You have a large rectangular board which is divided into $$$n \times m$$$ cells (the board has $$$n$$$ rows and $$$m$$$ columns). Each cell is either white or black.
You paint each white cell either red or blue. Obviously, the number of different ways to paint them is $$$2^w$$$, where $$$w$$$ is the number of white cells.
After painting the white cells of the board, you want to place the maximum number of dominoes on it, according to the following rules:
Let the value of the board be the maximum number of dominoes you can place. Calculate the sum of values of the board over all $$$2^w$$$ possible ways to paint it. Since it can be huge, print it modulo $$$998\,244\,353$$$.
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 3 \cdot 10^5$$$; $$$nm \le 3 \cdot 10^5$$$) — the number of rows and columns, respectively.
Then $$$n$$$ lines follow, each line contains a string of $$$m$$$ characters. The $$$j$$$-th character in the $$$i$$$-th string is * if the $$$j$$$-th cell in the $$$i$$$-th row is black; otherwise, that character is o.
Print one integer — the sum of values of the board over all $$$2^w$$$ possible ways to paint it, taken modulo $$$998\,244\,353$$$.
3 4 **oo oo*o **oo
3 4 **oo oo** **oo
2 2 oo o*
1 4 oooo