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.

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.

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.

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.