\[f_{i,j}=
\left\{
\begin{array}{lc}
f_{i-1,j}+P_{i,j}\\
f_{i,j-1}+Q_{i,j}\\
\end{array}
\right.\]
\[\Delta_{i,j}=\sum_{k=1}^j-Q_{i,j}
\]
\[f_{i,j}+\Delta_{i,j}=
\left\{
\begin{array}{lc}
f_{i-1,j}+\Delta_{i-1,j}+P_{i,j}+\sum\limits_{k=1}^j Q_{i-1,k}-Q_{i,k}\\
f_{i,j-1}+\Delta_{i-1,j-1}\\
\end{array}
\right.\]