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.*;
import java.io.*;
import java.math.BigInteger;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		InputReader in = new InputReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		new Task().go(in, out);
		out.close();
	}

}

class Task {
	public int maxn = 100010;
	HashMap<Integer, Integer>[] hm = new HashMap[maxn];
	HashMap<Integer, Long> ans = new HashMap<Integer, Long>();
	int[] a = new int[maxn];
	int n, m;
	public void go(InputReader in, PrintWriter out) {
		n = in.nextInt();
		for(int i=0; i<n; i++) {
			a[i] = in.nextInt();
			hm[i] = new HashMap<Integer, Integer>();
		}
		hm[0].put(a[0], 1);
		for(int i=1; i<n; i++) {
			Iterator it = hm[i-1].entrySet().iterator();
			while(it.hasNext()) {
				Map.Entry<Integer, Integer> e = (Map.Entry<Integer, Integer>)it.next();
				int first = gcd(e.getKey(), a[i]);
		//		out.println("e:"+" "+e.getKey()+ " " + e.getValue() + " " + a[i] + " "+ first);
				if(hm[i].containsKey(first)) {
					hm[i].put(first, hm[i].get(first) + e.getValue());
				}
				else hm[i].put(first, e.getValue());
			}
			
			if(hm[i].containsKey(a[i])) {
				hm[i].put(a[i], hm[i].get(a[i])+1);
			}
			else hm[i].put(a[i], 1);
		}
		for(int i=0; i<n; i++) {
			Iterator it = hm[i].entrySet().iterator();
			while(it.hasNext()) {
				Map.Entry<Integer, Integer> e = (Map.Entry<Integer, Integer>)it.next();
				if(ans.containsKey(e.getKey())) {
					ans.put(e.getKey(), ans.get(e.getKey()) + e.getValue());
				}
				else {
					ans.put(e.getKey(), (long)e.getValue());
				}
			}			
		}
		m = in.nextInt();
		for(int i=0; i<m; i++) {
			int x = in.nextInt();
			long res = ans.containsKey(x)?ans.get(x):0;
			out.println(res);
		}
	}
	
	public int gcd(int a, int b) {
		return b==0?a:gcd(b, a%b);
	}
	
}

class InputReader {
	BufferedReader bf;
	StringTokenizer st;

	InputReader(InputStreamReader is) {
		bf = new BufferedReader(is);
	}

	public String next() {
		if (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(bf.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

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

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

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