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.io.*;
import java.util.*;

public class D {

    int gcd(int a, int b) {
        return a == 0 ? b : gcd(b % a, a);
    }

    class Pair {

        int first, second;

        Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }
    }

    void solve() throws IOException {
        in = new InputReader("__std");
        out = new OutputWriter("__std");

        int n = in.readInt();
        Map<Integer, Long> res = new HashMap<Integer, Long>();
        List<Pair> gs = new ArrayList<Pair>();
        for (int i = 0; i < n; ++i) {
            int a = in.readInt();
            gs.add(new Pair(a, i));
            for (Pair g : gs) {
                g.first = gcd(g.first, a);
            }
            for (int j = 0; j < gs.size(); ) {
                Pair g1 = gs.get(j);
                Pair g2 = j < gs.size() - 1 ? gs.get(j + 1) : new Pair(-1, i + 1);
                if (g1.first == g2.first) {
                    gs.remove(j + 1);
                } else {
                    int d = g2.second - g1.second;
                    Long v = res.get(g1.first);
                    if (v == null) v = 0L;
                    res.put(g1.first, v + d);
                    ++j;
                }
            }
        }
        int q = in.readInt();
        while (q-- > 0) {
            int x = in.readInt();
            out.println(res.containsKey(x) ? res.get(x) : 0);
        }

        exit();
    }

    void exit() {
        //System.err.println((System.currentTimeMillis() - startTime) + " ms");
        out.close();
        System.exit(0);
    }

    InputReader in;
    OutputWriter out;

    //long startTime = System.currentTimeMillis();

    public static void main(String[] args) throws IOException {
        new D().solve();
    }

    class InputReader {

        private InputStream stream;

        private byte[] buffer = new byte[1024];
        private int pos, len;

        private int cur;

        private StringBuilder sb = new StringBuilder(32);

        InputReader(String name) throws IOException {
            if (name.equals("__std")) {
                stream = System.in;
            } else {
                stream = new FileInputStream(name);
            }
            cur = read();
        }

        private int read() throws IOException {
            if (len == -1) {
                throw new EOFException();
            }
            if (pos >= len) {
                pos = 0;
                len = stream.read(buffer);
                if (len == -1) return -1;
            }
            return buffer[pos++];
        }

        char readChar() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            char res = (char) cur;
            cur = read();
            return res;
        }

        int readInt() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (cur == -1) {
                throw new EOFException();
            }
            int sign = 1;
            if (cur == '-') {
                sign = -1;
                cur = read();
            }
            int res = 0;
            while (!whitespace()) {
                if (cur < '0' || cur > '9') {
                    throw new NumberFormatException();
                }
                res *= 10;
                res += cur - '0';
                cur = read();
            }
            return res * sign;
        }

        long readLong() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            return Long.parseLong(readToken());
        }

        double readDouble() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            return Double.parseDouble(readToken());
        }

        String readLine() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (cur != -1 && cur != '\r' && cur != '\n') {
                sb.append((char) cur);
                cur = read();
            }
            if (cur == '\r') {
                cur = read();
            }
            if (cur == '\n') {
                cur = read();
            }
            return sb.toString();
        }

        String readToken() throws IOException {
            if (cur == -1) {
                throw new EOFException();
            }
            while (whitespace()) {
                cur = read();
            }
            if (cur == -1) {
                throw new EOFException();
            }
            sb.setLength(0);
            while (!whitespace()) {
                sb.append((char) cur);
                cur = read();
            }
            return sb.toString();
        }

        boolean whitespace() {
            return cur == ' ' || cur == '\t' || cur == '\r' || cur == '\n' || cur == -1;
        }

        boolean eof() {
            return cur == -1;
        }
    }

    class OutputWriter {

        private PrintWriter writer;

        OutputWriter(String name) throws IOException {
            if (name.equals("__std")) {
                writer = new PrintWriter(System.out);
            } else {
                writer = new PrintWriter(name);
            }
        }

        void print(String format, Object ... args) {
            writer.print(new Formatter(Locale.US).format(format, args));
        }

        void println(String format, Object ... args) {
            writer.println(new Formatter(Locale.US).format(format, args));
        }

        void print(Object value) {
            writer.print(value);
        }

        void println(Object value) {
            writer.println(value);
        }

        void println() {
            writer.println();
        }

        void close() {
            writer.close();
        }
    }
}