System and method for analyzing, optimizing and/or designing spectral sensitivity curves for an imaging device

Abstract
A method and system for analyzing a color rendering capability of at least one color imaging device with multiple color channels obtaining includes obtaining spectral sensitivity curves for two or more of the multiple color channels in the color imaging device and determining an image quality value for the color imaging device from the spectral sensitivity curves for the two or more of the multiple color channels in the color imaging device.
Description


FIELD OF THE INVENTION

[0002] The invention relates generally to imaging and, more particularly, to a method and system for evaluating, optimizing and/or designing one or more spectral sensitivity curves for an imaging device.



BACKGROUND OF THE INVENTION

[0003] The practice of capturing color images with digital imaging devices or systems, such as a digital camera or color scanner, is widely spreading. Currently, these digital devices comprise a charge-coupled device or complementary metaloxide-semiconductor (CCD/CMOS) sensor array with a set of filters before it.


[0004] Ideally, these digital imaging devices capture color images in a substantially accurate and aesthetically pleasing manner.


[0005] There are many criteria which are utilized in the design and production of color imaging devices. An important consideration is the ability of the device to deliver color signals which can be used to create high quality color reproductions. To quantify the color quality capability of such devices, it is important to determine how the device's response to color stimuli corresponds to that of a human. Through psychophysical experiments, the Commission Internationale de l'Eclairage (CIE) has generated a standard set of color matching functions for the standard observer, representing the average human visual response to color. As the human eye has three types of cones, each with a different spectral sensitivity signature, there are three standard function specified by the CIE. Accordingly, most color imaging devices are set up with three channels and the spectral sensitivities in these imaging devices are initially designed to attempt to mimic the human visual system.


[0006] The spectral sensitivity functions for color imaging device channels should satisfy the Luther condition, that is the channel spectral sensitivities need not be exact duplicates of the CIE color-matching functions described above, but need to be a nonsingular transformation of them. In practice, it is not always possible to manufacture filters for imaging devices that satisfy the Luther condition, often due to the physical limitations of fabricating process. Measurement noise also plays an important role and will degrade the color accuracy even when spectral sensitivity curves fulfill the Luther condition.


[0007] Accordingly, a measure of goodness or quality factor for evaluating, optimizing, and/or designing spectral sensitivity curves for color imaging devices is desirable. Unfortunately, developing methods and/or systems for obtaining a measure of goodness or a quality factor has been challenging.


[0008] One quality factor, known as the Q-factor, for evaluating and designing spectral sensitivity functions is disclosed in H. E. J. Neugebauer, “Quality factor for filters whose spectral transmittances are different from color mixture curves, and its application to color photography,” J. Opt. Soc. Am. Vol. 46, No. 10, pg. 821-824 (1956), which is herein incorporated by reference. A major disadvantage of the Q-factor is that it is designed to evaluate only single spectral sensitivities.


[0009] Thus, it is easily possible to design an imaging device where all channels associate with high Q-factors, and still the system delivers color signals which cannot be used in creating high quality color reproductions. The trivial example of such a system is a three-channel device where all three channels are made with small deviations from the same spectral sensitivity signature. Although all three show high Q-factor, the result is a nearly monochrome image.


[0010] Another quality factor, known as the μ-factor, for evaluating and designing spectral sensitivity functions is disclosed in P. L. Vora and H. J. Trussell, “Measure of goodness of a set of color-scanning filters”, J. Opt. Soc. Am. A, Vol. 10, No. 7, pg. 1499-1503 (1993), which is herein incorporated by reference. The μ-factor is a quality factor which evaluates an arbitrary number of device channel sensitivity functions as an ensemble. More specifically, the μ-factor describes the difference between the orthonormal subspaces of the CIE color matching functions and the spectral sensitivity space. Generally, a μ-factor approximately equal to one is an indication of an imaging device expected to deliver high quality color reproduction. Unfortunately, some color imaging devices with a poor μ-factor can still generate a good image reproduction. Vora and Trussell have thus introduced a metric which does not have a straight forward correlation with expected image quality. Another problem with the μ-factor is that it does not penalize systems that by virtue of channel sensitivity choices tend to amplify system noise. Such noise is unavoidable in real systems and a system designer needs to carefully control it so as to avoid swamping the eventual color reproduction.


[0011] CIELAB color space is a non-linear transfromation of the CIE color matching functions used as an approximation to a perceptually uniform color space. A figure of merit for color scanners, based on locally-linearized CIELAB space, having an incorporated model for measurement of noise is present in G. Sharma et al. “Figure of merit for color scanners,” IEEE Trans. Image Processing, Vol. 6, No. 7, pg. 990-1001 (1997) which is herein incorporated by reference. The new figure has a high degree of perceptual relevance and also accounts for noise performance of sets of channel sensitivities. The noise aspect of Sharma's metric is, however completely independent of the input stimulus and thus is limited in its usefulness.



SUMMARY OF THE INVENTION

[0012] A method for determining a color rendering capability of at least one color imaging device with multiple color channels in accordance with one embodiment of the present invention includes a few steps. Spectral sensitivity curves for two or more of the multiple color channels in the color imaging device are obtained. An image quality value for the color imaging device is determined from the spectral sensitivity curves for the two or more of the multiple color channels in the color imaging device. The color rendering capability of the color imaging device can be evaluated based on the determined image quality value.


[0013] A method for designing a spectral sensitivity curve for one or more color channels of a color imaging device in accordance with another embodiment of the present invention includes selecting an image quality value and then determining a spectral sensitivity curve for at least one of the color channels of the color imaging device so that the spectral sensitivity curves for each of the color channels in the color imaging device results in the image quality value.


[0014] A method for determining the tolerances for one or more color channels in a color imaging device in accordance with another embodiment of the present invention includes a few steps. A spectral sensitivity curve for at least one of the multiple color channels in the color imaging device and an image quality value are obtained. Next, a first pair of upper and lower peak wavelength tolerances from the obtained spectral sensitivity for the at least one of the multiple color channels and the obtained image quality value. Additionally, a second pair of upper and lower tolerances on the width from the obtained spectral sensitivity curve for at least one of the multiple color channels and the obtained image quality value are determined.


[0015] An imaging device analyzing system in accordance with another embodiment of the present invention includes a source for spectral sensitivity curves for two or more of the multiple color channels in a color imaging device, an image quality processing system, and an evaluation system. The image quality processing system determines an image quality value for the color imaging device from the spectral sensitivity curves for the two or more of the multiple color channels in the color imaging device.


[0016] An imaging device designing system in accordance with another embodiment of the present invention includes a selection system and a design processing system. The selection system obtains an image quality value. The design processing system determines a spectral sensitivity curve for at least one of the color channels of the color imaging device so that the spectral sensitivity curves for each of the color channels in the color imaging device results in the image quality value.


[0017] A system for determining the tolerances for one or more color channels in a color imaging device in accordance with another embodiment of the present invention includes a source and a design processing system. The source provides a spectral sensitivity curve for at least one of the multiple color channels in the color imaging device. The design processing system determines a first pair of upper and lower tolerances for the obtained spectral sensitivity for the at least one of the multiple color channels and determines a second pair of upper and lower tolerances on the full width half maximum for the obtained spectral sensitivity curve for at least one of the multiple color channels.


[0018] With the present invention, an objective evaluation of the quality of color images captured by the evaluated imaging device is now provided using an analysis of the spectral sensitivity curves of channels in the imaging device. The resulting evaluation also provides information on how much room for improvement there is for the evaluated imaging device. The image quality of different imaging devices can now be compared.


[0019] Additionally, with the present invention spectral sensitivity curves for an imaging device can be designed or optimized. As a result, an imaging device with a desired level of image quality can be produced. Additionally, with the present invention determinations of image quality versus the cost of obtaining that level of image quality can be made.


[0020] Further, with the present invention tolerances for spectral sensitivity curves for an imaging device can be determined. These determined tolerances provide an evaluation of the tolerance range of the imaging device. Additionally, these determined tolerances can be used to select other sets of spectral sensitivity curves that might also be used with the same resulting image quality.







BRIEF DESCRIPTION OF THE DRAWINGS

[0021]
FIG. 1 is a block diagram of a system for evaluating, optimizing and/or designing one or more spectral sensitivity curves for an imaging device in accordance with one embodiment of the present invention;


[0022]
FIG. 2 is a block diagram of a color channel in an imaging device;


[0023]
FIG. 3A is a flow chart of a method for determining a color rendering capability of at least one color imaging device with multiple color channels in accordance with one embodiment of the present invention;


[0024]
FIG. 3B is a flow chart of a method for determining a color rendering capability of at least one color imaging device with multiple color channels in accordance with another embodiment of the present invention;


[0025]
FIG. 4A is a flow chart of a method for designing a spectral sensitivity curve for one or more color channels of a color imaging device in accordance with another embodiment of the present invention;


[0026]
FIG. 4B is a flow chart of a method for designing a spectral sensitivity curve for one or more color channels of a color imaging device in accordance with yet another embodiment of the present invention; and


[0027]
FIG. 5 is a flow chart of a method for determining the tolerances for one or more color channels in a color imaging device in accordance with another embodiment of the present invention.







DETAILED DESCRIPTION

[0028] A system 10 and method for evaluating, optimizing and/or designing one or more spectral sensitivity curves for an imaging device in accordance with one embodiment of the present invention is illustrated in FIGS. 1, 3A, 3B, 4A, 4B, and 5. The method in accordance with one embodiment includes determining an


[0029] Referring to FIG. 3A, a flow chart for analyzing a color rendering capability of at least one color imaging device with multiple color channels in accordance with one embodiment of the present invention is illustrated. In step 50, this method starts.


[0030] Next, in step 52 spectral sensitivity curves or functions for two or more of the multiple color channels in the color imaging device are obtained. Spectral sensitivity of a color imaging device or system is defined as the product of the spectral sensitivity of the imaging detector and the transmittance of the filter. A useful simplified model assumes the spectral sensitivity to be a smooth single-peaked curve in visible range with nonnegative values, although real channel spectral sensitivities may be more complex. In this particular embodiment, the spectral sensitivity curves are retrieved from memory 18 from a prior measurement of an imaging device, although the spectral sensitivity curves can be obtained in a variety of other manners, such as, from another memory storage device, by generating the spectral sensitivity curves hypothetically or by operator input via user input device 23.


[0031] By way of example only, the spectral sensitivity curves can be generated hypothetically by SS processing system 12. More specifically, the spectral sensitivities for the simplified model can be simulated by a combination of smooth cubic spline functions. The cubic spline function for instance with peak position at λ=λ0 is written as:
1C(λ)={w3+3w2(w-&LeftBracketingBar;λ-λ0&RightBracketingBar;)+3w(w-&LeftBracketingBar;λ-λ0&RightBracketingBar;)2-3(w-&LeftBracketingBar;λ-λ0&RightBracketingBar;)36w3&LeftBracketingBar;λ-λ0&RightBracketingBar;w(2w-&LeftBracketingBar;λ-λ0&RightBracketingBar;)36w3w&LeftBracketingBar;λ-λ0&RightBracketingBar;2w0&LeftBracketingBar;λ-λ0&RightBracketingBar;2w


[0032] where 2w is the width of the cubic spline function at one-fourth peak height (the corresponding width at half peak height is approximately {square root}{square root over (2)}w.


[0033] If we wish to describe a more complicated potential spectral sensitivity curve, one which may be non-symmetrical about its peak wavelength, then we can consider w1 and w2 which represent the left half and right half widths, respectively. Now our cubic spline function becomes
2C(λ)={w3+3w2(w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)+3w(w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)2-3(w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)36w30λ-Pλw2w3+3w2(w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)+3w(w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)2-3(w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)36w3-w1λ-Pλ0(2w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)36w3w2λ-Pλ2w2(2w-&LeftBracketingBar;λ-Pλ&RightBracketingBar;)36w3-2w1λ-Pλ-w10otherwise


[0034] For convenience we introduce w which is related to w1 and w2 in the following ways:


[0035]

3




w
2

-

w
1


=

2

Δ





w





so







w
1

=

w
-

Δ





w



,


w
2

=

w
+

Δ






w
.




and









Δ





w

=



w
2

-

w
1


2








[0036] Next, in step 54 the obtained spectral sensitivity curves from step 52 are used by the SS processing system 12 to determine a μ-factor. In this particular embodiment, the μ-factor is calculated by summing the q-factors of the orthonormalized vectors of the obtained spectral sensitivity curves and dividing the summation by three, although other manners for determining a μ-factor can be used. Since the process of determining a μ-factor and q-factors are known, they will not be described in detail here.


[0037] Next, in step 58 a color difference metric value, in this case a delta E (“E”) value, for the color imaging device is determined in SS processing system 12 from the μ-factor, although other combinations of the μ-factor and/or other quality factors could also be used to determine the color difference metric value. In this particular embodiment, a relationship between μ-factor and E stored in memory 18 is used by processor 16 to determine the color difference metric value. One example of such a derived relationship between μ-factor and E is set forth below:
1derived relationship between μ-factor and Eμ-factorMin Expected ΔEMax Expected ΔE0.9 2.24.80.912.04.70.921.94.40.931.84.00.941.83.80.951.63.50.961.53.20.971.33  0.981.22.50.991.12  


[0038] Based on this relationship, the color difference metric value in this particular embodiment is obtained by averaging the minimum and maximum expected E value expected for the determined μ-factor. For example, a μ-factor of 0.98 would result in color difference metric value of 1.85.


[0039] Next, in step 60 the color rendering capability of the color imaging device is evaluated based on the determined image quality value. In this particular embodiment, image quality value is compared against a standard to provide an evaluation, e.g. a standard might state that an image quality value of zero is ideal, an image quality value of 0 to 2.0 is acceptable, and an image quality value above 2.0 is unacceptable, although other types of evaluations could be used. By way of example only, the image quality values of two different imaging devices could also be compared against each other to identify the imaging device which would produce color images with better quality.


[0040] Although in this particular embodiment a color difference metric value is determined, other types of image quality values could also be determined, such as a color quality and noise sensitivity metric value. An image quality value is a number which correlates how well an image fits associated quality criteria from the view point of a typical human observer. A color quality metric value is an image quality value based on the criteria of how well the channel sensitivities of a device correlate with the human visual system. A color difference metric value is an image quality value which correlates with the magnitude of change in color a typical human observer would detect between two images. A color quality and noise sensitivity metric value an image quality value based on color criteria and an image quality value based on quantifying how the amplification of noise in a system affects perceived quality to a human observer.


[0041] Referring to FIG. 3B, a flow chart for evaluating a color rendering capability of at least one color imaging device with multiple color channels in accordance with one embodiment of the present invention is illustrated. In step 62, this method starts.


[0042] Next, in step 64 spectral sensitivity curves or functions for two or more of the multiple color channels in the color imaging device are obtained. Since the process in step 64 is identical to that described earlier in step 52, it will not described again here.


[0043] Next, in step 66 the obtained spectral sensitivity curves from step 52 are used by the SS processing system 12 to determine a Universal Measure of Goodness (UMG) factor. UMG takes into account the total noise of the system, both shot noise which is signal dependent and dark noise which is signal independent, and an expected average color difference. Total noise is measured through the sum of the shot noise covariance and the dark current noise covariance, while the expectation of the noise is still zero. For a standard set of object spectra, τ is the information content which would be delivered by the system described by the spectral sensitivity curves. Thus, τ is a function of the total noise and the average E. For the same standard set of object spectra, α is the information content which a perfectly noise-free colorimetric system would deliver. UMG is the ratio of τ to α.


[0044] Next, in step 70 a color quality and noise sensitivity metric value for the color imaging device is determined in SS processing system 12 from the UMG factor, although other combinations of the UMG factor and/or other quality factors could also be used to determine the color quality and noise sensitivity metric value. In this particular embodiment, a relationship between the UMG factor and E stored in memory 18 is used by processor 16 to determine the color difference metric value. Since the process in this step is the same as described earlier in step 58 except a color quality and noise sensitivity metric value is being determined here instead of a color difference metric value and a UMG factor is used here instead of a μ-factor, the process will not described again here.


[0045] One of the advantages of this method is the use of a noise sensitivity metric because it involves a consideration of image-dependent noise. Image dependent noise is noise dependent on the input signal level, rather than independent, white noise as described in greater detail in Gerald C. Holst, “CCD Arrays Cameras and Displays”, SPIE Optical Engineering Press 1998 which is herein incorporated by reference. By incorporating this practical noise model into the image quality metric value, this embodiment of the present invention generates an image quality metric value which is more coincident with what occurs in the real world.


[0046] Next, in step 72 the color rendering capability of the color imaging device is evaluated based on the determined color quality and noise sensitivity metric value. Since the process in step 68 is identical to that described earlier in step 56, except that the evaluation is based using a color quality and noise sensitivity metric value instead of a color difference metric value, it will not described again here.


[0047] Referring to FIG. 4A is a flow chart of a method for designing a spectral sensitivity curve for one or more color channels of a color imaging device in accordance with another embodiment of the present invention is illustrated. In step 74, this method starts. Next, in step 76, an image quality value is obtained. way of example only, user input device 23 can be used to select or input the image quality value or the value could be retrieved from a memory device. Again, depending upon the embodiment, a variety of different types of image quality metric values could be used, such as a color difference metric value or a color quality and noise sensitivity metric value.


[0048] Next, in step 78 the SS processing system 12 uses the obtained image quality value to obtain or retrieve one or more tables, sets, or enumerations of combinations of spectral sensitivity curves from memory 18. The one or more tables sets, or enumerations of combinations of spectral sensitivity curves can be obtained in a variety of different manners, such as based on the image quality value itself or on a portion of the image quality value, such as a μ-factor on which the image quality value is at least partially based or on other factors. Two illustrative examples of such tables set forth below. In this particular embodiment, the tables are stored in memory 18, although the tables could be stored elsewhere. The tables are accessed by processor 16 to determine the spectral sensitivity curve(s) which are unknown needed or desired for the particular application.


[0049] Next, in step 80 the known spectral sensitivity curves are used to identify a combination or combinations of spectral sensitivity curves in the obtained table that could be used for the particular application.


[0050] Next, in step 82 one of the identified combinations of spectral sensitivity curves is selected. A variety of factors could be used by SS processing system 12 to determine how this selection is made, such as which combination of spectral sensitivity curves would have the best color rendering capability or by an operator making a selection using user input device 23.


[0051] Next, in step 84 the missing and desired spectral sensitivity curve or curves are determined from the selected combination. The selected combination will contain the needed information and/or data on the missing and desired spectral sensitivity curve or curves.


[0052] By way of example only, one example of this method is set forth below. If, for example, one chooses to design a third channel for a three-channel system where an image quality value is selected that is based at least partly on a μ-factor with a desired value of 0.98, then Table I would be selected. Next, if for this example, the spectral sensitivities of the first two channels in a three-channel system are already given where channel 1 has a peak sensitivity at 600 nm, a full width half maximum of 100 nm (wr=50, described above) and a skewness of 5 nm (wr=5, described above) and channel 2 has a peak sensitivity at 540 nm, a full width half maximum of 140 nm (wG=70) and a skewness of 5 nm ( wG=5), then consulting the table, one possible solution would be found on the following line:
2SensitivityGreenCenter Peaks inWRWGWBΔWRΔWGΔWBPλGPλRPλBHalfAxisRHalfAxisB50704055554059744832


[0053] As shown here for the aformentioned channels 1 and 2, there is a satisfactory third channel with peak wavelength sensitivity of 448 nm, a full width half maximum of 80 nm and a skewness of 5 nm which would be determined to be the spectral sensitivity curve for this example. Although in this particular embodiment, the spectral sensitivity curve(s) is determined using tables, the selected image quality value, and the known spectral sensitivity curves, other methods for determining the spectral sensitivity curve may also be used.


[0054] Referring to FIG. 4B is a flow chart of a method for designing a spectral sensitivity curve for one or more color channels of a color imaging device in accordance with another embodiment of the present invention is illustrated. In step 86, this method starts. Next, in step 88, an image quality value is obtained. Since the process in step 88 is identical to that described earlier in step 76, it will not described again here.


[0055] Next, in step 90 the SS processing system 12 uses the obtained image quality value to obtain or retrieve one or more tables, sets, or enumerations of combinations of spectral sensitivity curves from memory 18. Since the process in step 90 is identical to that described earlier in step 78, it will not described again here.


[0056] Next, in step 92 one or more characteristics are used by SS processing system 12 to identify a combination or combinations of spectral sensitivity curves in the obtained table that could be used for the particular application. A variety of different characteristics, numbers of characteristics (one or more than one, and a variety of different combinations can be used as needed or desired for the particular application. The characteristics can be obtained in a variety of different manners, such as from memory 18 or via operator input using user input device 23.


[0057] Next, in step 94 one of the identified combinations of spectral sensitivity curves is selected. A variety of factors could be used by SS processing system 12 to determine how this selection is made, such as which combination of spectral sensitivity curves would have the best color rendering capability or by an operator making a selection using user input device 23.


[0058] Next, in step 96 the desired spectral sensitivity curves are obtained from the selected combination. The selected combination will contain the needed information and/or data on these spectral sensitivity curves.


[0059] One example of this particular embodiment is discussed below. If, for example, one chooses to design three channels for a three-channel system where the image quality metric value is based on a μ-factor with a desired value of 0.98, then Table I would be selected in this example. For that table, every channel sensitivity combination described in that table is associated with a Cμ-factor of 0.98. One could search for a characteristic such as a green curve which is easily manufactured. For example, say a channel with a peak sensitivity at 540 nm, a full width half maximum of 140 nm (WG=70) and a skewness of 5 nm ( WG=5) is easily made. Surveying Table I shows a possible second curve could have a peak sensitivity at 604 nm, a full width half maximum of 100 nm (wR=50) and a skewness of −5 nm (wR=−5). If the second curve with its negative skewness is considered difficult to manufacturer, the table can be further consulted by SS processing system 12 until a combination which meets all manufacturing criteria is met. For example, the following combination, also found in Table I, may be considered a good manufacturing candidate: the same first curve along with a second curve with peak sensitivity at 597 nm, a full width half maximum of 100 nm (wR=50) and a skewness of 5 nm (wR=5) and a third channel sensitivity with peak sensitivity at 448 nm, a full width half maximum of 80 nm (wB=40) and a skewness of 5 nm (wB=5)
3SensitivityGreenCenter Peaks inWRWGWBΔWRΔWGΔWBPλGPλRPλBHalfAxisRHalfAxisB507030−5505406044502150704055554059744832


[0060] Accordingly, with this method once an image quality value is selected, then one or more spectral sensitivity curves can be determined.


[0061] In yet another embodiment, as discussed earlier the μ-factor for an image quality value can be used to select a set or table of spectral sensitivity curves. Next, to select a combination of spectral sensitivity curves an optimization approach can be used by SS processing system 12 to select one of the combinations of spectral sensitivity curves. For example, three or more spectral sensitivity curves could be optimized by maximizing the image quality metric within one or more constraints. By way of example only, these constraints can be:


[0062] (1) Non-negativity


[0063] The transmittance of spectral sensitivity at each wavelength is non-negative.


[0064] (2) Smoothness


[0065] The second derivative of the physical sensitivity can be used as a measure of curvature and therefore as a measure of smoothness of the sensitivity.




|S
(λ,−1)−2S(λ,)+S(λ,+1)|=Δ1; where 2≦i≦30 Δ≦Δmax



[0066] (3) Boundedness


[0067] In general, the transmittance at each wavelength cannot exceed one, or a constant that is less than one.


[0068] (4) Single Peak


[0069] The transmittance of the filter has one global maximum, and without local maximum.


[0070] Although four constraints are discussed above, a variety of different types of constraints and combinations of them can be used depending upon the particular application and its requirements.


[0071] In FIG. 5 a flow chart of a method for determining the tolerances for one or more color channels in a color imaging device in accordance with another embodiment of the present invention is illustrated. In step 98, this method starts. Next, in step 100 a spectral sensitivity curve for at least one of the multiple color channels in the color imaging device is obtained in a manner as described in greater detail earlier. Meanwhile in step 102 an image quality value is obtained. Since methods and systems for obtaining spectral sensitivity curve(s) and/or image quality values are discussed earlier, they will not be described here again.


[0072] Next, in step 104 a first pair of upper and lower tolerances on the peak wavelength is determined for the obtained spectral sensitivity curves for one of the multiple color channels. These tolerances may be obtained by processor 16 through reference to the tables stored in memory 18, such as the tables which are set forth below as examples. The table used is selected based on the obtained image quality value as described in greater detail earlier. The tables are useful in determining desirable channel spectral sensitivities for three-channel imaging devices. These tables provide manufacturing guidance on the choice of curves. The μ-factor used in deriving the tables is a color quality metric. The tables describe tolerances on the specification of the “red” and “blue” channels in a three-channel system. The tolerances are in terms of peak wavelength error which maintain the μ-factor at or above the desired level. The first table maintains a μ-factor of at least 0.98, the second maintains at least a μ-factor of 0.95.


[0073] Next, in step 106 a second pair of upper and lower tolerances on the full width half maximum is determined from the obtained spectral sensitivity curve for one of the multiple color channels. These tolerances may also be obtained through reference to the tables, such as the exemplary tables incorporated below in the same manner as described above in step 104.


[0074] Next, in step 108 the spectral sensitivity curve or curves are evaluated based on the determined first and second pair of tolerances. For example, the first and second pair of tolerances may provide an indication on the ease or difficulty in reproducing an imaging device with the same color rendering capability. If the tolerances are small, then it will be difficult to obtain imaging devices with the same color rendering capability.



EXAMPLES of Two Tables

[0075]

4





TABLE I










Peak wavelength tolerances based on single-peak symmetric or asymmetric channel


sensitivities for three channel cameras with μ-factor of .98 or larger











Sensitivity

Green
Center Peaks in


















WR
WG
WB
ΔWR
ΔWG
ΔWB
PλG
PλR
PλB
HalfAxisR
HalfAxisB




















50
50
30
−5
−5
0
540
604
450
2
1


50
50
30
−5
−5
5
540
604
446
2
2


50
50
30
−5
−5
5
550
602
446
1
1


50
50
30
−5
0
−5
540
604
454
1
1


50
50
30
−5
0
0
540
604
450
2
2


50
50
30
−5
0
5
540
603
446
2
2


50
50
30
−5
5
0
540
603
450
2
1


50
50
30
−5
5
5
540
603
446
2
2


50
50
30
0
−5
0
540
601
450
2
1


50
50
30
0
−5
5
540
600
446
2
2


50
50
30
0
−5
5
550
598
446
2
1


50
50
30
0
0
−5
540
600
454
2
1


50
50
30
0
0
0
540
600
450
2
2


50
50
30
0
0
5
540
600
446
2
2


50
50
30
0
5
0
540
599
450
2
1


50
50
30
0
5
5
540
600
446
2
2


50
50
30
5
−5
0
540
598
450
1
1


50
50
30
5
−5
5
540
597
446
2
1


50
50
30
5
−5
5
550
595
446
1
1


50
50
30
5
0
−5
540
597
454
1
1


50
50
30
5
0
0
540
597
450
2
2


50
50
30
5
0
5
540
597
446
2
2


50
50
30
5
5
0
540
597
450
2
1


50
50
30
5
5
5
540
596
446
2
2


50
50
40
−5
−5
−5
540
640
454
3
2


50
50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
60
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50
60
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50
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50
60
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50
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50
60
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50
60
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50
60
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50
60
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50
60
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5
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50
60
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5
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50
60
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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5
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50
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50
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50
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50
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50
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50
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550
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50
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50
5
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50
5
5
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597
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50
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30
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560
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50
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30
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550
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50
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30
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50
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30
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50
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30
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550
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50
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30
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560
601
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50
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30
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50
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30
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50
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30
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50
70
30
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50
70
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0
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50
70
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50
70
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5
550
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50
70
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50
70
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50
70
30
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50
70
30
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50
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30
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5
0
550
603
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50
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30
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560
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50
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30
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5
5
540
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50
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30
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5
5
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603
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50
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560
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50
70
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50
70
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50
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50
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50
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50
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50
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50
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50
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50
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570
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50
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50
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50
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50
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50
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50
70
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50
70
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50
70
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550
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50
70
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5
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50
70
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50
70
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50
70
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50
70
30
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5
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50
70
30
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5
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550
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50
70
30
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5
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50
70
30
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5
5
540
601
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50
70
30
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5
5
550
599
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50
70
30
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5
5
560
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50
70
30
5
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550
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50
70
30
5
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560
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50
70
30
5
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570
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50
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30
5
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550
596
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50
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30
5
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560
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50
70
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570
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50
70
30
5
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580
595
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50
70
30
5
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5
550
596
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50
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30
5
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560
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50
70
30
5
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570
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50
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580
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50
70
30
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550
596
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50
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30
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50
70
30
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50
70
30
5
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560
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50
70
30
5
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570
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50
70
30
5
0
5
540
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1


50
70
30
5
0
5
550
596
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2


50
70
30
5
0
5
560
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50
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30
5
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5
570
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50
70
30
5
5
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550
597
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50
70
30
5
5
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560
595
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1


50
70
30
5
5
0
540
598
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1


50
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30
5
5
0
550
596
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2


50
70
30
5
5
0
560
595
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2


50
70
30
5
5
5
540
597
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2


50
70
30
5
5
5
550
597
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2


50
70
30
5
5
5
560
595
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50
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40
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540
604
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50
70
40
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550
603
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50
70
40
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560
601
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50
70
40
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50
70
40
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50
70
40
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50
70
40
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50
70
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50
70
40
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570
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50
70
40
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580
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50
70
40
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540
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50
70
40
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550
602
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50
70
40
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560
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50
70
40
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570
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50
70
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580
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50
70
40
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50
70
40
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
40
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5
540
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50
70
40
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550
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50
70
40
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5
560
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50
70
40
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570
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50
70
40
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50
70
40
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50
70
40
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50
70
40
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50
70
40
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550
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50
70
40
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50
70
40
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5
530
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50
70
40
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5
540
604
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50
70
40
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5
5
550
602
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50
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50
70
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50
70
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50
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50
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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540
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50
70
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550
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50
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50
70
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50
70
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50
70
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50
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50
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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5
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50
70
40
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5
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550
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50
70
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5
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50
70
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50
70
40
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5
530
602
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50
70
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50
70
40
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5
5
550
600
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50
70
40
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50
70
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5
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50
70
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50
70
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550
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50
70
40
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560
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50
70
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5
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570
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50
70
40
5
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580
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50
70
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5
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540
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50
70
40
5
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550
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50
70
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560
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50
70
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50
70
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580
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50
70
40
5
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540
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50
70
40
5
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5
550
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50
70
40
5
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560
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50
70
40
5
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570
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50
70
40
5
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5
580
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50
70
40
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540
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50
70
40
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550
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50
70
40
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50
70
40
5
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50
70
40
5
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540
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50
70
40
5
0
0
550
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50
70
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5
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560
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50
70
40
5
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570
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50
70
40
5
0
5
540
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2


50
70
40
5
0
5
550
596
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3
3


50
70
40
5
0
5
560
595
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3
3


50
70
40
5
0
5
570
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50
70
40
5
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5
580
596
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50
70
40
5
5
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540
598
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50
70
40
5
5
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550
597
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2


50
70
40
5
5
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560
595
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2


50
70
40
5
5
0
540
597
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3
2


50
70
40
5
5
0
550
596
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3
3


50
70
40
5
5
0
560
596
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2
2


50
70
40
5
5
0
570
595
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1
1


50
70
40
5
5
5
530
599
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1
1


50
70
40
5
5
5
540
597
448
3
2


50
70
40
5
5
5
550
596
448
3
3


50
70
40
5
5
5
560
596
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3
2


50
70
40
5
5
5
570
595
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2
2


50
70
50
−5
−5
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550
602
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50
70
50
−5
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560
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50
70
50
−5
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550
602
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50
70
50
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5
560
600
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50
70
50
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550
603
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50
70
50
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550
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50
70
50
−5
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560
601
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50
70
50
−5
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5
540
604
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0
0


50
70
50
−5
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5
550
602
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2


50
70
50
−5
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5
560
601
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1
2


50
70
50
−5
5
−5
550
603
455
1
1


50
70
50
−5
5
0
550
602
452
2
2


50
70
50
−5
5
5
540
604
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2


50
70
50
−5
5
5
550
603
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2


50
70
50
0
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550
599
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1
1


50
70
50
0
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560
597
455
1
1


50
70
50
0
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550
599
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2


50
70
50
0
−5
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560
597
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2
2


50
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50
0
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570
596
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1


50
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50
0
−5
5
550
599
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2
2


50
70
50
0
−5
5
560
597
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2
2


50
70
50
0
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5
570
597
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1
2


50
70
50
0
0
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550
599
455
1
1


50
70
50
0
0
−5
560
598
454
1
1


50
70
50
0
0
0
550
599
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2
2


50
70
50
0
0
0
560
598
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1
2


50
70
50
0
0
5
540
601
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1
2


50
70
50
0
0
5
550
599
449
2
2


50
70
50
0
0
5
560
598
449
2
2


50
70
50
0
5
−5
550
599
454
2
1


50
70
50
0
5
0
540
600
452
1
1


50
70
50
0
5
0
550
599
451
2
2


50
70
50
0
5
5
540
600
450
2
2


50
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50
0
5
5
550
599
449
2
2


50
70
50
0
−5
−5
560
594
454
1
1


50
70
50
5
−5
0
550
596
452
2
2


50
70
50
5
−5
0
560
594
452
2
2


50
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50
5
−5
5
550
595
449
2
2


50
70
50
5
−5
5
560
594
449
2
2


50
70
50
5
−5
5
570
593
449
1
1


50
70
50
5
0
−5
550
596
455
1
1


50
70
50
5
0
0
550
596
452
2
2


50
70
50
5
0
0
560
595
451
1
1


50
70
50
5
0
5
550
596
449
2
2


50
70
50
5
0
5
560
594
448
2
2


50
70
50
5
5
−5
550
596
454
1
1


50
70
50
5
5
0
550
596
452
2
2


50
70
50
5
5
5
540
597
449
1
1


50
70
50
5
5
5
550
597
449
2
2


60
50
30
−5
−5
−5
540
600
454
2
1


60
50
30
−5
−5
−5
550
595
454
2
1


60
50
30
−5
−5
0
540
599
450
2
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60
50
30
−5
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0
550
594
450
3
2


60
50
30
−5
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3
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60
50
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−5
−5
5
550
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3
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
60
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60
60
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550
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60
60
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60
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60
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60
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60
60
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60
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60
60
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60
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60
60
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5
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5
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60
60
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5
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60
60
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60
60
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60
60
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5
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60
60
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5
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60
60
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5
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60
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60
60
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5
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60
60
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5
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60
60
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60
60
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60
60
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5
5
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60
60
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5
5
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60
60
40
5
5
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587
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60
60
40
5
5
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60
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60
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60
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60
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60
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60
60
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60
60
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60
60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
60
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60
60
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60
60
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60
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60
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60
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60
60
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60
60
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60
60
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60
60
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60
60
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60
60
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60
60
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60
60
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60
60
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60
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60
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60
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70
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60
70
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
70
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60
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60
70
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
70
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60
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60
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60
70
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60
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60
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60
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60
70
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60
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
30
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70
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60
70
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60
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
70
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60
70
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60
70
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60
70
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540
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60
70
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550
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60
70
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560
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60
70
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570
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60
70
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580
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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540
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60
70
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550
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60
70
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560
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60
70
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60
70
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580
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60
70
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540
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60
70
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550
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60
70
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60
70
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60
70
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540
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60
70
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550
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60
70
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560
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60
70
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570
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60
70
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5
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540
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60
70
40
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550
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60
70
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5
560
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60
70
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570
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60
70
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60
70
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550
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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560
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60
70
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60
70
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580
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60
70
40
0
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590
597
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60
70
40
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5
540
597
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60
70
40
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70
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70
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70
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70
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70
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70
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70
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70
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60
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70
60
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70
60
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70
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70
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70
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2
2


70
70
50
0
5
5
560
577
449
2
2










[0076]

5





TABLE II










Peak wavelength tolerances based on single-peak symmetric or asymmetric channel


sensitivities for three channel cameras with μ-factor of .95 or larger













Green
Center Peaks in



Sensitivity
Sensitivity
Sensitivity
Red/Blue
Elipse Axes in


Widths
Skews
Peak
Peak Plane
Red/Blue Peak Plane

















WR
WG
WB
ΔWR
ΔWG
ΔWB
PλG
PλR
PλB
HalfAxisR
HalfAxisB




















50
50
30
−5
+TA, 13 −5
−5
530
604
454
3
2


50
50
30
−5
−5
−5
540
604
454
4
3


50
50
30
−5
−5
−5
550
601
454
4
3


50
50
30
−5
−5
−5
560
595
454
3
2


50
50
30
−5
−5
0
530
604
450
3
2


50
50
30
−5
−5
0
540
603
450
4
3


50
50
30
−5
−5
0
550
600
450
4
3


50
50
30
−5
−5
0
560
595
450
3
2


50
50
30
−5
−5
5
530
604
446
3
2


50
50
30
−5
−5
5
540
603
446
4
3


50
50
30
−5
−5
5
550
600
446
4
3


50
50
30
−5
−5
5
560
595
446
3
2


50
50
30
−5
0
−5
530
604
454
3
3


50
50
30
−5
0
−5
540
603
454
4
3


50
50
30
−5
0
−5
550
600
454
4
3


50
50
30
−5
0
0
530
605
450
3
3


50
50
30
−5
0
0
540
603
450
4
3


50
50
30
−5
0
0
550
600
450
4
3


50
50
30
−5
0
5
530
604
446
3
3


50
50
30
−5
0
5
540
602
446
4
3


50
50
30
−5
0
5
550
600
446
4
3


50
50
30
−5
0
5
560
595
446
1
1


50
50
30
−5
5
−5
530
604
454
4
3


50
50
30
−5
5
−5
540
602
454
4
3


50
50
30
−5
5
−5
550
600
454
3
2


50
50
30
−5
5
0
530
604
450
4
3


50
50
30
−5
5
0
540
603
450
4
3


50
50
30
−5
5
0
550
599
450
3
2


50
50
30
−5
5
5
530
604
446
4
3


50
50
30
−5
5
5
540
602
446
4
3


50
50
30
−5
5
5
550
599
446
3
2


50
50
30
0
−5
−5
530
601
454
3
2


50
50
30
0
−5
−5
540
600
454
4
3


50
50
30
0
−5
−5
550
597
454
4
3


50
50
30
0
−5
−5
560
590
454
3
2


50
50
30
0
−5
−5
570
575
454
2
2


50
50
30
0
−5
0
530
601
450
3
2


50
50
30
0
−5
0
540
600
450
4
3


50
50
30
0
−5
0
550
597
450
4
3


50
50
30
0
−5
0
560
590
450
4
2


50
50
30
0
−5
0
570
575
450
2
2


50
50
30
0
−5
5
530
601
446
3
2


50
50
30
0
−5
5
540
600
446
4
3


50
50
30
0
−5
5
550
597
446
4
3


50
50
30
0
−5
5
560
590
446
4
2


50
50
30
0
−5
5
570
576
446
2
2


50
50
30
0
0
−5
530
601
454
3
3


50
50
30
0
0
−5
540
599
454
4
3


50
50
30
0
0
−5
550
596
454
4
3


50
50
30
0
0
−5
560
589
454
1
1


50
50
30
0
0
0
530
601
450
3
3


50
50
30
0
0
0
540
600
450
4
3


50
50
30
0
0
0
550
596
450
4
3


50
50
30
0
0
0
560
590
450
2
2


50
50
30
0
0
5
530
601
446
3
3


50
50
30
0
0
5
540
600
446
4
3


50
50
30
0
0
5
550
596
446
4
3


50
50
30
0
0
5
560
589
446
3
2


50
50
30
0
5
−5
530
601
454
4
3


50
50
30
0
5
−5
540
599
454
4
3


50
50
30
0
5
−5
550
595
454
3
2


50
50
30
0
5
0
530
601
450
4
3


50
50
30
0
5
0
540
599
450
4
3


50
50
30
0
5
0
550
596
450
4
2


50
50
30
0
5
5
530
601
446
4
3


50
50
30
0
5
5
540
599
446
4
3


50
50
30
0
5
5
550
595
446
4
2


50
50
30
5
−5
−5
530
598
454
3
2


50
50
30
5
−5
−5
540
596
454
4
3


50
50
30
5
−5
−5
550
594
454
4
3


50
50
30
5
−5
−5
560
585
454
4
2


50
50
30
5
−5
−5
570
576
454
2
2


50
50
30
5
−5
0
530
597
450
3
2


50
50
30
5
−5
0
540
597
450
4
3


50
50
30
5
−5
0
550
593
450
4
3


50
50
30
5
−5
0
560
585
450
4
2


50
50
30
5
−5
0
570
576
450
2
2


50
50
30
5
−5
5
530
598
446
3
2


50
50
30
5
−5
5
540
597
446
4
3


50
50
30
5
−5
5
550
593
446
4
3


50
50
30
5
−5
5
560
584
446
4
2


50
50
30
5
−5
5
570
577
446
2
2


50
50
30
5
0
−5
530
598
454
3
3


50
50
30
5
0
−5
540
597
454
4
3


50
50
30
5
0
−5
550
593
454
4
3


50
50
30
5
0
−5
560
583
454
3
2


50
50
30
5
0
−5
570
572
454
1
1


50
50
30
5
0
0
530
597
450
3
3


50
50
30
5
0
0
540
596
450
4
3


50
50
30
5
0
0
550
592
450
4
3


50
50
30
5
0
0
560
583
450
3
2


50
50
30
5
0
0
570
573
450
1
2


50
50
30
5
0
5
530
597
446
3
3


50
50
30
5
0
5
540
596
446
4
3


50
50
30
5
0
5
550
592
446
4
3


50
50
30
5
0
5
560
583
446
3
2


50
50
30
5
0
5
570
574
446
1
1


50
50
30
5
5
−5
530
598
454
3
3


50
50
30
5
5
−5
540
595
454
4
3


50
50
30
5
5
−5
550
592
454
3
2


50
50
30
5
5
0
530
597
450
4
3


50
50
30
5
5
0
540
596
450
4
3


50
50
30
5
5
0
550
592
450
4
2


50
50
30
5
5
5
530
597
446
4
3


50
50
30
5
5
5
540
596
446
4
3


50
50
30
5
5
5
550
592
446
4
2


50
50
40
−5
−5
−5
530
604
455
3
3


50
50
40
−5
−5
−5
540
603
454
4
3


50
50
40
−5
−5
−5
550
601
454
4
3


50
50
40
−5
−5
−5
560
595
454
4
3


50
50
40
−5
−5
0
530
604
451
3
3


50
50
40
−5
−5
0
540
603
451
4
3


50
50
40
−5
−5
0
550
600
451
4
3


50
50
40
−5
−5
0
560
595
451
4
3


50
50
40
−5
−5
5
530
604
448
3
3


50
50
40
−5
−5
5
540
603
447
4
3


50
50
40
−5
−5
5
550
600
448
4
3


50
50
40
−5
−5
5
560
595
447
4
3


50
50
40
−5
0
−5
530
604
454
4
3


50
50
40
−5
0
−5
540
603
454
4
3


50
50
40
−5
0
−5
550
600
454
4
3


50
50
40
−5
0
−5
560
594
454
3
2


50
50
40
−5
0
0
530
604
451
4
3


50
50
40
−5
0
0
540
603
451
4
3


50
50
40
−5
0
0
550
600
451
4
3


50
50
40
−5
0
0
560
594
451
3
2


50
50
40
−5
0
5
530
604
447
4
3


50
50
40
−5
0
5
540
602
447
4
3


50
50
40
−5
0
5
550
599
448
4
3


50
50
40
−5
0
5
560
595
448
3
2


50
50
40
−5
5
−5
520
605
454
2
1


50
50
40
−5
5
−5
530
604
454
4
3


50
50
40
−5
5
−5
540
602
454
4
3


50
50
40
−5
5
−5
550
599
454
4
3


50
50
40
−5
5
0
520
604
451
2
2


50
50
40
−5
5
0
530
604
451
4
3


50
50
40
−5
5
0
540
603
451
4
3


50
50
40
−5
5
0
550
599
451
4
3


50
50
40
−5
5
5
520
604
448
2
2


50
50
40
−5
5
5
530
604
448
4
3


50
50
40
−5
5
5
540
602
447
4
3


50
50
40
−5
5
5
550
600
448
4
3


50
50
40
0
−5
−5
530
601
455
3
3


50
50
40
0
−5
−5
540
600
454
4
3


50
50
40
0
−5
−5
550
597
454
4
3


50
50
40
0
−5
−5
560
590
454
4
3


50
50
40
0
−5
−5
570
578
454
2
2


50
50
40
0
−5
0
530
601
451
3
3


50
50
40
0
−5
0
540
600
451
4
3


50
50
40
0
−5
0
550
597
451
4
3


50
50
40
0
−5
0
560
589
451
4
3


50
50
40
0
−5
0
570
578
450
3
2


50
50
40
0
−5
5
530
601
448
3
3


50
50
40
0
−5
5
540
599
447
4
3


50
50
40
0
−5
5
550
597
447
4
3


50
50
40
0
−5
5
560
589
447
4
3


50
50
40
0
−5
5
570
579
448
3
2


50
50
40
0
0
−5
530
601
454
4
3


50
50
40
0
0
−5
540
599
454
4
3


50
50
40
0
0
−5
550
596
454
4
3


50
50
40
0
0
−5
560
589
454
3
2


50
50
40
0
0
0
530
601
451
4
3


50
50
40
0
0
0
540
599
451
4
3


50
50
40
0
0
0
550
596
451
4
3


50
50
40
0
0
0
560
589
451
4
2


50
50
40
0
0
5
530
600
447
4
3


50
50
40
0
0
5
540
600
447
4
3


50
50
40
0
0
5
550
596
448
4
3


50
50
40
0
0
5
560
589
447
4
2


50
50
40
0
5
−5
520
601
454
2
2


50
50
40
0
5
−5
530
600
454
4
3


50
50
40
0
5
−5
540
599
454
4
3


50
50
40
0
5
−5
550
596
454
4
3


50
50
40
0
5
0
520
601
451
2
2


50
50
40
0
5
0
530
601
451
4
3


50
50
40
0
5
0
540
599
451
4
3


50
50
40
0
5
0
550
595
451
4
3


50
50
40
0
5
5
520
601
448
3
2


50
50
40
0
5
5
530
601
448
4
3


50
50
40
0
5
5
540
598
447
4
3


50
50
40
0
5
5
550
595
448
4
3


50
40
5
−5
−5
530
597
455
3
3


50
50
40
5
−5
−5
540
596
454
4
3


50
50
40
5
−5
−5
550
593
454
4
3


50
50
40
5
−5
−5
560
584
454
4
3


50
50
40
5
−5
−5
570
578
454
2
2


50
50
40
5
−5
0
530
598
451
3
3


50
50
40
5
−5
0
540
597
451
4
3


50
50
40
5
−5
0
550
593
451
4
3


50
50
40
5
−5
0
560
584
451
4
3


50
50
40
5
−5
0
570
578
451
3
2


50
50
40
5
−5
5
530
597
448
3
3


50
50
40
5
−5
5
540
596
447
4
3


50
50
40
5
−5
5
550
593
448
4
3


50
50
40
5
−5
5
560
584
448
5
3


50
50
40
5
−5
5
570
579
448
3
2


50
50
40
5
0
−5
530
597
454
4
3


50
50
40
5
0
−5
540
596
454
4
3


50
50
40
5
0
−5
550
592
454
4
3


50
50
40
5
0
−5
560
581
454
4
2


50
50
40
5
0
−5
570
575
454
2
2


50
50
40
5
0
0
530
597
451
4
3


50
50
40
5
0
0
540
596
451
4
3


50
50
40
5
0
0
550
592
451
4
3


50
50
40
5
0
0
560
581
451
4
2


50
50
40
5
0
0
570
575
451
2
2


50
50
40
5
0
5
530
597
447
4
3


50
50
40
5
0
5
540
596
447
4
3


50
50
40
5
0
5
550
592
448
4
3


50
50
40
5
0
5
560
581
448
4
2


50
50
40
5
0
5
570
576
447
2
2


50
50
40
5
5
−5
520
598
455
2
1


50
50
40
5
5
−5
530
598
454
4
3


50
50
40
5
5
−5
540
595
454
4
3


50
50
40
5
5
−5
550
591
454
4
3


50
50
40
5
5
0
520
598
451
2
2


50
50
40
5
5
0
530
597
451
4
3


50
50
40
5
5
0
540
595
451
4
3


50
50
40
5
5
0
550
591
451
4
3


50
50
40
5
5
5
520
598
448
2
2


50
50
40
5
5
5
530
597
448
4
3


50
50
40
5
5
5
540
596
447
4
3


50
50
40
5
5
5
550
592
448
4
3


50
50
40
5
5
5
560
583
448
2
1


50
50
50
−5
−5
−5
530
604
455
3
2


50
50
50
−5
−5
−5
540
603
454
4
3


50
50
50
−5
−5
−5
550
601
454
4
3


50
50
50
−5
−5
−5
560
596
454
3
2


50
50
50
−5
−5
0
530
605
452
3
3


50
50
50
−5
−5
0
540
604
452
4
4


50
50
50
−5
−5
0
550
601
451
4
3


50
50
50
−5
−5
0
560
596
451
3
2


50
50
50
−5
−5
5
530
604
450
3
3


50
50
50
−5
−5
5
540
604
449
4
4


50
50
50
−5
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550
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50
50
50
−5
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560
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50
50
50
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0
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530
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50
50
50
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0
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50
50
50
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0
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550
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50
50
50
−5
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0
530
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50
50
50
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50
50
50
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0
550
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50
50
50
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530
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50
50
50
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50
50
50
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50
50
50
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50
50
50
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50
50
50
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50
50
50
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50
50
50
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540
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50
50
50
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550
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50
50
50
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530
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50
50
50
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540
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50
50
50
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550
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50
50
50
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50
50
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50
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50
50
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50
50
50
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50
50
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50
50
50
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50
50
50
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50
50
50
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50
50
50
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50
50
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50
50
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50
50
50
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50
50
50
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560
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50
50
50
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50
50
50
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50
50
50
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50
50
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50
50
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50
50
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50
50
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50
50
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50
50
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50
50
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50
50
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50
50
50
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50
50
50
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50
50
50
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530
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50
50
50
0
5
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540
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50
50
50
0
5
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550
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50
50
50
0
5
5
530
601
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50
50
50
0
5
5
540
599
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50
50
50
0
5
5
550
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50
50
50
5
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50
50
50
5
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540
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50
50
50
5
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550
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50
50
50
5
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50
50
50
5
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50
50
50
5
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50
50
50
5
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540
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50
50
50
5
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550
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50
50
50
5
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50
50
50
5
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570
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50
50
50
5
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530
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50
50
50
5
−5
5
540
596
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50
50
50
5
−5
5
550
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50
50
50
5
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560
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50
50
50
5
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570
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50
50
50
5
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530
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50
50
50
5
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540
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50
50
50
5
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550
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50
50
50
5
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530
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50
50
50
5
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540
596
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50
50
50
5
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550
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4
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50
50
50
5
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50
50
50
5
0
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530
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50
50
50
5
0
5
540
596
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50
50
50
5
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5
550
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50
50
50
5
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5
560
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50
50
50
5
5
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530
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50
50
50
5
5
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540
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50
50
50
5
5
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550
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50
50
50
5
5
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530
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50
50
50
5
5
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540
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4
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50
50
50
5
5
0
550
592
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3
3


50
50
50
5
5
5
530
598
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3


50
50
50
5
5
5
540
596
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4
3


50
50
50
5
5
5
550
592
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3


50
60
30
−5
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530
604
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50
60
30
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540
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50
60
30
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50
60
30
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560
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50
60
30
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570
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50
60
30
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50
60
30
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530
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50
60
30
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50
60
30
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550
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50
60
30
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560
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50
60
30
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50
60
30
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50
60
30
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50
60
30
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50
60
30
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50
60
30
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550
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50
60
30
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560
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50
60
30
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570
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50
60
30
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60
30
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50
60
30
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
60
30
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
60
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50
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50
60
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50
60
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50
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50
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50
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50
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50
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580
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50
60
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50
60
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50
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50
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50
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50
60
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50
60
30
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50
60
30
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50
60
30
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50
60
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50
60
30
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50
60
30
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50
60
30
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50
60
30
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5
530
601
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50
60
30
0
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5
540
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50
60
30
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5
550
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50
60
30
0
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5
560
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50
60
30
0
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5
570
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50
60
30
0
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5
580
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50
60
30
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530
601
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50
60
30
0
5
−5
540
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3


50
60
30
0
5
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550
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50
60
30
0
5
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560
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50
60
30
0
5
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570
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50
60
30
0
5
0
530
601
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50
60
30
0
5
0
540
599
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3


50
60
30
0
5
0
550
598
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3


50
60
30
0
5
0
560
595
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3
3


50
60
30
0
5
0
570
593
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2
2


50
60
30
0
5
5
520
602
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1
1


50
60
30
0
5
5
530
601
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4
3


50
60
30
0
5
5
540
600
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4
3


50
60
30
0
5
5
550
597
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4
3


50
60
30
0
5
5
560
595
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3
3


50
60
30
0
5
5
570
593
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2
2


50
60
30
5
−5
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530
598
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2


50
60
30
5
−5
−5
540
596
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3


50
60
30
5
−5
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550
595
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3


50
60
30
5
−5
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560
592
454
4
3


50
60
30
5
−5
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570
589
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3
3


50
60
30
5
−5
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580
589
454
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3


50
60
30
5
−5
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590
593
454
1
2


50
60
30
5
−5
0
530
598
450
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2


50
60
30
5
−5
0
540
597
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3


50
60
30
5
−5
0
550
594
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3


50
60
30
5
−5
0
560
591
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3


50
60
30
5
−5
0
570
589
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3
3


50
60
30
5
−5
0
580
590
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3


50
60
30
5
−5
0
590
594
450
1
2


50
60
30
5
−5
5
530
598
446
3
2


50
60
30
5
−5
5
540
597
446
4
3


50
60
30
5
−5
5
550
594
446
4
3


50
60
30
5
−5
5
560
591
446
4
3


50
60
30
5
−5
5
570
589
446
3
3


50
60
30
5
−5
5
580
590
446
3
3


50
60
30
5
−5
5
590
594
446
1
2


50
60
30
5
0
−5
530
598
454
3
3


50
60
30
5
0
−5
540
596
454
4
3


50
60
30
5
0
−5
550
595
454
4
3


50
60
30
5
0
−5
560
591
454
4
3


50
60
30
5
0
−5
570
589
454
3
2


50
60
30
5
0
−5
580
590
454
2
2


50
60
30
5
0
0
530
597
450
3
3


50
60
30
5
0
0
540
597
450
4
3


50
60
30
5
0
0
550
594
450
4
3


50
60
30
5
0
0
560
591
450
4
3


50
60
30
5
0
0
570
590
450
3
2


50
60
30
5
0
0
580
590
450
2
2


50
60
30
5
0
5
530
597
446
3
3


50
60
30
5
0
5
540
597
446
4
3


50
60
30
5
0
5
550
594
446
4
3


50
60
30
5
0
5
560
591
446
4
3


50
60
30
5
0
5
570
589
446
3
3


50
60
30
5
0
5
580
590
446
2
2


50
60
30
5
5
−5
530
598
454
3
3


50
60
30
5
5
−5
540
596
454
4
3


50
60
30
5
5
−5
550
594
454
4
3


50
60
30
5
5
−5
560
592
454
3
3


50
60
30
5
5
−5
570
589
454
2
2


50
60
30
5
5
0
530
598
450
4
3


50
60
30
5
5
0
540
597
450
4
3


50
60
30
5
5
0
550
594
450
4
3


50
60
30
5
5
0
560
591
450
3
3


50
60
30
5
5
0
570
589
450
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2


50
60
30
5
5
5
520
599
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1
1


50
60
30
5
5
5
530
598
446
4
3


50
60
30
5
5
5
540
597
446
4
3


50
60
30
5
5
5
550
595
446
4
3


50
60
30
5
5
5
560
591
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3
3


50
60
30
5
5
5
570
589
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2
2


50
60
40
−5
−5
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530
605
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3


50
60
40
−5
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540
604
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3


50
60
40
−5
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550
601
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3


50
60
40
−5
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560
599
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4
3


50
60
40
−5
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570
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3
3


50
60
40
−5
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580
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50
60
40
−5
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590
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2


50
60
40
−5
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0
530
604
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3


50
60
40
−5
−5
0
540
603
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3


50
60
40
−5
−5
0
550
601
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4
3


50
60
40
−5
−5
0
560
598
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4
3


50
60
40
−5
−5
0
570
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3
3


50
60
40
−5
−5
0
580
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3
3


50
60
40
−5
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0
590
600
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1
2


50
60
40
−5
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5
530
604
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3


50
60
40
−5
−5
5
540
603
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4
3


50
60
40
−5
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5
550
602
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50
60
40
−5
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5
560
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4
3


50
60
40
−5
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5
570
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3


50
60
40
−5
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5
580
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50
60
40
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5
590
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50
60
40
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0
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530
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50
60
40
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0
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540
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50
60
40
−5
0
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550
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50
60
40
−5
0
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560
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4
3


50
60
40
−5
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570
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50
60
40
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580
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50
60
40
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0
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50
60
40
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0
530
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3


50
60
40
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0
0
540
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50
60
40
−5
0
0
550
601
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4
3


50
60
40
−5
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0
560
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4
3


50
60
40
−5
0
0
570
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3
3


50
60
40
−5
0
0
580
597
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1
2


50
60
40
−5
0
5
520
604
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2
2


50
60
40
−5
0
5
530
604
448
4
3


50
60
40
−5
0
5
540
603
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4
4


50
60
40
−5
0
5
550
601
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4
3


50
60
40
−5
0
5
560
598
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4
3


50
60
40
−5
0
5
570
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50
60
40
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5
580
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50
60
40
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5
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520
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50
60
40
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5
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530
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3


50
60
40
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5
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540
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50
60
40
−5
5
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550
601
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50
60
40
−5
5
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560
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50
60
40
−5
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570
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2
2


50
60
40
−5
5
0
520
605
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2


50
60
40
−5
5
0
530
604
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3


50
60
40
−5
5
0
540
603
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3


50
60
40
−5
5
0
550
601
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4
3


50
60
40
−5
5
0
560
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50
60
40
−5
5
0
570
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2
2


50
60
40
−5
5
5
520
605
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3


50
60
40
−5
5
5
530
604
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4
3


50
60
40
−5
5
5
540
603
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4
4


50
60
40
−5
5
5
550
602
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4
3


50
60
40
−5
5
5
560
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3
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50
60
40
−5
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5
570
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50
60
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530
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50
60
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540
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50
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50
60
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560
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50
60
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570
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50
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580
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50
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50
60
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50
60
40
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540
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50
60
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550
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50
60
40
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560
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50
60
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570
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50
60
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580
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50
60
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50
60
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530
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50
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540
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50
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550
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50
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560
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50
60
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570
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50
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580
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
60
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580
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50
60
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50
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50
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50
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50
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50
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50
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50
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50
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50
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5
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50
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50
60
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50
60
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50
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50
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50
60
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5
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50
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50
60
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50
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50
60
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5
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50
60
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5
530
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50
60
40
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5
5
540
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50
60
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5
5
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50
60
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50
60
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50
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50
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50
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50
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50
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50
60
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580
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50
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50
60
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
60
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570
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50
60
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580
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50
60
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50
60
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50
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50
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50
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50
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50
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50
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50
60
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50
60
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50
60
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50
60
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50
60
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50
60
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580
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50
60
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5
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50
60
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50
60
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50
60
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50
60
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50
60
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50
60
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580
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50
60
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50
60
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50
60
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50
60
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550
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50
60
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50
60
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50
60
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5
5
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50
60
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5
5
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530
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50
60
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5
5
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540
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4
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50
60
40
5
5
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550
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50
60
40
5
5
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560
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4
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50
60
40
5
5
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570
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3
3


50
60
40
5
5
5
520
598
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3
3


50
60
40
5
5
5
530
597
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4
3


50
60
40
5
5
5
540
597
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4
4


50
60
40
5
5
5
550
594
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50
60
40
5
5
5
560
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4
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50
60
40
5
5
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570
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50
60
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530
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50
60
50
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50
60
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550
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50
60
50
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560
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50
60
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570
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50
60
50
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580
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50
60
50
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530
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50
60
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540
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50
60
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550
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50
60
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560
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50
60
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570
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50
60
50
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580
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50
60
50
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530
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50
60
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540
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50
60
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550
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50
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560
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50
60
50
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570
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50
60
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580
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50
60
50
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530
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50
60
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50
60
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50
60
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50
60
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50
60
50
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530
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50
60
50
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540
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50
60
50
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550
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50
60
50
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560
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50
60
50
−5
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570
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50
60
50
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530
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50
60
50
−5
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5
540
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50
60
50
−5
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5
550
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50
60
50
−5
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560
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50
60
50
−5
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5
570
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50
60
50
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520
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1


50
60
50
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5
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530
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50
60
50
−5
5
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540
603
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4


50
60
50
−5
5
−5
550
601
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50
60
50
−5
5
−5
560
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3
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50
60
50
−5
5
0
520
605
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2


50
60
50
−5
5
0
530
604
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50
60
50
−5
5
0
540
602
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50
60
50
−5
5
0
550
601
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4
3


50
60
50
−5
5
0
560
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3
3


50
60
50
−5
5
5
520
605
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2


50
60
50
−5
5
5
530
604
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3


50
60
50
−5
5
5
540
603
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4


50
60
50
−5
5
5
550
601
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50
60
50
−5
5
5
560
598
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3


50
60
50
0
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530
601
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50
60
50
0
−5
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540
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50
60
50
0
−5
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550
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4


50
60
50
0
−5
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560
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50
60
50
0
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570
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50
60
50
0
−5
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580
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50
60
50
0
−5
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590
596
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1
2


50
60
50
0
−5
0
530
601
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3
3


50
60
50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
60
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50
60
50
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50
60
50
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1
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50
60
50
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5
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530
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50
60
50
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5
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540
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50
60
50
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5
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550
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50
60
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5
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50
60
50
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50
60
50
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50
60
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50
60
50
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5
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540
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50
60
50
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50
60
50
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5
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50
60
50
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50
60
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5
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50
60
50
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5
530
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50
60
50
0
5
5
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50
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50
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5
5
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50
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50
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5
5
560
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50
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50
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50
60
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5
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50
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5
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50
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50
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50
60
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50
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50
60
50
5
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50
60
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5
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530
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50
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540
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50
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5
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550
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50
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560
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50
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5
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570
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50
60
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5
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580
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50
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50
5
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590
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50
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50
5
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530
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50
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50
5
−5
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540
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50
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50
5
−5
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50
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50
5
−5
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50
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50
5
−5
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570
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50
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50
5
−5
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580
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50
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50
5
−5
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1
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50
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50
5
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−5
530
598
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50
60
50
5
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−5
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50
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50
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50
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50
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50
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50
60
50
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50
60
50
5
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540
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50
60
50
5
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550
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50
60
50
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50
60
50
5
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50
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50
5
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580
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50
60
50
5
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530
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50
60
50
5
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5
540
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50
60
50
5
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5
550
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50
60
50
5
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5
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50
60
50
5
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570
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50
60
50
5
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580
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50
60
50
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5
−5
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50
60
50
5
5
−5
530
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50
60
50
5
5
−5
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50
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50
5
5
−5
550
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3


50
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50
5
5
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50
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50
5
5
−5
570
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50
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50
5
5
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50
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50
5
5
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530
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50
60
50
5
5
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540
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50
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50
5
5
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550
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50
60
50
5
5
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560
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50
60
50
5
5
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570
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2
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50
60
50
5
5
5
520
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50
60
50
5
5
5
530
598
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50
60
50
5
5
5
540
596
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4


50
60
50
5
5
5
550
594
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3


50
60
50
5
5
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560
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50
60
50
5
5
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70
30
−5
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50
70
30
−5
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50
70
30
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50
70
30
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560
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50
70
30
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50
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30
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580
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50
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30
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50
70
30
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50
70
30
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50
70
30
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50
70
30
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50
70
30
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50
70
30
−5
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50
70
30
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50
70
30
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50
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50
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50
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50
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30
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50
70
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50
70
30
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
70
30
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50
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30
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50
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50
70
30
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50
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50
70
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50
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50
70
30
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50
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50
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50
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50
70
30
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50
70
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
70
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50
70
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50
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50
70
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50
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50
70
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50
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50
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50
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70
30
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50
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70
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50
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50
70
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50
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50
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50
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30
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50
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30
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50
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50
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50
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50
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30
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50
70
30
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3
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50
70
30
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2


50
70
30
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454
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50
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30
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50
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50
70
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560
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454
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50
70
30
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50
70
30
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454
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50
70
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50
70
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50
70
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50
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50
70
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50
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50
70
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50
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50
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50
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50
70
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50
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50
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50
70
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50
70
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
70
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50
70
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50
70
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50
70
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50
70
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50
70
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50
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50
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50
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50
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50
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50
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50
70
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50
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50
70
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50
70
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50
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50
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50
70
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50
70
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50
70
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50
70
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50
70
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
70
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50
70
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
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50
70
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50
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50
−5
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60
50
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450
5
3


60
50
30
0
5
0
550
587
450
4
3


60
50
30
0
5
5
530
597
446
4
3


60
50
30
0
5
5
540
592
446
5
3


60
50
30
0
5
5
550
587
446
4
3


60
50
30
5
−5
−5
530
596
454
3
2


60
50
30
5
−5
−5
540
592
454
4
3


60
50
30
5
−5
−5
550
580
454
5
3


60
50
30
5
−5
−5
560
580
454
4
2


60
50
30
5
−5
0
530
596
450
3
2


60
50
30
5
−5
0
540
591
450
5
3


60
50
30
5
−5
0
550
581
450
5
3


60
50
30
5
−5
0
560
581
450
4
3


60
50
30
5
−5
5
530
595
446
3
2


60
50
30
5
−5
5
540
591
446
5
3


60
50
30
5
−5
5
550
581
446
5
3


60
50
30
5
−5
5
560
581
446
4
3


60
50
30
5
0
−5
530
595
454
4
2


60
50
30
5
0
−5
540
590
454
5
3


60
50
30
5
0
−5
550
581
454
5
3


60
50
30
5
0
−5
560
579
454
2
2


60
50
30
5
0
0
530
595
450
4
3


60
50
30
5
0
0
540
590
450
5
3


60
50
30
5
0
0
550
580
450
5
3


60
50
30
5
0
0
560
580
450
3
2


60
50
30
5
0
5
530
595
446
4
3


60
50
30
5
0
5
540
589
446
5
3


60
50
30
5
0
5
550
581
446
5
3


60
50
30
5
0
5
560
580
446
3
2


60
50
30
5
5
−5
530
594
454
4
3


60
50
30
5
5
−5
540
588
454
5
3


60
50
30
5
5
−5
550
581
454
5
3


60
50
30
5
5
0
530
594
450
4
3


60
50
30
5
5
0
540
586
450
5
3


60
50
30
5
5
0
550
582
450
5
3


60
50
30
5
5
5
530
594
446
4
3


60
50
30
5
5
5
540
587
446
5
3


60
50
30
5
5
5
550
582
446
5
3


60
50
40
−5
−5
−5
530
601
455
4
3


60
50
40
−5
−5
−5
540
598
454
5
3


60
50
40
−5
−5
−5
550
591
454
5
3


60
50
40
−5
−5
−5
560
589
454
4
3


60
50
40
−5
−5
0
530
601
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4
3


60
50
40
−5
−5
0
540
598
451
5
3


60
50
40
−5
−5
0
550
591
451
5
3


60
50
40
−5
−5
0
560
590
451
4
3


60
50
40
−5
−5
5
530
601
448
4
3


60
50
40
−5
−5
5
540
598
448
5
3


60
50
40
−5
−5
5
550
591
447
5
3


60
50
40
−5
−5
5
560
590
447
4
3


60
50
40
−5
0
−5
530
600
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4
3


60
50
40
−5
0
−5
540
596
454
5
3


60
50
40
−5
0
−5
550
591
454
5
3


60
50
40
−5
0
0
530
600
451
4
3


60
50
40
−5
0
0
540
596
451
5
3


60
50
40
−5
0
0
550
591
451
5
3


60
50
40
−5
0
0
560
590
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2
1


60
50
40
−5
0
5
530
600
448
4
3


60
50
40
−5
0
5
540
596
448
5
3


60
50
40
−5
0
5
550
592
448
5
3


60
50
40
−5
0
5
560
591
448
2
2


60
50
40
−5
5
−5
520
602
455
2
1


60
50
40
−5
5
−5
530
600
454
4
3


60
50
40
−5
5
−5
540
596
454
5
3


60
50
40
−5
5
−5
550
593
454
4
3


60
50
40
−5
5
0
520
601
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2
2


60
50
40
−5
5
0
530
599
451
4
3


60
50
40
−5
5
0
540
595
451
5
3


60
50
40
−5
5
0
550
592
451
4
3


60
50
40
−5
5
5
520
602
448
3
2


60
50
40
−5
5
5
530
599
448
4
3


60
50
40
−5
5
5
540
595
447
5
3


60
50
40
−5
5
5
550
592
448
4
3


60
50
40
0
−5
−5
530
598
455
3
3


60
50
40
0
−5
−5
540
594
454
5
3


60
50
40
0
−5
−5
550
585
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5
3


60
50
40
0
−5
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560
585
454
4
3


60
50
40
0
−5
0
530
598
451
4
3


60
50
40
0
−5
0
540
594
451
5
3


60
50
40
0
−5
0
550
585
451
6
3


60
50
40
0
−5
0
560
586
451
4
3


60
50
40
0
−5
5
530
598
448
4
3


60
50
40
0
−5
5
540
594
447
5
3


60
50
40
0
−5
5
550
585
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6
3


60
50
40
0
−5
5
560
586
448
4
3


60
50
40
0
0
−5
530
597
454
4
3


60
50
40
0
0
−5
540
593
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5
3


60
50
40
0
0
−5
550
586
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5
3


60
50
40
0
0
−5
560
585
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3
2


60
50
40
0
0
0
530
597
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4
3


60
50
40
0
0
0
540
592
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5
3


60
50
40
0
0
0
550
586
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5
3


60
50
40
0
0
0
560
585
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3
2


60
50
40
0
0
5
530
597
447
4
3


60
50
40
0
0
5
540
592
448
5
3


60
50
40
0
0
5
550
586
448
5
3


60
50
40
0
0
5
560
586
448
3
2


60
50
40
0
5
−5
520
599
454
1
1


60
50
40
0
5
−5
530
596
454
4
3


60
50
40
0
5
−5
540
592
454
5
3


60
50
40
0
5
−5
550
588
454
4
3


60
50
40
0
5
0
520
599
451
2
2


60
50
40
0
5
0
530
597
451
4
3


60
50
40
0
5
0
540
591
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5
3


60
50
40
0
5
0
550
588
451
5
3


60
50
40
0
5
5
520
599
448
2
2


60
50
40
0
5
5
530
597
448
4
3


60
50
40
0
5
5
540
591
447
5
3


60
50
40
0
5
5
550
587
447
5
3


60
50
40
5
−5
−5
530
595
454
3
3


60
50
40
5
−5
−5
540
591
454
5
3


60
50
40
5
−5
−5
550
581
454
5
3


60
50
40
5
−5
−5
560
582
454
4
3


60
50
40
5
−5
0
530
596
451
3
3


60
50
40
5
−5
0
540
591
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5
3


60
50
40
5
−5
0
550
582
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5
3


60
50
40
5
−5
0
560
581
451
4
3


60
50
40
5
−5
5
530
595
448
4
3


60
50
40
5
−5
5
540
591
447
5
3


60
50
40
5
−5
5
550
582
447
5
3


60
50
40
5
−5
5
560
582
447
4
3


60
50
40
5
0
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530
595
454
4
3


60
50
40
5
0
−5
540
589
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5
3


60
50
40
5
0
−5
550
581
454
5
3


60
50
40
5
0
−5
560
581
454
3
2


60
50
40
5
0
0
530
594
451
4
3


60
50
40
5
0
0
540
588
451
5
3


60
50
40
5
0
0
540
547
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2
1


60
50
40
5
0
0
550
581
451
5
3


60
50
40
5
0
0
560
581
451
3
2


60
50
40
5
0
5
530
594
448
4
3


60
50
40
5
0
5
540
580
447
5
3


60
50
40
5
0
5
550
582
448
5
3


60
50
40
5
0
5
560
582
448
4
2


60
50
40
5
5
−5
530
594
454
4
3


60
50
40
5
5
−5
540
584
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5
3


60
50
40
5
5
−5
550
582
454
5
3


60
50
40
5
5
0
520
597
451
2
1


60
50
40
5
5
0
530
594
451
4
3


60
50
40
5
5
0
540
583
451
5
3


60
50
40
5
5
0
550
583
451
5
3


60
50
40
5
5
5
520
597
448
2
2


60
50
40
5
5
5
530
594
448
4
3


60
50
40
5
5
5
540
583
447
5
3


60
50
40
5
5
5
550
583
447
5
3


60
50
50
−5
−5
−5
530
601
455
3
2


60
50
50
−5
−5
−5
540
598
454
4
3


60
50
50
−5
−5
−5
550
592
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5
3


60
50
50
−5
−5
−5
560
588
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3
2


60
50
50
−5
−5
0
530
601
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3
3


60
50
50
−5
−5
0
540
598
452
4
4


60
50
50
−5
−5
0
550
592
451
5
3


60
50
50
−5
−5
0
560
589
451
3
2


60
50
50
−5
−5
5
530
601
450
3
3


60
50
50
−5
−5
5
540
598
449
4
3


60
50
50
−5
−5
5
550
592
448
5
3


60
50
50
−5
−5
5
560
588
449
3
2


60
50
50
−5
0
−5
530
600
455
4
3


60
50
50
−5
0
−5
540
597
454
4
4


60
50
50
−5
0
−5
550
591
454
4
3


60
50
50
−5
0
0
530
601
452
4
3


60
50
50
−5
0
0
540
597
451
4
4


60
50
50
−5
0
0
550
591
451
4
3


60
50
50
−5
0
5
530
600
450
4
3


60
50
50
−5
0
5
540
597
449
4
4


60
50
50
−5
0
5
550
591
448
4
3


60
50
50
−5
5
−5
530
600
454
4
3


60
50
50
−5
5
−5
540
596
454
4
3


60
50
50
−5
5
−5
550
592
454
4
3


60
50
50
−5
5
0
530
600
452
4
3


60
50
50
−5
5
0
540
596
451
4
4


60
50
50
−5
5
0
550
593
451
4
3


60
50
50
−5
5
5
530
600
449
4
3


60
50
50
−5
5
5
540
596
448
4
3


60
50
50
−5
5
5
550
592
449
4
3


60
50
50
0
−5
−5
530
599
455
3
2


60
50
50
0
−5
−5
540
595
454
4
3


60
50
50
0
−5
−5
550
585
454
5
3


60
50
50
0
−5
−5
560
583
454
4
3


60
50
50
0
−5
0
530
598
452
3
2


60
50
50
0
−5
0
540
595
452
4
3


60
50
50
0
−5
0
550
585
451
5
3


60
50
50
0
−5
0
560
583
451
4
3


60
50
50
0
−5
5
530
598
450
3
3


60
50
50
0
−5
5
540
595
449
4
3


60
50
50
0
−5
5
550
585
448
5
3


60
50
50
0
−5
5
560
583
449
4
3


60
50
50
0
0
−5
530
598
455
4
3


60
50
50
0
0
−5
540
594
454
4
3


60
50
50
0
0
−5
550
585
454
5
3


60
50
50
0
0
0
530
597
452
4
3


60
50
50
0
0
0
540
593
451
5
4


60
50
50
0
0
0
550
585
451
5
3


60
50
50
0
0
5
530
597
449
4
3


60
50
50
0
0
5
540
593
448
4
3


60
50
50
0
0
5
550
585
448
5
3


60
50
50
0
5
−5
530
597
454
4
3


60
50
50
0
5
−5
540
592
454
4
3


60
50
50
0
5
−5
550
587
454
4
3


60
50
50
0
5
0
530
597
452
4
3


60
50
50
0
5
0
540
592
451
5
3


60
50
50
0
5
0
550
587
451
4
3


60
50
50
0
5
5
530
597
449
4
3


60
50
50
0
5
5
540
592
448
5
3


60
50
50
0
5
5
550
587
448
4
3


60
50
50
5
−5
−5
530
596
455
3
2


60
50
50
5
−5
−5
540
592
454
4
3


60
50
50
5
−5
−5
550
581
454
5
3


60
50
50
5
−5
−5
560
579
454
4
3


60
50
50
5
−5
0
530
595
453
3
2


60
50
50
5
−5
0
540
592
452
4
3


60
50
50
5
−5
0
550
580
451
5
3


60
50
50
5
−5
0
560
580
451
4
3


60
50
50
5
−5
5
530
595
450
3
3


60
50
50
5
−5
5
540
591
449
4
3


60
50
50
5
−5
5
550
580
448
5
3


60
50
50
5
−5
5
560
579
448
4
3


60
50
50
5
0
−5
530
595
454
3
3


60
50
50
5
0
−5
540
590
454
4
3


60
50
50
5
0
−5
550
580
454
5
3


60
50
50
5
0
0
530
595
452
4
3


60
50
50
5
0
0
540
590
451
5
3


60
50
50
5
0
0
550
580
451
5
3


60
50
50
5
0
0
560
578
451
2
1


60
50
50
5
0
5
530
595
449
4
3


60
50
50
5
0
5
540
590
448
5
3


60
50
50
5
0
5
550
581
448
5
3


60
50
50
5
0
5
560
579
448
2
1


60
50
50
5
5
−5
530
594
454
4
3


60
50
50
5
5
−5
540
588
454
5
3


60
50
50
5
5
−5
550
581
454
4
3


60
50
50
5
5
0
530
594
452
4
3


60
50
50
5
5
0
540
588
451
5
3


60
50
50
5
5
0
550
581
451
4
3


60
50
50
5
5
5
530
594
449
4
3


60
50
50
5
5
5
540
588
449
5
3


60
50
50
5
5
5
550
581
448
4
3


60
60
30
−5
−5
−5
530
601
454
3
2


60
60
30
−5
−5
−5
540
598
454
4
3


60
60
30
−5
−5
−5
550
594
454
5
3


60
60
30
−5
−5
−5
560
586
454
5
3


60
60
30
−5
−5
−5
570
584
454
3
3


60
60
30
−5
−5
−5
580
584
454
1
2


60
60
30
−5
−5
0
530
601
450
3
2


60
60
30
−5
−5
0
540
598
450
4
3


60
60
30
−5
−5
0
550
594
450
5
3


60
60
30
−5
−5
0
560
586
450
5
3


60
60
30
−5
−5
0
570
584
450
4
3


60
60
30
−5
−5
0
580
584
450
1
2


60
60
30
−5
−5
5
530
601
446
3
2


60
60
30
−5
−5
5
540
599
446
4
3


60
60
30
−5
−5
5
550
594
446
5
3


60
60
30
−5
−5
5
560
586
446
5
3


60
60
30
−5
−5
5
570
584
446
4
3


60
60
30
−5
−5
5
580
585
446
2
2


60
60
30
−5
0
−5
530
600
454
3
3


60
60
30
−5
0
−5
540
598
454
4
3


60
60
30
−5
0
−5
550
593
454
5
3


60
60
30
−5
0
−5
560
589
454
4
3


60
60
30
−5
0
−5
570
587
454
3
2


60
60
30
−5
0
0
530
601
450
4
3


60
60
30
−5
0
0
540
598
450
4
3


60
60
30
−5
0
0
550
593
450
5
3


60
60
30
−5
0
0
560
589
450
4
3


60
60
30
−5
0
0
570
587
450
3
2


60
60
30
−5
0
5
530
601
446
4
3


60
60
30
−5
0
5
540
598
446
4
3


60
60
30
−5
0
5
550
593
446
5
3


60
60
30
−5
0
5
560
590
446
4
3


60
60
30
−5
0
5
570
587
446
3
2


60
60
30
−5
5
−5
530
600
454
4
3


60
60
30
−5
5
−5
540
597
454
4
3


60
60
30
−5
5
−5
550
593
454
4
3


60
60
30
−5
5
−5
560
590
454
4
3


60
60
30
−5
5
0
530
601
450
4
3


60
60
30
−5
5
0
540
597
450
4
3


60
60
30
−5
5
0
550
593
450
4
3


60
60
30
−5
5
0
560
591
450
4
3


60
60
30
−5
5
5
530
601
446
4
3


60
60
30
−5
5
5
540
598
446
4
3


60
60
30
−5
5
5
550
594
446
4
3


60
60
30
−5
5
5
560
590
446
4
3


60
60
30
0
−5
−5
530
599
454
3
2


60
60
30
0
−5
−5
540
596
454
4
3


60
60
30
0
−5
−5
550
590
454
5
3


60
60
30
0
−5
−5
560
584
454
5
3


60
60
30
0
−5
−5
570
583
454
3
3


60
60
30
0
−5
0
530
598
450
3
2


60
60
30
0
−5
0
540
595
450
4
3


60
60
30
0
−5
0
550
590
450
5
3


60
60
30
0
−5
0
560
584
450
5
3


60
60
30
0
−5
0
570
583
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3
3


60
60
30
0
−5
0
580
584
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1
1


60
60
30
0
−5
5
530
598
446
3
2


60
60
30
0
−5
5
540
595
446
4
3


60
60
30
0
−5
5
550
590
446
5
3


60
60
30
0
−5
5
560
584
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5
3


60
60
30
0
−5
5
570
583
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3
3


60
60
30
0
−5
5
580
584
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1
1


60
60
30
0
0
−5
530
598
454
4
3


60
60
30
0
0
−5
540
595
454
4
3


60
60
30
0
0
−5
550
589
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5
3


60
60
30
0
0
−5
560
583
454
5
3


60
60
30
0
0
−5
570
581
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3


60
60
30
0
0
−5
580
582
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1
1


60
60
30
0
0
0
530
598
450
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3


60
60
30
0
0
0
540
595
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3


60
60
30
0
0
0
550
590
450
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3


60
60
30
0
0
0
560
583
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5
3


60
60
30
0
0
0
570
582
450
3
3


60
60
30
0
0
0
580
582
450
1
2


60
60
30
0
0
5
530
598
446
4
3


60
60
30
0
0
5
540
595
446
4
3


60
60
30
0
0
5
550
589
446
5
3


60
60
30
0
0
5
560
583
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5
3


60
60
30
0
0
5
570
582
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3
3


60
60
30
0
0
5
580
583
446
1
2


60
60
30
0
5
−5
530
598
454
4
3


60
60
30
0
5
−5
540
595
454
4
3


60
60
30
0
5
−5
550
590
454
4
3


60
60
30
0
5
−5
560
585
454
4
3


60
60
30
0
5
−5
570
584
454
2
2


60
60
30
0
5
0
530
598
450
4
3


60
60
30
0
5
0
540
594
450
4
3


60
60
30
0
5
0
550
589
450
5
3


60
60
30
0
5
0
560
586
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4
3


60
60
30
0
5
0
570
584
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2
2


60
60
30
0
5
5
530
597
446
4
3


60
60
30
0
5
5
540
594
446
4
3


60
60
30
0
5
5
550
589
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5
3


60
60
30
0
5
5
560
586
446
4
3


60
60
30
0
5
5
570
584
446
2
2


60
60
30
5
−5
−5
530
596
454
3
2


60
60
30
5
−5
−5
540
593
454
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3


60
60
30
5
−5
−5
550
588
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3


60
60
30
5
−5
−5
560
583
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5
3


60
60
30
5
−5
−5
570
583
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3


60
60
30
5
−5
0
530
596
450
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2


60
60
30
5
−5
0
540
593
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3


60
60
30
5
−5
0
550
588
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3


60
60
30
5
−5
0
560
583
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5
3


60
60
30
5
−5
0
570
583
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3


60
60
30
5
−5
5
530
596
446
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2


60
60
30
5
−5
5
540
593
446
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3


60
60
30
5
−5
5
550
587
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3


60
60
30
5
−5
5
560
583
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3


60
60
30
5
−5
5
570
583
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3


60
60
30
5
0
−5
530
595
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2


60
60
30
5
0
−5
540
592
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3


60
60
30
5
0
−5
550
586
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3


60
60
30
5
0
−5
560
581
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3


60
60
30
5
0
−5
570
581
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3


60
60
30
5
0
0
530
595
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3


60
60
30
5
0
0
540
592
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3


60
60
30
5
0
0
550
586
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3


60
60
30
5
0
0
560
582
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4
3


60
60
30
5
0
0
570
582
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3


60
60
30
5
0
5
530
595
446
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3


60
60
30
5
0
5
540
592
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3


60
60
30
5
0
5
550
587
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3


60
60
30
5
0
5
560
582
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3


60
60
30
5
0
5
570
581
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3
3


60
60
30
5
5
−5
530
595
454
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3


60
60
30
5
5
−5
540
591
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3


60
60
30
5
5
−5
550
586
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3


60
60
30
5
5
−5
560
580
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3


60
60
30
5
5
−5
570
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2


60
60
30
5
5
0
530
595
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3


60
60
30
5
5
0
540
591
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3


60
60
30
5
5
0
550
586
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5
3


60
60
30
5
5
0
560
580
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3


60
60
30
5
5
0
570
579
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2


60
60
30
5
5
5
530
595
446
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3


60
60
30
5
5
5
540
592
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3


60
60
30
5
5
5
550
586
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3


60
60
30
5
5
5
560
581
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4
3


60
60
30
5
5
5
570
579
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2


60
60
40
−5
−5
−5
530
601
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3


60
60
40
−5
−5
−5
540
598
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60
60
40
−5
−5
−5
550
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3


60
60
40
−5
−5
−5
560
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3


60
60
40
−5
−5
−5
570
585
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3


60
60
40
−5
−5
−5
580
585
454
2
2


60
60
40
−5
−5
0
530
601
452
4
3


60
60
40
−5 −5
0
540
598
451
5
3


60
60
40
−5
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0
550
593
451
5
4


60
60
40
−5 −5
0
560
587
451
5
3


60
60
40
−5 −5
0
570
585
451
4
3


60
60
40
−5 −5
0
580
585
451
2
2


60
60
40
−5
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530
601
449
4
3


60
60
40
−5 −5
5
540
598
448
5
3


60
60
40
−5
−5
5
550
593
448
5
4


60
60
40
−5
−5
5
560
587
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3


60
60
40
−5
−5
5
570
586
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60
60
40
−5
−5
5
580
585
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60
60
40
−5
0
−5
530
601
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60
60
40
−5
0
−5
540
597
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3


60
60
40
−5
0
−5
550
593
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4


60
60
40
−5
0
−5
560
589
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3


60
60
40
−5
0
−5
570
587
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3


60
60
40
−5
0
0
520
602
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1
1


60
60
40
−5
0
0
530
600
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3


60
60
40
−5
0
0
540
597
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5
3


60
60
40
−5
0
0
550
593
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5
4


60
60
40
−5
0
0
560
589
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4
3


60
60
40
−5
0
0
570
588
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3


60
60
40
−5
0
5
520
602
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2
2


60
60
40
−5
0
5
530
601
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4
3


60
60
40
−5
0
5
540
598
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5
4


60
60
40
−5
0
5
550
593
448
5
4


60
60
40
−5
0
5
560
589
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4
3


60
60
40
−5
0
5
570
588
448
3
3


60
60
40
−5
5
−5
520
602
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2


60
60
40
−5
5
−5
530
600
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3


60
60
40
−5
5
−5
540
597
454
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3


60
60
40
−5
5
−5
550
593
454
5
3


60
60
40
−5
5
−5
560
591
454
4
3


60
60
40
−5
5
0
520
602
452
3
2


60
60
40
−5
5
0
530
600
451
4
3


60
60
40
−5
5
0
540
597
451
5
4


60
60
40
−5
5
0
550
593
451
5
4


60
60
40
−5
5
0
560
591
451
4
3


60
60
40
−5
5
5
520
602
449
3
2


60
60
40
−5
5
5
530
600
448
4
3


60
60
40
−5
5
5
540
598
448
5
4


60
60
40
−5
5
5
550
594
448
5
3


60
60
40
−5
5
5
560
591
448
4
3


60
60
40
0
−5
−5
530
598
455
4
3


60
60
40
0
−5
−5
540
595
455
5
3


60
60
40
0
−5
−5
550
590
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3


60
60
40
0
−5
−5
560
585
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5
3


60
60
40
0
−5
−5
570
584
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3


60
60
40
0
−5
−5
580
585
454
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2


60
60
40
0
−5
0
530
598
452
4
3


60
60
40
0
−5
0
540
595
451
5
3


60
60
40
0
−5
0
550
590
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5
4


60
60
40
0
−5
0
560
585
451
5
4


60
60
40
0
−5
0
570
585
451
4
3


60
60
40
0
−5
0
580
585
451
2
2


60
60
40
0
−5
5
530
598
449
4
3


60
60
40
0
−5
5
540
595
448
5
3


60
60
40
0
−5
5
550
589
448
5
3


60
60
40
0
−5
5
560
585
448
5
3


60
60
40
0
−5
5
570
585
448
4
3


60
60
40
0
−5
5
580
585
447
2
2


60
60
40
0
0
−5
530
598
455
4
3


60
60
40
0
0
−5
540
595
455
5
3


60
60
40
0
0
−5
550
590
454
5
3


60
60
40
0
0
−5
560
584
454
5
3


60
60
40
0
0
−5
570
583
454
3
3


60
60
40
0
0
−5
580
583
454
1
2


60
60
40
0
0
0
530
598
451
4
3


60
60
40
0
0
0
540
594
451
5
3


60
60
40
0
0
0
550
589
451
5
3


60
60
40
0
0
0
560
584
451
5
3


60
60
40
0
0
0
570
583
451
3
3


60
60
40
0
0
0
580
583
451
1
2


60
60
40
0
0
5
520
599
449
2
2


60
60
40
0
0
5
530
597
448
4
3


60
60
40
0
0
5
540
594
448
5
3


60
60
40
0
0
5
550
589
448
5
4


60
60
40
0
0
5
560
584
447
5
3


60
60
40
0
0
5
570
583
447
3
3


60
60
40
0
0
5
580
584
447
1
2


60
60
40
0
5
−5
520
599
455
2
2


60
60
40
0
5
−5
530
598
454
4
3


60
60
40
0
5
−5
540
595
454
5
3


60
60
40
0
5
−5
550
590
454
5
3


60
60
40
0
5
−5
560
586
454
4
3


60
60
40
0
5
−5
570
585
454
2
2


60
60
40
0
5
0
520
599
452
3
2


60
60
40
0
5
0
530
597
451
4
3


60
60
40
0
5
0
540
594
451
5
3


60
60
40
0
5
0
550
589
451
5
4


60
60
40
0
5
0
560
586
451
4
3


60
60
40
0
5
0
570
586
451
2
2


60
60
40
0
5
5
520
600
449
3
2


60
60
40
0
5
5
530
598
448
4
3


60
60
40
0
5
5
540
594
448
5
4


60
60
40
0
5
5
550
589
448
5
4


60
60
40
0
5
5
560
587
448
4
3


60
60
40
0
5
5
570
586
448
3
2


60
60
40
5
−5
−5
530
595
455
4
3


60
60
40
5
−5
−5
540
592
455
5
3


60
60
40
5
−5
−5
550
587
454
5
3


60
60
40
5
−5
−5
560
584
454
5
3


60
60
40
5
−5
−5
570
584
454
3
3


60
60
40
5
−5
0
530
595
452
4
3


60
60
40
5
−5
0
540
592
451
5
3


60
60
40
5
−5
0
550
587
451
5
3


60
60
40
5
−5
0
560
584
451
5
3


60
60
40
5
−5
0
570
584
451
3
3


60
60
40
5
−5
5
530
595
448
4
3


60
60
40
5
−5
5
540
592
448
5
3


60
60
40
5
−5
5
550
586
448
5
3


60
60
40
5
−5
5
560
584
447
5
3


60
60
40
5
−5
5
570
584
447
4
3


60
60
40
5
−5
5
580
584
448
1
1


60
60
40
5
0
−5
530
595
455
4
3


60
60
40
5
0
−5
540
592
455
5
3


60
60
40
5
0
−5
550
586
454
5
3


60
60
40
5
0
−5
560
583
454
5
3


60
60
40
5
0
−5
570
582
454
3
3


60
60
40
5
0
0
530
595
451
4
3


60
60
40
5
0
0
540
592
451
5
3


60
60
40
5
0
0
550
586
451
5
3


60
60
40
5
0
0
560
583
451
5
3


60
60
40
5
0
0
570
582
451
3
3


60
60
40
5
0
5
520
596
449
2
1


60
60
40
5
0
5
530
595
448
4
3


60
60
40
5
0
5
540
592
448
5
3


60
60
40
5
0
5
550
586
448
5
3


60
60
40
5
0
5
560
583
447
5
3


60
60
40
5
0
5
570
582
448
3
3


60
60
40
5
5
−5
520
597
455
2
2


60
60
40
5
5
−5
530
595
455
4
3


60
60
40
5
5
−5
540
591
454
5
3


60
60
40
5
5
−5
550
585
454
5
3


60
60
40
5
5
−5
560
581
454
4
3


60
60
40
5
5
−5
570
579
454
3
3


60
60
40
5
5
0
520
597
452
3
2


60
60
40
5
5
0
530
595
451
4
3


60
60
40
5
5
0
540
591
451
5
3


60
60
40
5
5
0
550
586
451
5
3


60
60
40
5
5
0
560
581
451
4
3


60
60
40
5
5
0
570
580
451
3
3


60
60
40
5
5
5
520
596
449
3
2


60
60
40
5
5
5
530
595
448
4
3


60
60
40
5
5
5
540
591
448
5
3


60
60
40
5
5
5
550
585
447
5
3


60
60
40
5
5
5
560
582
448
4
3


60
60
40
5
5
5
570
580
448
3
3


60
60
50
−5
−5
−5
530
601
456
3
3


60
60
50
−5
−5
−5
540
598
455
4
4


60
60
50
−5
−5
−5
550
593
454
5
4


60
60
50
−5
−5
−5
560
586
454
5
3


60
60
50
−5
−5
−5
570
583
454
3
3


60
60
50
−5
−5
−5
580
583
453
1
3


60
60
50
−5
−5
0
530
601
454
3
3


60
60
50
−5
−5
0
540
598
452
4
4


60
60
50
−5
−5
0
550
593
451
5
4


60
60
50
−5
−5
0
560
586
452
5
4


60
60
50
−5
−5
0
570
583
451
3
3


60
60
50
−5
−5
0
580
583
451
1
2


60
60
50
−5
−5
5
530
600
451
4
3


60
60
50
−5
−5
5
540
598
450
4
4


60
60
50
−5
−5
5
550
593
449
5
4


60
60
50
−5
−5
5
560
585
448
5
3


60
60
50
−5
−5
5
570
583
449
3
3


60
60
50
−5
−5
5
580
583
449
1
2


60
60
50
−5
0
−5
530
600
456
4
3


60
60
50
−5
0
−5
540
598
455
4
4


60
60
50
−5
0
−5
550
593
454
4
4


60
60
50
−5
0
−5
560
588
454
4
3


60
60
50
−5
0
−5
570
586
454
3
3


60
60
50
−5
0
0
530
601
453
4
3


60
60
50
−5
0
0
540
597
452
4
4


60
60
50
−5
0
0
550
592
451
4
4


60
60
50
−5
0
0
560
588
451
4
3


60
60
50
−5
0
0
570
586
451
3
3


60
60
50
−5
0
5
530
600
450
4
3


60
60
50
−5
0
5
540
597
449
4
4


60
60
50
−5
0
5
550
593
449
5
4


60
60
50
−5
0
5
560
589
449
4
3


60
60
50
−5
0
5
570
586
449
3
3


60
60
50
−5
5
−5
530
600
455
4
3


60
60
50
−5
5
−5
540
598
454
4
4


60
60
50
−5
5
−5
550
593
454
4
4


60
60
50
−5
5
−5
560
590
453
3
3


60
60
50
−5
5
0
520
602
454
2
2


60
60
50
−5
5
0
530
600
453
4
3


60
60
50
−5
5
0
540
597
451
4
4


60
60
50
−5
5
0
550
594
451
4
4


60
60
50
−5
5
0
560
590
451
3
3


60
60
50
−5
5
5
520
602
452
2
2


60
60
50
−5
5
5
530
600
450
4
3


60
60
50
−5
5
5
540
597
449
4
4


60
60
50
−5
5
5
550
593
448
4
4


60
60
50
−5
5
5
560
590
449
4
3


60
60
50
0
−5
−5
530
598
456
3
3


60
60
50
0
−5
−5
540
595
455
4
4


60
60
50
0
−5
−5
550
590
455
5
4


60
60
50
0
−5
−5
560
583
454
5
4


60
60
50
0
−5
−5
570
582
454
3
3


60
60
50
0
−5
0
530
598
454
3
3


60
60
50
0
−5
0
540
595
452
4
4


60
60
50
0
−5
0
550
590
451
5
4


60
60
50
0
−5
0
560
583
452
5
4


60
60
50
0
−5
0
570
582
451
3
3


60
60
50
0
−5
5
530
598
451
4
3


60
60
50
0
−5
5
540
595
450
4
4


60
60
50
0
−5
5
550
589
449
5
4


60
60
50
0
−5
5
560
584
448
5
4


60
60
50
0
−5
5
570
582
449
3
3


60
60
50
0
0
−5
530
598
455
4
3


60
60
50
0
0
−5
540
594
454
4
4


60
60
50
0
0
−5
550
589
454
5
4


60
60
50
0
0
−5
560
582
454
4
4


60
60
50
0
0
−5
570
581
454
3
3


60
60
50
0
0
0
530
597
453
4
3


60
60
50
0
0
0
540
595
452
4
4


60
60
50
0
0
0
550
589
451
5
4


60
60
50
0
0
0
560
582
451
4
4


60
60
50
0
0
0
570
581
451
3
3


60
60
50
0
0
5
530
598
450
4
3


60
60
50
0
0
5
540
594
449
4
4


60
60
50
0
0
5
550
589
449
5
4


60
60
50
0
0
5
560
582
448
4
4


60
60
50
0
0
5
570
581
449
3
3


60
60
50
0
5
−5
530
598
455
4
3


60
60
50
0
5
−5
540
594
454
4
4


60
60
50
0
5
−5
550
589
454
4
4


60
60
50
0
5
−5
560
585
454
4
3


60
60
50
0
5
−5
570
584
454
0
1


60
60
50
0
5
0
520
600
455
1
1


60
60
50
0
5
0
530
598
453
4
3


60
60
50
0
5
0
540
594
452
4
4


60
60
50
0
5
0
550
589
451
4
4


60
60
50
0
5
0
560
585
451
4
3


60
60
50
0
5
0
570
583
451
1
1


60
60
50
0
5
5
520
599
452
2
2


60
60
50
0
5
5
530
597
450
4
3


60
60
50
0
5
5
540
594
449
4
4


60
60
50
0
5
5
550
589
448
4
4


60
60
50
0
5
5
560
585
448
4
3


60
60
50
0
5
5
570
584
448
1
2


60
60
50
5
−5
−5
530
596
456
3
3


60
60
50
5
−5
−5
540
592
455
4
3


60
60
50
5
−5
−5
550
587
454
5
4


60
60
50
5
−5
−5
560
582
454
4
4


60
60
50
5
−5
−5
570
582
454
3
3


60
60
50
5
−5
0
530
595
454
3
3


60
60
50
5
−5
0
540
592
452
4
3


60
60
50
5
−5
0
550
586
451
5
4


60
60
50
5
−5
0
560
582
452
4
4


60
60
50
5
−5
0
570
582
451
3
3


60
60
50
5
−5
5
530
595
451
3
3


60
60
50
5
−5
5
540
592
450
4
3


60
60
50
5
−5
5
550
586
449
5
4


60
60
50
5
−5
5
560
582
448
4
4


60
60
50
5
−5
5
570
582
449
3
3


60
60
50
5
0
−5
530
595
455
3
3


60
60
50
5
0
−5
540
592
454
4
3


60
60
50
5
0
−5
550
586
454
5
4


60
60
50
5
0
−5
560
581
454
4
3


60
60
50
5
0
−5
570
580
454
3
3


60
60
50
5
0
0
530
595
453
4
3


60
60
50
5
0
0
540
592
452
4
4


60
60
50
5
0
0
550
586
452
5
4


60
60
50
5
0
0
560
581
451
4
3


60
60
50
5
0
0
570
580
451
3
3


60
60
50
5
0
5
530
595
450
4
3


60
60
50
5
0
5
540
591
449
4
4


60
60
50
5
0
5
550
586
449
5
4


60
60
50
5
0
5
560
581
449
4
3


60
60
50
5
0
5
570
580
449
3
3


60
60
50
5
5
−5
530
595
455
4
3


60
60
50
5
5
−5
540
592
454
4
4


60
60
50
5
5
−5
550
586
454
4
3


60
60
50
5
5
−5
560
579
454
4
3


60
60
50
5
5
−5
570
577
454
2
3


60
60
50
5
5
0
530
594
452
4
3


60
60
50
5
5
0
540
591
452
4
4


60
60
50
5
5
0
550
586
451
5
4


60
60
50
5
5
0
560
579
451
4
3


60
60
50
5
5
0
570
578
451
2
3


60
60
50
5
5
5
520
596
452
2
2


60
60
50
5
5
5
530
595
450
4
3


60
60
50
5
5
5
540
591
449
4
4


60
60
50
5
5
5
550
585
448
5
3


60
60
50
5
5
5
560
579
449
4
3


60
60
50
5
5
5
570
578
449
2
3


60
70
30
−5
−5
−5
530
602
455
3
2


60
70
30
−5
−5
−5
540
600
454
4
3


60
70
30
−5
−5
−5
550
598
454
4
3


60
70
30
−5
−5
−5
560
596
454
4
3


60
70
30
−5
−5
−5
570
596
454
3
3


60
70
30
−5
−5
−5
580
597
454
3
3


60
70
30
−5
−5
−5
590
600
454
2
3


60
70
30
−5
−5
−5
600
606
454
1
1


60
70
30
−5
−5
0
530
602
450
3
2


60
70
30
−5
−5
0
540
600
450
4
3


60
70
30
−5
−5
0
550
598
450
4
3


60
70
30
−5
−5
0
560
596
450
4
3


60
70
30
−5
−5
0
570
596
450
3
3


60
70
30
−5
−5
0
580
597
450
3
3


60
70
30
−5
−5
0
590
601
450
2
3


60
70
30
−5
−5
0
600
607
450
1
2


60
70
30
−5
−5
5
530
601
447
3
2


60
70
30
−5
−5
5
540
601
446
4
3


60
70
30
−5
−5
5
550
598
446
4
3


60
70
30
−5
−5
5
560
596
446
4
3


60
70
30
−5
−5
5
570
596
446
3
3


60
70
30
−5
−5
5
580
597
446
3
3


60
70
30
−5
−5
5
590
601
446
2
3


60
70
30
−5
−5
5
600
607
446
1
2


60
70
30
−5
0
−5
530
602
454
3
2


60
70
30
−5
0
−5
540
600
454
4
3


60
70
30
−5
0
−5
550
598
454
4
3


60
70
30
−5
0
−5
560
596
454
4
3


60
70
30
−5
0
−5
570
596
454
3
3


60
70
30
−5
0
−5
580
598
454
3
3


60
70
30
−5
0
−5
590
603
454
1
1


60
70
30
−5
0
0
530
602
451
3
2


60
70
30
−5
0
0
540
601
450
4
3


60
70
30
−5
0
0
550
598
450
4
3


60
70
30
−5
0
0
560
596
450
4
3


60
70
30
−5
0
0
570
596
450
3
3


60
70
30
−5
0
0
580
598
450
3
3


60
70
30
−5
0
0
590
603
450
1
2


60
70
30
−5
0
5
530
602
447
3
2


60
70
30
−5
0
5
540
600
446
4
3


60
70
30
−5
0
5
550
598
446
4
3


60
70
30
−5
0
5
560
597
446
4
3


60
70
30
−5
0
5
570
596
446
3
3


60
70

30
−5
0
5
580
598
446
3
3


60
70
30
−5
0
5
590
603
446
1
2


60
70
30
−5
5
−5
530
602
454
3
2


60
70
30
−5
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−5
540
600
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3


60
70
30
−5
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542
455
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60
70
30
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598
454
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60
70
30
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560
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454
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3


60
70
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570
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60
70
30
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580
600
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60
70
30
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0
530
601
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60
70
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0
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60
70
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0
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60
70
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60
70
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0
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
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60
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60
70
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60
70
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0
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60
70
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60
70
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60
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60
70
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0
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570
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60
70
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0
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580
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60
70
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0
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60
70
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0
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60
70
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60
70
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60
70
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60
70
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0
0
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60
70
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0
0
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60
70
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0
0
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60
70
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60
70
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0
0
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60
70
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0
0
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60
70
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0
0
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60
70
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0
0
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60
70
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0
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60
70
30
0
0
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60
70
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0
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60
70
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60
70
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0
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60
70
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60
70
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0
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60
70
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0
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60
70
30
0
5
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60
70
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0
5
0
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60
70
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0
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0
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60
70
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0
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0
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60
70
30
0
5
0
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60
70
30
0
5
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580
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60
70
30
0
5
5
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60
70
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0
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5
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60
70
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0
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60
70
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0
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5
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60
70
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0
5
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60
70
30
0
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5
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60
70
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5
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60
70
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5
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60
70
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60
70
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60
70
30
5
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570
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60
70
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60
70
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60
70
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5
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60
70
30
5
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530
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60
70
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5
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60
70
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5
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60
70
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560
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60
70
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60
70
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580
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60
70
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590
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60
70
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5
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60
70
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5
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60
70
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5
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
30
5
0
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60
70
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5
0
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60
70
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0
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60
70
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0
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60
70
30
5
0
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60
70
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5
0
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580
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3
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60
70
30
5
0
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590
596
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3


60
70
30
5
0
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600
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60
70
30
5
0
0
530
597
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3
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60
70
30
5
0
0
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60
70
30
5
0
0
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60
70
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5
0
0
560
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60
70
30
5
0
0
570
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3
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60
70
30
5
0
0
580
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3
3


60
70
30
5
0
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590
596
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60
70
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5
0
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60
70
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5
0
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60
70
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5
0
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60
70
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5
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60
70
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5
0
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60
70
30
5
0
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3
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60
70
30
5
0
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60
70
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5
0
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60
70
30
5
0
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60
70
30
5
5
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530
597
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60
70
30
5
5
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60
70
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5
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60
70
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60
70
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60
70
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60
70
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60
70
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5
5
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60
70
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60
70
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5
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60
70
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60
70
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5
5
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60
70
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60
70
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60
70
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60
70
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5
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60
70
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60
70
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60
70
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60
70
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60
70
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5
5
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590
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60
70
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530
601
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3


60
70
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3


60
70
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4
3


60
70
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60
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
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60
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60
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60
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60
70
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60
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60
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60
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60
70
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60
70
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60
70
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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40
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0
580
594
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60
70
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0
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
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60
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
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60
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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0
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60
70
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0
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60
70
40
0
0
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60
70
40
0
0
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60
70
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0
0
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60
70
40
0
0
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60
70
40
0
0
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4
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60
70
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0
0
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60
70
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0
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60
70
40
0
0
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60
70
40
0
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60
70
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5
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60
70
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60
70
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60
70
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60
70
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5
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60
70
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5
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60
70
40
0
5
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60
70
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0
5
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4
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60
70
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5
0
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4
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60
70
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0
5
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60
70
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0
5
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60
70
40
0
5
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60
70
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0
5
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3
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60
70
40
0
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60
70
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60
70
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60
70
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60
70
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0
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5
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60
70
40
0
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60
70
40
0
5
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3
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60
70
40
0
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60
70
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60
70
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60
70
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60
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60
70
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60
70
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60
70
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5
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2
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60
70
40
5
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600
603
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1
3


60
70
40
5
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0
520
596
454
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60
70
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5
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0
530
595
452
4
3


60
70
40
5
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4
3


60
70
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5
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60
70
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5
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60
70
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5
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60
70
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5
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3
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60
70
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5
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2
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60
70
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5
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60
70
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5
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450
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60
70
40
5
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4
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60
70
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5
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4
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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5
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60
70
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5
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4
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60
70
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60
70
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5
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60
70
40
5
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580
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3
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60
70
40
5
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454
2
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60
70
40
5
0
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60
70
40
5
0
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60
70
40
5
0
0
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4
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60
70
40
5
0
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60
70
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5
0
0
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60
70
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5
0
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4
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60
70
40
5
0
0
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60
70
40
5
0
0
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60
70
40
5
0
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2
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60
70
40
5
0
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60
70
40
5
0
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60
70
40
5
0
5
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60
70
40
5
0
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4
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60
70
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5
0
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60
70
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5
0
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4
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60
70
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5
0
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60
70
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5
0
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60
70
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5
0
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60
70
40
5
0
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60
70
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5
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60
70
40
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5
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3


60
70
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5
5
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
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60
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5
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
70
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60
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60
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60
70
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60
70
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60
70
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60
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60
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60
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60
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60
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60
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60
70
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
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60
70
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60
70
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60
70
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60
70
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60
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60
70
50
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60
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60
70
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60
70
50
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60
70
50
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60
70
50
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60
70
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60
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60
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60
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60
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60
70
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60
70
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60
70
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60
70
50
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60
70
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60
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60
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60
70
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60
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60
70
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60
70
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60
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60
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60
70
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60
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60
70
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60
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60
70
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60
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60
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60
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60
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60
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60
70
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60
70
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60
70
50
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60
70
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60
70
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60
70
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60
70
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60
70
50
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60
70
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60
70
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3


60
70
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60
70
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60
70
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60
70
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60
70
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60
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60
70
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0
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60
70
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0
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3


60
70
50
0
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60
70
50
0
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60
70
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0
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
70
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60
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50
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60
70
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0
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60
70
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60
70
50
0
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60
70
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0
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60
70
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0
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60
70
50
0
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60
70
50
0
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60
70
50
0
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60
70
50
0
0
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454
3
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60
70
50
0
0
0
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453
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3


60
70
50
0
0
0
550
594
452
4
4


60
70
50
0
0
0
560
593
451
4
4


60
70
50
0
0
0
570
593
451
3
4


60
70
50
0
0
0
580
595
451
3
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60
70
50
0
0
0
590
599
451
2
3


60
70
50
0
0
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599
454
2
2


60
70
50
0
0
5
530
598
452
4
3


60
70
50
0
0
5
540
596
450
4
3


60
70
50
0
0
5
550
594
449
4
4


60
70
50
0
0
5
560
593
449
4
4


60
70
50
0
0
5
570
593
449
3
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60
70
50
0
0
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580
595
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3
3


60
70
50
0
0
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590
599
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3


60
70
50
0
5
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530
599
456
3
3


60
70
50
0
5
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540
597
455
4
3


60
70
50
0
5
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550
595
455
4
4


60
70
50
0
5
−5
560
593
454
4
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60
70
50
0
5
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570
593
454
3
3


60
70
50
0
5
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580
596
453
2
3


60
70
50
0
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0
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2
2


60
70
50
0
5
0
530
598
454
4
3


60
70
50
0
5
0
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597
452
4
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60
70
50
0
5
0
550
595
452
4
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60
70
50
0
5
0
560
594
451
4
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60
70
50
0
5
0
570
594
451
3
3


60
70
50
0
5
0
580
596
451
2
3


60
70
50
0
5
5
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599
453
3
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60
70
50
0
5
5
530
598
451
4
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60
70
50
0
5
5
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597
450
4
4


60
70
50
0
5
5
550
595
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4
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60
70
50
0
5
5
560
594
449
4
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60
70
50
0
5
5
570
594
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3
3


60
70
50
0
5
5
580
596
449
2
3


60
70
50
5
−5
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530
596
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3
3


60
70
50
5
−5
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594
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4
3


60
70
50
5
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550
592
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4
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60
70
50
5
−5
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560
590
454
4
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60
70
50
5
−5
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570
590
454
3
3


60
70
50
5
−5
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580
591
454
3
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60
70
50
5
−5
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590
596
454
2
3


60
70
50
5
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600
602
454
1
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60
70
50
5
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0
530
595
454
3
3


60
70
50
5
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540
593
453
4
3


60
70
50
5
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0
550
592
452
4
4


60
70
50
5
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0
560
591
452
4
3


60
70
50
5
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570
590
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3
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60
70
50
5
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580
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451
3
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60
70
50
5
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590
596
451
2
3


60
70
50
5
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1
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60
70
50
5
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596
454
2
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60
70
50
5
−5
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530
596
452
3
3


60
70
50
5
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540
594
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4
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60
70
50
5
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5
550
592
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4
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60
70
50
5
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560
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449
4
3


60
70
50
5
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570
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3
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60
70
50
5
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580
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3
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60
70
50
5
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590
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2
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60
70
50
5
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1
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60
70
50
5
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530
596
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3
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60
70
50
5
0
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594
455
4
3


60
70
50
5
0
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550
593
454
4
3


60
70
50
5
0
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560
591
454
4
3


60
70
50
5
0
−5
570
590
454
3
3


60
70
50
5
0
−5
580
592
454
3
3


60
70
50
5
0
−5
590
596
454
2
3


60
70
50
5
0
0
520
597
456
1
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60
70
50
5
0
0
530
595
454
3
3


60
70
50
5
0
0
540
594
453
4
3


60
70
50
5
0
0
550
592
452
4
4


60
70
50
5
0
0
560
590
452
4
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60
70
50
5
0
0
570
590
452
3
3


60
70
50
5
0
0
580
592
451
3
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60
70
50
5
0
0
590
596
451
2
3


60
70
50
5
0
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453
2
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60
70
50
5
0
5
530
596
451
4
3


60
70
50
5
0
5
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594
450
4
3


60
70
50
5
0
5
550
592
450
4
4


60
70
50
5
0
5
560
590
449
4
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60
70
50
5
0
5
570
590
449
3
3


60
70
50
5
0
5
580
592
448
3
3


60
70
50
5
0
5
590
596
448
2
3


60
70
50
5
5
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530
596
456
3
3


60
70
50
5
5
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540
594
455
4
3


60
70
50
5
5
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550
593
454
4
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60
70
50
5
5
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560
591
454
4
3


60
70
50
5
5
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570
591
454
3
3


60
70
50
5
5
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580
593
454
2
3


60
70
50
5
5
−5
590
598
454
1
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60
70
50
5
5
0
520
597
456
2
2


60
70
50
5
5
0
530
596
453
3
3


60
70
50
5
5
0
540
594
452
4
3


60
70
50
5
5
0
550
593
452
4
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60
70
50
5
5
0
560
591
452
4
3


60
70
50
5
5
0
570
591
451
3
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60
70
50
5
5
0
580
593
451
2
3


60
70
50
5
5
0
590
598
451
1
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60
70
50
5
5
5
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597
453
3
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60
70
50
5
5
5
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596
451
4
3


60
70
50
5
5
5
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594
450
4
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60
70
50
5
5
5
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592
449
4
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60
70
50
5
5
5
560
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449
4
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60
70
50
5
5
5
570
591
448
3
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60
70
50
5
5
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449
2
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60
70
50
5
5
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598
449
1
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70
50
30
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530
596
454
3
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70
50
30
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454
5
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70
50
30
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70
50
30
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70
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70
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70
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70
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5
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70
50
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0
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4
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70
50
30
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5
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70
50
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454
4
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70
50
30
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594
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4
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70
50
30
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0
0
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5
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70
50
30
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0
0
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450
4
3


70
50
30
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0
5
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594
446
4
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70
50
30
−5
0
5
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446
5
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70
50
30
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589
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4
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70
50
30
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593
454
4
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70
50
30
−5
5
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454
5
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70
50
30
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5
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550
590
454
2
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70
50
30
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5
0
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593
450
5
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70
50
30
−5
5
0
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589
450
5
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70
50
30
−5
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550
590
450
3
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70
50
30
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5
5
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593
446
5
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70
50
30
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5
5
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5
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70
50
30
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5
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446
3
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70
50
30
0
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593
454
2
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70
50
30
0
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454
5
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70
50
30
0
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585
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5
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70
50
30
0
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594
450
3
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70
50
30
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5
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70
50
30
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5
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70
50
30
0
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593
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3
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70
50
30
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5
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70
50
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70
50
30
0
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454
4
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70
50
30
0
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70
50
30
0
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4
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70
50
30
0
0
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450
4
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70
50
30
0
0
0
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450
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70
50
30
0
0
0
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586
450
4
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70
50
30
0
0
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4
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70
50
30
0
0
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5
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70
50
30
0
0
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4
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70
50
30
0
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4
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70
50
30
0
5
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70
50
30
0
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586
454
3
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70
50
30
0
5
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589
450
5
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70
50
30
0
5
0
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585
450
5
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70
50
30
0
5
0
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587
450
3
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70
50
30
0
5
5
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589
446
5
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70
50
30
0
5
5
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585
446
5
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70
50
30
0
5
5
550
587
446
3
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70
50
30
5
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530
591
454
1
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70
50
30
5
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578
454
6
3


70
50
30
5
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580
454
5
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70
50
30
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592
450
2
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70
50
30
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6
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70
50
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70
50
30
5
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3
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70
50
30
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6
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70
50
30
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5
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70
50
30
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4
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70
50
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5
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70
50
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70
50
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4
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70
50
30
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70
50
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70
50
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4
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70
50
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6
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70
50
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70
50
30
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586
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4
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70
50
30
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70
50
30
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3
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70
50
30
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5
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70
50
30
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5
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70
50
30
5
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3
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70
50
30
5
5
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586
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5
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70
50
30
5
5
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70
50
30
5
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3
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70
50
40
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595
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4
2


70
50
40
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5
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70
50
40
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5
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70
50
40
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4
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70
50
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70
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70
50
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4
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70
50
40
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5
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70
50
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5
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70
50
40
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70
50
40
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5
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70
50
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4
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70
50
40
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5
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70
50
40
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0
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70
50
40
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0
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4
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70
50
40
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5
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70
50
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0
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5
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70
50
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5
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70
50
40
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5
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70
50
40
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5
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70
50
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3
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70
50
40
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5
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70
50
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5
0
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451
5
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70
50
40
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5
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451
3
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70
50
40
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597
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2
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70
50
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5
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448
5
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70
50
40
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5
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5
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70
50
40
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448
4
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70
50
40
0
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455
4
2


70
50
40
0
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454
6
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70
50
40
0
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5
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70
50
40
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4
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70
50
40
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451
6
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70
50
40
0
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5
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70
50
40
0
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448
4
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70
50
40
0
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447
6
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70
50
40
0
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5
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585
447
5
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70
50
40
0
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587
448
1
1


70
50
40
0
0
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530
591
454
4
3


70
50
40
0
0
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454
6
3


70
50
40
0
0
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550
586
454
5
3


70
50
40
0
0
0
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590
451
4
3


70
50
40
0
0
0
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451
6
3


70
50
40
0
0
0
550
587
451
5
3


70
50
40
0
0
5
530
590
448
5
3


70
50
40
0
0
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447
6
3


70
50
40
0
0
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586
448
5
3


70
50
40
0
5
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530
589
454
5
3


70
50
40
0
5
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585
454
5
3


70
50
40
0
5
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550
587
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4
2


70
50
40
0
5
0
530
588
451
5
3


70
50
40
0
5
0
540
585
451
5
3


70
50
40
0
5
0
550
587
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4
3


70
50
40
0
5
5
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588
448
5
3


70
50
40
0
5
5
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586
447
5
3


70
50
40
0
5
5
550
587
448
4
3


70
50
40
5
−5
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530
591
455
3
2


70
50
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5
−5
−5
540
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6
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70
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−5
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5
3


70
50
40
5
−5
0
530
590
451
4
2


70
50
40
5
−5
0
540
578
451
6
3


70
50
40
5
−5
0
550
581
451
5
3


70
50
40
5
−5
0
560
583
451
2
1


70
50
40
5
−5
5
530
590
448
4
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70
50
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5
−5
5
540
578
448
6
3


70
50
40
5
−5
5
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581
447
5
3


70
50
40
5
−5
5
560
583
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2
2


70
50
40
5
0
−5
530
588
454
4
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70
50
40
5
0
−5
540
579
454
6
3


70
50
40
5
0
−5
550
582
454
5
3


70
50
40
5
0
0
530
588
451
4
3


70
50
40
5
0
0
540
580
451
6
3


70
50
40
5
0
0
550
582
451
5
3


70
50
40
5
0
5
530
588
448
5
3


70
50
40
5
0
5
540
580
447
6
3


70
50
40
5
0
5
550
582
448
5
3


70
50
40
5
5
−5
530
584
454
5
3


70
50
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5
5
−5
540
582
454
5
3


70
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5
5
−5
550
583
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4
3


70
50
40
5
5
0
530
583
451
5
3


70
50
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5
5
0
540
581
451
5
3


70
50
40
5
5
0
550
584
451
4
3


70
50
40
5
5
5
530
582
447
5
3


70
50
40
5
5
5
540
581
447
5
3


70
50
40
5
5
5
550
583
447
4
3


70
50
50
−5
−5
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530
596
455
3
2


70
50
50
−5
−5
−5
540
589
454
5
3


70
50
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−5
−5
−5
550
587
454
5
3


70
50
50
−5
−5
0
530
596
453
3
2


70
50
50
−5
−5
0
540
589
452
5
3


70
50
50
−5
−5
0
550
587
451
5
3


70
50
50
−5
−5
5
530
596
450
3
2


70
50
50
−5
−5
5
540
589
449
5
3


70
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−5
5
550
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5
3


70
50
50
−5
0
−5
530
594
454
4
3


70
50
50
−5
0
−5
540
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454
5
3


70
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0
−5
550
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454
4
3


70
50
50
−5
0
0
530
595
452
4
3


70
50
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−5
0
0
540
588
451
5
4


70
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0
0
550
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451
4
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70
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−5
0
5
530
594
450
4
3


70
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0
5
540
588
448
5
4


70
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−5
0
5
550
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448
4
3


70
50
50
−5
5
−5
530
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454
4
3


70
50
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−5
5
−5
540
588
454
5
3


70
50
50
−5
5
0
530
593
452
4
3


70
50
50
−5
5
0
540
589
451
5
3


70
50
50
−5
5
5
530
593
449
4
3


70
50
50
−5
5
5
540
589
449
5
4


70
50
50
−5
5
5
550
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449
2
1


70
50
50
0
−5
−5
530
593
455
2
2


70
50
50
0
−5
−5
540
584
454
5
3


70
50
50
0
−5
−5
550
584
453
5
3


70
50
50
0
−5
0
530
593
452
3
2


70
50
50
0
−5
0
540
583
452
5
3


70
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50
0
−5
0
550
583
451
5
3


70
50
50
0
−5
5
530
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450
3
2


70
50
50
0
−5
5
540
583
449
5
3


70
50
50
0
−5
5
550
583
449
5
3


70
50
50
0
0
−5
530
592
455
4
3


70
50
50
0
0
−5
540
583
454
5
3


70
50
50
0
0
−5
550
584
454
4
3


70
50
50
0
0
0
530
591
452
4
3


70
50
50
0
0
0
540
583
451
5
4


70
50
50
0
0
0
550
585
451
4
3


70
50
50
0
0
5
530
591
450
4
3


70
50
50
0
0
5
540
583
448
5
3


70
50
50
0
0
5
550
585
449
4
3


70
50
50
0
5
−5
530
590
454
4
3


70
50
50
0
5
−5
540
584
454
5
3


70
50
50
0
5
−5
550
586
454
2
2


70
50
50
0
5
0
530
590
452
4
3


70
50
50
0
5
0
540
584
451
5
3


70
50
50
0
5
0
550
585
451
2
2


70
50
50
0
5
5
530
589
449
4
3


70
50
50
0
5
5
540
584
449
5
4


70
50
50
0
5
5
550
586
449
3
2


70
50
50
5
−5
−5
540
579
454
5
3


70
50
50
5
−5
−5
550
579
454
5
3


70
50
50
5
−5
0
530
591
453
2
2


70
50
50
5
−5
0
540
578
451
6
3


70
50
50
5
−5
0
550
580
451
5
3


70
50
50
5
−5
5
530
591
450
3
2


70
50
50
5
−5
5
540
578
449
6
3


70
50
50
5
−5
5
550
580
449
5
3


70
50
50
5
0
−5
530
589
455
4
3


70
50
50
5
0
−5
540
578
454
5
3


70
50
50
5
0
−5
550
581
453
4
3


70
50
50
5
0
0
530
589
452
4
3


70
50
50
5
0
0
540
579
451
5
3


70
50
50
5
0
0
550
580
451
4
3


70
50
50
5
0
5
530
589
450
4
3


70
50
50
5
0
5
540
578
449
6
4


70
50
50
5
0
5
550
581
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4
3


70
50
50
5
5
−5
530
587
454
4
3


70
50
50
5
5
−5
540
580
454
5
3


70
50
50
5
5
−5
550
582
454
3
2


70
50
50
5
5
0
530
586
452
4
3


70
50
50
5
5
0
540
580
451
5
3


70
50
50
5
5
0
550
581
451
3
2


70
50
50
5
5
5
530
586
449
4
3


70
50
50
5
5
5
540
580
449
5
3


70
50
50
5
5
5
550
582
448
3
2


70
60
30
−5
−5
−5
530
596
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3
2


70
60
30
−5
−5
−5
540
587
454
5
3


70
60
30
−5
−5
−5
550
583
454
5
3


70
60
30
−5
−5
−5
560
585
454
4
2


70
60
30
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0
530
595
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3
2


70
60
30
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3


70
60
30
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3


70
60
30
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0
560
585
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4
3


70
60
30
−5
−5
5
530
596
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3
2


70
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−5
−5
5
540
582
446
5
3


70
60
30
−5
−5
5
550
584
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5
3


70
60
30
−5
−5
5
560
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446
4
3


70
60
30
−5
0
−5
530
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454
4
2


70
60
30
−5
0
−5
540
584
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5
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70
60
30
−5
0
−5
550
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5
3


70
60
30
−5
0
−5
560
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3
2


70
60
30
−5
0
0
530
595
450
4
2


70
60
30
−5
0
0
540
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450
5
3


70
60
30
−5
0
0
550
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450
5
3


70
60
30
−5
0
0
560
586
450
3
2


70
60
30
−5
0
5
530
594
446
4
2


70
60
30
−5
0
5
540
584
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5
3


70
60
30
−5
0
5
550
585
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5
3


70
60
30
−5
0
5
560
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3
2


70
60
30
−5
5
−5
530
594
454
4
3


70
60
30
−5
5
−5
540
586
454
5
3


70
60
30
−5
5
−5
550
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454
4
3


70
60
30
−5
5
−5
600
602
454
1
1


70
60
30
−5
5
0
530
593
450
4
3


70
60
30
−5
5
0
540
586
450
5
3


70
60
30
−5
5
0
550
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450
4
3


70
60
30
−5
5
0
600
602
450
1
1


70
60
30
−5
5
5
530
593
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4
3


70
60
30
−5
5
5
540
586
446
5
3


70
60
30
−5
5
5
550
587
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4
3


70
60
30
−5
5
5
600
602
446
1
1


70
60
30
0
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−5
530
593
454
3
2


70
60
30
0
−5
−5
540
576
454
5
2


70
60
30
0
−5
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550
579
454
5
3


70
60
30
0
−5
−5
560
582
454
4
2


70
60
30
0
−5
0
530
593
450
3
2


70
60
30
0
−5
0
540
576
450
5
2


70
60
30
0
−5
0
550
580
450
5
3


70
60
30
0
−5
0
560
583
450
4
3


70
60
30
0
−5
5
530
593
446
3
2


70
60
30
0
−5
5
540
577
446
6
2


70
60
30
0
−5
5
550
580
446
5
3


70
60
30
0
−5
5
560
583
446
4
3


70
60
30
0
0
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530
592
454
4
2


70
60
30
0
0
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540
578
454
6
3


70
60
30
0
0
−5
550
582
454
5
3


70
60
30
0
0
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560
582
454
3
2


70
60
30
0
0
0
530
592
450
4
2


70
60
30
0
0
0
540
578
450
6
3


70
60
30
0
0
0
550
581
450
5
3


70
60
30
0
0
0
560
583
450
3
2


70
60
30
0
0
5
530
592
446
4
2


70
60
30
0
0
5
540
579
446
6
3


70
60
30
0
0
5
550
582
446
5
3


70
60
30
0
0
5
560
584
446
3
2


70
60
30
0
5
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530
591
454
4
2


70
60
30
0
5
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540
581
454
5
3


70
60
30
0
5
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550
583
454
5
3


70
60
30
0
5
0
530
591
450
4
3


70
60
30
0
5
0
540
581
450
5
3


70
60
30
0
5
0
550
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450
5
3


70
60
30
0
5
5
530
591
446
4
3


70
60
30
0
5
5
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581
446
6
3


70
60
30
0
5
5
550
583
446
5
3


70
60
30
5
−5
−5
530
591
454
2
1


70
60
30
5
−5
−5
540
574
454
6
2


70
60
30
5
−5
−5
550
578
454
5
3


70
60
30
5
−5
−5
560
580
454
4
2


70
60
30
5
−5
0
530
592
450
3
2


70
60
30
5
−5
0
540
573
450
6
2


70
60
30
5
−5
0
550
578
450
5
3


70
60
30
5
−5
0
560
581
450
4
2


70
60
30
5
−5
5
530
591
446
3
2


70
60
30
5
−5
5
540
574
446
6
2


70
60
30
5
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5
550
578
446
5
3


70
60
30
5
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5
560
581
446
4
3


70
60
30
5
0
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530
591
454
3
2


70
60
30
5
0
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540
573
454
6
3


70
60
30
5
0
−5
550
578
454
5
3


70
60
30
5
0
−5
560
580
454
3
2


70
60
30
5
0
0
530
591
450
4
2


70
60
30
5
0
0
540
574
450
6
3


70
60
30
5
0
0
550
578
450
5
3


70
60
30
5
0
0
560
581
450
3
2


70
60
30
5
0
5
530
590
446
4
2


70
60
30
5
0
5
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574
446
6
3


70
60
30
5
0
5
550
578
446
5
3


70
60
30
5
0
5
560
580
446
3
2


70
60
30
5
5
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530
589
454
4
3


70
60
30
5
5
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575
454
5
3


70
60
30
5
5
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550
579
454
5
2


70
60
30
5
5
0
530
589
450
4
3


70
60
30
5
5
0
540
576
450
6
3


70
60
30
5
5
0
550
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450
5
3


70
60
30
5
5
5
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589
446
4
2


70
60
30
5
5
5
540
577
446
6
3


70
60
30
5
5
5
550
580
446
5
3


70
60
40
−5
−5
−5
530
595
455
4
3


70
60
40
−5
−5
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540
582
455
5
3


70
60
40
−5
−5
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550
583
454
5
4


70
60
40
−5
−5
−5
560
586
454
4
3


70
60
40
−5
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0
530
595
452
4
3


70
60
40
−5
−5
0
540
582
451
5
3


70
60
40
−5
−5
0
550
584
451
5
4


70
60
40
−5
−5
0
560
586
451
4
3


70
60
40
−5
−5
5
530
594
448
4
3


70
60
40
−5
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5
540
582
448
6
3


70
60
40
−5
−5
5
550
584
448
5
4


70
60
40
−5
−5
5
560
586
447
4
3


70
60
40
−5
0
−5
530
594
455
4
3


70
60
40
−5
0
−5
540
584
455
6
3


70
60
40
−5
0
−5
550
585
454
5
3


70
60
40
−5
0
−5
560
587
454
3
3


70
60
40
−5
0
0
530
594
452
4
3


70
60
40
−5
0
0
540
584
451
6
3


70
60
40
−5
0
0
550
586
451
5
3


70
60
40
−5
0
0
560
587
451
3
3


70
60
40
−5
0
5
530
594
448
5
3


70
60
40
−5
0
5
540
584
448
6
3


70
60
40
−5
0
5
550
585
448
5
3


70
60
40
−5
0
5
560
587
447
3
3


70
60
40
−5
5
−5
530
593
455
5
3


70
60
40
−5
5
−5
540
586
454
5
3


70
60
40
−5
5
−5
550
587
454
5
3


70
60
40
−5
5
−5
600
602
454
1
1


70
60
40
−5
5
0
520
598
452
2
2


70
60
40
−5
5
0
530
593
451
5
3


70
60
40
−5
5
0
540
586
451
5
3


70
60
40
−5
5
0
550
587
451
5
3


70
60
40
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0
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70
60
40
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3
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70
60
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70
60
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70
60
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70
60
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70
60
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70
60
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0
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70
60
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0
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70
60
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0
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70
60
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0
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70
60
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6
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70
60
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0
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550
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70
60
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0
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0
560
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70
60
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0
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4
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70
60
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70
60
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70
60
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0
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70
60
40
0
0
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592
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4
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70
60
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0
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6
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70
60
40
0
0
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550
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454
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70
60
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0
0
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3
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70
60
40
0
0
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4
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70
60
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0
0
0
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70
60
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0
0
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70
60
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0
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70
60
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0
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70
60
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0
0
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70
60
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0
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5
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70
60
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0
0
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70
60
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0
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70
60
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0
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6
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70
60
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0
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70
60
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0
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70
60
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0
5
0
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5
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70
60
40
0
5
0
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6
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70
60
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0
5
0
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70
60
40
0
5
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2
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70
60
40
0
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595
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2
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70
60
40
0
5
5
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5
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70
60
40
0
5
5
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6
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70
60
40
0
5
5
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70
60
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0
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2
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70
60
40
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4
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70
60
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5
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6
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70
60
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5
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70
60
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5
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4
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70
60
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5
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4
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70
60
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6
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70
60
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70
60
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4
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70
60
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4
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70
60
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6
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70
60
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5
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70
60
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4
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70
60
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4
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70
60
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6
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70
60
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5
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70
60
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0
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3
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70
60
40
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0
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4
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70
60
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5
0
0
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6
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70
60
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5
0
0
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70
60
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0
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70
60
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5
0
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4
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70
60
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70
60
40
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6
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70
60
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5
0
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5
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70
60
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5
0
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70
60
40
5
5
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4
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70
60
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5
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6
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70
60
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5
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70
60
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1
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70
60
40
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70
60
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5
5
0
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6
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70
60
40
5
5
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70
60
40
5
5
0
560
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2
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70
60
40
5
5
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593
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1
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70
60
40
5
5
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5
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70
60
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5
5
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1
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70
60
40
5
5
5
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6
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70
60
40
5
5
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70
60
40
5
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2
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70
60
50
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3
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70
60
50
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70
60
50
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5
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70
60
50
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560
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3


70
60
50
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70
60
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70
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70
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70
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70
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70
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70
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70
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0
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594
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70
60
50
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0
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540
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70
60
50
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0
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550
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454
5
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70
60
50
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0
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560
585
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2


70
60
50
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0
0
530
594
453
4
3


70
60
50
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0
0
540
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70
60
50
−5
0
0
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451
5
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70
60
50
−5
0
0
560
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2
2


70
60
50
−5
0
5
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593
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4
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70
60
50
−5
0
5
540
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70
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50
−5
0
5
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5
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70
60
50
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0
5
560
586
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2
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70
60
50
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593
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4
3


70
60
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−5
5
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586
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5
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70
60
50
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550
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454
4
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70
60
50
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1
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70
60
50
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0
530
593
452
4
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70
60
50
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5
0
540
586
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5
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70
60
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0
550
586
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4
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70
60
50
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5
0
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1
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70
60
50
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5
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593
450
4
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70
60
50
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5
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5
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70
60
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4
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70
60
50
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1
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70
60
50
0
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592
456
3
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70
60
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0
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5
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70
60
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0
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5
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70
60
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0
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70
60
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0
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454
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70
60
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0
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70
60
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0
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70
60
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4
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70
60
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0
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4
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70
60
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70
60
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70
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70
60
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0
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70
60
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0
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70
60
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0
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70
60
50
0
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70
60
50
0
0
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70
60
50
0
0
0
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70
60
50
0
0
0
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70
60
50
0
0
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560
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3
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70
60
50
0
0
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4
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70
60
50
0
0
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70
60
50
0
0
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5
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70
60
50
0
0
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3
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70
60
50
0
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70
60
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0
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5
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70
60
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0
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4
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70
60
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0
5
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70
60
50
0
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70
60
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0
5
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70
60
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0
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70
60
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70
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70
60
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70
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70
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70
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70
60
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3
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70
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70
60
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70
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70
60
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3
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70
60
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6
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70
60
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70
60
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70
60
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70
60
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70
60
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70
60
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2
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70
60
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5
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70
60
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5
0
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70
60
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5
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70
60
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70
60
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70
60
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70
60
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70
60
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70
60
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70
60
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70
60
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70
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70
60
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70
60
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70
60
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70
60
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70
60
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70
70
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2
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70
70
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70
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70
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70
70
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3
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70
70
30
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454
1
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70
70
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2
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70
70
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70
70
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70
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70
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70
70
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1
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70
70
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3
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70
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70
70
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5
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70
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70
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70
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70
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70
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70
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70
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70
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3
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70
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70
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70
70
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70
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70
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70
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70
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70
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70
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70
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70
70
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70
70
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70
70
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70
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70
70
30
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2
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70
70
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70
70
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450
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70
70
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70
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560
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70
70
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70
70
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70
70
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70
70
30
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70
70
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70
70
30
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2
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70
70
30
0
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454
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2


70
70
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4
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70
70
30
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3


70
70
30
0
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570
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454
3
2


70
70
30
0
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530
594
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2
1


70
70
30
0
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540
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4
3


70
70
30
0
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70
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3
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3










[0077] Having thus described the basic concept of the invention, it will be rather apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only, and is not limiting. Various alterations, improvements, and modifications will occur and are intended to those skilled in the art, though not expressly stated herein. These alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and scope of the invention. Accordingly, the invention is limited only by the following claims and equivalents thereto.


Claims
  • 1. A method for determining a color rendering capability of at least one color imaging device with multiple color channels, the method comprising: obtaining spectral sensitivity curves for two or more of the multiple color channels in the color imaging device; and determining an image quality value for the color imaging device from the spectral sensitivity curves for the two or more of the multiple color channels in the color imaging device.
  • 2. The method as set forth in claim 1 wherein determining an image quality value further comprises determining a μ-factor based on the obtained spectral sensitivity curves, wherein the determining an image quality value is based on the μ-factor and at least one other quality factor.
  • 3. The method as set forth in claim 2 wherein the determining an image quality value is based on a relationship between the determined μ-factor and the at least one other quality factor, the image quality value being a substantial average of a minimum and a maximum value for the quality factor associated with the determined μ-factor.
  • 4. The method as set forth in claim 2 wherein the at least one other quality factor is a delta E factor.
  • 5. The method as set forth in claim 2 wherein the image quality value is a color difference metric value.
  • 6. The method as set forth in claim 1 wherein determining an image quality value further comprises determining a Universal Measure of Goodness factor based on the obtained spectral sensitivity curves, wherein the determining an image quality value is based on the Universal Measure of Goodness factor and at least one other quality factor.
  • 7. The method as set forth in claim 6 wherein the at least one other quality factor is a delta E factor.
  • 8. The method as set forth in claim 6 wherein the image quality value is a color quality and noise sensitivity metric value.
  • 9. The method as set forth in claim 1 further comprising evaluating the color rendering capability of the color imaging device based on the determined image quality value.
  • 10. The method as set forth in claim 7 wherein the evaluating further comprises comparing the image quality value of the color imaging device against an image quality standard.
  • 11. The method as set forth in claim 7 wherein the evaluating further comprises comparing the image quality values of two or more of the color imaging devices against each other.
  • 12. A method for designing a spectral sensitivity curve for one or more color channels of a color imaging device, the method comprising: selecting an image quality value; determining a spectral sensitivity curve for at least one of the color channels of the color imaging device so that the spectral sensitivity curves for each of the color channels in the color imaging device results in the image quality value.
  • 13. The method as set forth in claim 12 further comprising obtaining a spectral sensitivity curve for at least one of the color channels of the color imaging device, wherein the determining comprises determining a spectral sensitivity curve for at least one of the other color channels of the color imaging device so that the obtained spectral sensitivity curve with the determined spectral sensitivity curve results in the selected image quality value.
  • 14. The method as set forth in claim 12 wherein the determining further comprises determining spectral sensitivity curves for all of the color channels of the color imaging device so that the determined spectral sensitivity curves result in the image quality value.
  • 15. The method as set forth in claim 12 wherein the determining further comprises: identifying one of a plurality of sets of combinations of spectral sensitivity curves based on the selected image quality value; identifying one or more of the combinations of spectral sensitivity curves based on one or more known spectral sensitivity curves; and selecting one of the one or more the combinations of spectral sensitivity curves based on one or more factors, wherein the determining a spectral sensitivity curve comprises obtaining the spectral sensitivity curve from the selected one of the one or more the combinations of spectral sensitivity curves.
  • 16. The method as set forth in claim 12 wherein the determining further comprises: identifying one of a plurality of sets of combinations of spectral sensitivity curves based on the selected image quality value; identifying one or more of the combinations of spectral sensitivity curves based on one or more characteristics; and selecting one of the one or more the combinations of spectral sensitivity curves based on one or more factors, wherein the determining a spectral sensitivity curve comprises obtaining the spectral sensitivity curve from the selected one of the one or more the combinations of spectral sensitivity curves.
  • 17. The method as set forth in claim 12 wherein the image quality value is a color difference metric value.
  • 18. The method as set forth in claim 12 wherein the image quality value is a color quality and noise sensitivity metric value.
  • 19. A method for determining the tolerances for one or more color channels in a color imaging device, the method comprising: obtaining a spectral sensitivity curve for at least one of the multiple color channels in the color imaging device; obtaining an image quality value; determining a first pair of upper and lower peak wavelength tolerances from the obtained spectral sensitivity for the at least one of the multiple color channels and the obtained image quality value; and determining a second pair of upper and lower tolerances on the width from the obtained spectral sensitivity curve for at least one of the multiple color channels and the obtained image quality value.
  • 20. The method as set forth in claim 19 further comprising evaluating the spectral sensitivity curve based on the first and second pair of tolerances.
  • 21. The method as set forth in claim 19 wherein the determining a first pair and the determining a second pair comprise: identifying one of a plurality of sets of combinations of spectral sensitivity curves based on the obtained image quality value; and identifying one or more of the combinations of spectral sensitivity curves within the identified one of a plurality of sets of combinations of spectral sensitivity curves based on the obtained spectral sensitivity curve; selecting one of the one or more the combinations of spectral sensitivity curves based on one or more factors, wherein the determining a first pair and the determining a second pair are determined from the selected one of the one or more the combinations of spectral sensitivity curves.
  • 22. An imaging device analyzing system, the system comprising: a source for spectral sensitivity curves for two or more of the multiple color channels in a color imaging device; and an image quality processing system that determines an image quality value for the color imaging device from the spectral sensitivity curves for the two or more of the multiple color channels in the color imaging device.
  • 23. The system as set forth in claim 22 wherein the image quality processing system further comprises a μ-factor processing system that determines a μ-factor based on the obtained spectral sensitivity curves, wherein the image quality value is based on the μ-factor and at least one other quality factor.
  • 24. The system as set forth in claim 23 wherein the image quality processing system determines an image quality value based on a relationship between the determined μ-factor and the at least one other quality factor, the image quality value being a substantial average of a minimum and a maximum value for the quality factor associated with the determined μ-factor.
  • 25. The system as set forth in claim 23 wherein the at least one other quality factor is a delta E factor.
  • 26. The system as set forth in claim 26 wherein the image quality value is a color difference metric value.
  • 27. The system as set forth in claim 22 wherein the image quality processing system determines a Universal Measure of Goodness factor based on the obtained spectral sensitivity curves, wherein the image quality value is based on the Universal Measure of Goodness factor and at least one other quality factor.
  • 28. The system as set forth in claim 27 wherein the at least one other quality factor is a delta E factor.
  • 29. The system as set forth in claim 27 wherein the image quality value is a color quality and noise sensitivity metric value.
  • 30. The system as set forth in claim 22 further comprising an evaluation system that evaluates the color rendering capability of the color imaging device based on the determined image quality value.
  • 31. The system as set forth in claim 30 wherein the evaluation system further comprises a comparison system that compares the image quality value of the color imaging device against an image quality standard.
  • 32. The system as set forth in claim 30 wherein the evaluation system further comprises a comparison system that compares the image quality values of two or more of the color imaging devices against each other.
  • 33. An imaging device designing system, the system comprising: a selection system that obtains an image quality value; a design processing system that determines a spectral sensitivity curve for at least one of the color channels of the color imaging device so that the spectral sensitivity curves for each of the color channels in the color imaging device results in the image quality value.
  • 34. The system as set forth in claim 33 further comprising a source for a spectral sensitivity curve for at least one of the color channels of the color imaging device, wherein the determining comprises determining a spectral sensitivity curve for at least one of the other color channels of the color imaging device so that the obtained spectral sensitivity curve with the determined spectral sensitivity curve results in the selected image quality value.
  • 35. The system as set forth in claim 33 wherein the design processing system determines spectral sensitivity curves for all of the color channels of the color imaging device so that the determined spectral sensitivity curves result in the image quality value.
  • 36. The system as set forth in claim 33 wherein the design processing system further comprises: an identification processing system that identifies one of a plurality of sets of combinations of spectral sensitivity curves based on the selected image quality value and identifyies one or more of the combinations of spectral sensitivity curves based on one or more known spectral sensitivity curves; and a selection processing system that selects one of the one or more the combinations of spectral sensitivity curves based on one or more factors, wherein the design processing system obtains the spectral sensitivity curve from the selected one of the one or more the combinations of spectral sensitivity curves.
  • 37. The system as set forth in claim 33 wherein the design processing system further comprises: an identification processing system that identifies one of a plurality of sets of combinations of spectral sensitivity curves based on the selected image quality value and identifies one or more of the combinations of spectral sensitivity curves based on one or more characteristics; and a selection processing system that selects one of the one or more the combinations of spectral sensitivity curves based on one or more factors, wherein the design processing system obtains the spectral sensitivity curve from the selected one of the one or more the combinations of spectral sensitivity curves.
  • 38. The system as set forth in claim 33 wherein the image quality value is a color difference metric value.
  • 39. The system as set forth in claim 33 wherein the image quality value is a color quality and noise sensitivity metric value.
  • 40. A system for determining the tolerances for one or more color, channels in a color imaging device, the system comprising: a first source for a spectral sensitivity curve for at least one of the multiple color channels in the color imaging device; a second source for an image quality value; and a design processing system that determines a first pair of upper and lower peak wavelength tolerances from the obtained spectral sensitivity for the at least one of the multiple color channels and the obtained image quality value and determines a second pair of upper and lower tolerances on the width from the obtained spectral sensitivity curve for at least one of the multiple color channels and the obtained image quality value.
  • 41. The system as set forth in claim 40 further comprising an evaluation system that evaluates the spectral sensitivity curve based on the first and second pair of tolerances.
  • 42. The system as set forth in claim 40 wherein the design processing system further comprises: an identification processing system that identifies one of a plurality of sets of combinations of spectral sensitivity curves based on the obtained image quality value and identifies one or more of the combinations of spectral sensitivity curves within the identified one of a plurality of sets of combinations of spectral sensitivity curves based on the obtained spectral sensitivity curve; and a selection processing system that selects one of the one or more the combinations of spectral sensitivity curves based on one or more factors, wherein the determining a first pair and the determining a second pair are determined from the selected one of the one or more the combinations of spectral sensitivity curves.
Parent Case Info

[0001] This application claims the benefit of U.S. Provisional Patent Application Serial No. 60/191,800 filed on Mar. 24, 2000 which is herein incorporated by reference.

Provisional Applications (1)
Number Date Country
60191800 Mar 2000 US