NN country

Description:

Input:

The first line contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of cities.

The second line contains $$$n - 1$$$ integers $$$p_2, p_3, \ldots, p_n$$$ ($$$1 \le p_i < i$$$), where $$$p_i$$$ means that cities $$$p_i$$$ and $$$i$$$ are connected by road.

The third line contains a single integer $$$m$$$ ($$$1 \le m \le 2 \cdot 10^5$$$) — the number of bus routes.

Each of the next $$$m$$$ lines contains $$$2$$$ integers $$$a$$$ and $$$b$$$ ($$$1 \le a, b \le n$$$, $$$a \neq b$$$), meaning that there is a bus route between cities $$$a$$$ and $$$b$$$. It is possible that there is more than one route between two cities.

The next line contains a single integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of questions you are interested in.

Each of the next $$$q$$$ lines contains $$$2$$$ integers $$$v$$$ and $$$u$$$ ($$$1 \le v, u \le n$$$, $$$v \neq u$$$), meaning that you are interested if it is possible to get from city $$$v$$$ to city $$$u$$$ and what is the minimum number of buses you need to use for it.

Output:

Print the answer for each question on a separate line. If there is no way to get from one city to another, print $$$-1$$$. Otherwise print the minimum number of buses you have to use.

Sample Input:

7
1 1 1 4 5 6
4
4 2
5 4
1 3
6 7
6
4 5
3 5
7 2
4 5
3 2
5 3

Sample Output:

1
3
-1
1
2
3

Sample Input:

7
1 1 2 3 4 1
4
4 7
3 5
7 6
7 6
6
4 6
3 1
3 2
2 7
6 3
5 3

Sample Output:

1
-1
-1
1
-1
1

Note:

Routes for first sample are marked on the picture.