Marinada '24

[lang=hr] Josip slaže ciklus pjesama (playlistu u kojoj nakon zadnje pjesme ponovno svira prva) duljine $20$. U ciklus želi staviti neke od $25$ pjesama tako da se niti jedna pjesma ne ponovi, no, posebno, ako je u ciklusu pjesma $\emph{Previše Suza U Mom Pivu}$ onda nakon nje obavezno mora biti pjesma $\emph{Ne Zovi Mama Doktora}$, ako je u ciklusu pjesma $\emph{Kiše Jesenje}$ nakon nje mora biti pjesma $\emph{Marina}$ i ako je u ciklusu pjesma $\emph{Marina}$ onda nakon nje mora biti pjesma $\emph{Mi Plešemo}$. Koliko takvih ciklusa postoji? Rješenje upišite u znanstvenom zapisu s tri decimale, sve bez razmaka (npr. 2.800*10^(39)). [/lang] [lang=en] Josip is creating a song cycle (a playlist where after the last song, the first one plays again) of length $20$. He wants to include some of the $25$ songs in the cycle (songs cannot reapeat), but with special conditions: if the song $\emph{Previše Suza U Mom Pivu}$ is in the cycle, it must be immediately followed by the song $\emph{Ne Zovi Mama Doktora}$; if the song $\emph{Kiše Jesenje}$ is in the cycle, it must be immediately followed by $\emph{Marina}$; and if $\emph{Marina}$ is in the cycle, it must be immediately followed by $\emph{Mi Plešemo}$. How many such cycles exist? Write your answer in scientific notation with three decimal places, without spaces (e.g., 2.800*10^(39)). [/lang]