Graph Algorithms · Hard problem

A network has routers $s,a,b,c,d,e,t$ and weighted links $sa{:}3, sb{:}5, ac{:}2, bc{:}1, ad{:}6, cd{:}3, ce{:}4, dt{:}4, et{:}3, be{:}6$. If router $c$ fails (removed, along with every link touching it), by how much does the shortest-path distance from $s$ to $t$ increase?