Hunter

In a hunting ground there are $N$ animals, each living at a particular spot. A hunter may only shoot from $M$ firing positions that all lie on one straight line. Treat that line as the $x$-axis, so each firing position is given by an $x$-coordinate $x_1, x_2, \dots, x_M$. Each animal lives at a spot written with an $x$- and a $y$-coordinate: $(a_1, b_1), (a_2, b_2), \dots, (a_N, b_N)$. Every coordinate value describing an animal's position is a positive integer.

If the hunter's gun has range $L$, then from a single firing position the hunter can catch any animal whose distance is at most $L$. Here the distance between a firing position $x_i$ and an animal at $(a_j, b_j)$ is defined as $|x_i - a_j| + b_j$.

For example, consider the hunting ground drawn below. (Firing positions are small squares and animal positions are small circles.) If the range $L$ is $4$, the dashed region is the area that can be hunted from the third firing position counted from the left.

Given the firing positions and the animal positions, write a program that prints how many animals can be caught.

The first line contains the number of firing positions $M$ ($1 \le M \le 100{,}000$), the number of animals $N$ ($1 \le N \le 100{,}000$), and the range $L$ ($1 \le L \le 1{,}000{,}000{,}000$), separated by spaces.

The second line contains the $M$ $x$-coordinates of the firing positions, given as positive integers separated by spaces.

Each of the next $N$ lines contains one animal's position as its $x$-coordinate followed by its $y$-coordinate, given as positive integers separated by spaces.

No two firing positions coincide, and no two animals share the same position. Every coordinate value is a positive integer not greater than $1{,}000{,}000{,}000$.

Print, on a single line, the number of animals that can be caught, as a non-negative integer.