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 double PI = 3.14159265359;
int gcd(int a, int b) {
  while (a) a ^= b ^= a ^= b %= a;
  return b;
}
int main() {
  int sparse[18][100500] = {0};
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &sparse[0][i]);
  for (int i = 1; i < 18; ++i) {
    for (int j = 0; j < n; ++j) {
      sparse[i][j] = sparse[i - 1][j];
      if (j + (1 << (i - 1)) < n)
        sparse[i][j] = gcd(sparse[i][j], sparse[i - 1][j + (1 << (i - 1))]);
    }
  }
  unordered_map<int, long long> ans;
  for (int i = 0; i < n; ++i) {
    int a = i;
    int g = sparse[0][i];
    while (a < n) {
      g = gcd(sparse[0][a], g);
      int b = a;
      int k = 18;
      while (b < n && k >= 0) {
        if (b + (1 << k) <= n && gcd(sparse[k][b], g) == g) b += (1 << k);
        --k;
      }
      ans[g] += b - a;
      a = b;
    }
  }
  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; ++i) {
    int x;
    scanf("%d", &x);
    auto iter = ans.find(x);
    cout << (iter == ans.end() ? 0LL : iter->second) << "\n";
  }
  return 0;
}