Problem: Given a sequence of integers a1, ..., an and q queries x1, ..., xq on it. For each query xi you have to count the number of pairs (l, r) such that 1 ≤ l ≤ r ≤ n and gcd(al, al + 1, ..., ar) = xi.

<image> is a greatest common divisor of v1, v2, ..., vn, that is equal to a largest positive integer that divides all vi.

Input

The first line of the input contains integer n, (1 ≤ n ≤ 105), denoting the length of the sequence. The next line contains n space separated integers a1, ..., an, (1 ≤ ai ≤ 109).

The third line of the input contains integer q, (1 ≤ q ≤ 3 × 105), denoting the number of queries. Then follows q lines, each contain an integer xi, (1 ≤ xi ≤ 109).

Output

For each query print the result in a separate line.

Examples

Input

3
2 6 3
5
1
2
3
4
6


Output

1
2
2
0
1


Input

7
10 20 3 15 1000 60 16
10
1
2
3
4
5
6
10
20
60
1000


Output

14
0
2
2
2
0
2
2
1
1

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.util.TreeMap;
import java.util.ArrayList;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Random;
import java.util.HashMap;
import java.io.BufferedReader;
import java.util.List;
import java.util.Map;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.Set;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author shu_mj @ http://shu-mj.com
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    Scanner in;
    PrintWriter out;

    public void solve(int testNumber, Scanner in, PrintWriter out) {
        this.in = in;
        this.out = out;
        run();
    }

    void run() {
        Map<Integer, Long> ans = new TreeMap<Integer, Long>();
        Map<Integer, Long> crt = new TreeMap<Integer, Long>();
        Map<Integer, Long> next = new TreeMap<Integer, Long>();
        for (int i : in.nextIntArray(in.nextInt())) {
            next.clear();
            for (Map.Entry<Integer, Long> e : crt.entrySet()) {
                inc(next, Num.gcd(e.getKey(), i), e.getValue());
            }
            inc(next, i, 1);
            for (Map.Entry<Integer, Long> e : next.entrySet()) {
                inc(ans, e.getKey(), e.getValue());
            }
            { Map<Integer, Long> t = crt; crt = next; next = t; }
        }
        for (int i : in.nextIntArray(in.nextInt())) {
            if (!ans.containsKey(i)) out.println(0);
            else out.println(ans.get(i));
        }
    }

    private void inc(Map<Integer, Long> cnt, int k, long v) {
        if (!cnt.containsKey(k)) cnt.put(k, v);
        else cnt.put(k, cnt.get(k) + v);
    }
}

class Scanner {
    BufferedReader br;
    StringTokenizer st;

    public Scanner(InputStream in) {
        br = new BufferedReader(new InputStreamReader(in));
        eat("");
    }

    private void eat(String s) {
        st = new StringTokenizer(s);
    }

    public String nextLine() {
        try {
            return br.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    public boolean hasNext() {
        while (!st.hasMoreTokens()) {
            String s = nextLine();
            if (s == null)
                return false;
            eat(s);
        }
        return true;
    }

    public String next() {
        hasNext();
        return st.nextToken();
    }

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

    public int[] nextIntArray(int n) {
        int[] is = new int[n];
        for (int i = 0; i < n; i++) {
            is[i] = nextInt();
        }
        return is;
    }

}

class Num {

    public static int gcd(int a, int b) {
        while (b != 0) {
            int c = a;
            a = b;
            b = c % b;
        }
        if (a < 0) a = -a;
        return a;
    }

}