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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
map<int, long long> query;
int n, gcd[20][100000], q;
int GCD(int a, int b) {
  if (a < b) swap(a, b);
  while (a != 0 && b != 0) a %= b, swap(a, b);
  return a;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int a = 0; a < n; a++) cin >> gcd[0][a];
  for (int a = 1; a < 20; a++)
    for (int b = 0; b + (1 << a) <= n; b++)
      gcd[a][b] = GCD(gcd[a - 1][b], gcd[a - 1][b + (1 << (a - 1))]);
  for (int a = 0; a < n; a++) {
    int b = 0, c = a;
    for (; c < n;) {
      int d = c;
      b = GCD(b, gcd[0][c]);
      for (int e = 19; e >= 0; e--)
        if (d + (1 << e) <= n && gcd[e][d] % b == 0) d += (1 << e) - 1;
      query[b] += d - c + 1;
      c = d + 1;
    }
  }
  cin >> q;
  for (int a = 0, b; a < q; a++) cin >> b, cout << query[b] << "\n";
  return 0;
}