Problem Statement

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.

• 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.

• Takahashi writes on a blackboard the digit written on the square the piece is on.

• 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.

• 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

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

Output

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

Constraints

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

Sample Input 1

2 2 1
31
41

Sample Output 1

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.

Sample Input 2

2 3 4
777
777

Sample Output 2

1

X can only become 77777777.

Sample Input 3

10 10 300
3181534389
4347471911
4997373645
5984584273
1917179465
3644463294
1234548423
6826453721
5892467783
1211598363

Sample Output 3

685516949

Be sure to find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分