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 {
	int GCD(int a, int b) {
		int t = Math.min(a, b);
		b = Math.max(a, b);
		a = t;

		while (b % a != 0) {
			t = b % a;
			b = a;
			a = t;
		}

		return a;
	}

	void solve() throws IOException {
		TreeMap<Integer, Long> results = new TreeMap<Integer, Long>();
		TreeMap<Integer, Long> local_results = new TreeMap<Integer, Long>();

		int n = nextInt();
		for (int i = 0; i < n; ++i) {
			int numb = nextInt();

			TreeMap<Integer, Long> next_local_results = new TreeMap<Integer, Long>();
			next_local_results.put(numb, (long) 1);

			Iterator<Integer> gcds = local_results.keySet().iterator();
			while (gcds.hasNext()) {
				int gcd = gcds.next();
				int next_gcd = GCD(numb, gcd);

				Long local_result = local_results.get(gcd);
				Long next_local_result = next_local_results.get(next_gcd);
				if (next_local_result != null) {
					next_local_result += local_result;
				} else {
					next_local_result = local_result;
				}

				next_local_results.put(next_gcd, next_local_result);
			}

			local_results = next_local_results;
			gcds = local_results.keySet().iterator();
			while (gcds.hasNext()) {
				int gcd = gcds.next();
				
				Long local_result = local_results.get(gcd);
				Long result = results.get(gcd);
				if (result != null) {
					result += local_result;
				} else {
					result = local_result;
				}

				results.put(gcd, result);
			}
		}

		int q = nextInt();
		for (int e = 0; e < q; ++e) {
			int val = nextInt();

			long result = 0;
			if (results.containsKey(val)) {
				result = results.get(val);
			}

			out.println(result);
		}
	}

	void run() throws IOException {
		// reader = new BufferedReader(new FileReader("B-large.in"));
		reader = new BufferedReader(new InputStreamReader(System.in));
		tokenizer = null;
		// out = new PrintWriter(new FileWriter("B-large.out"));
		out = new PrintWriter(new OutputStreamWriter(System.out));
		solve();
		reader.close();
		out.flush();
	}

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

	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter out;

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}
}