Problem Statement

There is a grid with H rows and W columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left of the grid.
Each square of the grid is holed or not. There are exactly N holed squares: $(a_1, b_1), (a_2, b_2), \dots, (a_N, b_N)$.
When the triple of positive integers (i, j, n) satisfies the following condition, the square region whose top-left corner is (i, j) and whose bottom-right corner is (i + n - 1, j + n - 1) is called a holeless square.

• $i + n - 1 \leq H$.
• $j + n - 1 \leq W$.
• For every pair of non-negative integers (k, l) such that $0 \leq k \leq n - 1, 0 \leq l \leq n - 1, square (i + k, j + l)$ is not holed.

How many holeless squares are in the grid?

Input

The input is given from Standard Input in the following format:
H W N
a_1 b_1
a_2 b_2
$\vdots$
a_N b_N

Output

Print the number of holeless squares.

Constraints

• $1 \leq H, W \leq 3000$
• $0 \leq N \leq \min(H \times W, 10^5)$
• $1 \leq a_i \leq H$
• $1 \leq b_i \leq W$
• All (a_i, b_i) are pairwise different.
• All input values are integers.

Sample Input 1

2 3 1
2 3

Sample Output 1

6

There are six holeless squares, listed below. For the first five, n = 1, and the top-left and bottom-right corners are the same square.

• The square region whose top-left and bottom-right corners are (1, 1).
• The square region whose top-left and bottom-right corners are (1, 2).
• The square region whose top-left and bottom-right corners are (1, 3).
• The square region whose top-left and bottom-right corners are (2, 1).
• The square region whose top-left and bottom-right corners are (2, 2).
• The square region whose top-left corner is (1, 1) and whose bottom-right corner is (2, 2).

Sample Input 2

3 2 6
1 1
1 2
2 1
2 2
3 1
3 2

Sample Output 2

0

There may be no holeless square.

Sample Input 3

1 1 0

Sample Output 3

1

The whole grid may be a holeless square.

Sample Input 4

3000 3000 0

Sample Output 4

9004500500

见题面 Input 部分

见题面 Output 部分