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, a[100086], b[100086][18];
map<int, long long> Sum;
int gcd(int x, int y) { return y ? gcd(y, x % y) : x; }
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i), b[i][0] = a[i];
  for (int j = 1; j <= 17; ++j)
    for (int i = 1; i <= n; ++i)
      b[i][j] = gcd(b[i][j - 1], b[min(i + (1 << j - 1), n)][j - 1]);
  for (int i = 1; i <= n; ++i) {
    int val = a[i], last = i, pos = i;
    while (pos <= n) {
      while (1) {
        int k = 1;
        while (pos + (1 << k) - 1 <= n && b[pos][k] % val == 0) ++k;
        --k;
        pos = pos + (1 << k) - 1;
        if (pos == n || a[pos + 1] % val != 0) break;
      }
      Sum[val] += pos - last + 1;
      last = ++pos;
      val = gcd(val, a[pos]);
    }
  }
  scanf("%d", &q);
  while (q--) {
    int x;
    scanf("%d", &x);
    printf("%I64d\n", Sum[x]);
  }
  return 0;
}