Problem Description

Juanyun found a toy at home today. This toy is made up of several circular regions, arranged as shown in the figure below:

In it, the 1st, 3rd, and 5th columns each have $341{,}799$ circular regions, while the 2nd and 4th columns each have $2$ circular regions.

Now, Dylan wants to fill each circular region with a lowercase letter, such that for any two tangent circular regions, the letters in them cannot both be vowels.

Here, vowels refer to the five letters $\texttt{a},\texttt{e},\texttt{i},\texttt{o},\texttt{u}$.

Now, Juanyun's good friend Xiao 🧿 wants to know the number of ways to fill in the letters. Please help him compute the result, and output it modulo $998{,}244{,}353$.

Output Format

This is an output-only fill-in-the-blank problem. You only need to compute the result and submit it. The answer for this problem is an integer. When submitting, you only need to write a program that outputs this integer. Any extra output will cause you to receive no score.

Hint

Translated by ChatGPT 5