Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
> I trust that you know the proper order of these powerful French words > starting from p and m better than me. ;-) I sent them an email asking if anything had been done about this bug, and saying that we would remove the code otherwise. Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
On Friday, 8 May 2015 14:06:58 UTC+1, Nathann Cohen wrote: > > > maybe we should just keep posting strong-worded statements about quality > of > > that code, > > perhaps in French ;-) > > I prefer your technique. You are waiting for me to do something about it, > right? > I trust that you know the proper order of these powerful French words starting from p and m better than me. ;-) > > Nathann > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
> maybe we should just keep posting strong-worded statements about quality of > that code, > perhaps in French ;-) I prefer your technique. You are waiting for me to do something about it, right? Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
On Friday, 8 May 2015 10:13:26 UTC+1, Nathann Cohen wrote: > > > Was it about the same version of their code? > > I cannot swear that they have not changed a single character of their > code in the meantime. What I can tell for sure is that the same error > still exists at the same line of their file, on the copy I downloaded > this morning. > > > Maybe we should tell the code authors that we will have to remove it > from > > Sage if they will not fix the bug? > > (and not have certainly wrong code in Sage?) > > Maybe ... Just thinking that they might ignore that email too... >_< > maybe we should just keep posting strong-worded statements about quality of that code, perhaps in French ;-) > > Nathann > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
> Was it about the same version of their code? I cannot swear that they have not changed a single character of their code in the meantime. What I can tell for sure is that the same error still exists at the same line of their file, on the copy I downloaded this morning. > Maybe we should tell the code authors that we will have to remove it from > Sage if they will not fix the bug? > (and not have certainly wrong code in Sage?) Maybe ... Just thinking that they might ignore that email too... >_< Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
On Friday, 8 May 2015 09:27:57 UTC+1, Nathann Cohen wrote:
>
> Small update on the 'modular decomposition story'.
>
> Today I ran valgrind on the code, and ended up finding where the error
> comes from. Around line 972 of dm.c, one can find:
>
> for(v = n-1; v>=0; v--)
> if(ds[v-1] != -1){
> L2[v]=v;
> while( pile[sommet] < ds[v-1])
> L2[pile[sommet--]]=v;
> }
>
> Now, because v can be equal to 0 in the loop, ds[v-1] is actually
> ds[-1] and leads, unsurprisingly, to a wrong area of the memory.
> Valgrind reports it like that:
>
> ==23980== 1 errors in context 3 of 4:
> ==23980== Invalid read of size 4
> ==23980==at 0x40269D: algo2 (dm.c:972)
>
> Thus it is rather obvious where the error comes from (there are some
> other occurrences of the same problem). I was about to write an email
> to the authors, when I noticed that. I had already sent an email
> with the very same information, i.e. line number+explanation+short
> tutorial on valgrind, and that was... one year ago. On the 6th of
> April 2014, to be specific.
>
Was it about the same version of their code?
Maybe we should tell the code authors that we will have to remove it from
Sage if they will not fix the bug?
(and not have certainly wrong code in Sage?)
>
> So that is not a problem of having to debug under mac OS X.
>
> Nathann
>
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Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Small update on the 'modular decomposition story'.
Today I ran valgrind on the code, and ended up finding where the error
comes from. Around line 972 of dm.c, one can find:
for(v = n-1; v>=0; v--)
if(ds[v-1] != -1){
L2[v]=v;
while( pile[sommet] < ds[v-1])
L2[pile[sommet--]]=v;
}
Now, because v can be equal to 0 in the loop, ds[v-1] is actually
ds[-1] and leads, unsurprisingly, to a wrong area of the memory.
Valgrind reports it like that:
==23980== 1 errors in context 3 of 4:
==23980== Invalid read of size 4
==23980==at 0x40269D: algo2 (dm.c:972)
Thus it is rather obvious where the error comes from (there are some
other occurrences of the same problem). I was about to write an email
to the authors, when I noticed that. I had already sent an email
with the very same information, i.e. line number+explanation+short
tutorial on valgrind, and that was... one year ago. On the 6th of
April 2014, to be specific.
So that is not a problem of having to debug under mac OS X.
Nathann
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Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hello ! > Thank you very much. With your help I was able to compile the library from > the "new" sources and it is working properly now, although just for me of > course. "Good" :-P > I understand your disappointment because of not being able to solve > the issue for everybody. > > I am willing to write to the author of the C code but I do not know what > exactly to ask him to do. The main problem is that the code works right in > some architectures (at least in ours and in the one of the author I guess). Well... Probably that it would be cool if they could try to test and debug it under Mac OS X (seems like it aways fails on this architecture), for there are known bugs and that their code returns wrong results on this platform. I don't exactly know how to make them understand that this is important O_o > So what is needed the most is active involvement from some other Sage user > interested in having the modular_decomposition package to work in a > different architecture so as detect what should be modified in the C code to > make it work in that architecture too. Is there someone out there? Someone with a mac. Someone who preferably knows french, as the all comments are in french. > I really appreciate your effort to make modular decomposition available in > Sage because for some of us this is very useful. I think that keeping > modular_decomposition as an optional package should be useful for testing > purposes in different architectures until the portability problem with the > source code is identified and solved. I have to day that I am a bit pessimistic. The code has been in Sage's source tree for years already :-/ Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hi Nathann, Thank you very much. With your help I was able to compile the library from the "new" sources and it is working properly now, although just for me of course. I understand your disappointment because of not being able to solve the issue for everybody. I am willing to write to the author of the C code but I do not know what exactly to ask him to do. The main problem is that the code works right in some architectures (at least in ours and in the one of the author I guess). So what is needed the most is active involvement from some other Sage user interested in having the modular_decomposition package to work in a different architecture so as detect what should be modified in the C code to make it work in that architecture too. Is there someone out there? I really appreciate your effort to make modular decomposition available in Sage because for some of us this is very useful. I think that keeping modular_decomposition as an optional package should be useful for testing purposes in different architectures until the portability problem with the source code is identified and solved. Thanks, Paulo On Saturday, May 2, 2015 at 12:33:11 PM UTC-3, Nathann Cohen wrote: > > Hello ! > > > I would like to know if there is any workaround for solving this issue > for > > version 6.6. Unfortunately, there is no dm.c and no random.c in the sage > 6.6 > > directory structure so as to replace them and so I do not know how to > > proceed. > > Sigh... Modular decomposition. A story of many disappointments. > > No, right now you will not find those two files in Sage's source code. > They are, however, contained in the optional package that is > downloaded when you run "sage -i modular_decomposition", and all that > is done on them is compile them into a shared library named > libmodulardecomposition (if I remember correctly. Not of my own > computer at the moment) located in SAGE_ROOT/local/lib/. If you > compile this shared library from the new sources, there should not be > any problem. If you do not know how, open the archive and look at > "spkg-install", it contains the lines that do that. > > I feel a bit guilty telling you how to make it work on your computer; > for we have a REAL problem with this package. What we need is to get > the original authors to solve it. > > 1) The old version of the sources (those that we ship) returns wrong > results. For instance on yours, as you were the one who reported it > first. > > 2) The new version of the sources apparently returns correct results > on your architecture (and on mine), but not on all of them. Look > at this ticket I opened when you first reported it: > http://trac.sagemath.org/ticket/13744 > > As you can see, the "new" version still triggers segfaults or wrong > results on some machines that we use to test Sage. Thus, my attempts > at upgrading Sage's version of the code were (rather legitimately) > refused. > > I am stuck with those files, and I do not like this situation (at > all). We ship something which returns wrong results, the problem is > fixed by updating to a new version which returns wrong results too or > even segfaults, and of course I get absolutely no answer from the > authors, whom I reminded regularly of the problem. > > To be honest, I feel like removing this from Sage. That was part of > the reason behind that more recent change, which made it an optional > package. > > Really, the best you could do to help us is send an email to the > authors. Tell them about your problem, and how cool it would be if it > worked, as this situation is bad advertisement for everybody. > Computing modular decompositions is cool and everything, but we can't > just keep buggy code in Sage, even if we raise a warning whenever it > is used :-/ > > Nathann > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hello ! > I would like to know if there is any workaround for solving this issue for > version 6.6. Unfortunately, there is no dm.c and no random.c in the sage 6.6 > directory structure so as to replace them and so I do not know how to > proceed. Sigh... Modular decomposition. A story of many disappointments. No, right now you will not find those two files in Sage's source code. They are, however, contained in the optional package that is downloaded when you run "sage -i modular_decomposition", and all that is done on them is compile them into a shared library named libmodulardecomposition (if I remember correctly. Not of my own computer at the moment) located in SAGE_ROOT/local/lib/. If you compile this shared library from the new sources, there should not be any problem. If you do not know how, open the archive and look at "spkg-install", it contains the lines that do that. I feel a bit guilty telling you how to make it work on your computer; for we have a REAL problem with this package. What we need is to get the original authors to solve it. 1) The old version of the sources (those that we ship) returns wrong results. For instance on yours, as you were the one who reported it first. 2) The new version of the sources apparently returns correct results on your architecture (and on mine), but not on all of them. Look at this ticket I opened when you first reported it: http://trac.sagemath.org/ticket/13744 As you can see, the "new" version still triggers segfaults or wrong results on some machines that we use to test Sage. Thus, my attempts at upgrading Sage's version of the code were (rather legitimately) refused. I am stuck with those files, and I do not like this situation (at all). We ship something which returns wrong results, the problem is fixed by updating to a new version which returns wrong results too or even segfaults, and of course I get absolutely no answer from the authors, whom I reminded regularly of the problem. To be honest, I feel like removing this from Sage. That was part of the reason behind that more recent change, which made it an optional package. Really, the best you could do to help us is send an email to the authors. Tell them about your problem, and how cool it would be if it worked, as this situation is bad advertisement for everybody. Computing modular decompositions is cool and everything, but we can't just keep buggy code in Sage, even if we raise a warning whenever it is used :-/ Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Dear Nathann, I have just installed sage 6.6 and found out that the bug is still there and that I am not able to apply the same workaround as before. I used to replace dm.c and random.c, apply touch to modular_decomposition.pyx and do sage -b. That used to be enough. But I do not know how to reproduce this workaround in version 6.6. I did the following. I installed sage 6.6 by uncompressing sage-6.6-x86_64-Linux-Ubuntu_14.04_x86_64.tar.gz. Since sage complained that modular_decomposition package was not installed, I proceeded to install the package using "sage -i modular_decomposition" plus "sage -b". Now the package is installed, but modular_decomposition behaves as it did when I frst started this post (except that it nows displays a warning claiming that it is known to return wrong results). I would like to know if there is any workaround for solving this issue for version 6.6. Unfortunately, there is no dm.c and no random.c in the sage 6.6 directory structure so as to replace them and so I do not know how to proceed. Thank you for your help. Best, Paulo On Saturday, November 24, 2012 at 12:00:21 AM UTC-3, Nathann Cohen wrote: > > The ticket is now waiting to be reviewed :-) > > http://trac.sagemath.org/sage_trac/ticket/13744 > > Nathann > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
The ticket is now waiting to be reviewed :-) http://trac.sagemath.org/sage_trac/ticket/13744 Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hell !! > Indeed it worked! Good ! > Now I can report that the bug I have reported is solved. Well.. It is solved on your (unique) version of Sage :-P I haven't written the patch yet. I wait for an answer from the code's author, and then it will be ready to be reviewed :-) > Thank you very much Nathann! Well, thank you for reporting the bug ! ;-) Have fn ! Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hello Nathann,
Oh. Well, perhaps you need to do something like "touch
> modular_decomposition.pyx" when you are in the
> sage/graphs/modular_decomposition folder. Then run "sage -b".
> modular_decomposition.pyx is the actual Sage code, that depends on the .c
> file you modified. It should be enough. Tell me how it goes !! I will keep
> this thread updated about the fix.
>
Indeed it worked!
I've just:
1) Replaced the the files: dm.c, dm_english.c and random.c from Fabien's
tar to devel/sage-main/sage/graphs/modular_decomposition/src taking care of
commenting the line "#include "dm_english.h" in dm.c.
2) "touch modular_decomposition.pyx"
3) "sage -b" (for this I had to install the g++ package)
Now I can report that the bug I have reported is solved. Look:
sage: P = Graph('Dl_')
sage: P.is_prime()
False
sage: P.complement().is_prime()
False
sage: P.modular_decomposition()
('Prime', [2, 0, 4, ('Parallel', [1, 3])])
sage: P.complement().modular_decomposition()
('Prime', [('Serie', [3, 1]), 4, 0, 2])
sage: for g in graphs(7):
: if g.is_prime() and not g.complement().is_prime():
: g.graph6_string()
:
sage:
Thank you very much Nathann!
Paulo
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Re: [sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hello !! > So, I downloaded the most current version of the source code from > http://www.liafa.jussieu.fr/~fm/algos/dm.tar, compiled it and run the exact > same code codifying the graph P. This time I got the right answer: H O_O So either Fabien modified it since I wrote to him about the bug you reported, or he updated it without me knowing since the last time... Well, looks like we have an easy way out then ! I will just have to create a patch that replaces the current file, and we'll be done ;-) > Introducing some changes into the file dm.c by hand seem to be not enough > to make sage recompile it and change the behaviour of the command > "P.modular_decomposition()" afterwards. Could you please tell how could I > sage know that it must recompile dm.c after I modify it? Oh. Well, perhaps you need to do something like "touch modular_decomposition.pyx" when you are in the sage/graphs/modular_decomposition folder. Then run "sage -b". modular_decomposition.pyx is the actual Sage code, that depends on the .c file you modified. It should be enough. Tell me how it goes !! I will keep this thread updated about the fix. Nathann -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hello Nathann,
You're absolutely right! The problem is due to
sage/graph/modular_decomposition/src/dm.c. I've managed to compile it in C,
coded the graph P and got:
Premier
+--3
+--1
+--5
+--2
+--4
So, I downloaded the most current version of the source code from
http://www.liafa.jussieu.fr/~fm/algos/dm.tar, compiled it and run the exact
same code codifying the graph P. This time I got the right answer:
Premier
+--2
+--0
+--4
+-Parallele
| +--1
| +--3
So, the bug seem to be fixed in the most current version from Fabien's
webpage.
Introducing some changes into the file dm.c by hand seem to be not enough
to make sage recompile it and change the behaviour of the command
"P.modular_decomposition()" afterwards. Could you please tell how could I
sage know that it must recompile dm.c after I modify it?
Best,
Paulo
On Thursday, November 22, 2012 12:04:56 PM UTC-3, Nathann Cohen wrote:
>
> Hello Paulo !
>
> You did, and thank you for that !
>
> The trouble is that the bug does not come from Sage, but rather from the
> piece of code we call to solve the problem. In
> sage/graph/modular_decomposition/src/ there is a dm.c file that contains
> the "smart" code, and contains a line at the top of the file :
> #define DEBUG 0
>
> I set it to 1, so that the C code can tell us by itself what is actually
> happening before Sage does anything, and I get as output on your instance
> (translated from french) :
> Final Tree:
> Prime
> +--3
> +--1
> +--5
> +--2
> +--4
>
> Well.. It just means that I have to forward the bug you found to the
> software's author :-)
>
> I just create a trac ticket about that :
> http://trac.sagemath.org/sage_trac/ticket/13744
>
> Nathann
>
> On Wednesday, November 21, 2012 4:07:46 PM UTC+1, Paulo Seijas wrote:
>>
>> Hi,
>>
>> I think I have found a serious bug on Graph.modular_decomposition.
>> Clearly, a graph is prime if and only if its complement is so. Nevertheless:
>>
>> sage: P = Graph('Dl_')
>> sage: P.is_prime()
>> True
>> sage: P.complement().is_prime()
>> False
>>
>> This behaviour seems to derive from Graph.modular_decomposition. Look:
>>
>> sage: P.modular_decomposition()
>> ('Prime', [2, 0, 4, 1, 3])
>> sage: P.complement().modular_decomposition()
>> ('Prime', [('Serie', [3, 1]), 4, 0, 2])
>>
>> This is not the only example where you can observe this behavior. To
>> generate easily many examples try, for instance:
>>
>> sage: for g in graphs(7):
>> : if g.is_prime() and not g.complement().is_prime():
>> : g.graph6_string()
>> :
>> 'Fl_K?'
>> 'FlGK?'
>> 'FlSK?'
>> 'FnsK?'
>> 'Fl[K?'
>> 'FheL?'
>> 'FlUL?'
>> 'F|UL?'
>> 'Fl]L?'
>> 'FlsKG'
>> 'FlUKG'
>> 'FluKG'
>> 'FnV[G'
>> 'FlT[G'
>> 'F|tkG'
>> 'Fl]KG'
>> 'Fl[KW'
>> 'Fn|KG'
>> 'Fn|kG'
>> 'F|LLG'
>> 'FnnLG'
>> 'Flg[?'
>> 'F|g[?'
>> 'Fli[?'
>> 'Flg{?'
>> 'Fn{[?'
>> 'Fn}[?'
>> 'FzN{?'
>> 'F~H[?'
>>
>> Best regards,
>> Paulo
>>
>>
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[sage-support] Re: Serious bug in Graph.modular_decomposition (which propagates to Graph.is_prime)
Hello Paulo !
You did, and thank you for that !
The trouble is that the bug does not come from Sage, but rather from the
piece of code we call to solve the problem. In
sage/graph/modular_decomposition/src/ there is a dm.c file that contains
the "smart" code, and contains a line at the top of the file :
#define DEBUG 0
I set it to 1, so that the C code can tell us by itself what is actually
happening before Sage does anything, and I get as output on your instance
(translated from french) :
Final Tree:
Prime
+--3
+--1
+--5
+--2
+--4
Well.. It just means that I have to forward the bug you found to the
software's author :-)
I just create a trac ticket about that :
http://trac.sagemath.org/sage_trac/ticket/13744
Nathann
On Wednesday, November 21, 2012 4:07:46 PM UTC+1, Paulo Seijas wrote:
>
> Hi,
>
> I think I have found a serious bug on Graph.modular_decomposition.
> Clearly, a graph is prime if and only if its complement is so. Nevertheless:
>
> sage: P = Graph('Dl_')
> sage: P.is_prime()
> True
> sage: P.complement().is_prime()
> False
>
> This behaviour seems to derive from Graph.modular_decomposition. Look:
>
> sage: P.modular_decomposition()
> ('Prime', [2, 0, 4, 1, 3])
> sage: P.complement().modular_decomposition()
> ('Prime', [('Serie', [3, 1]), 4, 0, 2])
>
> This is not the only example where you can observe this behavior. To
> generate easily many examples try, for instance:
>
> sage: for g in graphs(7):
> : if g.is_prime() and not g.complement().is_prime():
> : g.graph6_string()
> :
> 'Fl_K?'
> 'FlGK?'
> 'FlSK?'
> 'FnsK?'
> 'Fl[K?'
> 'FheL?'
> 'FlUL?'
> 'F|UL?'
> 'Fl]L?'
> 'FlsKG'
> 'FlUKG'
> 'FluKG'
> 'FnV[G'
> 'FlT[G'
> 'F|tkG'
> 'Fl]KG'
> 'Fl[KW'
> 'Fn|KG'
> 'Fn|kG'
> 'F|LLG'
> 'FnnLG'
> 'Flg[?'
> 'F|g[?'
> 'Fli[?'
> 'Flg{?'
> 'Fn{[?'
> 'Fn}[?'
> 'FzN{?'
> 'F~H[?'
>
> Best regards,
> Paulo
>
>
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