Planar Graph

Description:

Input:

The first line contains two space-separated integers n and m (3 ≤ n, m ≤ 10⁵) — the number of vertexes and edges of the graph. Next m lines contain the edges of the graph: the i-th line contains two space-separated integers u_i and v_i (1 ≤ u_i, v_i ≤ n) — the numbers of vertexes, connecting the i-th edge. The next n lines contain the positions of the planar graph vertexes on the plane: the i-th line contains a pair of space-separated integers x_i and y_i (|x_i|, |y_i| ≤ 10⁹) — the coordinates of the i-th vertex of the graph on the plane.

The next line contains integer q (1 ≤ q ≤ 10⁵) — the number of queries. Then follow q lines that describe the queries: the i-th line contains the sequence of space-separated integers k_i, a₁, a₂, ..., a_ki (1 ≤ a_j ≤ n; k_i > 2), where k_i is the cycle length in the i-th query, a_j are numbers of the vertexes that form a cycle. The numbers of vertexes in the cycle are given in the clockwise or counterclockwise order. The given cycles are simple, that is they cannot go through a graph vertex more than once. The total length of all cycles in all queries does not exceed 10⁵.

It is guaranteed that the given graph contains no bridges, articulation points, loops and multiple edges. It is guaranteed that the edge segments can have common points only at the graph's vertexes.

Output:

For each query print a single integer — the number of vertexes inside the cycle or on it. Print the answers in the order, in which the queries follow in the input. Separate the numbers by spaces.

Sample Input:

3 3
1 2
2 3
3 1
0 0
1 0
0 1
1
3 1 2 3

Sample Output:

3

Sample Input:

5 8
1 2
2 3
3 4
4 1
1 5
2 5
3 5
4 5
0 0
2 0
2 2
0 2
1 1
1
4 1 2 3 4

Sample Output:

5

Sample Input:

4 5
1 2
2 3
3 4
4 1
2 4
0 0
1 0
1 1
0 1
3
3 1 2 4
3 4 2 3
4 1 2 3 4

Sample Output:

3
3
4