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## Problem Statement

You have recently gained a large piece of free real estate!

The real estate may be represented as a grid of size *M* × *N*. These grid squares may consist of flat open ground, ponds or forests.

You wish to build some houses on flat open ground. Due to the principles of *Feng Shui*, these houses must be at most *K* minutes walk away from a pond. You can walk from a grid square to any grid square that shares an edge in 1 minute, but you cannot walk through ponds or forests.

How many grid squares are suitable for building your houses?

## Input

The first line of input contains three integers, *M*, *N* and *K*.

The next *M* lines of input contain strings of *N* characters, indicating the contents of the grid.

'.' represents flat ground, '#' represents forest and '*' represents a pond.

## Output

The first and only line of output should contain a single integer, denoting the number of grid squares that you can build houses on.

## Limits

For all subtasks, 1 ≤ *M*, *N*, *M* × *N* ≤ 1000000 and 1 ≤ *K* ≤ 10^{9}.

Subtask 1 (65%): There is at most one pond.

Subtask 2 (15%): There are no forests.

Subtask 3 (20%): There are no more constraints.

Subtask 4 (0%): Sample test cases.

## Sample Input 1

3 3 3 ... .#. .*.

## Sample Output 1

6

## Sample Input 2

5 5 8 ..... .*#*. .#.#. .*#*. .....

## Sample Output 2

16

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 65 | 11 | 1s | 256MB | Minimum |

2 | 15 | 10 | 1s | 256MB | Minimum |

3 | 20 | 32 | 1s | 256MB | Minimum |

4 | 0 | 2 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o realestate -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512