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.IOException;
import java.io.InputStreamReader;
import java.io.FileReader;
import java.util.HashMap;
import java.util.Set;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Agostinho Junior
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
	OutputWriter out;
	InputReader in;
	public void solve(int testNumber, InputReader in, OutputWriter out) {
		this.in = in; this.out = out;
		final int n = in.readInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.readInt();
		}
		final int q = in.readInt();
		int[] x = new int[q];
		HashMap<Integer, Long> count = new HashMap<Integer, Long>();
		for (int i = 0; i < q; i++) {
			x[i] = in.readInt();
			count.put(x[i], 0L);
		}
		HashMap<Integer, Long> curCount = new HashMap<Integer, Long>();
		for (int i = 0; i < n; i++) {
			HashMap<Integer, Long> newCount = new HashMap<Integer, Long>();
			for (int key: curCount.keySet()) {
				int gcd = XMath.gcd(key, a[i]);
				long temp = newCount.containsKey(gcd) ? newCount.get(gcd) : 0;
				newCount.put(gcd, curCount.get(key) + temp);
			}
			long temp = newCount.containsKey(a[i]) ? newCount.get(a[i]) : 0;
			newCount.put(a[i], temp + 1);
			for (int key: newCount.keySet()) if (count.containsKey(key)) {
				count.put(key, count.get(key) + newCount.get(key));
			}
			curCount = newCount;
		}
		for (int xi: x) {
			out.println(count.get(xi));
		}
	}
}

class OutputWriter {
	private PrintWriter output;
	public OutputWriter() {
		this(System.out);
	}
	public OutputWriter(OutputStream out) {
		output = new PrintWriter(out);
	}
	public OutputWriter(Writer writer) {
		output = new PrintWriter(writer);
	}
	public void println(Object o) {
		output.println(o);
	}
	public void close() {
		output.close();
	}
}

class InputReader {
	private BufferedReader input;
	private StringTokenizer line = new StringTokenizer("");
	public InputReader() {
		this(System.in);
	}
	public InputReader(InputStream in) {
		input = new BufferedReader(new InputStreamReader(in));
	}
	public InputReader(String s) {
		try {
			input = new BufferedReader(new FileReader(s));
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	public void fill() {
		try {
			if(!line.hasMoreTokens()) line = new StringTokenizer(input.readLine());
		} catch(IOException io) { io.printStackTrace(); System.exit(0);}
	}
	public int readInt() {
		fill();
		return Integer.parseInt(line.nextToken());
	}
}

class XMath {
	public static int gcd(int a, int b) {
		int c;
		while (b > 0) {
			c = a % b;
			a = b;
			b = c;
		}
		return a;
	}
}