##### Canadian Computing Olympiad: 2016 Day 2, Problem 2

Your country has a problem with zombies. That is, it has zombies, which are a problem. Thankfully, you are gainfully employed at the Forensic Institute for Zoology and Zombie Emerging Studies (FIZZES), and your job is simply to give a measure of how bad the problem is.

You have mapped out your country on an -by- array of cells marked with non-negative integers.

You have the exact locations of all the zombies, and know that no two zombies are in the same location. The cells containing a zombie are marked with `0`

. Next, all the unmarked cells touching a cell (where touching a cell means touching on any side or corner of a cell; so each cell touches up to other cells) marked with `0`

are marked with `1`

. Then, all the unmarked cells touching a cell marked with `1`

are marked with `2`

. This process continues until all the cells are marked. These numbers indicate the level of concern your office has about the spread of zombies.

A small example is shown below.

```
2 2 1 1 1 2
2 1 1 0 1 2
2 1 0 1 1 2
2 1 1 1 2 2
2 2 2 2 2 3
```

Your boss has given you an integer , and you must determine the number of cells which are marked with the integer .

#### Input Specification

The first line of input will contain two space-separated integers and indicating the size of the grid. The next line will contain the number , indicating the number of cells that contain zombies. The next lines each contain two space separated integers indicating the row and column of the th zombie . No two zombies are in the same cell: thus if then . The last line will contain the integer .

For of the marks available, and .

For an additional of the marks available, .

For an additional of the marks available, .

#### Output Specification

Output the number of cells in the grid that are marked with the integer .

#### Sample Input

```
5 6
2
3 3
2 4
2
```

#### Sample Output

`15`

#### Explanation

The sample input is the example shown above, which has `2`

's.

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