Score : $500$ points

Problem Statement

We have a grid with $H$ rows and $W$ columns.

We choose $K$ cells in this grid uniformly at random. The score is the number of cells in the minimum rectangle (whose edges are parallel to the axes of the grid) that contains all of the chosen cells.

Find the expected score modulo $998244353$.

Constraints

• $1\leq H,W \leq 1000$
• $1\leq K \leq HW$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$H$ $W$ $K$

Output

Print the answer.

2 2 2

665496238

The score equals $4$ in the following two cases: if cells $(1,1)$ and $(2,2)$ are chosen, or cells $(1,2)$ and $(2,1)$ are chosen. The other four cases yield a score of $2$.

Thus, the expected score equals $\frac{4 \times 2 + 2 \times 4} {6} = \frac{8}{3}$. Since $665496238 \times 3 \equiv 8\pmod{998244353}$, you should print $665496238$.

10 10 1

1

314 159 2653

639716353