306:. If R and B were to have been used, these would have non-zero values even in a B&W scene, requiring all three data-carrying signals. This was important in the early days of color television, because old black and white TV signals had no U and V signals present, meaning the color TV would just display it as B&W TV out of the box. In addition, black and white receivers could take the Y′ signal and ignore the U- and V-color signals, making Y′UV backward-compatible with all existing black-and-white equipment, input and output. If the color-TV standard wouldn't have used color difference signals, it could mean a color TV would make funny colors out of a B&W broadcast or it would need additional circuitry to translate the B&W signal to color. It was necessary to assign a narrower bandwidth to the chrominance channel because there was no additional bandwidth available. If some of the luminance information arrived via the chrominance channel (as it would have if RB signals were used instead of differential UV signals), B&W resolution would have been compromised.
2543:
far above 100% of the range (e.g., outside the standard 16–235 luma range (and 16–240 chroma range) for TVs and HD content, or outside 0–255 for standard definition on PCs). Unless these values are dealt with they will usually be "clipped" (i.e., limited) to the valid range of the channel affected. This changes the hue of the color, which is very undesirable, so it is therefore often considered better to desaturate the offending colors such that they fall within the RGB gamut. Likewise, when RGB at a given bit depth is converted to YUV at the same bit depth, several RGB colors can become the same Y′UV color, resulting in information loss.
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color brighter at the cost of the other and by how much it should be shifted. The higher (or the lower when negative) the U and V values are, the more saturated (colorful) the spot gets. The closer the U and V values get to zero, the lesser it shifts the color meaning that the red, green and blue lights will be more equally bright, producing a grayer spot. This is the benefit of using color difference signals, i.e. instead of telling how much red there is to a color, it tells by how much it is more red than green or blue. In turn this meant that when the U and V signals would be zero or absent, it would just display a
2333:
1759:
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1807:. This decision further impacted on the matrix for the Y′UV↔RGB conversion so that its member values are also slightly different. As a result, with SDTV and HDTV there are generally two distinct Y′UV representations possible for any RGB triple: a SDTV-Y′UV and an HDTV-Y′UV one. This means in detail that when directly converting between SDTV and HDTV, the luma (Y′) information is roughly the same but the representation of the chroma (U & V) channel information needs conversion. Still in coverage of the
1979:
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885:
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2328:{\displaystyle {\begin{aligned}{\begin{bmatrix}Y'\\U\\V\end{bmatrix}}&={\begin{bmatrix}0.2126&0.7152&0.0722\\-0.09991&-0.33609&0.436\\0.615&-0.55861&-0.05639\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}\\{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}&={\begin{bmatrix}1&0&1.28033\\1&-0.21482&-0.38059\\1&2.12798&0\end{bmatrix}}{\begin{bmatrix}Y'\\U\\V\end{bmatrix}}\end{aligned}}}
1754:{\displaystyle {\begin{aligned}{\begin{bmatrix}Y'\\U\\V\end{bmatrix}}&={\begin{bmatrix}0.299&0.587&0.114\\-0.14713&-0.28886&0.436\\0.615&-0.51499&-0.10001\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}},\\{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}&={\begin{bmatrix}1&0&1.13983\\1&-0.39465&-0.58060\\1&2.03211&0\end{bmatrix}}{\begin{bmatrix}Y'\\U\\V\end{bmatrix}}.\end{aligned}}}
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earliest color NTSC standard which used a chroma subsampling of 4:1:1 (where the horizontal color resolution is quartered while the vertical is full resolution) so that the picture carried only a quarter as much color resolution compared to brightness resolution. Today, only high-end equipment processing uncompressed signals uses a chroma subsampling of 4:4:4 with identical resolution for both brightness and color information.
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1379:{\displaystyle {\begin{aligned}R'&=Y'+V{\frac {1-W_{R}}{V_{\text{max}}}}=Y'+{\frac {V}{0.877}}=Y'+1.14V,\\G'&=Y'-U{\frac {W_{B}(1-W_{B})}{U_{\text{max}}W_{G}}}-V{\frac {W_{R}(1-W_{R})}{V_{\text{max}}W_{G}}}\\&=Y'-{\frac {0.232U}{0.587}}-{\frac {0.341V}{0.587}}=Y'-0.395U-0.581V,\\B'&=Y'+U{\frac {1-W_{B}}{U_{\text{max}}}}=Y'+{\frac {U}{0.492}}=Y'+2.033U.\end{aligned}}}
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2369:
38:
94:
102:
2535:. It is a way of encoding RGB information, and the actual color displayed depends on the actual RGB colorants used to display the signal. Therefore, a value expressed as Y′UV is only predictable if standard RGB colorants are used (i.e. a fixed set of primary chromaticities, or particular set of red, green, and blue).
532:
543:
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and color volume) of RGB (whether it be BT.601 or Rec. 709) is far smaller than the range of colors and brightnesses allowed by Y′UV. This can be very important when converting from Y′UV (or Y′CbCr) to RGB, since the formulas above can produce "invalid" RGB values – i.e., values below 0% or very
301:
The UV representation of chrominance was chosen over straight R and B signals because U and V are color difference signals. In other words, the U and V signals tell the television to shift the color of a certain spot without altering its brightness. Or the U and V signals tell the monitor to make one
2495:
artifacts. When the NTSC standard was created in the 1950s, this was not a real concern since the quality of the image was limited by the monitor equipment, not the limited-bandwidth signal being received. However today's modern television is capable of displaying more information than is contained
2463:
The I and Q axes were chosen according to bandwidth needed by human vision, one axis being that requiring the most bandwidth, and the other (fortuitously at 90 degrees) the minimum. However, true I and Q demodulation was relatively more complex, requiring two analog delay lines, and NTSC receivers
2454:
Therefore, the resulting U and V signals can be substantially "compressed". In the NTSC (Y′IQ) and PAL systems, the chrominance signals had significantly narrower bandwidth than that for the luminance. Early versions of NTSC rapidly alternated between particular colors in identical image areas to
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by recording a picture's color information at reduced resolution. Only half the horizontal resolution compared to the brightness information is kept (termed 4:2:2 chroma subsampling), and often the vertical resolution is also halved (giving 4:2:0). The 4:x:x standard was adopted due to the very
2436:). The Y′ channel saves all the data recorded by black and white cameras, so it produces a signal suitable for reception on old monochrome displays. In this case, the U and V are simply discarded. If displaying color, all three channels are used, and the original RGB information can be decoded.
242:
All these formats are based on a luma component and two chroma components describing the color difference from gray. In all formats other than Y′IQ, each chroma component is a scaled version of the difference between red/blue and Y; the main difference lies in the scaling factors used, which is
2916:
MATLAB toolbox for color science computation and accurate color reproduction (by Jesus Malo and Maria Jose Luque, Universitat de
Valencia). It includes CIE standard tristimulus colorimetry and transformations to a number of non-linear color appearance models (CIE Lab, CIE CAM,
2443:. The human eye has fairly little spatial sensitivity to color: the accuracy of the brightness information of the luminance channel has far more impact on the image detail discerned than that of the other two. Understanding this human shortcoming, standards such as
1947:
1811:
the Rec. 709 color space is almost identical to Rec. 601 and covers 35.9%. In contrast to this UHDTV with Rec. 2020 covers a much larger area and thus its very own matrix was derived for YCbCr (no YUV/Y′UV, since decommissioning of analog TV).
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infrastructure. They needed a signal transmission method that was compatible with black-and-white (B&W) TV while being able to add color. The luma component already existed as the black and white signal; they added the UV signal to this as a solution.
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Nevertheless, the relationship between them in the standard case is simple. In particular, the Y' channels of both are linearly related to each other, both Cb and U are related linearly to (B-Y), and both Cr and V are related linearly to (R-Y).
2487:). Furthermore, NTSC and PAL encoded color signals in a manner that causes high bandwidth chroma and luma signals to mix with each other in a bid to maintain backward compatibility with black and white television equipment, which results in
352:
880:{\displaystyle {\begin{aligned}Y'&=W_{R}R'+W_{G}G'+W_{B}B'=0.299R'+0.587G'+0.114B',\\U&=U_{\text{max}}{\frac {B'-Y'}{1-W_{B}}}\approx 0.492(B'-Y'),\\V&=V_{\text{max}}{\frac {R'-Y'}{1-W_{R}}}\approx 0.877(R'-Y').\end{aligned}}}
2555:. However, while related, they are different formats with different scale factors; additionally, unlike YCbCr, Y’UV has historically used two different scale factors for the U component vs. the V component. Not scaled matrix is used in
166:
correlate of luminance. Likewise, U and V were chosen to differentiate the U and V axes from those in other spaces, such as the x and y chromaticity space. See the equations below or compare the historical development of the math.
2559:'s PhotoYCC. U and V are bipolar signals which can be positive or negative, and are zero for grays, whereas YCbCr usually scales all channels to either the 16–235 range or the 0–255 range, which makes Cb and Cr
2527:
digital video format also uses Y′CbCr at the common chroma subsampling rate of 4:2:2, primarily for compatibility with previous analog video standards. This stream can be easily mixed into any output format needed.
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In BT.470 a mistake was made because 0.115 was used instead of 0.114 for blue and 0.493 was the result instead of 0.492. In practice that did not affect the decoders because the approximation 1/2.03 was used.
342:, which is further rotated) standard defines the following constants, derived from BT.470 System M primaries and white point using SMPTE RP 177 (same constants called matrix coefficients were used later in
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in these lossy signals. To keep pace with the abilities of new display technologies, attempts were made since the late 1970s to preserve more of the Y′UV signal while transferring images, such as
1984:
1826:
1404:
904:
548:
357:
335:) source. Weighted values of R, G, and B are summed to produce Y′, a measure of overall brightness or luminance. U and V are computed as scaled differences between Y′ and the B and R values.
1821:
1764:
For small values of Y' it is possible to get R, G, or B values that are negative so in practice we clamp the RGB results to the interval or more correctly clamp inside the Y'CbCr.
1969:
The conversion matrices for analog form of BT.709 are these, but there is no evidence those were ever used in practice (instead only actually described form of BT.709 is used, the
2451:
reduce the bandwidth of the chrominance channels considerably. (Bandwidth is in the temporal domain, but this translates into the spatial domain as the image is scanned out.)
527:{\displaystyle {\begin{aligned}W_{R}&=0.299,\\W_{G}&=1-W_{R}-W_{B}=0.587,\\W_{B}&=0.114,\\U_{\text{max}}&=0.436,\\V_{\text{max}}&=0.615.\end{aligned}}}
2351:
Equal values of red, green and blue (i.e. levels of gray) yield 0 for U and V. Black, RGB=(0, 0, 0), yields YUV=(0, 0, 0). White, RGB=(1, 1, 1), yields YUV=(1, 0, 0).
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2781:
3034:
2519:
streams in the MPEG-2 format, which uses a fully defined Y′CbCr color space, although retaining the established process of chroma subsampling.
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2823:
2616:
2986:
48:
3336:
151:
so that a black-and-white receiver would still be able to receive and display a color picture transmission in the receiver's native
73:
158:
As for etymology, Y, Y′, U, and V are not abbreviations. The use of the letter Y for luminance can be traced back to the choice of
3253:
2455:
make them appear adding up to each other to the human eye, while all modern analogue and even most digital video standards use
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3379:
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1942:{\displaystyle {\begin{aligned}W_{R}&=0.2126,\\W_{G}&=1-W_{R}-W_{B}=0.7152,\\W_{B}&=0.0722\\\end{aligned}}}
2843:
2925:
2777:
3389:
3115:
2355:
2959:
3120:
140:. Today, the term YUV is commonly used in the computer industry to describe colorspaces that are encoded using
2804:"ST 170:2004 - SMPTE Standard - For Television — Composite Analog Video Signal — NTSC for Studio Applications"
3483:
2597:"EG 28:1993 - SMPTE Engineering Guideline - Annotated Glossary of Essential Terms for Electronic Production"
199:
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162:
primaries. This lends itself naturally to the usage of the same letter in luma (Y′), which approximates a
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These formulas are traditionally used in analog televisions and equipment; digital equipment such as
1808:
1803:
compared to the previously selected values in the SDTV system. For HDTV these values are provided by
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This article is about an analogue color encoding used in PAL. For the digital pixel format, see
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Another advantage of Y′UV is that some of the information can be discarded in order to reduce
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The scope of the terms Y′UV, YUV, YCbCr, YPbPr, etc., is sometimes ambiguous and overlapping.
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from the luma to the chroma-carrying wire, and vice versa, in analogue equipment (including
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PAL signals in Y′UV are computed from R'G'B' (only SECAM IV used linear RGB) as follows:
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The weights used to compute Y′ (top row of matrix) are identical to those used in the
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2751:
2476:
2722:
3394:
2913:
224:, unusually based on non-gamma-corrected (linear) RGB, making the Y component true
125:
2523:, a video codec from 1991, used a modified YUV 4:2:0 colorspace. The professional
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of Y'PbPr suited for video and image compression and transmission formats such as
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components U and V. The prime symbol (') denotes that the luma is calculated from
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determined by color primaries and the intended numeric range (compare the use of
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Limiting of YUV digital video signals (BBC publication) Authors: V.G. Devereux
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Example of U-V color plane, Y′ value = 0.5, represented within RGB color gamut
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2507:
Instead of Y′UV, Y′CbCr was used as the standard format for (digital) common
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The primary advantage of luma/chroma systems such as Y′UV, and its relatives
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1780:
HDTV Rec. 709 (quite close to SDTV Rec. 601) compared with UHDTV
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Equivalently, substituting values for the constants and expressing them as
2844:""Super Hi-Vision" as Next-Generation Television and Its Video Parameters"
93:
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Furthermore, the range of colors and brightnesses (known as the color
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In TV formats, color information (U and V) was added separately via a
3130:
3067:
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Y′ value of 0.5, with untruncated gamut shown by the center rectangle
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analogue color TV standard. A color is described as a Y′ component (
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may be in need of reorganization to comply with
Knowledge (XXG)'s
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Poynton, Charles (2003). "YUV and luminance considered harmful".
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The resulting ranges of Y′, U, and V respectively are , , and .
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31:
2678:"Projective Transformations of I. C. I. Color Specifications"
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considered harmful: A plea for precise terminology in video"
2479:
to transfer a digital signal, as all they carry is analogue
105:
An image along with its Y′, U, and V components respectively
893:
Inverting the above transformation converts Y′UV to RGB:
3476:
For the vision capacities of organisms or machines, see
155:
format, with no need for extra transmission bandwidth.
55:
2866:
http://downloads.bbc.co.uk/rd/pubs/reports/1987-22.pdf
2428:, is that they remain compatible with black and white
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902:
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346:, although it uses 1/2 instead of 0.436 and 0.615):
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3000:
2778:"World Analogue Television Standards and Waveforms"
2363:UV planes in a range of Y= using the BT.709 matrix
2327:
1941:
1753:
1378:
879:
526:
2880:Digital video and HDTV algorithms and interfaces
1393:gives these formulas for BT.470 System M (PAL):
58:to make improvements to the overall structure.
2960:
2515:. Digital television and DVDs preserve their
136:RGB input and that it is different from true
8:
281:). In Y′IQ, the UV plane is rotated by 33°.
2938:– library for analog TV transmission using
2467:However, this color modulation strategy is
2967:
2953:
2945:
2752:"BT.470: Conventional television systems"
2682:Journal of the Optical Society of America
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74:Learn how and when to remove this message
2921:YUV, YCbCr, YPbPr color space and models
2416:Luminance/chrominance systems in general
1795:decided to change the basic values for W
319:Y′UV signals are typically created from
289:Y′UV was invented when engineers wanted
92:
2588:
2361:
2784:from the original on 27 February 2019
2741:, Pitman Publishing, 1971, pp 161-163
2358:and digital video cameras use Y′CbCr.
258:
7:
2563:quantities which are 128 for grays.
2483:, which is either YUV, YIQ, or even
1815:BT.709 defines these weight values:
2676:Macadam, David L. (1 August 1937).
2739:Principles of Television Reception
25:
2932:between RGB, YUV, YCbCr and YPbPr
2928:for image and video processing –
2551:Y′UV is often used as a term for
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1:
2737:W. Wharton & D. Howorth,
279:YCbCr § R'G'B' to Y'PbPr
2432:(largely due to the work of
2638:Poynton, Charles. "YUV and
3520:
3390:Colour Index International
2471:, particularly because of
188:is the separation used in
85:
3474:
2982:
2816:10.5594/SMPTE.ST170.2004
27:Mathematical color model
2810:: 1–21. November 2004.
2609:10.5594/SMPTE.EG28.1993
1966:values are from above.
259:§ SDTV with BT.470
2940:software-defined radio
2702:10.1364/JOSA.27.000294
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310:Conversion to/from RGB
234:is the format used in
216:is the format used in
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2846:. Information Display
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3407:Federal Standard 595
2987:List of color spaces
2780:. 27 February 2019.
2665:CIE 1960 color space
2625:on 30 November 2017.
2547:Relation with Y′CbCr
2533:absolute color space
1980:
1822:
1809:CIE 1931 color space
1400:
900:
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171:Related color models
164:perceptually uniform
2694:1937JOSA...27..294M
2511:algorithms such as
2504:(1987) connectors.
56:editing the article
2907:Poynton, Charles.
2727:FXScript Reference
2603:: 1–45. May 1993.
2577:Chroma subsampling
2457:chroma subsampling
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2723:RGB and YUV Color
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2509:video compression
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315:SDTV with BT.470
291:color television
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3395:CI list of dyes
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3322:Imaginary color
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3106:rg chromaticity
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2832:on 8 June 2018.
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2531:Y′UV is not an
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2434:Georges Valensi
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338:PAL (NTSC used
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304:grayscale image
295:black-and-white
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190:component video
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153:black-and-white
134:gamma-corrected
112:, also written
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54:Please help by
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3141:SMPTE 240M/"C"
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2902:External links
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2688:(8): 294–297.
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2477:RCA connectors
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1782:Rec. 2020
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3373:and standards
3371:Color systems
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3068:CIELUV (1976)
3066:
3064:
3063:CIELAB (1976)
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2926:Color formats
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2724:
2721:Maller, Joe.
2718:
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2410:Y′ value of 1
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2374:Y′ value of 0
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1805:Rec. 709
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261:with a fixed
260:
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127:
123:
120:found in the
119:
115:
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103:
95:
89:
78:
75:
67:
57:
51:
50:
45:This article
43:
34:
33:
30:
19:
3484:Color vision
3173:
3165:
2992:Color models
2887:. Retrieved
2879:
2872:
2860:
2848:. Retrieved
2838:
2830:the original
2807:
2798:
2786:. Retrieved
2772:
2760:. Retrieved
2755:
2746:
2738:
2733:
2726:
2717:
2705:. Retrieved
2685:
2681:
2671:
2660:
2649:
2639:
2623:the original
2600:
2591:
2565:
2550:
2537:
2530:
2506:
2466:
2462:
2453:
2438:
2419:
2348:color space.
1968:
1960:
1953:
1951:
1814:
1786:
1766:
1763:
1388:
892:
889:
536:
337:
318:
300:
288:
251:
244:
241:
179:
174:
157:
146:
113:
109:
108:
70:
64:October 2015
61:
46:
29:
3504:Color space
3462: [
3417:ICC profile
2976:Color space
2889:18 November
2808:St 170:2004
2758:. p. 9
2756:www.itu.int
2500:(1977) and
2493:cross color
238:television.
118:color model
3307:Hexachrome
3116:Wide-gamut
3058:UVW (1964)
3053:YUV (1960)
3048:RGB (1931)
3043:XYZ (1931)
2601:Eg 28:1993
2583:References
149:subcarrier
128:) and two
3459:JIS Z8102
3242:Rec. 2100
3230:Rec. 2100
3225:Rec. 2020
3156:Rec. 2100
3151:Rec. 2020
2850:1 January
2640:luminance
2489:dot crawl
2473:crosstalk
2441:bandwidth
2253:−
2245:−
2094:−
2086:−
2066:−
2058:−
1890:−
1877:−
1676:−
1668:−
1514:−
1506:−
1486:−
1478:−
1300:−
1249:−
1240:−
1211:−
1193:−
1134:−
1109:−
1068:−
1043:−
943:−
857:−
840:≈
824:−
808:−
756:−
739:≈
723:−
707:−
421:−
408:−
226:luminance
138:luminance
116:, is the
3498:Category
3422:ISCC–NBS
3312:HSL, HSV
3297:Coloroid
3292:ColorADD
3220:Rec. 709
3215:Rec. 601
3146:Rec. 709
3136:Rec. 601
3121:ProPhoto
3078:CIECAM16
3073:CIECAM02
3025:CIECAM16
3010:CIECAM02
2914:Colorlab
2788:16 April
2782:Archived
2762:16 April
2707:12 April
2571:See also
2561:unsigned
2557:Photo CD
2525:CCIR 601
2296:′
2196:′
2184:′
2172:′
2144:′
2132:′
2120:′
2000:′
1719:′
1619:′
1607:′
1595:′
1564:′
1552:′
1540:′
1420:′
1391:matrices
1357:′
1333:′
1284:′
1269:′
1236:′
1189:′
1039:′
1024:′
1000:′
976:′
927:′
912:′
864:′
853:′
815:′
804:′
763:′
752:′
714:′
703:′
665:′
651:′
637:′
623:′
602:′
581:′
556:′
3442:Pantone
3437:Ostwald
3427:Munsell
3332:OSA-UCS
2690:Bibcode
2521:Cinepak
2502:S-Video
2268:2.12798
2256:0.38059
2248:0.21482
2233:1.28033
2097:0.05639
2089:0.55861
2069:0.33609
2061:0.09991
1973:form):
1691:2.03211
1679:0.58060
1671:0.39465
1656:1.13983
1517:0.10001
1509:0.51499
1489:0.28886
1481:0.14713
285:History
275:
263:
198:is any
3482:
3282:CcMmYK
3131:DCI-P3
2936:hacktv
2917:etc.).
2822:
2654:CIELUV
2615:
2513:MPEG-2
2051:0.0722
2046:0.7152
2041:0.2126
1933:0.0722
1906:0.7152
1847:0.2126
518:0.615.
344:BT.601
196:Y′CbCr
186:Y'PbPr
130:chroma
3466:]
3327:Oklab
3275:Other
3266:YCoCg
3261:xvYCC
3249:YPbPr
3237:ICtCp
3210:YCbCr
3191:SECAM
3186:YDbDr
3126:scRGB
3111:Adobe
3020:CAM16
2884:(PDF)
2553:YCbCr
2540:gamut
2498:SCART
2469:lossy
2426:YDbDr
2339:Notes
2081:0.615
2074:0.436
1971:YCbCr
1799:and W
1501:0.615
1494:0.436
1471:0.114
1466:0.587
1461:0.299
1364:2.033
1345:0.492
1252:0.581
1243:0.395
1224:0.587
1217:0.341
1206:0.587
1199:0.232
988:0.877
843:0.877
742:0.492
658:0.114
644:0.587
630:0.299
491:0.436
464:0.114
437:0.587
378:0.299
329:green
293:in a
222:PAL-N
218:SECAM
214:YDbDr
142:YCbCr
88:YCbCr
3452:list
3385:ANPA
3380:ACES
3337:PCCS
3287:CMYK
3203:NTSC
3166:Y′UV
3101:sRGB
3015:iCAM
2891:2016
2852:2013
2820:ISBN
2790:2021
2764:2021
2709:2014
2613:ISBN
2491:and
2485:CVBS
2447:and
2445:NTSC
2424:and
2422:Y′IQ
2356:HDTV
2346:Y′IQ
1959:and
1952:The
1793:ATSC
1791:the
1789:HDTV
1787:For
1007:1.14
333:blue
331:and
250:and
236:NTSC
232:Y′IQ
220:and
208:JPEG
206:and
204:MPEG
180:Y′UV
126:luma
110:Y′UV
3447:RAL
3432:NCS
3412:HKS
3402:DIC
3362:TSL
3357:YJK
3352:HWB
3347:RYB
3317:HCL
3302:LMS
3254:MAC
3198:YIQ
3179:PAL
3174:YUV
3088:RGB
3035:CIE
3002:CAM
2812:doi
2698:doi
2605:doi
2449:PAL
1964:max
1957:max
1319:max
1157:max
1091:max
962:max
792:max
691:max
506:max
479:max
340:YIQ
325:red
321:RGB
277:in
257:in
254:max
247:max
160:XYZ
122:PAL
114:YUV
18:YUV
3500::
3464:ja
3342:RG
2818:.
2806:.
2754:.
2725:,
2696:.
2686:27
2684:.
2680:.
2631:^
2611:.
2599:.
327:,
144:.
3486:.
2968:e
2961:t
2954:v
2893:.
2854:.
2814::
2792:.
2766:.
2711:.
2700::
2692::
2607::
2317:]
2311:V
2304:U
2293:Y
2286:[
2279:]
2273:0
2263:1
2240:1
2228:0
2223:1
2217:[
2212:=
2203:]
2193:B
2181:G
2169:R
2162:[
2151:]
2141:B
2129:G
2117:R
2110:[
2103:]
2035:[
2030:=
2021:]
2015:V
2008:U
1997:Y
1990:[
1961:V
1954:U
1930:=
1921:B
1917:W
1909:,
1903:=
1898:B
1894:W
1885:R
1881:W
1874:1
1871:=
1862:G
1858:W
1850:,
1844:=
1835:R
1831:W
1801:B
1797:R
1745:.
1740:]
1734:V
1727:U
1716:Y
1709:[
1702:]
1696:0
1686:1
1663:1
1651:0
1646:1
1640:[
1635:=
1626:]
1616:B
1604:G
1592:R
1585:[
1576:,
1571:]
1561:B
1549:G
1537:R
1530:[
1523:]
1455:[
1450:=
1441:]
1435:V
1428:U
1417:Y
1410:[
1370:.
1367:U
1361:+
1354:Y
1350:=
1342:U
1337:+
1330:Y
1326:=
1315:U
1308:B
1304:W
1297:1
1291:U
1288:+
1281:Y
1277:=
1266:B
1258:,
1255:V
1246:U
1233:Y
1229:=
1220:V
1202:U
1186:Y
1182:=
1167:G
1163:W
1153:V
1147:)
1142:R
1138:W
1131:1
1128:(
1123:R
1119:W
1112:V
1101:G
1097:W
1087:U
1081:)
1076:B
1072:W
1065:1
1062:(
1057:B
1053:W
1046:U
1036:Y
1032:=
1021:G
1013:,
1010:V
1004:+
997:Y
993:=
985:V
980:+
973:Y
969:=
958:V
951:R
947:W
940:1
934:V
931:+
924:Y
920:=
909:R
871:.
868:)
861:Y
850:R
846:(
832:R
828:W
821:1
812:Y
801:R
788:V
784:=
777:V
770:,
767:)
760:Y
749:B
745:(
731:B
727:W
720:1
711:Y
700:B
687:U
683:=
676:U
669:,
662:B
655:+
648:G
641:+
634:R
627:=
620:B
614:B
610:W
606:+
599:G
593:G
589:W
585:+
578:R
572:R
568:W
564:=
553:Y
515:=
502:V
494:,
488:=
475:U
467:,
461:=
452:B
448:W
440:,
434:=
429:B
425:W
416:R
412:W
405:1
402:=
393:G
389:W
381:,
375:=
366:R
362:W
323:(
272:2
269:/
266:1
252:V
245:U
228:.
210:.
192:.
90:.
77:)
71:(
66:)
62:(
52:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
