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 N = 1e5 + 7;
map<int, long long> dp;
map<int, int> mp[N];
int a[N], n;
int gcd(int a, int b) { return (b == 0 ? a : gcd(b, a % b)); }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  mp[0][a[0]] = 1;
  dp[a[0]] = 1;
  for (int i = 1; i < n; i++) {
    mp[i][a[i]] = 1;
    for (auto it : mp[i - 1]) mp[i][gcd(it.first, a[i])] += it.second;
    for (auto it : mp[i]) dp[it.first] += it.second;
  }
  int q;
  cin >> q;
  vector<long long> ans;
  for (int i = 0; i < q; i++) {
    int x;
    cin >> x;
    ans.push_back(dp[x]);
  }
  for (auto x : ans) cout << x << "\n";
  cout << flush;
  return 0;
}