\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
\@nameuse{bbl@beforestart}
\babel@aux{english}{}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {2}{2}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{3}{3/3}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {3}{3}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{4}{4/4}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {4}{4}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{5}{5/6}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {5}{6}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{6}{7/7}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {7}{7}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{7}{8/9}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {8}{9}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{8}{10/10}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {10}{10}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{9}{11/13}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {11}{13}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{10}{14/15}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {14}{15}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{11}{16/16}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{12}{17/17}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {17}{17}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{13}{18/18}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {18}{18}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{14}{19/19}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {19}{19}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{15}{20/20}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {20}{20}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{16}{21/22}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {21}{22}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{17}{23/23}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{18}{24/24}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{19}{25/26}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {25}{26}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{20}{27/27}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {27}{27}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{21}{28/28}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {28}{28}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{22}{29/29}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {29}{29}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{23}{30/30}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {30}{30}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{24}{31/32}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {31}{32}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{25}{33/33}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {33}{33}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{26}{34/35}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {34}{35}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{27}{36/36}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {36}{36}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{28}{37/37}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {37}{37}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{29}{38/38}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {38}{38}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{30}{39/39}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {39}{39}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{31}{40/41}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {40}{41}}}
\@writefile{nav}{\headcommand {\beamer@partpages {1}{41}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{41}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{41}}}
\@writefile{nav}{\headcommand {\beamer@documentpages {41}}}
\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {31}}}
\gdef \@abspage@last{41}
