Consider an ~n \times n~ grid whose squares may have traps. It is not allowed to move to a square with a trap.

Your task is to calculate the number of paths from the upper-left square to the lower-right square. You can only move right or down.

Input

• The first input line has an integer ~n~: the size of the grid.

After this, there are ~n~ lines that describe the grid. Each line has ~n~ characters: . denotes an empty cell, and * denotes a trap.

Output

• Print the number of paths modulo ~10^9+7~.

Constraints

• ~1 \le n \le 1000~

Example Input

4
....
.*..
...*
*...

Example Output

3