Is it possible to pagebreak aligned equations? Unicorn Meta Zoo #1: Why another podcast? ...

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Is it possible to pagebreak aligned equations?



Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraToo much spacing of the paragraph before a long equation in Align environmentautomatically split begin{align*} content in two pagesWhat to do to have an equation going over the pageNice display of proof steps without eqnarrayHow to avoid page breaks locally in aligned equations, with allowdisplaybreaks enabledMultiline equation, label once and support page breakSplitting a matrix into several pagessplit subequations in two pagesHow to display an equation that is 3 pages longhypdvips causing content to overflow into footerHow Do I Horizontally Center An Operator Relative To Aligned Equations Above and BelowMulti-page equations — problemAligned equations in LaTeXAligned multiline equationsdmath and alignementHow to get rid of small indent after a defined “aligned equation” environmentChange left margin for long equationsCreating Bold Equations in align EnvironmentSplit equations inside align environment with amsmath and mathtoolsAligned equations with comments/explanations












123















The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.



The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the displaybreak command.



Is there an alternative way to achieve a pagebreak inside an aligned equation?



Here's a sample ofthe equations I'm using



begin{equation}
begin{aligned}
...\
...\ %I need to pagebreak here
...\
end{aligned}end{equation}









share|improve this question




















  • 1





    What about the split environment?

    – Stephan Lehmke
    Apr 12 '12 at 18:05






  • 3





    About begin{equation}begin{aligned}: Would begin{align}...notag \ label{where you want it} \ end{align} (or the split environment as mentioned by Stephan Lehmke) be a possible alternative for you?

    – Stephen
    Apr 12 '12 at 18:09











  • @Stephen I'll try it now, but according to AucTeX split can't be broken either. align+notag seems like a good idea. I wasn't using it because that would involve managing dozens of notags. But I suppose I could use it only on the problematic equations.

    – Malabarba
    Apr 12 '12 at 21:15






  • 4





    if you only want one number you can use the starred form of the environment and use tag once rather than the unstarred form and use notag on all but one line

    – David Carlisle
    Apr 12 '12 at 22:22
















123















The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.



The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the displaybreak command.



Is there an alternative way to achieve a pagebreak inside an aligned equation?



Here's a sample ofthe equations I'm using



begin{equation}
begin{aligned}
...\
...\ %I need to pagebreak here
...\
end{aligned}end{equation}









share|improve this question




















  • 1





    What about the split environment?

    – Stephan Lehmke
    Apr 12 '12 at 18:05






  • 3





    About begin{equation}begin{aligned}: Would begin{align}...notag \ label{where you want it} \ end{align} (or the split environment as mentioned by Stephan Lehmke) be a possible alternative for you?

    – Stephen
    Apr 12 '12 at 18:09











  • @Stephen I'll try it now, but according to AucTeX split can't be broken either. align+notag seems like a good idea. I wasn't using it because that would involve managing dozens of notags. But I suppose I could use it only on the problematic equations.

    – Malabarba
    Apr 12 '12 at 21:15






  • 4





    if you only want one number you can use the starred form of the environment and use tag once rather than the unstarred form and use notag on all but one line

    – David Carlisle
    Apr 12 '12 at 22:22














123












123








123


53






The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.



The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the displaybreak command.



Is there an alternative way to achieve a pagebreak inside an aligned equation?



Here's a sample ofthe equations I'm using



begin{equation}
begin{aligned}
...\
...\ %I need to pagebreak here
...\
end{aligned}end{equation}









share|improve this question
















The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.



The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the displaybreak command.



Is there an alternative way to achieve a pagebreak inside an aligned equation?



Here's a sample ofthe equations I'm using



begin{equation}
begin{aligned}
...\
...\ %I need to pagebreak here
...\
end{aligned}end{equation}






equations page-breaking






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Jul 18 '17 at 9:54









David Carlisle

501k4211471897




501k4211471897










asked Apr 12 '12 at 17:56









MalabarbaMalabarba

2,58792029




2,58792029








  • 1





    What about the split environment?

    – Stephan Lehmke
    Apr 12 '12 at 18:05






  • 3





    About begin{equation}begin{aligned}: Would begin{align}...notag \ label{where you want it} \ end{align} (or the split environment as mentioned by Stephan Lehmke) be a possible alternative for you?

    – Stephen
    Apr 12 '12 at 18:09











  • @Stephen I'll try it now, but according to AucTeX split can't be broken either. align+notag seems like a good idea. I wasn't using it because that would involve managing dozens of notags. But I suppose I could use it only on the problematic equations.

    – Malabarba
    Apr 12 '12 at 21:15






  • 4





    if you only want one number you can use the starred form of the environment and use tag once rather than the unstarred form and use notag on all but one line

    – David Carlisle
    Apr 12 '12 at 22:22














  • 1





    What about the split environment?

    – Stephan Lehmke
    Apr 12 '12 at 18:05






  • 3





    About begin{equation}begin{aligned}: Would begin{align}...notag \ label{where you want it} \ end{align} (or the split environment as mentioned by Stephan Lehmke) be a possible alternative for you?

    – Stephen
    Apr 12 '12 at 18:09











  • @Stephen I'll try it now, but according to AucTeX split can't be broken either. align+notag seems like a good idea. I wasn't using it because that would involve managing dozens of notags. But I suppose I could use it only on the problematic equations.

    – Malabarba
    Apr 12 '12 at 21:15






  • 4





    if you only want one number you can use the starred form of the environment and use tag once rather than the unstarred form and use notag on all but one line

    – David Carlisle
    Apr 12 '12 at 22:22








1




1





What about the split environment?

– Stephan Lehmke
Apr 12 '12 at 18:05





What about the split environment?

– Stephan Lehmke
Apr 12 '12 at 18:05




3




3





About begin{equation}begin{aligned}: Would begin{align}...notag \ label{where you want it} \ end{align} (or the split environment as mentioned by Stephan Lehmke) be a possible alternative for you?

– Stephen
Apr 12 '12 at 18:09





About begin{equation}begin{aligned}: Would begin{align}...notag \ label{where you want it} \ end{align} (or the split environment as mentioned by Stephan Lehmke) be a possible alternative for you?

– Stephen
Apr 12 '12 at 18:09













@Stephen I'll try it now, but according to AucTeX split can't be broken either. align+notag seems like a good idea. I wasn't using it because that would involve managing dozens of notags. But I suppose I could use it only on the problematic equations.

– Malabarba
Apr 12 '12 at 21:15





@Stephen I'll try it now, but according to AucTeX split can't be broken either. align+notag seems like a good idea. I wasn't using it because that would involve managing dozens of notags. But I suppose I could use it only on the problematic equations.

– Malabarba
Apr 12 '12 at 21:15




4




4





if you only want one number you can use the starred form of the environment and use tag once rather than the unstarred form and use notag on all but one line

– David Carlisle
Apr 12 '12 at 22:22





if you only want one number you can use the starred form of the environment and use tag once rather than the unstarred form and use notag on all but one line

– David Carlisle
Apr 12 '12 at 22:22










4 Answers
4






active

oldest

votes


















132














In relation to the comments I want to answer this question.



First of all to allow page breaks inside equations you have to set the command allowdisplaybreaks. Without setting this one no page break occurs.



Using a simple align-environment. Of course as @DavidCarlisle suggested you can use the star variant to suppress the numbering and set a specific tag by tag.



The environment split can't handle page breaks.



documentclass{article}
usepackage{amsmath}
usepackage{kantlipsum}
usepackage{showframe}
allowdisplaybreaks

begin{document}
kant[1-3]
begin{align*}
a\
b\
c\
d\
etag{stepcounter{equation}theequation}\
f\
g\
h\
i
end{align*}
end{document}





share|improve this answer


























  • The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

    – Sibbs Gambling
    Dec 28 '14 at 9:12






  • 1





    It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

    – Troy Woo
    Feb 9 '15 at 15:42






  • 10





    What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

    – Evgeni Sergeev
    Jul 29 '17 at 10:57



















18














Additionally to the above answers, as asked in comments, the command allowdisplaybreaks from amsmath can be used locally do a display break by using the begingroup and endgroup commands:



begingroup
allowdisplaybreaks
begin{align}
....
end{align}
endgroup





share|improve this answer































    12














    Just add the allowdisplaybreaks command from the amsmath package to the preamble of your document. Works only with the math environments provided by this package. So you can use align.






    share|improve this answer



















    • 6





      Isn't this all covered in the other answer?

      – Johannes_B
      Nov 5 '17 at 9:13






    • 3





      @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

      – Chill2Macht
      Sep 18 '18 at 16:41





















    0














    I am posting my version because it took me some time to figure that out and i hope it will help others also.



    allowdisplaybreaks goes before begin{document} and it is used only once. Then a very general code example for an equation is the following



    begin{align} 
    sum{...a very large expression...} &= sum{...another large expression...} nonumber \
    &= sum{...a result which is also large but needs to be aligned under first "="...} nonumber \
    {...again a large expression...} &= {...still a large expression...} \
    &= {... a final large expression...}
    end{align}


    If nonumber is not used, latex will assign numbers to every line break which for the majority of cases is useless. That worked for me






    share|improve this answer










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      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      132














      In relation to the comments I want to answer this question.



      First of all to allow page breaks inside equations you have to set the command allowdisplaybreaks. Without setting this one no page break occurs.



      Using a simple align-environment. Of course as @DavidCarlisle suggested you can use the star variant to suppress the numbering and set a specific tag by tag.



      The environment split can't handle page breaks.



      documentclass{article}
      usepackage{amsmath}
      usepackage{kantlipsum}
      usepackage{showframe}
      allowdisplaybreaks

      begin{document}
      kant[1-3]
      begin{align*}
      a\
      b\
      c\
      d\
      etag{stepcounter{equation}theequation}\
      f\
      g\
      h\
      i
      end{align*}
      end{document}





      share|improve this answer


























      • The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

        – Sibbs Gambling
        Dec 28 '14 at 9:12






      • 1





        It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

        – Troy Woo
        Feb 9 '15 at 15:42






      • 10





        What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

        – Evgeni Sergeev
        Jul 29 '17 at 10:57
















      132














      In relation to the comments I want to answer this question.



      First of all to allow page breaks inside equations you have to set the command allowdisplaybreaks. Without setting this one no page break occurs.



      Using a simple align-environment. Of course as @DavidCarlisle suggested you can use the star variant to suppress the numbering and set a specific tag by tag.



      The environment split can't handle page breaks.



      documentclass{article}
      usepackage{amsmath}
      usepackage{kantlipsum}
      usepackage{showframe}
      allowdisplaybreaks

      begin{document}
      kant[1-3]
      begin{align*}
      a\
      b\
      c\
      d\
      etag{stepcounter{equation}theequation}\
      f\
      g\
      h\
      i
      end{align*}
      end{document}





      share|improve this answer


























      • The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

        – Sibbs Gambling
        Dec 28 '14 at 9:12






      • 1





        It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

        – Troy Woo
        Feb 9 '15 at 15:42






      • 10





        What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

        – Evgeni Sergeev
        Jul 29 '17 at 10:57














      132












      132








      132







      In relation to the comments I want to answer this question.



      First of all to allow page breaks inside equations you have to set the command allowdisplaybreaks. Without setting this one no page break occurs.



      Using a simple align-environment. Of course as @DavidCarlisle suggested you can use the star variant to suppress the numbering and set a specific tag by tag.



      The environment split can't handle page breaks.



      documentclass{article}
      usepackage{amsmath}
      usepackage{kantlipsum}
      usepackage{showframe}
      allowdisplaybreaks

      begin{document}
      kant[1-3]
      begin{align*}
      a\
      b\
      c\
      d\
      etag{stepcounter{equation}theequation}\
      f\
      g\
      h\
      i
      end{align*}
      end{document}





      share|improve this answer















      In relation to the comments I want to answer this question.



      First of all to allow page breaks inside equations you have to set the command allowdisplaybreaks. Without setting this one no page break occurs.



      Using a simple align-environment. Of course as @DavidCarlisle suggested you can use the star variant to suppress the numbering and set a specific tag by tag.



      The environment split can't handle page breaks.



      documentclass{article}
      usepackage{amsmath}
      usepackage{kantlipsum}
      usepackage{showframe}
      allowdisplaybreaks

      begin{document}
      kant[1-3]
      begin{align*}
      a\
      b\
      c\
      d\
      etag{stepcounter{equation}theequation}\
      f\
      g\
      h\
      i
      end{align*}
      end{document}






      share|improve this answer














      share|improve this answer



      share|improve this answer








      edited Jul 18 '17 at 9:54


























      community wiki





      2 revs, 2 users 82%
      Marco Daniel














      • The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

        – Sibbs Gambling
        Dec 28 '14 at 9:12






      • 1





        It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

        – Troy Woo
        Feb 9 '15 at 15:42






      • 10





        What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

        – Evgeni Sergeev
        Jul 29 '17 at 10:57



















      • The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

        – Sibbs Gambling
        Dec 28 '14 at 9:12






      • 1





        It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

        – Troy Woo
        Feb 9 '15 at 15:42






      • 10





        What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

        – Evgeni Sergeev
        Jul 29 '17 at 10:57

















      The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

      – Sibbs Gambling
      Dec 28 '14 at 9:12





      The tag thing is not working for me. I found this stepcounter{equation}tag{theequation}label{myeq1} working.

      – Sibbs Gambling
      Dec 28 '14 at 9:12




      1




      1





      It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

      – Troy Woo
      Feb 9 '15 at 15:42





      It somehow solves my problem of a mildly underfull split equation...it didn't break, but fudge the spaces a little bit...why...?

      – Troy Woo
      Feb 9 '15 at 15:42




      10




      10





      What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

      – Evgeni Sergeev
      Jul 29 '17 at 10:57





      What's the correct way to set allowdisplaybreaks locally? Just directly saying it inside a group surrounding the align*? Or inside the align*?

      – Evgeni Sergeev
      Jul 29 '17 at 10:57











      18














      Additionally to the above answers, as asked in comments, the command allowdisplaybreaks from amsmath can be used locally do a display break by using the begingroup and endgroup commands:



      begingroup
      allowdisplaybreaks
      begin{align}
      ....
      end{align}
      endgroup





      share|improve this answer




























        18














        Additionally to the above answers, as asked in comments, the command allowdisplaybreaks from amsmath can be used locally do a display break by using the begingroup and endgroup commands:



        begingroup
        allowdisplaybreaks
        begin{align}
        ....
        end{align}
        endgroup





        share|improve this answer


























          18












          18








          18







          Additionally to the above answers, as asked in comments, the command allowdisplaybreaks from amsmath can be used locally do a display break by using the begingroup and endgroup commands:



          begingroup
          allowdisplaybreaks
          begin{align}
          ....
          end{align}
          endgroup





          share|improve this answer













          Additionally to the above answers, as asked in comments, the command allowdisplaybreaks from amsmath can be used locally do a display break by using the begingroup and endgroup commands:



          begingroup
          allowdisplaybreaks
          begin{align}
          ....
          end{align}
          endgroup






          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered May 12 '18 at 8:27









          Mr GMr G

          315211




          315211























              12














              Just add the allowdisplaybreaks command from the amsmath package to the preamble of your document. Works only with the math environments provided by this package. So you can use align.






              share|improve this answer



















              • 6





                Isn't this all covered in the other answer?

                – Johannes_B
                Nov 5 '17 at 9:13






              • 3





                @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

                – Chill2Macht
                Sep 18 '18 at 16:41


















              12














              Just add the allowdisplaybreaks command from the amsmath package to the preamble of your document. Works only with the math environments provided by this package. So you can use align.






              share|improve this answer



















              • 6





                Isn't this all covered in the other answer?

                – Johannes_B
                Nov 5 '17 at 9:13






              • 3





                @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

                – Chill2Macht
                Sep 18 '18 at 16:41
















              12












              12








              12







              Just add the allowdisplaybreaks command from the amsmath package to the preamble of your document. Works only with the math environments provided by this package. So you can use align.






              share|improve this answer













              Just add the allowdisplaybreaks command from the amsmath package to the preamble of your document. Works only with the math environments provided by this package. So you can use align.







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Oct 18 '17 at 16:26









              Vassilis ChasiotisVassilis Chasiotis

              336311




              336311








              • 6





                Isn't this all covered in the other answer?

                – Johannes_B
                Nov 5 '17 at 9:13






              • 3





                @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

                – Chill2Macht
                Sep 18 '18 at 16:41
















              • 6





                Isn't this all covered in the other answer?

                – Johannes_B
                Nov 5 '17 at 9:13






              • 3





                @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

                – Chill2Macht
                Sep 18 '18 at 16:41










              6




              6





              Isn't this all covered in the other answer?

              – Johannes_B
              Nov 5 '17 at 9:13





              Isn't this all covered in the other answer?

              – Johannes_B
              Nov 5 '17 at 9:13




              3




              3





              @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

              – Chill2Macht
              Sep 18 '18 at 16:41







              @Johannes_B To be fair, the other answer doesn't clarify that this only works with the environments from amsmath, so that the solution doesn't work with, for example, a custom math environment. This answer does clarify that.

              – Chill2Macht
              Sep 18 '18 at 16:41













              0














              I am posting my version because it took me some time to figure that out and i hope it will help others also.



              allowdisplaybreaks goes before begin{document} and it is used only once. Then a very general code example for an equation is the following



              begin{align} 
              sum{...a very large expression...} &= sum{...another large expression...} nonumber \
              &= sum{...a result which is also large but needs to be aligned under first "="...} nonumber \
              {...again a large expression...} &= {...still a large expression...} \
              &= {... a final large expression...}
              end{align}


              If nonumber is not used, latex will assign numbers to every line break which for the majority of cases is useless. That worked for me






              share|improve this answer










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                I am posting my version because it took me some time to figure that out and i hope it will help others also.



                allowdisplaybreaks goes before begin{document} and it is used only once. Then a very general code example for an equation is the following



                begin{align} 
                sum{...a very large expression...} &= sum{...another large expression...} nonumber \
                &= sum{...a result which is also large but needs to be aligned under first "="...} nonumber \
                {...again a large expression...} &= {...still a large expression...} \
                &= {... a final large expression...}
                end{align}


                If nonumber is not used, latex will assign numbers to every line break which for the majority of cases is useless. That worked for me






                share|improve this answer










                New contributor




                Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.























                  0












                  0








                  0







                  I am posting my version because it took me some time to figure that out and i hope it will help others also.



                  allowdisplaybreaks goes before begin{document} and it is used only once. Then a very general code example for an equation is the following



                  begin{align} 
                  sum{...a very large expression...} &= sum{...another large expression...} nonumber \
                  &= sum{...a result which is also large but needs to be aligned under first "="...} nonumber \
                  {...again a large expression...} &= {...still a large expression...} \
                  &= {... a final large expression...}
                  end{align}


                  If nonumber is not used, latex will assign numbers to every line break which for the majority of cases is useless. That worked for me






                  share|improve this answer










                  New contributor




                  Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.










                  I am posting my version because it took me some time to figure that out and i hope it will help others also.



                  allowdisplaybreaks goes before begin{document} and it is used only once. Then a very general code example for an equation is the following



                  begin{align} 
                  sum{...a very large expression...} &= sum{...another large expression...} nonumber \
                  &= sum{...a result which is also large but needs to be aligned under first "="...} nonumber \
                  {...again a large expression...} &= {...still a large expression...} \
                  &= {... a final large expression...}
                  end{align}


                  If nonumber is not used, latex will assign numbers to every line break which for the majority of cases is useless. That worked for me







                  share|improve this answer










                  New contributor




                  Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  share|improve this answer



                  share|improve this answer








                  edited 25 mins ago









                  Phelype Oleinik

                  26.1k54791




                  26.1k54791






                  New contributor




                  Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  answered 27 mins ago









                  Captain NakosCaptain Nakos

                  1




                  1




                  New contributor




                  Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.





                  New contributor





                  Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






                  Captain Nakos is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






























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