Chef Rami and Inventions

In Chef Rami's kitchen, there is a long counter divided into $N$ sections (numbered $1$ through $N$). For each valid $i$, there are $a_i$ raw meals stacked on top of each other in section $i$. Chef Rami has a special cooking device. This device can take all the meals that are stacked in some section and instantly cook them. He may perform the following operations in any order any number of times