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 MX = int(1e5) + 10;
map<int, long long> mp;
int f[20][MX];
int n, q;
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
void init() {
  for (int i = 1; i < 20; i++) {
    for (int j = 1; j <= n; j++) {
      if (j < (1 << i)) continue;
      f[i][j] = gcd(f[i - 1][j], f[i - 1][j - (1 << (i - 1))]);
    }
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &f[0][i]);
  }
  init();
  for (int i = 1; i <= n; i++) {
    int temp = f[0][i];
    int pos = i;
    while (temp != 1 && pos > 0) {
      for (int j = 19; j >= 0; j--) {
        if (f[j][pos] == 0) continue;
        if (f[j][pos] % temp == 0) {
          pos -= 1 << j;
          mp[temp] += 1 << j;
        }
      }
      temp = gcd(temp, f[0][pos]);
    }
    if (pos) {
      mp[1] += pos;
    }
  }
  scanf("%d", &q);
  for (int i = 0; i < q; i++) {
    int temp;
    scanf("%d", &temp);
    printf("%I64d\n", mp[temp]);
  }
}