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 $998244353$.

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 ?.

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.

Sample Input 1

2 3
0?1
?1?

Sample Output 1

6

The following six grids are in $S$.

011  011  001
010  011  110

001  011  011
111  110  111

Sample Input 2

5 3
101
010
101
010
101

Sample Output 2

0

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

Sample Input 3

18 18
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????
??????????????????

Sample Output 3

462237431

Be sure to find the count modulo $998244353$.