C - Bowls and Dishes

Score : $300$ points

Problem Statement

We have $N$ dishes numbered $1, 2, \dots, N$ and $M$ conditions numbered $1, 2, \dots, M$.
Condition $i$ is satisfied when both Dish $A_i$ and Dish $B_i$ have (one or more) balls on them.
There are $K$ people numbered $1, 2, \dots, K$. Person $i$ will put a ball on Dish $C_i$ or Dish $D_i$.
At most how many conditions will be satisfied?

Constraints

• All values in input are integers.
• $2 ≤ N ≤ 100$
• $1 ≤ M ≤ 100$
• $1 ≤ A_i < B_i ≤ N$
• $1 ≤ K ≤ 16$
• $1 ≤ C_i < D_i ≤ N$

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $B_1$

$\vdots$

$A_M$ $B_M$

$K$

$C_1$ $D_1$

$\vdots$

$C_K$ $D_K$

Output

Print the answer.

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

2

For example, if People $1, 2, 3$ put their balls on Dishes $1, 3, 2$, respectively, Conditions $1$ and $2$ will be satisfied.

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

4

For example, if People $1, 2, 3, 4$ put their balls on Dishes $3, 1, 2, 4$, respectively, all conditions will be satisfied.

6 12
2 3
4 6
1 2
4 5
2 6
1 5
4 5
1 3
1 2
2 6
2 3
2 5
5
3 5
1 4
2 6
4 6
5 6

9