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Elly and some of her friends (possibly none) are going to the movies. Their company consists of **numFriends** people, including Elly. Since they don't want to be spread across the entire hall, they decided to sit either in the same row or in the same column (though not necessarily next to one another).

Your are given a String[] **hall** representing the layout of seats in the theater that are already taken. The j-th character of the i-th element of **hall** will be '#' if the seat at row i, column j is already taken and '.' if it is empty.

Print the number of different ways for Elly and her friends to choose **numFriends** different empty seats so that their seating requirement is fulfilled. Two ways are considered different if there exists a person in their company that will sit in different seats in these two ways.

The first line of the input gives the number of test cases, **T** (1 <= **T** <= 200).

Each test case starts with three positive integers **numFriends**, which is between 1 and 8, inclusive, and **r**, **c**, which is between 1 and 50, inclusive.

For next **r** lines, length **c** string representing r-th line of **hall** is given.

For each test case, print the number of different ways as explained in the problem statement, in one line.

```
4
2 3 4
.#..
.##.
....
2 3 3
..#
.##
...
5 4 8
..####..
.###.##.
.######.
#.#.#.#.
8 1 8
........
```

```
34
16
0
40320
```