At the Nova Theatre, the balcony seats can be seen as a grid with $M$ rows and $N$ columns. The theatre is packed and the seats are all filled. At the end of the play, $K$ people in the balcony stand to give their applause. The $i^{\text{th}}$ of these $K$ people is sitting in row $r_i$, column $c_i$. The rest of the $M\times N$ people will only stand if at least two people adjacent to them are standing. How many people will end up standing?

Constraints

$K\le M\times N$
$1\le r_i\le M$ for all $1\le i\le K$
$1\le c_i\le N$ for all $1\le i\le K$

Subtask 1 [10%]

$M=2$
$1\le N\le 100000$
$1\le K\le 100000$

Subtask 2 [30%]

$1\le M,N\le 1000$
$1\le K\le 100000$

Subtask 3 [10%]

$1\le M,N\le 100000$
$1\le K\le 1000$

Subtask 4 [50%]

$1\le M,N\le 100000$
$1\le K\le 100000$

Input Specification

The first line will contain three space-separated integers, $M,N,K$.
The next $K$ lines each contain two space-separated integers, $r_i$ and $c_i$, representing the $i^{\text{th}}$ person initially standing.

Sample Input 1

3 4 5
1 1
1 2
1 3
2 1
3 1

Sample Output 1

9

Explanation for Sample 1

Initially, the grid appears as:

S S S O
S O O O
S O O O

where S denotes someone standing and O denotes someone sitting.
Then it becomes:

S S S O
S S O O
S O O O

Then:

S S S O
S S S O
S S O O

Finally:

S S S O
S S S O
S S S O

No more people stand, so the $9$ people end up standing.

Sample Input 2

3 5 4
1 1
3 1
1 4
2 5

Sample Output 2

7

Sample Input 3

3 5 4
1 1
3 1
1 3
2 4

Sample Output 3

12