Bouquet

A robot stands inside a building with $N$ floors. Each floor has $M$ rooms arranged in a single row, so all rooms of the building form an $N \times M$ rectangle. Some rooms each contain one flower. The robot is learning to gather bouquets.

When the robot is in a room, it may:

• If it is not in the leftmost room, move to the adjacent room to the left on the same floor.
• If it is not in the rightmost room, move to the adjacent room to the right on the same floor.
• If it is not on the bottom floor, move to the room directly below the current one, one floor down.

The robot only moves horizontally or downward; it never moves up.

Whenever it enters a room that contains a flower, it always picks that flower and adds it to the bouquet.

All flowers are distinct, and a bouquet's appearance depends on the order in which the flowers were added. Two bouquets are considered different if they consist of different flowers, or if the flowers were added in a different order.

The robot starts in any room of the top floor and finishes in any room of the bottom floor. Furthermore, the robot always chooses a route that picks at least one flower on every floor.

Determine how many different bouquets the robot could end up having gathered. Output the answer modulo $10^9 + 7$.

The first line contains two integers $N$ and $M$.

Each of the next $N$ lines describes one floor (starting from the top) with $M$ characters; the $i$-th character tells whether the $i$-th room from the left on that floor contains a flower:

• O — the room has no flower.
• X — the room has a flower.

It is guaranteed that every floor contains at least one flower.

Output the number of different bouquets the robot can gather, modulo $10^9 + 7$.

• $1 \le N \le 500$
• $1 \le M \le 300$