Directed Graphs and Network Flows · Challenge problem

A distribution network has two depots $s_1,s_2$ and two stores $t_1,t_2$, linked through two warehouses $a,b$ with capacities $c(s_1,a)=5$, $c(s_1,b)=3$, $c(s_2,a)=2$, $c(s_2,b)=6$, $c(a,t_1)=4$, $c(a,t_2)=3$, $c(b,t_1)=3$, $c(b,t_2)=5$ (each depot can ship as much as its own arcs allow). What is the maximum total amount of goods that can reach the two stores combined?