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 CGCDSSQ {

	static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
	static BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));

	static int n;
	static int[] a;
//	static int[][] m;
	static Map<Integer, Long> res;
	
	static void process() throws Exception {
		Map<Integer, Long> cur = new HashMap<>();
		Map<Integer, Long> prev = new HashMap<>();
		for (int i = 0; i < n; i++) {
			cur.clear();
			cur.put(a[i], cur.getOrDefault(a[i], 0L) + 1);
			res.put(a[i], res.getOrDefault(a[i], 0L) + 1);
			for (int k: prev.keySet()) {
				int new_gcd = gcd(a[i], k);
				long prev_gcd_count = prev.get(k);
				res.put(new_gcd, res.getOrDefault(new_gcd, 0L) + prev_gcd_count);
				cur.put(new_gcd, cur.getOrDefault(new_gcd, 0L) + prev_gcd_count);
			}
			Map<Integer, Long> tmp = cur;
			cur = prev;
			prev = tmp;
		}
	}
	
	static int gcd(int a, int b) {
		int tmp = 0;
		while (b != 0) {
			tmp = b;
			b = a % b;
			a = tmp;
		}
		return a;
	}

	public static void main(String[] args) throws Exception {
		//		writer = new BufferedWriter(new FileWriter("output.txt"));
		n = Integer.parseInt(reader.readLine());
		a = Arrays.asList(reader.readLine().split(" ")).stream().mapToInt(Integer::parseInt).toArray();
		int q = Integer.parseInt(reader.readLine());
		res = new HashMap<>();
		process();
		while (q-- != 0) {
			writer.write(String.format("%d", res.getOrDefault(Integer.parseInt(reader.readLine()), 0L)));
			writer.newLine();
		}
		writer.close();
		reader.close();
	}

}