Problem Description

lxhgww's nickname is "Little L" because he loves L-shaped objects.

Little L's living room is a rectangular area of size $r \times c$. He wants to cover the entire living room with L-shaped floor tiles. Some positions in the living room have pillars and cannot be covered with tiles.

Little L wants to know how many different ways there are to cover the entire living room with L-shaped tiles.

It should be noted that, as shown in the figure below, the lengths of the two ends of the L-shaped tile can vary, but they cannot be zero.

After the installation, all areas without pillars in the living room must be covered with tiles, and the same area cannot be covered multiple times.

Input Format

The first line of input contains two integers, $r$ and $c$, representing the size of the living room.

Following are $r$ lines, each containing $c$ characters. The characters can be either _ or *. _ indicates an empty position that must be covered with a tile, and * indicates a position with a pillar that cannot be covered.

Output Format

Output a single line containing an integer, which represents the number of ways to cover the entire living room. Since this number may be very large, output the remainder of this number divided by $20110520$.

Sample Input and Output

Sample Input #1

2 2
*_
__

Sample Output #1

1

Sample Input #2

3 3
 ___
 _*_
 ___

Sample Output #2

8

Notes

Data Size and Constraints

见题面 Input 部分

见题面 Output 部分