Problem Statement

We have a tree with $N$ vertices numbered $1$ to $N$. The $i$-th edge in this tree connects Vertex $a_i$ and Vertex $b_i$.
Consider painting each of these edges white or black. There are $2^{N-1}$ such ways to paint the edges. Among them, how many satisfy all of the following $M$ restrictions?

• The $i$-th $(1 \\leq i \\leq M)$ restriction is represented by two integers $u_i$ and $v_i$, which mean that the path connecting Vertex $u_i$ and Vertex $v_i$ must contain at least one edge painted black.

Constraints

• $2 \\leq N \\leq 50$
• $1 \\leq a_i,b_i \\leq N$
• The graph given in input is a tree.
• $1 \\leq M \\leq \\min(20,\\frac{N(N-1)}{2})$
• $1 \\leq u_i < v_i \\leq N$
• If $i \\not= j$, either $u_i \\not=u_j$ or $v_i\\not=v_j$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$N$ $a_1$ $b_1$ $:$ $a_{N-1}$ $b_{N-1}$ $M$ $u_1$ $v_1$ $:$ $u_M$ $v_M$

Output

Print the number of ways to paint the edges that satisfy all of the $M$ conditions.

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Sample Input 1

3
1 2
2 3
1
1 3

Sample Output 1

3

The tree in this input is shown below:

All of the $M$ restrictions will be satisfied if Edge $1$ and $2$ are respectively painted (white, black), (black, white), or (black, black), so the answer is $3$.

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Sample Input 2

2
1 2
1
1 2

Sample Output 2

1

The tree in this input is shown below:

All of the $M$ restrictions will be satisfied only if Edge $1$ is painted black, so the answer is $1$.

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Sample Input 3

5
1 2
3 2
3 4
5 3
3
1 3
2 4
2 5

Sample Output 3

9

The tree in this input is shown below:

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Sample Input 4

8
1 2
2 3
4 3
2 5
6 3
6 7
8 6
5
2 7
3 5
1 6
2 8
7 8

Sample Output 4

62

The tree in this input is shown below: