Tree and Constraints

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

inputFormat

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

outputFormat

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

样例

2
1 2
1
1 2

1