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.Arrays;
import java.util.HashMap;
import java.util.Scanner;

public class MainD_2 {
	MyScanner sc = new MyScanner();
	Scanner sc2 = new Scanner(System.in);
	final int MOD = 1000000007;
	int[] dx = { 1, 0, 0, -1 };
	int[] dy = { 0, 1, -1, 0 };

	void run() {
		int n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		HashMap<Integer, Long> res = new HashMap<Integer, Long>();
		HashMap<Integer, Integer> divisor = new HashMap<Integer, Integer>();
		HashMap<Integer, Integer> nextDivisor = new HashMap<Integer, Integer>();

		for (int i = 0; i < n; i++) {
			nextDivisor.clear();
			for (int k : divisor.keySet()) {
				if (nextDivisor.containsKey(gcd(k, a[i]))) {
					int tmp = nextDivisor.get(gcd(k, a[i]));
					nextDivisor.put(gcd(k, a[i]), tmp + divisor.get(k));
				} else {
					nextDivisor.put(gcd(k, a[i]), divisor.get(k));
				}
			}
			nextDivisor.put(a[i],
					nextDivisor.containsKey(a[i]) ? nextDivisor.get(a[i]) + 1
							: 1);
			// swap
			HashMap<Integer, Integer> tmp = divisor;
			divisor = nextDivisor;
			nextDivisor = tmp;

			for (int k : divisor.keySet()) {
				res.put(k, res.containsKey(k) ? res.get(k) + divisor.get(k)
						: divisor.get(k));
			}
		}
		StringBuilder out = new StringBuilder();
		int q = sc.nextInt();
		while (q-- > 0) {
			int x = sc.nextInt();
			out.append((res.containsKey(x) ? res.get(x) : 0) + "\n");
		}
		System.out.print(out);
	}

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

	public static void main(String[] args) {
		new MainD_2().run();
	}

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	void debug2(int[][] array) {
		for (int i = 0; i < array.length; i++) {
			for (int j = 0; j < array[i].length; j++) {
				System.out.print(array[i][j]);
			}
			System.out.println();
		}
	}

	class MyScanner {
		int nextInt() {
			try {
				int c = System.in.read();
				while (c != '-' && (c < '0' || '9' < c))
					c = System.in.read();
				if (c == '-')
					return -nextInt();
				int res = 0;
				do {
					res *= 10;
					res += c - '0';
					c = System.in.read();
				} while ('0' <= c && c <= '9');
				return res;
			} catch (Exception e) {
				return -1;
			}
		}

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

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

		String next() {
			try {
				StringBuilder res = new StringBuilder("");
				int c = System.in.read();
				while (Character.isWhitespace(c))
					c = System.in.read();
				do {
					res.append((char) c);
				} while (!Character.isWhitespace(c = System.in.read()));
				return res.toString();
			} catch (Exception e) {
				return null;
			}
		}
	}
}