Problem Statement

There is a grid $A$ with $H$ rows and $W$ columns. The cell in the $i$-th row from the top and the $j$-th column from the left contains an integer $A_{(i, j)}$.

Let the function $f(A)$ be the answer to the following problem.

You start at cell $(1, 1)$, and repeatedly move from your current cell to the adjacent cell on the right $(i, j+1)$ or the adjacent cell below $(i+1, j)$.

However, you cannot make a move that goes outside the grid.

Furthermore, letting $x$ be the value written in the current cell and $y$ be the value written in the destination cell, $x \lt y$ must hold.

How many ways are there to move to cell $(H, W)$?

Here, $2$ ways of moving $(P_1 \dots P_N)$ and $(Q_1 \dots Q_M)$ are considered different if $N \neq M$, or if there exists at least $1$ index $i$ such that $P_i \neq Q_i$.

($P_i, Q_i$ denote a move to the right or down.)

There are $M^{HW}$ grids with $H$ rows and $W$ columns in which each cell contains an integer satisfying $1 \le A_{(i, j)} \le M$.

Output the sum of the values of $f(A)$ over all these grids, modulo $998244353$.

Constraints

• $2 \le H, W \le 2,000$
• $1 \le M \le 10^9$
• All inputs are integers

Input

$H\ W\ M$

Output

Output the answer.

Sample

2 2 3

6

2 2 2

0

1000 1000 100000

866431467