E - Akari

Score : $500$ points

Problem Statement

We have a grid with $H$ rows and $W$ columns. Let square $(i, j)$ be the square at the $i$-th row and $j$-th column in this grid.
There are $N$ bulbs and $M$ blocks on this grid. The $i$-th bulb is at square $(A_i, B_i)$, and the $i$-th block is at square $(C_i, D_i)$. There is at most one object - a bulb or a block - at each square.
Every bulb emits beams of light in four directions - up, down, left, and right - that extend until reaching a square with a block, illuminating the squares on the way. A square with a bulb is also considered to be illuminated. Among the squares without a block, find the number of squares illuminated by the bulbs.

Constraints

• $1 \le H, W \le 1500$
• $1 \le N \le 5 \times 10^5$
• $1 \le M \le 10^5$
• $1 \le A_i \le H$
• $1 \le B_i \le W$
• $1 \le C_i \le H$
• $1 \le D_i \le W$
• $(A_i, B_i) \neq (A_j, B_j)\ \ (i \neq j)$
• $(C_i, D_i) \neq (C_j, D_j)\ \ (i \neq j)$
• $(A_i, B_i) \neq (C_j, D_j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$H$ $W$ $N$ $M$

$A_1$ $B_1$

$A_2$ $B_2$

$A_3$ $B_3$

$\hspace{15pt} \vdots$

$A_N$ $B_N$

$C_1$ $D_1$

$C_2$ $D_2$

$C_3$ $D_3$

$\hspace{15pt} \vdots$

$C_M$ $D_M$

Output

Print the number of squares illuminated by the bulbs among the squares without a block.

3 3 2 1
1 1
2 3
2 2

7

Among the squares without a block, all but square $(3, 2)$ are illuminated.

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

8

Among the squares without a block, the following eight are illuminated:

• Square $(1, 1)$
• Square $(1, 2)$
• Square $(1, 3)$
• Square $(1, 4)$
• Square $(2, 2)$
• Square $(3, 3)$
• Square $(3, 4)$
• Square $(4, 4)$

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

24

In this case, all the squares without a block are illuminated.