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 gcd(int a, int b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
int arr[100001];
int main() {
  int n, q, i, j, x;
  map<int, long long int> divisors, ans;
  cin >> n;
  for (i = 0; i < n; i++) cin >> arr[i];
  for (i = 0; i < n; i++) {
    map<int, long long int> nxtdivisors;
    map<int, long long int>::iterator it = divisors.begin();
    while (it != divisors.end()) {
      nxtdivisors[gcd(it->first, arr[i])] += it->second;
      it++;
    }
    nxtdivisors[arr[i]]++;
    swap(nxtdivisors, divisors);
    it = divisors.begin();
    while (it != divisors.end()) {
      ans[it->first] += it->second;
      it++;
    }
  }
  cin >> q;
  while (q--) {
    cin >> x;
    cout << ans[x] << endl;
  }
}