Show that splitting an edge in a flow network yields an equivalent network. More formally, suppose that flow network G contains edge .u; /, and we create a new flow network G0 by creating a new vertex x and replacing .u; / by new edges .u; x/ and .x; / with c. u; x/ D c. x; / D c. u; /. Show that a maximum flow in G0 has the same value as a maximum flow in G.