Balls of Three Colors
time limit per test
2 seconds
memory limit per test
512 mebibytes
input
standard input
output
standard output

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 $$$998\,244\,353$$$.

Input

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

Output

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

Examples

Input
1 1 1
Output
6
Input
4 1 1
Output
0
Input
1 1 2
Output
6