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.

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.

Examples

Input

3
1 2
2 3
1
1 3

Output

3

Input

2
1 2
1
1 2

Output

1

Input

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

Output

9

Input

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

Output

62

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