27413 2009-07-18 04:40:40 -0700 Built-up (vulgar) fractions using the Unicode fraction slash (or other methods) not supported 2010-02-10 11:42:45 -0800 1 1 1 Unclassified WebKit Text 528+ (Nightly build) All All UNCONFIRMED P2 Normal --- 0 pub-webkit webkit-unassigned alex ap emacemac7 mitz pub-webkit robburns1 oldest_to_newest 132904 0 pub-webkit 2009-07-18 04:40:40 -0700 Unicode contains only a handful of precomposed vulgar fractions (viz, ½; ⅓, ⅔; ¼, ¾; ⅕, ⅖, ⅗, ⅘; ⅙, ⅚; ⅛, ⅜, ⅝, ⅞). In particular, 16ths and 32nds, which are frequently used with imperial units, are not included. The preferred solution, as suggested in an e-mail [1] sent to the WhatWG mailing list, would be to let a sequence of one or more digits 0--9 followed by a fraction slash [U+2044] followed by one or more digits 0--9 be rendered as a built-up fraction. This behaviour is defined in Unicode, and Unicode Technical Report No. 20 explicitly says that this solution is appropriate for use in mark-up languages and not only in plain text. Ideally, digits specifically designed for use in built-up fractions should be used when available in the font used. Otherwise, scaling normal digits to 60% height and 65% width, as suggested in the PostScript Language Cookbook, would seem to be appropriate as fall-back. It should also be noted that MathML does not seem to support vulgar fractions at all, neither as specified nor as implemented in (other) browsers. The correct behaviour is specified in Unicode 5.0, Chapter 6 `Punctuation' [2], Section 6.1 `General Punctuation', heading `General Punctuation: U+2000--U+206F', subheading `Other Punctuation', subsubheading `Fraction Slash' (p. 154): “Fraction Slash. “U+2044 FRACTION SLASH is used between digits to form numeric fractions, such as 2/3, 3/9, and so on. The standard form of a fraction built using the fraction slash is defined as follows: Any sequence of one or more decimal digits, followed by the fraction slash, followed by any sequence of one or more decimal digits. Such a fraction should be displayed as a unit, such as ¾ or $\frac34$ [vertical built-up fraction]. The precise choice of display can depend upon additional formatting information. “If the displaying software is incapable of mapping the fraction to a unit, then it can also be displayed as a simple linear sequence as a fallback (for example, 3/4). If the fraction is to be separated from a previous number, then a space can be used, choosing the appropriate width (normal, thin, zero width, and so on). For example, 1 + ZERO WIDTH SPACE + 3 + FRACTION SLASH + 4 is displayed as 1¾.” [1] <http://lists.whatwg.org/pipermail/whatwg-whatwg.org/2009-April/019340.html> [2] <http://unicode.org/book/ch06.pdf> This bug is also reported elsewhere as <https://bugzilla.mozilla.org/show_bug.cgi?id=500293>. 148562 1 alex 2009-09-20 08:03:09 -0700 The support for beveled fractions is in MathML: <mfrac beveled='true'><mn>1</mn></mn>2</mn></mfrac> That should do exactly what you want. This should be able to be implemented in the fraction rendering support being worked on for MathML. Trying to detect and adjust the line boxes give the recognition of a certain Unicode character without markup surrounding that and an associated style rule seems onerous as well as possibly an incorrect behavior. 148581 2 39837 pub-webkit 2009-09-20 16:42:02 -0700 Created attachment 39837 MathML bevelled fraction example 148582 3 pub-webkit 2009-09-20 16:57:22 -0700 I am not sure I understand why you think following Unicode would be incorrect. In any case, that does not matter if it would be too onerous. Please note (as mentioned in [1] linked to in the original bug report) that the example of a bevelled fraction in the MathML specification (added as an attachment) does not suggest that <mfrac bevelled='true'/> (MathML uses British spelling, apparently) should be rendered as a vulgar fraction. I do agree, however, that it seems reasonable to handle <mfrac bevelled='true'><mn/><mn/></mfrac> or <mfrac bevelled='true'><mn>[0-9]+</mn><mn>[0-9]+</mn></mfrac> as a special case and render it as a vulgar fraction, and this is probably the best option if handling the Unicode fraction slash is not feasible. 148583 4 alex 2009-09-20 17:14:54 -0700 (In reply to comment #3) > I am not sure I understand why you think following Unicode would be incorrect. > In any case, that does not matter if it would be too onerous. Because you are suggesting the before and after characters have their font size changed without a wrapping inline. That is certainly more than kerning two characters. Also, to make this work, the baseline of the before and after characters would have to change. That also seems more than normal placement of line boxes for character glyphs. The attachment point of the before and after characters would most certainly have to be special cased. > Please note (as mentioned in [1] linked to in the original bug report) that the > example of a bevelled fraction in the MathML specification (added as an > attachment) does not suggest that > <mfrac bevelled='true'/> > (MathML uses British spelling, apparently) should be rendered as a vulgar > fraction. That's just a suggestion and used to show how a much more complicated fraction could be rendered. I think it is perfectly reasonable to have a single fraction render close, if not exact, as you'd want. Since I'm working on the MathML stuff, your request is a reasonable goal for simple fractions involving numbers. 148586 5 pub-webkit 2009-09-20 17:43:08 -0700 (In reply to comment #4) > (In reply to comment #3) > > I am not sure I understand why you think following Unicode would be incorrect. > > Because you are suggesting the before and after characters have their font size > changed without a wrapping inline. [...] Fair enough. I do appreciate your concern and do not wish to start a meta-discussion. > Since I'm working on the MathML stuff, your request is a reasonable goal for > simple fractions involving numbers. That is great! 167529 6 robburns1 2009-11-30 23:49:09 -0800 I'm not sure how the cocoa text system and NSText fits into the WebKit open source project, but this is really an enhancement needed in the cocoa text system. Right now some AAT fonts do the job quite nicely, but my sense is that OpenType fonts do not have the control to do this (because I haven't found an OpenType font that does it on any platform). So therefore I think with OpenType fonts it is up tot he text rendering engine to implement the Unicode fraction slash behavior. For AAT fonts this behavior can be implemented in the font, but it would be nice for the rendering engine to do so if the font doesn't have any of that intelligence. Obviously MathML should handle fractions in the MathML way, but I do think we should be getting Unicode fractions even in plain text without any special fraction markup (including in HTML). 169031 7 robburns1 2009-12-05 01:40:33 -0800 Just to clarify my earlier comment, I think this bug should be treated as a Unicode bug only. A separate bug could be filed for MathML fraction support, but this bug as reported by O. Anderson is about Unicode fraction support. These two issues are kept quite distinct since the Unicode fraction approach involves using the fraction slash (U+2044), while the fraction slash will be absent from the MathML. Therefore there is no conflict between the two approaches. It may also make sense to file a bug with Apple Radar since the Unicode fraction slash support would need to come from Apple’s cocoa text system (or any other text system used by WebKit). Specifically I think that the Cocoa Text system should provide the advanced Unicode support for layout from any font by synthesizing, if necessary, the fraction numerator and denominator glyphs and laying them out appropriately. However, more advanced fonts could provide specific fraction glyphs so that the glyph synthesis is not necessary. Finally there is an issue where AAT fonts might already provide the complete layout of the font glyphs into a complete fraction. This means that either the automatic fraction rendering has to be disabled for AAT fonts or some algorithm is needed within the cocoa text system to recognize AAT fonts that already provide font-level fractions (for example Apple Chancery provides complete Unicode support within the font, but I think that is not possible with an OpenType font. see for example, http://en.wikipedia.org/wiki/File:AppleChancery4and221-225thsExample.png). 189430 8 alex 2010-02-10 11:37:53 -0800 In reading chapter 6 from the unicode standard, I agree that this is not a MathML related issue. While you can build such representations using MathML, following the mapping suggestions from chapter 6 would not be implemented using the MathML code directly. Although, such an implementation might use the MathML rendering objects for fractions. 39837 2009-09-20 16:42:02 -0700 2009-09-20 16:42:02 -0700 MathML bevelled fraction example f3008.gif image/gif 11254 pub-webkit R0lGODlhoQAzAPMAAP///93d3WZmZu7u7qqqqjMzM5mZmSIiIru7u3d3d0RERAAAAMzMzIiIiFVV VRERESH5BAAAAAAAIf5oIEltYWdlIGdlbmVyYXRlZCBieSBHTlUgR2hvc3RzY3JpcHQgKGRldmlj ZT1wcG1yYXcpCiBJbWFnZSBnZW5lcmF0ZWQgYnkgR05VIEdob3N0c2NyaXB0IChkZXZpY2U9cHBt cmF3KQoALAAAAAChADMAAAT+EAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAAB AAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQA AAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAA AAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAA AAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACD+AAAAAAAAAAAAAQAA AAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAA AAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAA AAAAAIAAAAAAAAAAAAAEQQAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAA AAAAAAIAAAAAAAAAABCAMQAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAA AAAACAAAAABACgAAQAD+AAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAA AAAAIAAAAACAOQgAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAA AACA4CQAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAA AAaqtBAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAQFgMA AAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAD+AAAAAAAAAAQAAAAAQAsB ACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAUCgAAAAAAAAA gAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAgBYCAAAAAAAA AgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAARjAAAAAAAAACAAAAAATgMAAAABAAAAAAAAAAAI AAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAaCEAAAQAAAAAAAAAACAA AAAAAAAAAAABAAD+AAAAAAAACAAAAABzEAAAQAAAAAAAAAAABp4BAAAAAAAAABAAAAAAAAAAAIAA AAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACNBCAAAAAAAAQAAAAAAAAAAAAAIA AAAAAAAAABAAAAAAAAAAjIJpIQAAAAAAAAAEAAAAnAMAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAA AAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAC0EAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAA AAAAAAAAAQAAAIAWAgAACAAAAAAAAABjwQAAAAAAAAAAAAIAAAD+AAAAAAAQAAAAAAAAAACAAAAA AAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAFaCAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAA AAAAAAAQLQQAAAAAAACAAAAAzAEAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAA AAAAAEAAAAAAAAAAAAACAAAAAKCFAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAADQ QgAAAAEAAAAAAACgJAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAA AAAABAAAAAD+AAAAACBACwEAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAooUAAAAA AAAAEAAA2AoAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAA AABAAAAAAAC0EAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAWggAACAAAAAAAAAg KQABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAA EExqqYQAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAD+AAAAQLQQAAAAAAAAAAIAxjMAAAAA ABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAA QAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAQAsBAAAEAAAAAACAPAAgAAAAAAAAAAAA AQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAE AAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAAiBYCAAAAAAAAQACAEwAAAAAAAAIAAAAAAAAAABAA AAAAAAD+AACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAA AAAAAAAAAAACAAAAAAAAAAAQAAAAAGghAACAAAAAAABgPAYABAAAAAAAAAAAIAAAAAAAAAAAAAEA AAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAA AAAAAAAAIAAAAAAAAACgBNVSCQEAAAAAAAhAOgAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAA AAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAD+AAABAAAAAAAAAAAIAAAAAAAAAABAAAAA AAAAAAAAAgAAAAAAAAAAEAAAAAAAlAQAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAA AAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAEBQSimlFFRKKQcA AAAAACAAAAAAAAAAAAABWgMAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAA AAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAA AAD+AAIAAAAACAUAABAAAAAAAAAARIJODQAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAKKWU UkopqJRSSimllFJKQaWUUkoppZRSCiqllFJKKaWUMhAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAA AAAgWAQAAAAAAAAAAQAArQBOAgAACAAAAAAAAAAAQAAAAAAAEJphCQYAAAAAAAAAABAAAAAAAAAA AIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAEUIIIYQQQgwACAAAAAAAAAAAQAAAAACYNwAA AAIAAAAAAABAAHAsAgAAAAAAAIAAAAAAAAAAAAD+BEGM4poCAAAAIAAAAAAAAAAAAAEAAAAAAAAA AAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAQSmllFJQKaUcAAAAAACAAAAAAAAAAAAAdAkAAAAAAAAA IAAAAJBOAwAAAAEAAAAAGAMAAAgAAAAAwAI4aMABAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACA AAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAACExQAAAEAAAAAAAAAAAACy RwAAAAAAAAAQpAQAAAAAAACAAACwAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAj+ AAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAABAgw8AAAAAAAAAAAQAgEAAUA4AACAA AAAAQEoAAAABAAAAABAjBxCIAAAAAAAAAABAAAAAAAAgklMDAgAAAAAAAAAAEAAAAAAAAABCg4al AAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAACAYwAAAAAIAEipECFWSAdAoAQAAAAAAAAAgpQA AAAAAAAAELjkDhEDAAAAgAAAAAAAAAAAAARoBXASAAAAACAAAAAAAAAAAAABACCIUVxTAAAIAAAA AAAAAABAAAAAAAAAAAAAAgAAAAAAAABbMAD+AAAAADQG0IKEPRYSMY8BAAAEAAAAAEgJAAAgAAAA AABAIDAAAQAAAAAAAAAACAAAAAAAAhiLQAAAAAAAAABgDAIAAAAAAABYAPCgMQAAAAAAAIAAAAAA AAAAAAAEAAAAAAAAAAAgAAAAJwAAAAAAARAAtAMAAAAwiAAAAAAAAAAAQJASAAAAAAAAAAIAAAAA AAAAABAAAAAAAAAAAIAAgHQaAAAAAAAEAACQEgAAAAAgAAAAABYAAAAAAQAAAAAAAAAACAAAAAAA AAAAQAAAAAAAAMB4BgIAAAAAAACAShAAAAAAAAAAAIAABKWUUucopRR0AAAAAFBKKaWgMgD+AAAA AAAAAAEAAAAAAADsEQgAAAAAAAAAKUEAAAAAAAAAYgQeQBAAAAAAAAAQAAAAAAAAAACAAAAAAAAA AAAABAAAcgAAAAAAIAAAgNMAAAAAAAEAAAAAAAAAAAhSAgAAAAAAAEAAAAAAAAAAAAACAAAAIKVC hFgwBAKAcgAAAACAAAAAUgIAAAAABAAAl9whYgAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAABQ CUAAAAAAAAAAWwyC0QAAAAAAAAAQAAAAACAlAACAAAAAAAAAAAAABAAAAAAAAADQIANoEfZYOgAo AQEAAAAAAAAgJQgAAAAAAAAACMDAAAD+AAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgACAsRgAAAAA AATtgbQAaAwAACAAAAAAAAAAAABBSgAAAAAAAAAIgEhODQAAAABAAAAAQADQDgAAgpCIeQwAAAAA EAAAQEoAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAABIBQAIAAAAAJCKEarB lgAAAAAAAAAAAgAAAACkBAAAEAAAAAAArQBOggAAAAAAAAAAAARAJQAAAIAhACAAAAAQlFJKnQOV UsoBAAAASimolFIGAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEABQGgAAAAAAgAAEBgD+CgAAAAAE AAAAAAAAAAAgSAkAAAAAAAAAAQhgLAIAAAAACAAAAAAATgMAQAAAAAAAAAAAAAIAAEgJAAAAABAA AAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAwbwAAAQAAAAAAAAAACAAAAAAAAAAAQAAA AACAEAAAAAIAAAAAAJBOAxAAAAAAAAAAAICALQZGAwAAAAAEAAAAAAAAgJQgAAAAAAAAAAAAAQAA AAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIgHAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAA AAAAAAAgAACwRwAAAAAAAQAAtAf+0gKgMQgAAAAAAAAAAEAAAAApAQAAAAACAAAAIjk1AAAQAAAA AAAAAACAAAAAAAAAAAAABAAAAAAACwEAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAA gEAAUA4CAAAAAAAAQCrQCNVaAgAAAACAAAAAAAAAAJASBAAAAAAAAAC0YAAnAQAAAAAAAAEAAAAA AAAAAAgAAAAAAAAAAEBgHgAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABOkAoAQA AAAAIAAAABAYACgAAAEAAAAAAAAAAAgAACAlAAAAAEAAAAAggLEIAAACAAAAAAD+AAAAEAAAAAAA AAAAgAAAAAAAKgEAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAABASMY9BAAAAAAAA AAAAAgAAAAAAAAAAEAAAAAAAAABCgAAAAAAAAAAAAEynAQAAAAAAACAAAAAAAAAAAAABAAAAAAAA AADIFgIAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAhgAAAAAAAAQAAAAAAAAA ACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAMAeAQBAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAABJAQAA gAAAAAAAAAAAAAQAAAAAAAD+AAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAA AAIAAAAAAAAAABAAAAAAAAAAAoEAKAcAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAATwMAAAAAAAAA CAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAg AAAAAAAAAAAAAQAApAOAEgAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAADsAQAAABAAAAAAAAAAAIAA AAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAD+AEAAAAAAAAAAAAAC AAAAAAAAQEiQmMcAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgA AAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAA AAAYAgAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAA AAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAA AAAAAAAQAAAAAAAAAACmgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAA AAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAA AAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAA AAAAAAQAAABABAAh+QQAAAAAACwAAAAAoQAzAAAE/hAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAA AAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAA AIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAA AAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAA CAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAg /gAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACA AAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAAC AAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABEEAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgA AAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQgDEAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAA AAAAAAAAAAEAAAAAAAAAAAgAAAAAQAoAAEAA/gAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAA AAAAAAAAAAQAAAAAAAAAACAAAAAAgDkIAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAA AAAAAAAAEAAAAAAAAAAAgOAkAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAA AAAAAABAAAAAAAAAAAAGqrQQAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAA AAAAAAABAAAAEBYDAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAA/gAA AAAAAAAEAAAAAEALAQAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAA AAAAAFAoAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAA AAAAQIAWAgAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEYwAAAAAAAAAgAAAAAE4D AAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAGgh AAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAA/gAAAAAAAAgAAAAAcxAAAEAAAAAAAAAAAAaeAQAAAAAA AAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAjQQgAAAAAA AEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAIyCaSEAAAAAAAAABAAAAJwDAAAAIAAAAAAAAAAA AAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAtBACAAAAAAAAAAAAA BAAAAAAAAAAAIAAAAAAAAAAAAAEAAACAFgIAAAgAAAAAAAAAY8EAAAAAAAAAAAACAAAA/gAAAAAA EAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABWggAAAAAAAAIAAAAAAAAAABA AAAAAAAAAAAAAgAAAAAAAAAAEC0EAAAAAAAAgAAAAMwBAAAAAAQAAAAAAAAAACAAAAAAAAAAAAAB AAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAACghQAAEAAAAAAAAAAAgAAAAAAAAAAAAAQA AAAAAAAAACAAAAAA0EIAAAABAAAAAAAAoCQIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAA AAAAAAAAgAAAAAAAAAAAAAQAAAAA/gAAAAAgQAsBAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAA AAAAAAAAAKKFAAAAAAAAABAAANgKAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAA AAAAAAAACAAAAAAAAAAAQAAAAAAAtBAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAA AFoIAAAgAAAAAAAAICkAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAA AAAAAIAAAAAAAAAAABBMaqmEAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAA/gAAAEC0EAAA AAAAAAACAMYzAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAA AAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAEALAQAABAAAAAAA gDwAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAA AACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAIgWAgAAAAAAAEAAgBMAAAAA AAACAAAAAAAAAAAQAAAAAAAA/gAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAA AAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAABoIQAAgAAAAAAAYDwGAAQAAAAAAAAA ACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAA gAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAoATVUgkBAAAAAAAIQDoAAAAAAABAAAAAAAAAAAAA AgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAA/gAAAQAAAAAAAAAA CAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAJQEAIAAAAAAAAAAAAAEAAAAAAAAAAAg AAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAA AABAUEoppRRUSikHAAAAAAAgAAAAAAAAAAAAAVoDAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIA AAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAA AAAAAAAAQAAAAAAAAAAA/gACAAAAAAgFAAAQAAAAAAAAAESCTg0AAAAAAAAABAAAAAAAAAAAIAAA AAAAAAAAAAEAACillFJKKaiUUkoppZRSSkGllFJKKaWUUgoqpZRSSimllDIQAAAAAAAAAACAAAAA AAAAAAAABAAAAAAAAAAAIFgEAAAAAAAAAAEAAK0ATgIAAAgAAAAAAAAAAEAAAAAAABCaYQkGAAAA AAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAABFCCCGEEEIMAAgAAAAA AAAAAEAAAAAAmDcAAAACAAAAAAAAQABwLAIAAAAAAACAAAAAAAAAAAAA/gRBjOKaAgAAACAAAAAA AAAAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAEEppZRSUCmlHAAAAAAAgAAAAAAA AAAAAHQJAAAAAAAAACAAAACQTgMAAAABAAAAABgDAAAIAAAAAMACOGjAAQAAAAAAAAAAAgAAAAAA AAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAhMUA AABAAAAAAAAAAAAAskcAAAAAAAAAEKQEAAAAAAAAgAAAsAAAAAAAAAQAAAAAAAAAACAAAAAAAAAA AAABAAAAAAAAAAAI/gAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAQIMPAAAAAAAA AAAEAIBAAFAOAAAgAAAAAEBKAAAAAQAAAAAQIwcQiAAAAAAAAAAAQAAAAAAAIJJTAwIAAAAAAAAA ABAAAAAAAAAAQoOGpQAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAgGMAAAAACABIqRAhVkgH QKAEAAAAAAAAAIKUAAAAAAAAABC45A4RAwAAAIAAAAAAAAAAAAAEaAVwEgAAAAAgAAAAAAAAAAAA AQAgiFFcUwAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAWzAA/gAAAAA0BtCChD0WEjGPAQAA BAAAAABICQAAIAAAAAAAQCAwAAEAAAAAAAAAAAgAAAAAAAIYi0AAAAAAAAAAYAwCAAAAAAAAWADw oDEAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAACcAAAAAAAEQALQDAAAAMIgAAAAAAAAAAECQ EgAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAIB0GgAAAAAABAAAkBIAAAAAIAAAAAAWAAAAAAEA AAAAAAAAAAgAAAAAAAAAAEAAAAAAAADAeAYCAAAAAAAAgEoQAAAAAAAAAACAAASllFLnKKUUdAAA AABQSimloDIA/gAAAAAAAAABAAAAAAAA7BEIAAAAAAAAAClBAAAAAAAAAGIEHkAQAAAAAAAAEAAA AAAAAAAAgAAAAAAAAAAAAAQAAHIAAAAAACAAAIDTAAAAAAABAAAAAAAAAAAIUgIAAAAAAABAAAAA AAAAAAAAAgAAACClQoRYMAQCgHIAAAAAgAAAAFICAAAAAAQAAJfcIWIAACAAAAAAAAAAAAABAAAA AAAAAAAIAAAAAAAAUAlAAAAAAAAAAFsMgtEAAAAAAAAAEAAAAAAgJQAAgAAAAAAAAAAAAAQAAAAA AAAA0CADaBH2WDoAKAEBAAAAAAAAICUIAAAAAAAAAAjAwAAA/gAAAAAAAAIAAAAAAAAAABAAAAAA AAAAAIAAgLEYAAAAAAAE7YG0AGgMAAAgAAAAAAAAAAAAQUoAAAAAAAAACIBITg0AAAAAQAAAAEAA 0A4AAIKQiHkMAAAAABAAAEBKAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAA SAUACAAAAACQihGqwZYAAAAAAAAAAAIAAAAApAQAABAAAAAAAK0AToIAAAAAAAAAAAAEQCUAAACA IQAgAAAAEJRSSp0DlVLKAQAAAEopqJRSBgAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAUBoAAAAA AIAABAYA/goAAAAABAAAAAAAAAAAIEgJAAAAAAAAAAEIYCwCAAAAAAgAAAAAAE4DAEAAAAAAAAAA AAACAABICQAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAMG8AAAEAAAAAAAAA AAgAAAAAAAAAAEAAAAAAgBAAAAACAAAAAACQTgMQAAAAAAAAAACAgC0GRgMAAAAABAAAAAAAAICU IAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACIBwAAAAAAAAQAAAAAAAAAACA AAAAAAAAAAAABAAAAAAAAAAAIAAAsEcAAAAAAAEAALQH/tICoDEIAAAAAAAAAABAAAAAKQEAAAAA AgAAACI5NQAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAsBACAAAAAAAAAAAAABAAAAAAAAAAAI AAAAAAAAAABAAAAAAIBAAFAOAgAAAAAAAEAq0AjVWgIAAAAAgAAAAAAAAACQEgQAAAAAAAAAtGAA JwEAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABAYB4AAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAA AAAAAAAAAATpAKAEAAAAACAAAAAQGAAoAAABAAAAAAAAAAAIAAAgJQAAAABAAAAAIICxCAAAAgAA AAAA/gAAABAAAAAAAAAAAIAAAAAAACoBAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAA AAAQEjGPQQAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAQoAAAAAAAAAAAABMpwEAAAAAAAAgAAAA AAAAAAAAAQAAAAAAAAAAyBYCAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAIYA AAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAADAHgEAQAAAAAAAAAAAAAIAAAAA AAAAABAAAAAASQEAAIAAAAAAAAAAAAAEAAAAAAAA/gAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAA AAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAKBACgHAAAAAAAABAAAAAAAAAAAIAAAAAAA AAAAAE8DAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAA AAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAKQDgBIAAAgAAAAAAAAAAEAAAAAAAAAAAAACAAAA7AEA AAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAA /gBAAAAAAAAAAAAAAgAAAAAAAEBIkJjHAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAA AAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAA AAQAAAAAAAAAACAAAAAAGAIAAAABAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAAAAgAAAAAAAAAA EAAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAABA AAAAAAAAAAAAAgAAAAAAAAAAEAAAAAAAAAAApoAAAAAAAAAAAAAEAAAAAAAAAAAgAAAAAAAAAAAA AQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAAAAAAAAAAAIAAAAAAAAAAAAAE AAAAAAAAAAAgAAAAAAAAAAAAAQAAAAAAAAAACAAAAAAAAAAAQAAAAAAAAAAAAAIAAAAAAAAAABAA AAAAAAAAAIAAAAAAAAAAAAAEAAAAQAQAOw==