(Reingold, Nievergelt, and Deo [1977]) A manufacturer of integrated circuits makes chips that have 16 elements arranged in a $4 \times 4$ array. These elements are interconnected between some adjacent horizontal or vertical elements. Figure 8.22 shows some sample interconnection patterns. A photomask of the interconnection pattern is used to deposit interconnections on a chip. Two patterns are considered the same if the same photomask could be used for each. For instance, by flipping the photomask over on a diagonal, it can be used for both the interconnection patterns shown in Figure 8.22. Thus, they are considered the same. How many photomasks are required in order to lay out all possible interconnection patterns? Formulate this problem as a coloring problem by defining an appropriate $D, R$, and $G$. However, do not attempt to compute $G^*$ or to solve the problem completely with the tools developed so far.