Omkar and Time Travel

Description:

Input:

The first line contains an integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$)  — the number of tasks that Okabe needs to complete.

$$$n$$$ lines follow. The $$$k$$$-th of these lines contain two integers $$$a_k$$$ and $$$b_k$$$ ($$$1 \leq a_k < b_k \leq 2n$$$)  — the time at which Okabe needs to complete the $$$k$$$-th task and the time that he realizes this respectively. All $$$2n$$$ of these times are distinct (so every time from $$$1$$$ to $$$2n$$$ inclusive appears exactly once in the input).

The next line contains a single integer $$$t$$$ ($$$1 \leq t \leq n$$$)  — the size of the set $$$s$$$ of tasks that lead to the funny scene.

The last line contains $$$t$$$ integers $$$s_1, s_2, \ldots, s_t$$$  — ($$$1 \leq s_k \leq n$$$, the numbers $$$s_1, s_2, \ldots, s_t$$$ are distinct)  — the set $$$s$$$ of tasks.

Output:

Output a single integer  — the number of times that Okabe time travels until all tasks in the set $$$s$$$ are simultaneously completed, modulo $$$10^9 + 7$$$.

Sample Input:

2
1 4
2 3
2
1 2

Sample Output:

3

Sample Input:

2
1 4
2 3
1
1

Sample Output:

2

Sample Input:

1
1 2
1
1

Sample Output:

1

Sample Input:

6
10 12
3 7
4 6
2 9
5 8
1 11
3
2 4 6

Sample Output:

17

Sample Input:

16
31 32
3 26
17 19
4 24
1 28
15 21
12 16
18 29
20 23
7 8
11 14
9 22
6 30
5 10
25 27
2 13
6
3 8 2 5 12 11

Sample Output:

138

Note:

For the first sample, all tasks need to be completed in order for the funny scene to occur.

Initially, the time is $$$0$$$. Nothing happens until time $$$3$$$, when Okabe realizes that he should have done the $$$2$$$-nd task at time $$$2$$$. He then time travels to time $$$2$$$ and completes the task.

As the task is done now, he does not time travel again when the time is again $$$3$$$. However, at time $$$4$$$, he travels to time $$$1$$$ to complete the $$$1$$$-st task.

This undoes the $$$2$$$-nd task. This means that the $$$2$$$-nd task is not currently completed, meaning that the funny scene will not occur at this point even though the $$$1$$$-st task is currently completed and Okabe had previously completed the $$$2$$$-nd task.

Once it is again time $$$3$$$ he travels back to time $$$2$$$ once more and does the $$$2$$$-nd task again.

Now all tasks are complete, with Okabe having time travelled $$$3$$$ times.

The second sample has the same tasks for Okabe to complete. However, this time the funny scene only needs the first task to be completed in order to occur. From reading the above sample you can see that this occurs once Okabe has time travelled $$$2$$$ times.