\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}{2/3}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {2}{3}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{3}{4/4}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {4}{4}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{4}{5/5}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {5}{5}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{5}{6/6}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {6}{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}{8/8}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {8}{8}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{8}{9/11}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {9}{11}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{9}{12/12}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {12}{12}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{10}{13/14}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {13}{14}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{11}{15/15}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {15}{15}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{12}{16/16}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{13}{17/17}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {17}{17}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{14}{18/21}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {18}{21}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{15}{22/23}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {22}{23}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{16}{24/24}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{17}{25/25}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {25}{25}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{18}{26/26}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {26}{26}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{19}{27/27}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {27}{27}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{20}{28/29}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {28}{29}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{21}{30/31}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {30}{31}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{22}{32/32}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {32}{32}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{23}{33/33}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {33}{33}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{24}{34/34}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {34}{34}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{25}{35/35}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {35}{35}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{26}{36/37}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {36}{37}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{27}{38/38}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {38}{38}}}
\@writefile{nav}{\headcommand {\beamer@partpages {1}{38}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{38}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{38}}}
\@writefile{nav}{\headcommand {\beamer@documentpages {38}}}
\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {27}}}
\gdef \@abspage@last{38}