## Day 2, Problem 2 - Zombie Apocalypse

Your country has a problem with zombies. That is, it has zombies, which are a problem. Thankfully, you are gainfully employed at the Forsenic 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 an N-by-M 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 8 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 Q, and you must determine the number of cells which are marked with the integer Q.

### Input Format

The first line of input will contain two space-separated integers N and M (1 ≤ N ≤ 109; 1 ≤ M ≤ 109) indicating the size of the grid. The next line contains the number K (1 ≤ K ≤ 2000), indicating the number of cells that contain zombies. The next K lines each contain two space-separated integers ri ci indicating the row and column of the i-th zombie (1 ≤ riN; 1 ≤ ciM). No two zombies are in the same cell: thus if ij then (ri, ci) ≠ (rj, cj). The last line will contain the integer Q (0 ≤ QN + M).

For 5 of the 25 marks available, N ≤ 1000 and M ≤ 1000.
For an additional 5 of the 25 marks available, K ≤ 50.
For an additional 5 of the 25 marks available, N ≤ 1000.

### Output Format

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

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

```15
```

### Explanation

The sample input is the example shown above, which has 15 2's.

Point Value: 15 (partial)
Time Limit: 2.00s
Memory Limit: 64M