Chef and Recipes

Chef is making $N$ atomic soups numbered $1$ through $N$. Each soup is either a *base* atomic soup or a composition of other atomic soups. For each valid $i$, if soup $i$ is not a base soup, one unit of this soup is made by mixing together one unit of soup $c_{i, 1}$, one unit of soup $c_{i, 2}$, and so on to one unit of soup $c_{i, P_i}$. Note that these $P_i$ soup units are not necessarily from