You have a pawn at point $(0, 0, 0)$ on a three dimensional grid. In one move you can increase either the $x$, $y$ or $z$ coordinate by one. In how many ways can you reach point $(X, Y, Z)$?

Input

A single line contains three integers $X,\,Y$ and $Z$.

Output

Print the answer modulo $998244353$.

Constraints

• $0 \leq X, Y, Z \leq 10^5$

Example 1

Input:

0 1 4

Output:

5

Example 2

Input:

1 1 1

Output:

6

Example 3

Input:

94451 13922 46410

Output:

534902695