Very simple problem

Description:

Input:

The first line contains integer n — the number of vertices of the polygon (3 ≤ n ≤ 100000). The polygon description is following: n lines containing coordinates of the vertices in clockwise order (integer x and y not greater than 10⁹ by absolute value). It is guaranteed that the given polygon is nondegenerate and convex (no three points lie on the same line).

The next line contains integer t (1 ≤ t ≤ 20) — the number of points which you should count the answer for. It is followed by t lines with coordinates of the points (integer x and y not greater than 10⁹ by absolute value).

Output:

The output should contain t integer numbers, each on a separate line, where i-th number is the answer for the i-th point.

Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).

Sample Input:

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

Sample Output:

2

Sample Input:

3
0 0
0 5
5 0
2
1 1
10 10

Sample Output:

1
0

Sample Input:

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

Sample Output:

5
3
3
4