Q1351 A city consists of a rectangular grid of roads, with $m$ roads running east-west and $n$ running north-south. Every east-west road intersects every north-south road. A construction vehicle travels around the city, visiting each intersection once (and only once) and finally returning to its starting point. As it travels it builds a fence down the middle of each road it uses: thus it constructs, in effect, a single long fence which eventually loops back on itself. How many city blocks are now inside the fence?