The Texago Corporation has four oil fields, four refineries, and four distribution centers in the locations identified in the following tables. Using units of thousands of barrels of crude oil (and its equivalent in refined products), the following tables show the maximum number of units that can be shipped per day from each oil field to each refinery and from each refinery to each distribution center.

The Texago management now wants to determine a plan for how many units to ship from each oil field to each refinery and from each refinery to each distribution center that will maximize the total number of units reaching the distribution centers.

What is the maximum flow (in thousands of barrels of oil) that can flow through the network?

\begin{tabular}{|c|c|c|c|c|c|} \hline \multirow[b]{2}{*}{ Refinery } & \multicolumn{5}{|c|}{ Distribution Center } \\ \hline & Pittsburgh & Atlanta & Ka & ity & San Francisco \\ \hline New Orleans & 5 & 9 & & & 4 \\ \hline Charleston & 8 & 7 & & & 5 \\ \hline Seattle & 4 & 6 & & & 8 \\ \hline \multirow[t]{2}{*}{ St. Louis } & 12 & 11 & & & 7 \\ \hline & \multicolumn{5}{|c|}{ Refinery } \\ \hline Oil Field & New Orleans & Ch & ton & Seattle & St. Louis \\ \hline Texas & 11 & & & 2 & 8 \\ \hline California & 5 & & & 8 & 7 \\ \hline Alaska & 7 & & & 12 & 6 \\ \hline Middle & 8 & & & 4 & 15 \\ \hline East & & & & & \\ \hline \end{tabular}