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 \min(500\,000, 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~

~1 \le M, N \le 500\,000~

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