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.