### Problem Statement

We have a grid $A$ with $N$ rows and $M$ columns. Initially, $0$ is written on every square.  
Let us perform the following operation.

-   For each integer $i$ such that $1 \le i \le N$, in the $i$-th row, turn the digits in zero or more leftmost squares into $1$.
-   For each integer $j$ such that $1 \le j \le M$, in the $j$-th column, turn the digits in zero or more topmost squares into $1$.

Let $S$ be the set of grids that can be obtained in this way.

You are given a grid $X$ with $N$ rows and $M$ columns consisting of `0`, `1`, and `?`.  
There are $2^q$ grids that can be obtained by replacing each `?` with `0` or `1`, where $q$ is the number of `?` in $X$. How many of them are in $S$?  
This count can be enormous, so find it modulo $998244353$.

### Input

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

```
$N$ $M$
$X_{1,1} X_{1,2} \dots X_{1,M}$
$X_{2,1} X_{2,2} \dots X_{2,M}$
$\vdots$
$X_{N,1} X_{N,2} \dots X_{N,M}$
```

### Output

Print an integer representing the answer.

### Constraints

-   $N$ and $M$ are integers.
-   $1 \le N,M \le 18$
-   $X$ is a grid with $N$ rows and $M$ columns consisting of `0`, `1`, and `?`.

6

The following six grids are in S.

011  011  001
010  011  110

001  011  011
111  110  111

0

X may have no ?, and the answer may be 0.