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<long long, long long> T;
long long n, q, u, i, j, A[200000], C[200000 * 20], D[200000 * 20];
long long gcd(long long x, long long y) {
  if (!y) return x;
  return gcd(y, x % y);
}
int main() {
  scanf("%I64d", &n);
  for (i = 1; i <= n; i++) scanf("%I64d", &A[i]);
  for (i = 1; i <= n; i++) {
    for (j = 1; j <= u; j++) C[j] = gcd(C[j], A[i]);
    C[++u] = A[i], D[u] = 1;
    long long x = 1;
    for (j = 2; j <= u; j++)
      if (C[j] != C[x])
        C[++x] = C[j], D[x] = D[j];
      else
        D[x] += D[j];
    u = x;
    for (j = 1; j <= u; j++) T[C[j]] += D[j];
  }
  scanf("%I64d", &q);
  for (i = 1; i <= q; i++) {
    scanf("%I64d", &u);
    printf("%I64d\n", T[u]);
  }
}