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 n, q;
int cur, pre;
set<int> S[2];
map<int, long long> M[2];
map<int, long long> Map;
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int main() {
  scanf("%d", &n);
  int x;
  scanf("%d", &x);
  cur = 0;
  S[cur].insert(x);
  Map[x]++;
  M[cur][x]++;
  for (int i = 2; i <= n; i++) {
    scanf("%d", &x);
    pre = cur;
    cur ^= 1;
    S[cur].insert(x);
    Map[x]++;
    M[cur][x]++;
    for (set<int>::iterator it = S[pre].begin(); it != S[pre].end(); ++it) {
      int y = *it;
      int Gcd = gcd(x, y);
      S[cur].insert(Gcd);
      Map[Gcd] += M[pre][y];
      M[cur][Gcd] += M[pre][y];
    }
    S[pre].clear();
    M[pre].clear();
  }
  scanf("%d", &q);
  while (q--) {
    scanf("%d", &x);
    printf("%I64d\n", Map[x]);
  }
  return 0;
}