There is a grid with $H$ horizontal rows and $W$ vertical columns, where each square contains a digit between $1$ and $9$. For each pair of integers (i, j) such that $1 \leq i \leq H$ and $1 \leq j \leq W$, the digit written on the square at the $i$-th row from the top and $j$-th column from the left is $c_{i, j}$.
Using this grid, Takahashi and Aoki will play together. First, Takahashi chooses a square and puts a piece on it. Then, the two will repeat the following procedures, 1. through 4., $N$ times.

1. Takahashi does one of the following two actions.
   • Move the piece to another square that shares a row with the square the piece is on.
   • Do nothing.
2. Takahashi writes on a blackboard the digit written on the square the piece is on.
3. Aoki does one of the following two actions.
   • Move the piece to another square that shares a column with the square the piece is on.
   • Do nothing.
4. Aoki writes on the blackboard the digit written on the square the piece is on.

After that, there will be $2N$ digits written on the blackboard. Let $d_1, d_2, \ldots, d_{2N}$ be those digits, in the order they are written. The two boys will concatenate the $2N$ digits in this order to make a $2N$-digit integer $X := d_1d_2\ldots d_{2N}$.
Find the number, modulo $998244353$, of different integers that $X$ can become.

Input is given from Standard Input in the following format:
$H\ W\ N$
$c_{1, 1}\ c_{1, 2}\ \cdots\ c_{1, W}$
$c_{2, 1}\ c_{2, 2}\ \cdots\ c_{2, W}$
$\vdots$
$c_{H, 1}\ c_{H, 2}\ \cdots\ c_{H, W}$

Print the number, modulo $998244353$, of different integers that $X$ can become.

$2≤H,W≤10\\
1 \leq N \leq 300\\
1 \leq c_{i, j} \leq 9$
All values in input are integers.

5

Below is one possible scenario.

• First, Takahashi puts the piece on (1, 2).
• Takahashi moves the piece from (1, 2) to (1, 1), and then writes the digit $3$ written on (1, 1).
• Aoki moves the piece from (1, 1) to (2, 1), and then writes the digit $4$ written on (2, 1).

In this case, we have $X = 34$.
Below is another possible scenario.

• First, Takahashi puts the piece on (2, 2).
• Takahashi keeps the piece on (2, 2), and then writes the digit $1$ written on (2, 2).
• Aoki moves the piece from (2, 2) to (1, 2), and then writes the digit $1$ written on (1, 2).

In this case, we have $X = 11$. Other than these, $X$ can also become $33,\ 44$, or $43$, but nothing else.
That is, there are five integers that $X$ can become, so we print $5$.

1

X can only become $77777777$.