Problem Description

We have obtained a satellite photo of land and water conditions, which can be seen as a rectangle consisting of $n$ rows and $m$ columns. Each grid in the rectangle is either land (represented by a period . ) or water (represented by a hash #).

Although the satellite photo clearly distinguishes between land and water, the specific types of land are not clear. We now understand that for a grid that is water, the land grids reachable within $k$ steps in all four directions (up, down, left, right) will form a beach. For example, the following diagram shows the case for $k=2$, where the blue grids represent water and the yellow grids represent land that forms the beach.

Your task is to calculate the number of grids that belong to the "beach" based on the satellite photo. Note: The satellite photo only captures the part that includes water, and beaches near the water may extend beyond the boundaries of the satellite photo. You can assume that there is no water outside the satellite photo.

Input Format

The first line of input contains three integers $n$, $m$, and $k$ separated by spaces, representing the number of rows and columns of the satellite photo, and the range $k$ within which land forms a beach.

The next $n$ lines each contain a string. The length of each string is exactly $m$, representing a row of the satellite photo, where:

• A hash # represents a water area;
• A period . represents a land area.

Output Format

Output a single integer on one line, representing the number of beach grids.

Sample Input and Output

Sample Input #1

2 4 2
##.#
...#

Sample Output #1

26

Sample Input #2

5 10 3
.........#
..########
.........#
#....###.#
..####...#

Sample Output #2

103

Notes/Hints

For $40\%$ of the data, $n=m=1$ holds;
For $100\%$ of the data, $1 \leq n, m \leq 100$ and $1 \leq k \leq 10$ hold.

见题面 Input 部分

见题面 Output 部分