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   \begin{align}
 
   \begin{align}
 
F(P,A) =    \begin{cases}
 
F(P,A) =    \begin{cases}
3x + 5y +    , A<P= 1 \\
+
\binom{P+A-1}{A-1}     &, A < P \\
7x - 2y + 4z , A>=P
+
\sum_{i=1}^{P-1} \binom{A}{i}\binom{P-1}{i-1}  + \binom{A}{P} &, A \ge P
 
\end{cases}
 
\end{cases}
 
   \end{align}
 
   \end{align}
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