Eulerian and Hamiltonian Graphs · Hard problem

A plow town has intersections $A,B,C,D,E,F$ with roads $AE, BE, BC, AF, EF, DE, DF, CE, AC$ (nine roads, no others). The plow must start at $A$, finish at $F$, and clear every road, retracing a road (building a short duplicate stretch) only where necessary. What is the minimum number of roads that must be duplicated?