Chef got Recipes

Chef has $N$ dishes, numbered $1$ through $N$. For each valid $i$, dish $i$ is described by a string $D_i$ containing only lowercase vowels, i.e. characters 'a', 'e', 'i', 'o', 'u'. A *meal* consists of exactly two dishes. Preparing a meal from dishes $i$ and $j$ ($i \neq j$) means concatenating the strings $D_i$ and $D_j$ in an arbitrary order into a string $M$ describing the meal. Chef *likes