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;
const int N = 1e5 + 1;
int a[N];
int gcd(int a, int b) {
  while (b) {
    a %= b;
    swap(a, b);
  }
  return a;
}
int main() {
  int n, q;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }
  map<int, long long> prev;
  map<int, long long> gc;
  int g, v, u;
  long long tmp;
  for (int i = 1; i <= n; ++i) {
    v = a[i];
    for (auto it = prev.begin(); it != prev.end();) {
      u = it->first;
      tmp = it->second;
      prev.erase(it++);
      g = gcd(u, v);
      gc[g] += tmp;
      prev[g] += tmp;
    }
    prev[v] += 1;
    gc[v] += 1;
  }
  cin >> q;
  int x;
  for (int i = 0; i < q; ++i) {
    cin >> x;
    cout << gc[x] << endl;
  }
  return 0;
}