Problem Statement

There is an $N \times M$ grid and a player standing on it.
Let (i,j) denote the square at the i-th row from the top and j-th column from the left of this grid.
Each square of this grid is black or white, which is represented by $N strings S_1,S_2,\dots,S_N$ of length M as follows:

• if the j-th character of S_i is ., square (i,j) is white;
• if the j-th character of S_i is #, square (i,j) is black.

The grid is said to be beautiful when the following condition is satisfied.

• For every pair of integers (i,j) such that $1 \le i \le N, 1 \le j \le M$, if square (i,j) is black, the square under (i,j) and the square to the immediate lower right of (i,j) are also black (if they exist).
• Formally, all of the following are satisfied.
• If square (i,j) is black and square (i+1,j) exists, square (i+1,j) is also black.
• If square (i,j) is black and square (i+1,j+1) exists, square (i+1,j+1) is also black.

Takahashi can paint zero or more white squares black, and he will do so to make the grid beautiful.
Find the number of different beautiful grids he can make, modulo 998244353.
Two grids are considered different when there is a square that has different colors in those two grids.

Input

The input is given from Standard Input in the following format:
N M
S_1
S_2
$\vdots$
S_N

Output

Print the answer as an integer.

Constraints

• $1 \le N,M \le 2000$
• S_i is a string of length M consisting of . and #.

Sample Input 1

2 2
.#
..

Sample Output 1

3

He can make the following three different beautiful grids:
.# .# ##
.# ## ##

Sample Input 2

5 5
....#
...#.
..#..
.#.#.

...

Sample Output 2

92

Sample Input 3

25 25
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Sample Output 3

604936632

Find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分