 stores 100 in the first register 30 and 25 in the second register 31. FIG. 3B shows 100 in the first register 30 and 100 in the second register. Examples of the image processing unit 22 storing 1 in 31 are shown.
In FIG. 3, the direction indicated by X is the main scanning direction, and the direction indicated by Y is the sub-scanning direction, and a part of the image based on the image data is illustrated. Note that the grids in the figure indicate the pixels that constitute the image.
[0031]
When storing 100 in the first register 30 and 25 in the second register 31, the image processing unit 22 having the above-described configuration uses the addition value of the adder 32 as indicated by hatching in FIG. , One pixel for every 100 pixels arranged in the main scanning direction X, and for each line adjacent in the sub-scanning direction Y, a pixel to be thinned out by shifting a distance of 25 pixels in the main scanning direction X. Locate the location.
Similarly, when 100 is stored in the first register 30 and 1 is stored in the second register 31, the image processing unit 22 determines the main scanning direction based on the value added by the adder 32, as shown in FIG. Identify the position of the pixel to be thinned out by shifting one pixel for every 100 pixels arranged in X, and one pixel in the main scanning direction X in each line adjacent in the sub-scanning direction Y I do.
[0032]
The resolution conversion unit 33 that has obtained the instruction signal indicating the execution of the reduction process from the control unit 10 sequentially thins out the pixels at the positions specified as described above and stores the pixels in the image memory 20.
As described above, in each line formed by arranging a plurality of pixels in the main scanning direction X, by specifying the positions of the thinned pixels in the line adjacent to the sub-scanning direction Y so as not to be continuous in the sub-scanning direction Y, It is possible to prevent white or black vertical streaks occurring in the sub-scanning direction Y.
[0033]
When the instruction signal from the control unit 10 indicates that the enlargement process is to be performed, the resolution conversion unit 33 determines whether the pixel at the position indicated by hatching in FIG. By inserting an interpolation pixel forward or backward in the main scanning direction X, enlargement processing can be executed.
[0034]
(Embodiment 2)
Hereinafter, the configuration of the image processing unit 22 according to the second embodiment will be described. Note that the overall configuration of the multifunction peripheral 1 according to the present embodiment is the same as that of the above-described first embodiment, and a description thereof will be omitted. The same components of the image processing unit 22 are denoted by the same reference numerals, and description thereof is omitted.
[0035]
FIG. 4 is a block diagram illustrating a configuration example of the image processing unit 22 according to the second embodiment. The image processing unit 22 according to the present embodiment further includes a random number generation circuit 34.
In the image processing unit 22 according to the present embodiment, similarly to the image processing unit 22 in the above-described first embodiment, the resolution conversion unit 33 transmits an instruction signal for instructing a reduction process or an enlargement process from the control unit 10 to the CODEC 18. For the decoded image data, the addition value calculated by the adder 32 is obtained, and further, the random number generated by the random number generation circuit 34 is also obtained.
[0036]
The random number generating circuit 34 in the present embodiment is for generating, for example, three numerical values of 1, 2, and 3 at random, and the resolution conversion unit 33 outputs the image data input from the CODEC 18 from the adder 32. It operates as selection means for selecting one position corresponding to a numerical value input from the random number generation circuit 34 from the input position and two positions adjacent to the position in the main scanning direction X. At the position, pixels are thinned out or interpolated and stored in the image memory 20 in accordance with an instruction signal input from the control unit 10.
Since the random number generating circuit 34 selects one from three numerical values, a complicated circuit configuration is not required.
[0037]
FIG. 5 is a diagram for explaining a resolution conversion process by the image processing unit 22 according to the second embodiment, and shows a reduction process with a scaling factor of 99%, as in FIG. 5A shows an example in which the image processing unit 22 stores 100 in the first register 30 and 25 in the second register 31. FIG. 5B shows 100 in the first register 30 and 100 in the second register. Examples of the image processing unit 22 storing 1 in 31 are shown.
In FIG. 5 as well, the direction indicated by X is the main scanning direction, and the direction indicated by Y is the sub-scanning direction, and the grids in the figure indicate the pixels that constitute the image.
[0038]
When storing 100 in the first register 30 and 25 in the second register 31, the image processing unit 22 configured as described above specifies one pixel for every 100 pixels among the pixels arranged in the main scanning direction X. In addition, one pixel out of three pixels adjacent to the one pixel in the main scanning direction X indicated by hatching in FIG. 5A is composed of two pixels adjacent to the one pixel in the main scanning direction X. , Based on the numerical value input from the random number generation circuit 34, and specifies the position of the pixel to be thinned or interpolated.
In each line adjacent in the sub-scanning direction Y, the positions of pixels to be thinned out or interpolated are specified by shifting the interval from 22 pixels to 26 pixels in the main scanning direction X.
[0039]
Similarly, when 100 is stored in the first register 30 and 1 is stored in the second register 31, one pixel is specified for every 100 pixels among the pixels arranged in the main scanning direction X. One of three pixels adjacent to the one pixel in the main scanning direction X indicated by hatching in FIG. 5B and two pixels adjacent to the one pixel in the main scanning direction X is input from the random number generation circuit 34. A pixel is selected based on the numerical value obtained, and is specified as a position of a pixel to be thinned or interpolated.
[0040]
In addition, the resolution conversion unit 33 that has obtained the instruction signal indicating the execution of the reduction processing from the control unit 10 sequentially thins out the pixels at the positions specified as described above and stores the pixels in the image memory 20.
As described above, in each line in which a plurality of pixels are arranged in the main scanning direction X, the positions of the thinned pixels in the lines adjacent in the sub-scanning direction Y are specified while being shifted in the main scanning direction X, and the specified positions are determined. By selecting one position from the vicinity and thinning out the pixels at the selected position, it is possible to prevent the positions of the thinned pixels from continuing in the oblique direction and to flexibly change the positions of the thinned pixels within a predetermined area. Can be.
[0041]
When the instruction signal from the control unit 10 indicates that the enlargement process is to be performed, the resolution conversion unit 33 performs the main scanning of the pixel at the position specified based on the addition value calculated by the adder 32 as described above. By inserting the interpolation pixel forward or backward in the direction X, the enlargement processing can be executed.
[0042]
In each of the embodiments described above, the resolution conversion processing in the main scanning direction X of the image is described, but the resolution conversion processing in the sub-scanning direction Y is also applicable. Further, for each line adjacent in the sub-scanning direction Y, the positions of pixels to be thinned out or interpolated are specified by shifting the interval of 25 pixels or 1 pixel in the main scanning direction X, but these values are limited to these values. I can't.
[0043]
【The invention's effect】
In the case of the first invention, a plurality of pixels arranged linearly are defined as one unit, and each unit adjacent in a direction perpendicular to the arrangement direction of the plurality of pixels is a predetermined number of pixels in the arrangement direction. By specifying the position of the pixel at an interval and by thinning or interpolating the pixel at the specified position, the pixel to be thinned or interpolated in each unit is not continuous in the direction perpendicular to the arrangement direction, and is white or black. It is possible to perform reduction processing or enlargement processing in which deterioration of image quality due to prevention of vertical streaks is reduced.
In each unit, the position of the pixel to be thinned or interpolated is specified at a predetermined number of pixels while being shifted, so that the position of the pixel to be thinned or interpolated is determined at random. Can be simplified.
[0044]
In the case of the second invention, for each unit adjacent in the direction perpendicular to the arrangement direction of the plurality of pixels arranged linearly, the position of the pixel is specified at intervals of a predetermined number of pixels in the arrangement direction. Then, by thinning out or interpolating pixels at the specified position and one of the positions near the position, it is possible to prevent the pixels to be thinned out or interpolated in each unit from continuing in the vertical direction. In addition, the pixels to be thinned or interpolated, which are located at intervals of a plurality of units in the vertical direction, can be appropriately shifted in the arrangement direction, and may be generated at intervals of the plurality of units. It is possible to realize a reduction process or an enlargement process in which a sharp white or black vertical streak is prevented and deterioration of image quality is reduced.
[0045]
In the case of the third aspect, based on the received magnification, a predetermined number of pixels indicating an interval for shifting the position of the pixel to be thinned out or interpolated in each unit is set, so that the reduction ratio or the enlargement ratio indicated by the magnification is set. Accordingly, the positions of the pixels to be thinned out or interpolated can be set as appropriate, and a reduction process or an enlargement process with reduced image quality deterioration can be realized.
[Brief description of the drawings]
FIG. 1 is a block diagram illustrating a configuration example of a multifunction peripheral according to the present invention.
FIG. 2 is a block diagram illustrating a configuration example of an image processing unit according to the first embodiment.
FIG. 3 is a diagram for explaining resolution conversion processing by an image processing unit according to the first embodiment;
FIG. 4 is a block diagram illustrating a configuration example of an image processing unit according to a second embodiment;
FIG. 5 is a diagram for explaining a resolution conversion process performed by an image processing unit according to the second embodiment.
[Explanation of symbols]
1 MFP 10 control unit (setting means)
22 Image processing unit (specification means)
33 Resolution conversion unit (magnification means, selection means)

Claims (3)

From an image in which a plurality of pixels are arranged in a matrix, the plurality of pixels arranged in a straight line are taken as one unit, and one pixel in each unit is thinned out or interpolated based on the received magnification, and In an image processing device that reduces or enlarges
For each unit adjacent in the direction perpendicular to the arrangement direction in which a plurality of pixels included in the unit are arranged, identification means for identifying the position of the pixel at an interval of a predetermined number of pixels in the arrangement direction,
An image processing apparatus comprising: a scaling unit that thins out or interpolates pixels at a position specified by the specifying unit. From an image in which a plurality of pixels are arranged in a matrix, the plurality of pixels arranged in a straight line are taken as one unit, and one pixel in each unit is thinned out or interpolated based on the received magnification, and In an image processing device that reduces or enlarges
For each unit adjacent in the direction perpendicular to the arrangement direction in which a plurality of pixels included in the unit are arranged, identification means for identifying the position of the pixel at an interval of a predetermined number of pixels in the arrangement direction,
Selecting means for selecting a position of a pixel to be thinned or interpolated from the position specified by the specifying means, and a position of a pixel at the position and a pixel nearby in the arrangement direction;
An image processing apparatus comprising: a scaling unit that thins out or interpolates pixels at a position selected by the selection unit. Setting means for setting the predetermined number of pixels based on the magnification,
3. The image processing apparatus according to claim 1, wherein the specifying unit is configured to specify a pixel position at intervals of the number of pixels set by the setting unit. 4.

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