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;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
int main() {
  int n;
  cin >> n;
  map<int, long long> cnt;
  map<int, long long> last;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    map<int, long long> next;
    last[x]++;
    for (map<int, long long>::iterator j = last.begin(); j != last.end(); j++) {
      int g = gcd(j->first, x);
      next[g] += j->second;
      cnt[g] += j->second;
    }
    last = next;
  }
  int q;
  cin >> q;
  while (q--) {
    int x;
    cin >> x;
    cout << cnt[x] << '\n';
  }
  return 0;
}