P1539 [TJOI2011] 01 Matrix

An $n \times m$ $01$ matrix, in which some positions are already fixed. Positions marked '.' can be filled with $0$ or $1$. Count the number of matrices for which the difference between any two adjacent positions is $1$ (i.e., adjacent cells sharing a side have different values), and output the answer modulo $10007$.

The first line contains two integers $n, m$. Then follows an $n \times m$ matrix consisting of $\verb!0!,\verb!1!,\verb!.!$.

Output a single integer: the number of matrices satisfying the condition, modulo $10007$.

### Constraints and Conventions For $100\%$ of the testdata, $n \times m \le 225$. Translated by ChatGPT 5