[BlindMath] Learning High School Math

Fri Jul 23 04:41:58 UTC 2021

Hi Shail,

I don't know the current state of Microsoft equation editor, as the newest Word I have is 2013, where the math is not even properly read.

Thus I may be out of date with this, but back in those times, in order to write math expressions, you had to switch to the equation editor, type the formula and switch back. When you wanted to edit what you wrote, you had to activate the editor again, make the changes and return.

While this approach is probably usable when writing documents, where you usually type the equations just once and have enough time to do it, the situation in a school is very different.

In a class, your software should meet two critical criteria:

* Speed, with about 30 minutes or less to complete a test, you usually don't have much time to waste.

* Reliability, the last thing you want during a test is to get stuck.

I have worked with various versions of word from 2003 to 2013, and from my experience, it doesn't fill any of them. :)

Like, that thing gets regularly stuck even in a normal text, you don't need any special notation to get in trouble. Also, constant opening of an equation editor is definitely not compliant with the speed requirement.

Heh, I still remember our exercises from quantum physics, we had to calculate the output speed of an electron thrown out of cesium under a light shine of certain frequency.

The calculation was not even algebraically difficult, it took just few lines, the problem were complicated numbers, ranking from really small to really big (this is an overal characteristics of these exercises).

As a fearless combinator, I've happily combined the physics algebra with various mathematical tricks to get the most accurate result possible.

And I've calculated the output speed to be 5*10^26ms^-1, 1000000000000000000 times faster than the speed of light!

I guess uncle Albert would have a lot to explain if he saw my quantum physics homeworks. :D

Now seriously, when doing the calculations, you don't really have the time to switch every line of it. You have to think out the plan, write down the equations, add the numbers (which you need to dynamically lookup from the task heading, copy your calculations to a calculator to get actual results and copy what you get back.

You make a mistake from time to time, either numerical or algebraical, and you have to lookup the exact place you've messed. Some calculations can take from 10 to 20 lines, as you usually need to note all lines where you substitute a second formula to your primary, some calculations contain wild numbers like the Avocadro constant, mass of a electron or the Boltzman constant, combined with either very small or big numbers requiring the *10^x suffix.

Imagine like 5 of these numbers, combined with constants and complicated units, in a structure with fractions and combined positive and negative exponents, and you get a pretty nice knot to deal with.

It's not difficult, but it requires direct access to things, the ability to quickly select and copy whole parts of the equation and most importantly, the ability to solve an equation in place, as rewriting a copied expression is the fastest way which will save the typing and prevent losing things.

The equation editor I saw in Word 2013 couldn't do any of this. It was not just required to open any formula in it, but the stability of the editor itself also did not seem very convincing, not even talking about more advanced operations.

May be the situation has improved over the time, I don't know. Just keep in mind you need:

* To be able to edit equations directly in text, without switching to editors.

* To be able to duplicate a line and rewrite the expression quickly in place as a next step in the algebraic solving process.

* To be able to copy/cut/delete any part of an equation quickly, simply by selecting it with shift+arrows and pressing relevant shortcuts.

* To be able to quickly prepare an equation for calculator like Python, or whatever your school allows, so you can get the results efficiently.

If Word 2016 can do all of this, then I guess it might be possible to use it.

also note that these recommendations are given from my personal experience as a sound-only student, it's possible that the braille users have different needs (I can't judge that).

I've always used Notepad and AsciiMath on Windows (except for my usage of lambda, but that's another story), and the efficiency of this setup (Notepad is really the fastest editor I saw on Windows) made it possible to do the job sufficiently quickly (there were even times I finished as the first of the fully sighted class without a single mistake :) ).

I suggest that your daughter tried to write a test in time conditions the same as on a real exam with all setups you're currently considering. She can then pick up the format showing the best results, may be after few tries to get used to them first.

As for the OpenStax books, and the overal MathML situation... heh

This has always been a quite funny topic. As far as I know (others may correct me in this), jaws and NVDA with its Access8math addon are currently the only software to read MathML.

Jaws, from my experience, works quite sufficiently... If it works.

The problem is, at least on my computer, it was simply not able to read some equations, after a long period of silence, it said simply blank.

Sometimes, opening the problematic equation allowed to read it in the tree-like hierarchy, which you need anyway when you see a complicated formula for the first time to get familiar with it.

Sometimes, however, instead of the equation being opened, the math server of Jaws got completely freezed, holding CPU usage at 80% without doing anything (the only way from it was to kill the process).

It was really nice, when I was solving an exercise and this was the case of the equation with result. :D

Also tables were read incorrectly at some places, it took me a while to find out, when there were multiple equals signs, Jaws got upto the second or thirdone, and then behaved like there wasn't anything left (not presenting the next = sign, so I really believed it at the time).

The fact, that Jaws simply ignores all symbols it doesn't know is then just a peculiarity, which can also have quite interesting consequences taking in the fact that you usually assume * or , when there is nothing spoken. I also had some heureka! revelations from this, and not just on OpenStax. :)

Access8math is better at parsing MathML and NVDA has overall better dictionary, but at least for me, Access8math was a nightmare to use.

I don't want to blame the authors now, who I'm sure put a lot of effort to get it working, but the extension always sliced the formula to parts presented with little time gaps, which were quite noticeable even with the lowest possible delay set in the settings.

Also, for some reason, when browsing an equation in a tree-like mode, the extension prefixed each single node with "item xy" string, what almost made me crazy when I was studying the equations of the backpropagation algorithm of neural networks (this was the only way to do it).

So, as you can see, there are two main programs, with both major advantages and disadvantages.

I was studying Calculus from OpenStax and other topics from other books on Windows, and it was always a game. I used Jaws as my default reader, and made the best out of my deductive skills to reveal in time when it hidden something from me.

I'm not saying I was always immediately successful, but it was certainly possible.

As far as I know, there is currently no single working solution. One has to be creative, that's the only way (in almost all aspects of blindness, not just mathematics).

Best regards

Rastislav

Dňa 21. 7. 2021 o 9:45 Shail M napísal(a):

> Hi [@Rastislav](mailto:rastislav.kish at protonmail.com),
>
> Thanks for sharing your perspective. It’s really helpful.
>
> I really liked the ASCII math notations as they are really very close to the real Math content but I think, the support of Unicode Matth in Microsoft Word makes things more easier. This integration allows to write the text as well as Science/Math content (using Equation Editor) in the same document seamlessly so no more relying on notepad. The school district uses Microsoft Office but with the help of vision teacher, she can get the homework in accessible format (Unicode Math) and then complete it right there either in Onenote or Word. JAWS seems to be able to read the Math content in Word successfully so that’s one peace of mind.
>
> You mentioned about the OpenStax site earlier. Is this site fully accessible to you? I found the content good and useful but found it hard to be read correctly by screen readers. I tried a combination of browsers (Microsoft Edge Chromium, Google Chrome and Firefox) and Screen Reader (JAWS, NVDA) and found that the only combination that works is NVDA + Firefox due to better support of Math ML in Firefox. I understand that you are Linux user but wondering if you have used site successfully on Windows?
>
> The hard part is that NVDA doesn’t seems to be able to read equations correctly if they are written in Equation editor in Word. JAWS does a lot better in this area but then it fails to read Math content in browsers correctly.
>
> I am still trying to figure what works well in a seamless way, like reading the questions from OpexStax and then writing it in Word and solving it there. Any suggestions are most welcome.
>
> I didn’t knew a thing about the possible diagnosis of the sound problem and the solution you mentioned. I’ll certainly try it out as it’s a night mare when the JAWS stops speaking which causes a lot of confusion to my daughter.
>
> Thanks
>
> Shail
>
> -----Original Message-----
> From: BlindMath [<blindmath-bounces at nfbnet.org>](mailto:blindmath-bounces at nfbnet.org) On Behalf Of Rastislav Kish via BlindMath
> Sent: Tuesday, July 20, 2021 5:53 PM
> To: Eric Mandell via BlindMath [<blindmath at nfbnet.org>](mailto:blindmath at nfbnet.org)
> Cc: Rastislav Kish [<rastislav.kish at protonmail.com>](mailto:rastislav.kish at protonmail.com)
> Subject: Re: [BlindMath] Learning High School Math
>
> Hi Shail,
>
> as for the usage of LaTeX upto the university...
>
> I'd say this is mostly a thing of personal choice. Unless your daughter's university specifically requires LaTeX for some reason, she can use whatever she wants,
>
> even Microsoft Word (no kidding, I really saw a physics book written in Word).
>
> There are countless preprocessors and text formats like Markdown and its flavors out there, so she can write anything from math in AsciiMath to Chemistry formulas in SMILE notation in pretty much any way she likes.
>
> I personally always select tools according to their strenghts and weaknesses, so they perfectly fit my goal.
>
> AsciiMath is not just easily readable, but also very close to the syntax of Python and SageMath, so I can work with it easily if needed.
>
> On the other hand, LaTeX for example gives more control over the output's design, what's mostly not important for me (I can't check it myself anyway), but there are people who care about it a lot and thus, they might find LaTeX as a better choice.
>
> Plus, if your daughter really finds a place for mathematics in her heart, another thing to realise is, that this is a truly big field, mostly combined with other big fields (it's called the science of all sciences for a reason).
>
> Learning "just another of the possible notations", should be a piece of cake, without the need for an intensive practice.
>
> In fact, if she'll really enjoy the subject, I recommend learning LaTeX even if she did not have future plans for it, it can't hurt, just help.
>
> I personally don't use it much, but I still know at least the basics, so I can read documents in it and write my own if needed.
>
> As for the math by sound, heh, now I use Orca on Linux, but back in my days on Windows, I was using Jaws as well. :) Jaws is a great screenreader, however, under two conditions:
>
> * It works properly
>
> * Its user is aware of its abilities, settings, and can make it to help them, instead of the opposite
>
> As for the speed problems and hanging, this is mostly a blind shot, but, did you try a sound-card state keeping program?
>
> I mean, the modern soundcards are often configured to shut down after a period of inactivity, for example one second or less.
>
> They wake up again as the new sound data come, but with various sideeffects like losing of first sillables, messing up the volume, time delay and other ugly things.
>
> Thus, when I see a screenreader being slow and doing weird things, the first thing I check is whether a solution for this problem has been applied.
>
> I recommend Silenzio:
>
> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstefankiss.sk%2Fmodules.php%3Fname%3DDownloads%26d_op%3Dgetit%26lid%3D112&data=04%7C01%7C%7C23618403d2e042587e0a08d94be20e73%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637624256540532584%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=c8ZI5%2FHkJDru260sCwgFmt7vqE95NWVmL6c3GyWmEAQ%3D&reserved=0
>
> It's a lightweight program, that will run in the background and continuously send silence to the soundcard, keeping it awake and responsive.
>
> I have a Windows installation on one of my partitions here, using it mostly as a testing environment, when I want to add a Windows support to my programs. Without this utility, it would be absolutely unusable.
>
> Of course, if one wants to quickly and efficiently work with math by sound, perfectly working screenreader is an absolute must, that's a no-brainer.
>
> As for the command line, I can't say I'd prefer it overall, GUI is more practical in many aspects like saving one's memory, time to refresh it and in general offers easier multitasking, not even mentioning advantages of a semantic interface for accessibility.
>
> But some tasks are definitely more practical from terminal, like compiling code, using pandoc or other console based programs like Python.
>
> Installing dependencies is also among them. :)
>
> If you had any troubles installing math_scanner, feel free to ask, especially on Windows, if you'll be installing there, I can send you my Tesseract binaries if you want, there are currently no official available.
>
> For Linux installations, you can simply use the main branch of the repository, the Windows support is experimentally added in the windowsSupport branch.
>
> Also, as for Pandoc, just few tips, you might want to check out this:
>
> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2FCDSoft%2Fpp&data=04%7C01%7C%7C23618403d2e042587e0a08d94be20e73%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637624256540532584%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=D3hY9lUkaSTY1N8iGTUibC0MSU%2B3YdKpWzqvTbdyJU0%3D&reserved=0
>
> and this:
>
> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2Fvbwx%2Fpandoc-asciimath&data=04%7C01%7C%7C23618403d2e042587e0a08d94be20e73%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637624256540542541%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=Hc5%2BfW3LJ%2FPkjRvuGExa6Sw9QtwFF0a3vIf3SDKIdu0%3D&reserved=0
>
> Best regards
>
> Rastislav
>
> Dňa 16. 7. 2021 o 21:52 Shail M napísal(a):
>
>> Hi Rastislav,
>
>>
>
>> Thanks for providing suggestions and detailed information. I really appreciate your help.
>
>>
>
>> I looked into AsciiMath and as you mentioned, it seems simple to read and write compared to Latex but the underlying reason for using Latex is that it is capable of helping her all the way to graduation or post-graduation if she wishes to pursue. As per my understanding, Latex won't just help in Math but also in Physics, Chemistry, Graphs, Charts etc.
>
>>
>
>> It amazing to know that you were able to deal with all this complexity without using Braille. I am not sure what screen reader is available on Linux but JAWS on Windows is pretty bad. Memory Hog as well as very frequently stops speaking and then we have to ALT + TAB to switch to different window and then come back to previous window and it will start working magically again.
>
>>
>
>> I also prefer using command line rather than GUI and have been suggesting daughter to use the same as I find the command line more accessible as well.
>
>>
>
>> I'll certainly try using Math Scanner and hopefully, it will help in converting image to text.
>
>>
>
>> Also, thanks for providing reference to Pandoc software. I was looking for a software that could generate different formats like Word/PDF and this software seems like single stop shop for that purpose.
>
>>
>
>> Again, thanks for your feedback.
>
>>
>
>> Thanks
>
>> Shail
>
>>
>
>> -----Original Message-----
>
>> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Rastislav
>
>> Kish via BlindMath
>
>> Sent: Tuesday, July 13, 2021 6:15 PM
>
>> To: blindmath at nfbnet.org
>
>> Cc: Rastislav Kish <rastislav.kish at protonmail.com>
>
>> Subject: Re: [BlindMath] Learning High School Math
>
>>
>
>> Hello Shail,
>
>>
>
>> personally, my universal answer for high-school math is AsciiMath.
>
>>
>
>> AsciiMath is a math format like LaTeX, just much easier to both read and write.
>
>>
>
>> In fact, it's so natural that I was able to work with quite massive expressions without really paying attention to what I'm doing and still get them right.
>
>>
>
>>
>
>> The naturality of AsciiMath is also an advantage when exchanging data, teachers can check it in the plain form without any visualisation, on the other hand, they can write equations without any special software or other equipment.
>
>>
>
>>
>
>> The editor I used was simply Notepad back on Windows, now on Linux, my 'swiss-army knife' is Pluma.
>
>>
>
>> Word doesn't in my view offer any significant advantages for math and on the other hand, has quite few caveats one must deal with like the spelling corrector, letters capitalizer or the overall program slowness.
>
>>
>
>>
>
>> When a teacher had a test already prepared in Word, I usually just copied everything to Pluma and returned the results in a plain-text format.
>
>>
>
>>
>
>> That did not necessarily need to be the case though, for example on math we did not have pre-printed tests at all, the teacher simply wrote tasks on the table, dictating as she was writing so I could catch everything.
>
>>
>
>>
>
>> Also one more thing to note, I may be in minority on this, but I solve everything exclusively by sound, no braille involved.
>
>>
>
>>
>
>> As for education and training, Openstax is a very good resource with accessible high-school as well as some university level math. All topics i read were well and comprehensively explained, providing also some exercises for training.
>
>>
>
>>
>
>> As for dealing with math in images, I have developed math_scanner:
>
>>
>
>> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithu
>
>> b.com%2FRastislavKish%2Fmath_scanner&data=04%7C01%7C%7C23618403d2e
>
>> 042587e0a08d94be20e73%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637
>
>> 624256540542541%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2
>
>> luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=r39lzvv1k6vazrob
>
>> DBvk%2FgO6ElCYaWUl32%2Bt%2FLVMQzg%3D&reserved=0
>
>>
>
>> which has been showing some promising results so far. There is already an experimental Windows support for now in a separate branch and my early tests on the proprietary platform vent quite good.
>
>>
>
>>
>
>> The only problem is, that it's a bit complicated to setup, I initially thought that anyone can easily learn to work with command line and install the few dependencies if there are detailed instructions.
>
>>
>
>> But after testing it with few people, I don't think so anymore. :)
>
>>
>
>>
>
>> Plus the whole project is for now a bit of a experiment, there is no long and deep testing behind it, so there may be hidden pitfalls in terms of accuracy and reliability.
>
>>
>
>>
>
>> So it depends on your daughter's personality. If she has technical talent and is cunning enough to use an experimental tool, I think she should be able to make use of it.
>
>>
>
>>
>
>> She could join the Windows version testing in that case, mostly for the Tesseract binaries, which I have compiled and which are not yet globally available.
>
>>
>
>>
>
>> On the other hand, if math is just an obligation for her, I think she should be able to pass it without very special efforts, in fact, the effortless passing part was even my case, as math_scanner is a quite recent work.
>
>>
>
>>
>
>> As for the university-level math, this is a slightly more complicated field. Not that much, there are just more things in equations to pay attention to, their layout tends to be more sophisticated due to the usage of sums, integrals, etc. there are more special math symbols to take care of and finally, the amount of information contained in an equation or expression is typically much higher than in high-school.
>
>>
>
>> MathML is a great way to deal with it, even though it requires some fiddling if one wants to write in AsciiMath and show in MathML, pandoc is quite good in this but it's a terminal app (so again, command line skills necessary, although there might be graphical wrappers, I did not check this option as terminal is faster for me in this case).
>
>>
>
>>
>
>> Best regards
>
>>
>
>>
>
>> Rastislav
>
>>
>
>>
>
>> Dňa 13. 7. 2021 o 22:52 Shail M via BlindMath napísal(a):
>
>>> Hi All,
>
>>>
>
>>> I have a basic question regarding understanding and solving problems in High School Math.
>
>>>
>
>>> Background:
>
>>> My daughter is vision impaired and currently studying in High School and will be learning Algebra 2 in coming year. She knows Braille but is learning Nemeth. Also, learning LaTeX. Apart from this, she knows and uses Equation Editor to some extent in Microsoft Word and has Braille display "Mantis Q40". She uses JAWS and also learning NVDA currently.
>
>>>
>
>>> While we are waiting for the session by Mr. Hussain, yet it will be happening in August which will late for us as school will open by August end. We are trying to figure out few things ahead of time. There are various aspects of learning Math and looking for feedback so that we can improve on the process.
>
>>> Below are the list of various actions that need to be performed:
>
>>>
>
>>> * Reading Math problems
>
>>> * Solving Math Problems (Show your work)
>
>>> * Reading concepts and problems/solutions over the web.
>
>>>
>
>>> The biggest problem is that there is no single software capable enough of handling Math content single handedly.
>
>>>
>
>>> For each of the action above, the approach we are taking:
>
>>>
>
>>> * Reading Math Problems:
>
>>> * The teacher gives assignment to all the students. Normally, it's given in Onenote but we can request the teacher to provide the Math content in Word using the Equation Editor. This way, JAWS can read the problem to her correctly. NVDA fails to read the content correctly written using Equation Editor. Math Player also doesn't read it correctly either. So, JAWS is winner here. Another solution is to use Immersive reader feature of Word.
>
>>> * Solving Math Problems:
>
>>> * Solve the problems in Word using the Equation Editor. Another solution is to use LaTeX in editor like Texmaker or TexWorks and generate a PDF with the question and corresponding solution. Both gets complex with lengthy equations.
>
>>> * Reading concepts and problems/solutions over the web:
>
>>> * Now, from the learning perspective, it is sometimes needed to search for the Math concept online and listen to the solution/approach. Most of the sites are inaccessible as they contains the Math content as image. Few of them uses MathJax/MathML and therefore, can be read. Now, here, JAWS fails to read correctly (in fact, it was consuming full CPU and very high memory as well) the Math content. NVDA over Firefox seems to be the best bet which was able to read the problem/solution correctly.
>
>>>
>
>>> The problem is that one need to be an expert in both JAWS and NVDA which is really tough as each comes with different set of commands. Also, Math Player requires 32 bit of Microsoft Word but then it also requires Math Type software to create Math content which adds additional dependency on external software.
>
>>>
>
>>> She has a TVI and other support in the class but looking forward to help her solve Math problems independently.
>
>>>
>
>>> Any ideas on simplifying the approach. Can you please share the approach taken which worked for you?
>
>>>
>
>>> Thanks for helping solving the mystery of learning Math.
>
>>>
>
>>> Thanks
>
>>> Shail
>
>>> _______________________________________________
>
>>> BlindMath mailing list
>
>>> BlindMath at nfbnet.org
>
>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbne
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>>> t
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>>> .org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%
>
>>> 7
>
>>> C7944d2de762c455280ac08d94664efb2%7C84df9e7fe9f640afb435aaaaaaaaaaaa%
>
>>> 7
>
>>> C1%7C0%7C637618221590993124%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwM
>
>>> D
>
>>> AiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=7ar
>
>>> %
>
>>> 2BT%2Btocqnp1IYiJjgw1TprLCpC42URm%2FfcdyZLxb0%3D&reserved=0
>
>>> To unsubscribe, change your list options or get your account info for BlindMath:
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>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbne
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>>> t
>
>>> .org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Frastislav.kish%2540
>
>>> p
>
>>> rotonmail.com&data=04%7C01%7C%7C7944d2de762c455280ac08d94664efb2%
>
>>> 7
>
>>> C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637618221590993124%7CUnkn
>
>>> o
>
>>> wn%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwi
>
>>> L
>
>>> CJXVCI6Mn0%3D%7C1000&sdata=Hg%2BnwZ9s0YeqT9rX0QQmfNIyPg%2FCigKk%2
>
>>> B
>
>>> 8SC76ZqlKw%3D&reserved=0 BlindMath Gems can be found at
>
>>> <https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.
>
>>> b
>
>>> lindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7C7944d2de7
>
>>> 6
>
>>> 2c455280ac08d94664efb2%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C6
>
>>> 3
>
>>> 7618221590993124%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoi
>
>>> V
>
>>> 2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=g4TxVSmPcYVsKy
>
>>> R LndGKcvMK9BREek%2Fy8yYQXvfmXlo%3D&reserved=0>
>
>>
>
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