Problem Statement

Pay attention to the special input format.

There are $N$ points $(X_i,Y_i)$ in the $xy$-plane. You are given these points in the input.

Also, $Q$ pairs of integers $(A_j,B_j)$ are given. Define $f(A_j,B_j)$ as the number of indices $i$ satisfying $Y_i \ge A_j \times X_i + B_j$.

Find $\displaystyle \sum^{Q}_{j=1} f(A_j,B_j)$.

Here, $Q$ gets very large, so $(A_j,B_j)$ are not given directly. Instead, $G_0$, $R_a$, and $R_b$ are given, and $(A_j,B_j)$ are generated as follows:

• First, for $n \ge 0$, define $G_{n+1} = (48271 \times G_n) \mod (2^{31}-1)$.
• For $j=1,2,\dots,Q$, generate $(A_j,B_j)$ as follows:
• $A_j = -R_a + (G_{3j - 2} \mod (2 \times R_a + 1) )$
  • $B_j = -R_b + ((G_{3j - 1} \times (2^{31}-1) + G_{3 j}) \mod (2 \times R_b + 1) )$

From this method, it can be shown that $A_j$ and $B_j$ satisfy the following constraints:

• $-R_a \le A_j \le R_a$
• $-R_b \le B_j \le R_b$

Constraints

• All input values are integers.
• $1 \le N \le 5000$
• $1 \le Q \le 10^7$
• $|X_i|, |Y_i| \le 10^8$
• The pairs $(X_i,Y_i)$ are distinct.
• $0 \le G_0 < (2^{31}-1)$
• $0 \le R_a \le 10^8$
• $0 \le R_b \le 10^{16}$

Input

The input is given from Standard Input in the following format:

N
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N
Q
G_0 R_a R_b

Output

Print the answer as an integer.