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 where you only can 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 $10^9+7$.

Note that this time, there might be traps in the top-left or bottom-right squares.

Constraints

• $1 \le n \le 1000$

Example

Input:

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

Output:

3