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 INF = (-1u) / 2;
const long long int INF2 = (-1ull) / 2;
long long int a, b, i, d[1011000], j, k, n, m, timer = 0, l, r, x, y;
long long int c[1011000], cnt = 0, fl = 0, a2, a3 = -1000000, ans = 0;
long long int GCD(long long int a, long long int b) {
  if (b == 0)
    return a;
  else
    return GCD(b, a % b);
};
map<long long int, long long int> mp1, mp2, res;
map<long long int, long long int>::iterator it;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> c[i];
    mp1.clear();
    for (it = mp2.begin(); it != mp2.end(); it++) {
      mp1[GCD((*it).first, c[i])] += (*it).second;
    }
    mp1[c[i]]++;
    for (it = mp1.begin(); it != mp1.end(); it++) {
      res[(*it).first] += (*it).second;
    }
    swap(mp1, mp2);
  }
  cin >> m;
  for (i = 0; i < m; i++) {
    cin >> x;
    cout << res[x] << endl;
  }
  return 0;
}