Problem Statement

The Yuki Kingdom can be regarded as an infinitely extending coordinate plane, and there is exactly $1$ city on each of its lattice points (points whose $x$ and $y$ coordinates are both integers). In the Yuki Kingdom, every city has the following $4$ types of warp panels installed.

• By stepping on warp panel $1$ in city $(x, y)$, you can warp to city $(x+a, y+b)$.
• By stepping on warp panel $2$ in city $(x, y)$, you can warp to city $(x-a, y-b)$.
• By stepping on warp panel $3$ in city $(x, y)$, you can warp to city $(x+c, y+d)$.
• By stepping on warp panel $4$ in city $(x, y)$, you can warp to city $(x-c, y-d)$.

In the Yuki Kingdom live $N$ citizens numbered $1, 2, \ldots , N$, and citizen $i$ ($1\leq i\leq N$) lives in city $(x_i, y_i)$. The king, Yuki-kun, has decided to divide the $N$ citizens into groups so that the following conditions are satisfied.

• Citizen $i$ and citizen $j$ belong to the same group if and only if it is possible to move from city $(x_i, y_i)$ to city $(x_j, y_j)$ by stepping on warp panels a finite number of times (possibly $0$ times).
• Each group contains at least $1$ citizen.

It can be proved that these conditions determine the grouping uniquely and without contradiction. How many groups will the citizens be divided into?

Input

$a\ b\ c\ d$
$N$
$x_1\ y_1$
$\ldots$
$x_N\ y_N$

• $0\leq a, b, c, d\leq 10^9$
• $(a, b)\neq (0, 0)$
• $(c, d)\neq (0, 0)$
• $(a, b)\neq (c, d)$
• $1\leq N\leq 10^5$
• $0\leq x_i, y_i\leq 10^9$
• All inputs are integers.

Output

Output the number of groups the citizens are divided into.

Sample

1 2 2 2
4
1 2
3 3
1 0
3 1

2

0 1 1 0
2
314159265 358979323
314159265 358979323

1

2 0 3 0
5
1 0
2 3
5 4
4 3
1 2

4

7 6 8 9
10
80 0
53 48
62 51
15 27
55 18
31 79
6 81
95 76
44 99
28 84

5