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 = 2e9;
const int MOD = 1e9 + 7;
const int N = 1e5 + 10;
int a[N];
int gcd(int x, int y) {
  while (y) {
    int tmp = y;
    y = x % y;
    x = tmp;
  }
  return x;
}
int main() {
  int n, q;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", a + i);
  map<int, long long> ans;
  map<int, int> div;
  map<int, int> ndiv;
  for (int i = 1; i <= n; i++) {
    ndiv.clear();
    for (auto &j : div) ndiv[gcd(j.first, a[i])] += j.second;
    ndiv[a[i]]++;
    swap(div, ndiv);
    for (auto &j : div) ans[j.first] += j.second;
  }
  scanf("%d", &q);
  while (q--) {
    int x;
    scanf("%d", &x);
    printf("%I64d\n", ans[x]);
  }
}