Problem Statement

You are given a grid $S$ with $H$ rows and $W$ columns consisting of 1, 2, 3, and ?. The character at the $i$-th row and $j$-th column is $S_{i,j}$.

By replacing each ? in $S$ with 1, 2, or 3, we can obtain $3^q$ different grids, where $q$ is the number of ?. Among these grids, how many satisfy the following condition? Print the count modulo $998244353$.

• Any two adjacent (edge-sharing) cells contain different digits.

Constraints

• $1 \leq H, W$
• $H \times W \leq 200$
• $H$ and $W$ are integers.
• $S$ is a grid with $H$ rows and $W$ columns consisting of 1, 2, 3, and ?.

Input

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

H W
S_{1,1}S_{1,2}\ldots S_{1,W}
S_{2,1}S_{2,2}\ldots S_{2,W}
\vdots
S_{H,1}S_{H,2}\ldots S_{H,W}

Output

Print the answer.