Valet Parking

Your friend works as a valet where $N$ cars show up in a shift. The $i$-th car will arrive $T_i$ seconds after the current moment, and the car can wait for at most $Y_i$ seconds. That is, your friend can only start parking the car from time $T_i$ to $T_i+Y_i$ (inclusive). Additionally, it takes $X_i$ time to park the $i$-th car, which means he cannot park any other cars for $X_i$ seconds starti