Balls of Three Colors

There are $r$ red, $g$ green, and $b$ blue balls. How many ways are there to arrange all these balls in a row such that any two adjacent balls have different colors? Since this number can be very large, output its remainder when divided by the prime number $998\,244\,353$.

You are given three integers separated by spaces: $r$, $g$, and $b$. Each of the integers is from $1$ to $10^5$ inclusive.

Output a single integer: the required number of ways modulo $998\,244\,353$.