Hate Stagnant Water

On a rainy day, Sejong went out to buy water for his parents. While waiting at a crosswalk, he saw water pooling on it because the crosswalk was not flat.

The crosswalk is an $N\times M$ rectangular grid. The cell at the front row on Sejong's side, far left, is row 1, column 1. The cell far right in that row is row 1, column $M$.

Drains are installed in $K$ cells of the crosswalk. A cell drains water if one of its vertically or horizontally adjacent cells has a drain or is already drained, and that adjacent cell's height is lower than or equal to its own. A cell without a drain that does not drain is called a standing water cell.

Sejong solved A+B and got new shoes. He does not want to dirty them, so he tries to cross without stepping on any standing water cell. His new shoes are a rectangle that covers $h$ consecutive rows and $w$ consecutive columns. When Sejong steps, the shoe always fits exactly onto the grid cells, and he never turns his foot.

Given the height of each cell, write a program that counts the number of ways Sejong can place one foot on the crosswalk without dirtying his shoes.

The first line contains two integers $N$ and $M$, separated by a space. ($1 \le N, M \le 1000$)

The second line contains two integers $h$ and $w$, the length and width of Sejong's shoes, separated by a space. ($1 \le h \le N$, $1 \le w \le M$)

The next $N$ lines contain $M$ integers each. On line $i+2$, the integers $H_{i,1}, H_{i,2}, \cdots, H_{i,M}$ are separated by spaces. $H_{i,j}$ is the height of the cell at row $i$, column $j$. ($1 \le H_{i,j} \le 100$)

Line $N+3$ contains an integer $K$, the number of drains. ($1 \le K \le N \times M$)

The next $K$ lines each contain two integers $r$ and $c$, separated by a space, meaning there is a drain at row $r$, column $c$. No position is repeated. ($1 \le r \le N$, $1 \le c \le M$)

Print the number of ways Sejong can place one foot on the crosswalk.