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.

What is rational number modulo 998244353?

We can prove that the sought expected value is always a rational number.
Moreover, under the Constraints of this problem, when the value is represented as $\frac{P}{Q}$ by two coprime integers P and Q, we can prove that there is a unique integer R such that $R \times Q \equiv P\pmod{998244353}$ and $0 \leq R \lt 998244353.$ Find such R.

Input

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

Output

Print the answer.

Constraints

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

Sample Input 1

2 2 2

Sample Output 1

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.

Sample Input 2

10 10 1

Sample Output 2

1

Sample Input 3

314 159 2653

Sample Output 3

639716353

见题面 Input 部分

见题面 Output 部分