JP2013181818A - Shape measuring instrument and shape measuring method for shape steel - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a shape measuring instrument for shape steel which can be not only installed to a horizontal roll having a small diameter but also can be applied to a shape steel having thin flange thickness, and a shape measuring method.SOLUTION: An instrument 20 for measuring a shape of a shape steel 17 during a universal mill 10 including a vertical pair of horizontal rolls 11, 12 and a horizontal pair of vertical rolls 13 rolls the shape steel 17 having a flange 15 and a web 16 includes a flexible rod 22 flexible in an axis orthogonal direction and having a tip part being a contact piece 21 brought into contact with a flange edge surface 15a, a support member 23 fixed to side surface parts 11a, 12a of the horizontal rolls 11, 12 to support the tip part of the flexible rod 22, a drive part 24 connected to a rear end part of the flexible rod 22 to move the flexible rod 22 in the axial direction thereof, and a displacement meter 25 connected to the drive part 24 to measure a movement amount of the flexible rod 22.

Description

  The present invention relates to an apparatus and method for measuring the shape of a shape steel having a web and a flange, such as an H-section steel, and more particularly to an apparatus and method for measuring the amount of web deviation.

  In the H-section steel rolling line, first, using the breakdown mill shown in FIG. 10A, reverse rolling is performed in the order of A1, A2, A3, and A4, and a beam blank (rolling material dedicated to H-section steel) is used. Form. Next, reverse rolling is repeated between the first coarse universal mill of FIG. 10B, the edger mill of FIG. 10C, and the second coarse universal mill of FIG. 10D to reduce the thickness of the beam blank. Reduce the flange width. Thereafter, one-pass rolling is performed with the finishing universal mill shown in FIG. 10 (E), the X-shaped flange is corrected to the H shape, and the final product shape is finished.

  In the rolling of section steel by a universal mill, rolling is performed in a state where the positions of the web center (center line in the thickness direction of the web) and the mill center (line passing through the center in the barrel length direction of the left and right saddle rolls) are shifted. Then, the position of the web moves according to the amount of misalignment between the centers, and the web is biased. In particular, if the shape steel is warped or the web bites into the horizontal roll at an angle, the misalignment between the web center and the mill center increases further, and the amount of web deviation at the front and rear ends of the shape steel increases. To do.

  Conventionally, the inspection of the amount of deviation of the web has been performed by cutting a predetermined portion of the rolled H-shaped steel with a heat saw, collecting a cross-sectional sample, and an inspector measuring the size of the collected cross-sectional sample. . Further, in Patent Document 1, a pair of left and right flange width upper end distance measuring devices and flange width lower end distance measuring devices are arranged opposite to each other above and below the shape steel, and the flange end portions are adjusted while adjusting the distance between the height direction and the horizontal direction. To measure the distance up to and calculate the flange width and its thickness with the calculation control device, and on the flange width, the web surface distance measurement device is attached to the side of the lower end distance measurement device so that the position can be adjusted in the horizontal direction, An on-line dimension measuring apparatus for a shape steel is disclosed in which a web thickness is obtained by measuring a distance to a web surface, and a web deviation amount is calculated using each distance measurement value.

  However, the above-described conventional technique has a problem that it takes time to calculate the amount of deviation of the web, so that not only the dimension measurement of the shape steel cannot be performed in real time but also the apparatus cost is increased.

  Therefore, Patent Document 2 discloses an invention of an apparatus and a method for measuring the shape of a shape steel when the shape steel having a flange and a web is rolled by a universal mill. In this invention, a web deviation measuring device for measuring the distance to the shape steel is arranged on each of the pair of upper and lower horizontal rolls, and the distance from the flange end face measured by each web deviation measuring device to the web deviation measuring device. Based on the above, the amount of deviation of the web is calculated by the control device.

Japanese Patent Laid-Open No. 04-2113014 JP 2011-235338 A

  In patent document 2, as a web deviation measuring device, a main component is a differential transformer (differential transformer type displacement meter) and a roller-like contactor that is connected to the differential transformer and contacts a flange end surface of the section steel. And an embodiment using an optical displacement meter as a main component.

However, when the web deviation measuring device is composed of a differential transformer and a roller-shaped contact, the differential transformer has a length of a few tens of mm even if the length is short. There is a problem that a space for installing the measuring device cannot be secured on the side surface of the horizontal roll. Incidentally, the minimum diameter of the horizontal roll in which the web deviation measuring device of this embodiment can be installed is about 2000 mm.
Moreover, in order to make a contactor contact a flange end surface, it is necessary to insert a contactor into the gap between the horizontal roll and the saddle roll, but depending on the shape steel size, the flange thickness may be less than 10 mm. In order to cope with a shape steel having a thin flange, it is necessary that the contact is not only thinner and smaller but also has sufficient strength. However, it is not only difficult to manufacture contacts that satisfy these conditions, but it is expensive.

  On the other hand, when the web deviation measuring device is an optical displacement meter, the cooling water and scale for cooling the roll are scattered around the mill, so the light irradiated from the optical displacement meter is scattered and the scaled water or scale Will be scattered. Therefore, there is a problem that accurate dimension measurement of the shape steel is extremely difficult.

  The present invention has been made in view of such circumstances, and it is possible to provide a shape measuring apparatus and a shape measuring method for a shape steel that can be applied not only to a horizontal roll having a small diameter but also to a shape steel having a thin flange thickness. The purpose is to provide.

In order to achieve the above object, the first invention is a universal mill incorporating a pair of upper and lower horizontal rolls and a pair of left and right saddle rolls, and when rolling the shape steel having a flange and a web, the shape of the shape steel A device for measuring
The front end is a contact that abuts against the flange end surface, a flexible rod that is flexible in the direction perpendicular to the axis, a support member that is fixed to the side surface of the horizontal roll and supports the tip of the flexible rod, and the flexible rod A drive unit connected to the rear end portion and moving the flexible rod in the axial direction thereof, and a displacement meter connected to the drive unit and measuring the movement amount of the flexible rod are provided.
Here, the “tip portion” refers to the tip portion of the “tip portion”, and the “tip portion” includes the “tip portion”.

The second invention is a universal mill incorporating a pair of upper and lower horizontal rolls and a pair of left and right saddle rolls. When rolling a shape steel having a flange and a web, the shape of the shape steel according to the first invention is provided. A method of measuring the shape of the shape steel using a measuring device,
The support member is fixed to a side surface portion of the horizontal roll and the tip portion of the flexible rod is supported by the support member, and an intermediate portion of the flexible rod is bent so that the drive unit and the displacement meter are connected to the horizontal roll. A step of arranging the arbor of the horizontal roll or the horizontal roll of
A step of causing the contact to intermittently protrude by moving the flexible rod in the axial direction of the horizontal roll and abutting the contact with a flange end surface;
Deriving the moving distance of the contact to the flange end surface based on the data of the moving amount of the flexible rod measured by the displacement meter;
And a step of calculating a deviation amount of the web based on the derived movement distance of the contact to the flange end surface.

  In 1st and 2nd invention, let the front-end | tip part of the flexible rod which has flexibility be a contactor. By moving the flexible rod in the axial direction in accordance with the rotation of the horizontal roll, the contact is intermittently projected outward in the radial direction of the horizontal roll, and the contact is brought into contact with the flange end surface. And the movement distance of the contact to a flange end surface is derived | led-out by measuring the axial movement amount of this flexible rod with the displacement meter connected with the flexible rod via the drive part. At that time, by using a flexible rod whose rigidity in the direction perpendicular to the axis is lower than that in the axial direction, the moving distance of the contact to the flange end surface can be accurately measured even when the intermediate part of the flexible rod is curved. It becomes possible.

  In addition, in the horizontal roll in which the shape measuring apparatus for the shaped steel according to the first invention is installed, the distance x from the contact (not in the projecting state) to the rolling surface of the horizontal roll is known when the shape measuring apparatus is installed. That is, since the measurement has been completed, the distance B from the flange end surface to the web surface on the flange end surface side can be calculated as x−δ if the moving distance δ of the contact to the flange end surface can be measured.

  In the shape measuring apparatus for shape steel according to the first aspect of the present invention, it is preferable that a regulating member for regulating the direction of the contact is provided so that the contact contacts the end face of the flange perpendicularly.

  When the contact comes into contact with the flange end surface during rolling, the contact moves in the direction of conveying the shape steel by friction with the flange end surface, and then returns to the original position by the restoring force of the flexible rod. At that time, the contactor moves greatly (overshoot) in the direction opposite to the conveying direction, and the pendulum motion is performed with the support member as a fulcrum. In this configuration, when the contact moves in the direction opposite to the conveying direction, the restricting member prevents overshoot of the contact, and the contact stops at a position where it abuts perpendicularly to the flange end surface.

  The shape measuring apparatus for shape steel according to the first invention may further include an impact sensor for measuring an impact force when the contact contacts the flange end surface.

  The point of contact of the contact with the flange end face can be identified from the change in the shape of the time history graph that shows the distance of movement of the contact, but contact can be obtained by capturing the peak time of the impact force measured by the impact sensor. It becomes possible to easily specify the point in time when the child comes into contact with the flange end surface.

  Moreover, 3rd invention is a universal mill provided with the shape measuring apparatus of the shape steel based on 1st invention.

  In the shape measuring apparatus and the shape measuring method of the shaped steel according to the present invention, the end of the flange is measured by measuring the amount of axial movement of the flexible rod that is flexible in the direction perpendicular to the axis. Therefore, it can be installed on a horizontal roll having a small diameter by curving the intermediate portion of the flexible rod. Moreover, since the contact is made into a rod shape, the invention can be applied to a steel having a thin flange thickness.

It is the partial schematic diagram which looked at the universal mill by which the shape measuring device of the shape steel which concerns on the 1st Embodiment of this invention was installed was seen from the conveyance direction of the shape steel. It is the partial schematic diagram which looked at the universal mill in which the same shape measuring apparatus was installed from the conveyance orthogonal direction. It is a schematic diagram of the same shape measuring apparatus. (A)-(D) are the schematic diagrams for demonstrating the motion of a contactor. It is a schematic diagram of the time history waveform which shows the movement distance of a contact. It is a time history graph which shows an example of the movement distance waveform of the contact measured by the displacement meter. It is the schematic diagram which showed the modification of the installation method of the same shape measuring apparatus. It is a partial schematic diagram of the shape measuring apparatus of the shape steel which concerns on the 2nd Embodiment of this invention. It is a schematic diagram of the time history waveform which shows the movement distance of a contactor, and the output of an impact sensor. It is a schematic diagram for demonstrating the manufacturing process of the H-section steel by the conventional H-section steel rolling line, (A) is a breakdown mill, (B) is a 1st rough universal mill, (C) is an edger mill, ( D) is a second coarse universal mill, and (E) is a finishing universal mill.

  Next, embodiments of the present invention will be described with reference to the accompanying drawings for understanding of the present invention.

[First Embodiment]
The partial model which looked at the universal mill 10 in which the shape measuring apparatus 20 (henceforth only a "shape measuring apparatus") of the shape steel which concerns on the 1st Embodiment of this invention was installed was seen from the conveyance direction of the shape steel 17. FIG. 1 shows a diagram, and FIG. 2 shows a partial schematic view of the universal mill 10 as viewed from the direction orthogonal to the conveyance. In the following description, with respect to the shape measuring device 20, the side closer to the flange end surface 15a of the shaped steel 17 is referred to as the “front” side, and the far side is referred to as the “rear” side.

The universal mill 10 includes a pair of horizontal rolls 11 and 12 arranged above and below across a conveyance line through which the shaped steel 17 is conveyed, and a pair of eaves rolls 13 arranged on the left and right across the conveyance line, This is a rolling mill for rolling a section steel 17 having a flange 15 and a web 16 such as an H-section steel.
The shape measuring device 20 is a device that measures the shape of the shape steel 17 when rolling the shape steel 17 and is installed on both side surface portions 11 a of the upper horizontal roll 11 and both side surface portions 12 a of the lower horizontal roll 12. Has been. The universal mill 10 to which the shape measuring device 20 can be applied may be either a rough universal mill or a finishing universal mill.
Hereinafter, the shape measuring device 20 installed on one side surface portion 11a of the upper horizontal roll 11 will be described as an example.

FIG. 3 shows a schematic diagram of the shape measuring apparatus 20. The shape measuring device 20 includes a flexible rod 22 that is flexible in the direction orthogonal to the axis (material axis), a support member 23 that is fixed to the side surface portion 11a of the horizontal roll 11 and rotatably supports the tip portion of the flexible rod 22. A drive unit 24 connected to the rear end of the flexible rod 22 and moving the flexible rod 22 in the axial direction thereof, and a displacement meter 25 connected to the rear end of the drive unit 24 and measuring the movement amount of the flexible rod 22; It has.
In addition, a spring 27 that applies an urging force toward the drive unit 24 to the flexible rod 22 is attached to a connecting portion between the flexible rod 22 and the drive unit 24.

The flexible rod 22 is composed of an inner rod 22a made of a steel wire that is closely adhered and spirally wound, and an outer tube 22b that covers the inner rod 22a. Is attached. The tip surface of the contact 21 that contacts the flange end surface 15a is hemispherical in order to reduce friction during contact.
Since the inner rod 22a has high axial rigidity and low axial orthogonal rigidity, even when the intermediate portion of the flexible rod 22 is curved, the amount of movement of the contact 21 is transferred to the displacement meter 25 via the drive unit 24. Can communicate. The outer tube 22b is made of a flexible material such as a synthetic resin such as vinyl chloride.

  As the drive unit 24, a solenoid actuator having a housing 24b in which a solenoid (not shown) is built and an iron core 24a that passes through the solenoid can be used. In the solenoid actuator, when a current is passed through the solenoid, a magnetic field is generated in the solenoid, and the iron core 24a in the solenoid moves linearly. The solenoid actuator has a feature that the response speed is high and the controllability is excellent.

  The displacement meter 25 includes, for example, a contact-type differential transformer type displacement having a cylindrical portion 25b having a bottomed cylindrical shape and a rod 25a that is inserted into the cylindrical portion 25b and advances and retracts in the axial direction of the cylindrical portion 25b. A meter can be used. The differential transformer type displacement meter has high accuracy, has a wide measurement range (for example, 0 to 300 mm), and can be used even in a bad environment. As the displacement meter 25, another displacement meter such as a magnetostrictive displacement meter may be used.

In the shape measuring apparatus 20, the rear end portion of the inner rod 22a is connected to the front end portion of the iron core 24a penetrating the drive unit 24, and the front end portion of the rod 25a of the displacement meter 25 is connected to the rear end portion of the iron core 24a.
When the drive unit 24 is operated, the iron core 24a moves to the flexible rod 22 side, the inner rod 22a connected to the iron core 24a moves to the contact 21 side, and the contact 21 protrudes from the outer tube 22b. On the other hand, when the drive unit 24 is stopped, the iron core 24a is moved to the displacement gauge 25 side by the urging force of the spring 27, the inner rod 22a connected to the iron core 24a is moved to the displacement gauge 25 side, and the contactor 21 is retracted. To do.
In addition, the movement distance of the contact 21 is calculated | required by measuring the movement amount of the iron core 24a connected with the contact 21 via the inner rod 22a with the displacement meter 25. FIG.

  The flexible rod 22 is disposed on the side surface portion 11a of the horizontal roll 11 in a state where the intermediate portion is curved, and the drive unit 24 and the displacement meter 25 are installed on the arbor 14 that is the roll axis of the horizontal roll 11 ( (See FIG. 1). An output signal from the displacement meter 25 is output to the outside through a slip ring (not shown) installed in a roll chock (not shown) that supports the arbor 14.

When the moving speed of the flange end surface 15a (conveying speed of the shaped steel 17) is V ₀ and the speed of the tip of the contact 21 is V _S (see FIG. 4A), the tip of the contact 21 is the horizontal roll 11 Since it is located radially inward from the rolling surface 11b (see FIG. 2), V ₀ > V _S , and the flange end surface 15a moves in the conveying direction at a relative speed V ₀ -V _S with respect to the contact 21. ing. In the present embodiment, the tip of the flexible rod 22 including the contact 21 rotates in the conveying direction of the shaped steel 17 with the support member 23 as a fulcrum, thereby preventing the tip of the contact 21 from being worn. Yes.

  In addition, a plate-like regulating member 26 that regulates the direction of the contact 21 is provided on one side surface of the support member 23 (upstream in the conveying direction of the shaped steel 17). When the tip portion of the flexible rod 22 contacts the regulating member 26, the direction of the contact 21 is regulated. The restricting member 26 is disposed so that the surface with which the tip of the flexible rod 22 contacts is parallel to a virtual surface including the central axis of the horizontal roll 11.

Contact 21 protrudes radially outwardly of the horizontal roll 11 and contacts the flange end face 15a (see FIG. 4 (B)), the contact 21 times in the conveying direction together with the flange end face 15a at a relative speed _V 0 -V _S Move (see FIG. 4C). When the contactor 21 moves away from the flange end surface 15a due to the retreat of the contactor 21, the flexible rod 22 (inner rod 22a) has a restoring force in the direction perpendicular to the axis. The tip of the flexible rod 22 comes into contact with the restricting member 26 (see FIG. 4D). Thereby, the contact 21 stops at a position where it abuts on the flange end surface 15a perpendicularly.

  Next, a method of measuring the amount of deviation of the web 16 using the shape measuring device 20 having the above-described configuration when rolling the shape steel 17 with the universal mill 10 will be described.

(1) The support member 23 is fixed to the side surface portion 11a of the horizontal roll 11 and the tip portion of the flexible rod 22 is rotatably supported by the support member 23, and the intermediate portion of the flexible rod 22 is curved to drive the drive portion 24. The displacement meter 25 is disposed on the arbor 14 of the horizontal roll 11. As described above, the minimum diameter of the roll on which the conventional web deviation measuring device can be installed was about 2000 mm. However, the shape measuring device 20 of the shape steel according to the present embodiment is 1000 mm or less (for example, about 800 mm). It can be applied to a small-diameter horizontal roll having a diameter.

  As shown in FIG. 4A, when the intermediate portion of the flexible rod 22 is bent, the drive unit 24 and the displacement meter 25 are arranged on the conveyance direction side of the shape steel 17, that is, the upstream in the conveyance direction. It is desirable that the regulating member 26 is installed on the side of the upstream side in the conveyance direction of the support member 23 while being curved so as to be convex toward the side. With such an arrangement, when the tip of the flexible rod 22 (inner rod 22a) rotates in the transport direction, the restoring force in the direction opposite to the transport direction has a restoring force in the direction opposite to the transport direction due to the property of becoming straight. The tip of the flexible rod 22 abuts on the regulating member 26.

(2) For each rotation of the horizontal roll 11, the drive unit 24 is operated to move the inner rod 22 a to the contact 21, thereby causing the contact 21 to protrude outward in the radial direction of the horizontal roll 11. The child 21 is brought into contact with the flange end surface 15a. Specifically, when the contact 21 comes closest to the flange end surface 15a of the shaped steel 17, the drive unit 24 is operated to cause the contact 21 to protrude, and the contact 21 is brought into perpendicular contact with the flange end surface 15a. After a certain time (for example, 0.1 second) has elapsed since the contact 21 has come into contact with the flange end surface 15a, the drive unit 24 is stopped, the contact 21 is moved backward, and returned to the original position.

(3) Based on the output value of the moving amount of the iron core 24a measured by the displacement meter 25 (moving amount data of the inner rod 22a), the moving distance of the contact 21 to the flange end surface 15a is calculated by a computing means such as a computer. Derived using (not shown).
FIG. 5 is a schematic diagram of a time history waveform indicating the moving distance of the contact 21. From the same figure, when the rolling is not performed, the time history waveform indicating the moving distance of the contact 21 has a clean trapezoidal shape, but when the rolling is performed, the moving distance of the contact 21 is indicated. It can be seen that the time history waveform becomes a maximum waveform after passing through the inflection point. FIG. 6 shows an example of the movement distance waveform of the contact 21 measured by the displacement meter 25.
The said inflection point has shown the time of the contactor 21 contact | abutting to the flange end surface 15a. Therefore, the movement distance waveform of the contactor 21 measured by the displacement meter 25 is image-analyzed to identify the inflection point, whereby the movement distance of the contactor 21 to the flange end surface 15a can be derived.

(4) Based on the derived movement distance of the contact 21 to the flange end surface 15a, the amount of bias of the web 16 is calculated using a computing means such as a computer.
As shown in FIG. 2, the distance x from the contact 21 that does not protrude (original position) to the rolling surface 11 b of the horizontal roll 11 has been measured when the shape measuring device 20 is installed. Accordingly, the distance B from the flange end surface 15a to the surface of the web 16 on the flange end surface 15a side is calculated as x−δ by measuring the moving distance δ of the contact 21 to the flange end surface 15a using the shape measuring device 20. can do.

  FIG. 7 shows a modification of the installation method of the shape measuring apparatus 20, and shows an example in which the drive unit 24 and the displacement meter 25 are also installed on the side surface part 11 a of the horizontal roll 11.

[Second Embodiment]
FIG. 8 shows a partial schematic diagram of the shape measuring apparatus 30 according to the second embodiment of the present invention.
The shape measuring device 30 is different from the shape measuring device 20 described above in that an impact sensor 31 is interposed between the flexible rod 22 and the drive unit 24.
The impact sensor 31 is used to measure the impact force when the contact 21 comes into contact with the flange end surface 15a. As the impact sensor 31, a load cell used for load measurement or the like can be used.

  FIG. 9 is a schematic diagram showing a time history waveform of the moving distance of the contact 21 and a time history waveform of the output (impact force) of the impact sensor 31. From the figure, it can be seen that when the contact 21 abuts on the flange end surface 15a, the output of the impact sensor 31 increases instantaneously. Therefore, by grasping the peak time of the output measured by the impact sensor 31, it becomes possible to easily specify the time when the contact 21 abuts on the flange end surface 15a.

  Although the embodiments of the present invention have been described above, the present invention is not limited to the configurations described in the above-described embodiments, and is considered within the scope of the matters described in the claims. Other embodiments and modifications are also included. For example, in the above embodiment, the protruding contact is retracted by the urging force of a spring, but the contact may be protruded and retracted by the drive unit. In the above embodiment, the flexible rod is configured by the inner rod made of a spiral steel wire and the outer tube covering the inner rod. However, the flexible rod is configured by another material that is flexible in the direction perpendicular to the axis, such as a plastic rod. You may do it.

10: Universal mill, 11, 12: Horizontal roll, 11a, 12a: Side face, 11b: Rolled surface, 13: Saddle roll, 14: Arbor, 15: Flange, 15a: Flange end face, 16: Web, 17: Shape steel 20, 30: Shape measuring device (shape steel shape measuring device), 21: contact, 22: flexible rod, 22a: inner rod, 22b: outer tube, 23: support member, 24: drive unit, 24a: iron core 24b: housing, 25: displacement meter, 25a: rod, 25b: cylindrical part, 26: regulating member, 27: spring, 31: impact sensor

Claims (5)

A universal mill incorporating a pair of upper and lower horizontal rolls and a pair of left and right saddle rolls, and a device for measuring the shape of a shape steel when rolling the shape steel having a flange and a web,
The front end is a contact that abuts against the flange end surface, a flexible rod that is flexible in the direction perpendicular to the axis, a support member that is fixed to the side surface of the horizontal roll and supports the tip of the flexible rod, and the flexible rod A shaped steel comprising: a drive unit connected to a rear end part and moving the flexible rod in an axial direction thereof; and a displacement meter connected to the drive part and measuring a movement amount of the flexible rod. Shape measuring device.   2. The shape measuring apparatus for shape steel according to claim 1, further comprising a regulating member for regulating the direction of the contact so that the contact contacts the flange end face perpendicularly. .   3. The shape measuring apparatus for shape steel according to claim 1, further comprising an impact sensor for measuring an impact force when the contact contacts the flange end surface. The shape measurement of the shape steel according to any one of claims 1 to 3, when rolling a shape steel having a flange and a web in a universal mill incorporating a pair of upper and lower horizontal rolls and a pair of left and right saddle rolls. A method for measuring the shape of the shape steel using an apparatus,
The support member is fixed to a side surface portion of the horizontal roll and the tip portion of the flexible rod is supported by the support member, and an intermediate portion of the flexible rod is bent so that the drive unit and the displacement meter are connected to the horizontal roll. A step of arranging the arbor of the horizontal roll or the arbor of the horizontal roll;
A step of causing the contact to intermittently protrude by moving the flexible rod in the axial direction of the horizontal roll and abutting the contact with a flange end surface;
Deriving the moving distance of the contact to the flange end surface based on the data of the moving amount of the flexible rod measured by the displacement meter;
And a step of calculating a deviation amount of the web based on the derived movement distance of the contact to the flange end surface.   A universal mill provided with the shape measuring apparatus of the shape steel of any one of Claims 1-3.

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