Flu Spread

Problem Background

Special for beginners, ^_^

Problem Description

A group of susceptible people live in a grid-shaped dormitory area, which is an $n \times n$ matrix. Each grid point is a room that may be occupied or empty. On the first day, some people in certain rooms catch the flu. Each subsequent day, a person with the flu infects their neighbors (those already sick do not change), while empty rooms are not contagious.

Output the number of people with the flu on day $m$.

Input Format

The first line contains an integer $n$ (not exceeding 100), representing an $n \times n$ dormitory grid.

The next $n$ lines each contain $n$ characters: . means the room is occupied by a healthy person on day 1, # means the room is empty, @ means the room is occupied by a person with the flu on day 1.

The following line contains an integer $m$ (not exceeding 100).

Output Format

Output the number of people with the flu on day $m$.

Sample Input

5
. . . . #
. # . @ .
. # @ . .
# . . . .
. . . . .
4

Sample Output

16

Constraints

1 second, 1024 KiB for each test case.