Problem Statement

chinerist wants to hold a programming contest and has created $N$ problems. The problems are numbered from $1$ to $N$ in advance.

Each problem has $2$ values: its "quality", represented by an integer at least $0$, and its "genre", represented by an integer between $1$ and $M$, inclusive. The quality and genre of problem $i\ (1\le i\le N)$ are $A_i,\ B_i$.

These problems will be presented in some order, and the participants will solve them.

This contest has $K$ participants, and it is known that the $i\ (1\le i\le K)$-th participant solves $C_i$ problems, in order starting from the first problem presented.

The "satisfaction" of each participant is $($the sum of the qualities of the problems they solved$) + X \times ($the number of distinct genres among the problems they solved$)$.

Find the maximum possible value of the sum of the participants' satisfaction.

Input

$N$ $M$ $X$
$A_1$ $B_1$
$A_2$ $B_2$
$\vdots$
$A_N$ $B_N$
$K$
$C_1$ $C_2$ $\dots$ $C_K$

• $1 \le N \le 2\times 10^5$
• $1 \le M \le 2\times 10^5$
• $0 \le X \le 10^7$
• $0 \le A_i \le 10^7\ (1\le i \le N)$
• $1 \le B_i \le M\ (1\le i \le N)$
• $1 \le K \le 2\times 10^5$
• $0 \le C_i \le N\ (1\le i \le K)$
• All input values are integers.

Output

Output the answer.

Print a newline at the end.

Sample

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

29

3 2 2
10 1
3 2
5 1
3
0 0 0

0

15 4 5
6 3
40 1
20 3
5 2
16 3
10 4
21 1
6 2
30 2
5 3
47 1
1 2
5 1
19 4
38 4
6
5 7 1 3 11 12

1168