Problem: You are given a convex polygon. Count, please, the number of triangles that contain a given point in the plane and their vertices are the vertices of the polygon. It is guaranteed, that the point doesn't lie on the sides and the diagonals of the polygon.

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).

Examples

Input

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


Output

2


Input

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


Output

1
0


Input

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


Output

5
3
3
4

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Polygon implements Runnable {
    private void solve() throws IOException {
        int n = nextInt();
        long[] x = new long[n];
        long[] y = new long[n];
        for (int i = 0; i < n; ++i) {
            x[i] = nextLong();
            y[i] = nextLong();
        }
        int t = nextInt();
        for (int it = 0; it < t; ++it) {
            long px = nextLong();
            long py = nextLong();
            long res = 0;
            for (int i = 0; i < n; ++i) {
                long x1 = x[i];
                long y1 = y[i];
                int ii = i + 1;
                if (ii == n) ii = 0;
                long x2 = x[ii];
                long y2 = y[ii];
                if ((x2 - x1) * (py - y1) - (y2 - y1) * (px - x1) >= 0) {
                    res = -1;
                    break;
                }
            }
            if (res < 0) {
                writer.println(0);
                continue;
            }
            int j = 0;
            int cnt = 0;
            for (int i = 0; i < n; ++i) {
                while (true) {
                    int jj = j + 1;
                    if (jj == n) jj = 0;
                    if ((x[jj] - x[i]) * (py - y[i]) - (y[jj] - y[i]) * (px - x[i]) > 0)
                        break;
                    j = jj;
                    ++cnt;
                }
                res += (long) cnt * (cnt - 1) / 2;
                res += (long) (n - 1 - cnt) * (n - 1 - cnt - 1) / 2;
                --cnt;
            }
            if (res % 2 != 0) throw new RuntimeException();
            res /= 2;
            res = (long) n * (n - 1) * (n - 2) / 6 - res;
            writer.println(res);
        }
    }

    public static void main(String[] args) {
        new Polygon().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}