The intersection of King and Alain Streets needs widening and improvement. The possibilities include
1. Widen King
2. Widen Main
3. Add a left-turn lane on King
4. Add a left-turn lane on Alain
5. Add traffic lights at the intersection
6. Add traffic lights at the intersection with advanced green for Alain
7. Add traffic lights at the intersection with advanced green for King
A left-turn lane can be installed only if the street in question is widened. A left-turn lane is necessary if the street has traffic lights with an advanced green. The city cannot afford to widen both streets. How many mutually exclusive projects are there?