Since childhood, the cordel poet Severino has kept tales heard at countryside markets: singing duels, enchanted creatures, and brave deeds passed down through generations. Now he is preparing his greatest booklet, an adventure where, in each chapter, the reader chooses how the story continues. To avoid losing any ending, Severino spread the pages of his outline on the floor and connected each choice with a piece of string.

Seen from above, the outline resembles a tree structure: there are $$$N$$$ chapters numbered from $$$1$$$ to $$$N$$$, with chapter $$$1$$$ being the beginning of every story. The outline follows these rules:

• Each connection links a chapter to one of its immediate continuations;
• For each connection, Severino must choose an uppercase letter between A and Z;
• No chapter may have two continuations with the same letter;
• Each chapter with no continuations ends a complete story, described by the sequence of letters on the path from chapter $$$1$$$ to it.

Severino also noticed that changing letters in the outline does not always change the booklet: two assignments of letters are considered equivalent when they produce exactly the same set of complete stories.

Severino wants to know how many distinct sets of complete stories can be obtained from this outline among all possible assignments of letters. Since the answer can be very large, he asks you to report it modulo $$$998244353$$$.