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 $$$998\,244\,353$$$.
1 1 1
6
4 1 1
0
1 1 2
6