Ex - E or m

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: $N$ $M$ $X_{1,1} X_{1,2} \dots X_{1,M}$ $X_{2,1} X_{2,2} \dots X_{2,M}$ $\vdots$ $X_{N,1} X_{N,2} \dots X_{N,M}$ [samples]