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.*;
import static java.lang.Math.*;
import java.util.*;
import java.util.function.*;
import java.lang.*;

public class Main {
    final static boolean debug = false;
    final static String fileName = "";
    final static boolean useFiles = false;

    public static void main(String[] args) throws FileNotFoundException {
        long start;
        if (debug)
            start = System.nanoTime();
        InputStream inputStream;
        OutputStream outputStream;
        if (useFiles) {
            inputStream = new FileInputStream(fileName + ".in");
            outputStream = new FileOutputStream(fileName + ".out");
        } else {
            inputStream = System.in;
            outputStream = System.out;
        }
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task(in, out);
        solver.solve();
        if(debug)
            out.println((System.nanoTime() - start) / 1e+9);
        out.close();
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public double nextDouble(){
        return Double.parseDouble(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong(){
        return Long.parseLong(next());
    }

    public byte nextByte(){
        return Byte.parseByte(next());
    }
}

class Point{
    int X, Y;
    Point(int x, int y){
        X = x;
        Y = y;
    }
}

class Task {
    long area(Point a, Point b, Point c){
        return (b.X - a.X) * (long)(c.Y - a.Y) - (c.X - a.X) * (long)(b.Y - a.Y);
    }
    public void solve() {
        int n = in.nextInt();
        Point[] points = new Point[n];
        for (int i = 0; i < n; i++) {
            points[i] = new Point(in.nextInt(), in.nextInt());
        }
        int t = in.nextInt();
        for (int test = 0; test < t; test++) {
            Point p = new Point(in.nextInt(), in.nextInt());
            boolean inside = true;
            for (int i = 0; i < n; i++) {
                if (area(p, points[i], points[(i + 1) % n]) > 0) {
                    inside = false;
                    break;
                }
            }
            if (!inside) {
                out.println(0);
                continue;
            }
            long result = 0;
            for (int i = 0, j = 1; i < n; i++) {
                for (; area(points[i], points[j], p) < 0; j = (j + 1) % n) ;
                int x = (j - i + n - 1) % n;
                result += x * (long) (x - 1) / 2;
            }
            out.println(n * (long) (n - 1) * (long) (n - 2) / 6 - result);
        }
    }

    private InputReader in;
    private PrintWriter out;

    Task(InputReader in, PrintWriter out) {
        this.in = in;
        this.out = out;
    }
}