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 getint() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || '9' < ch) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f * x;
}
int gcd(int x, int y) {
  if (!y) return x;
  return gcd(y, x % y);
}
map<int, long long> ans, last, now;
map<int, long long>::iterator it;
int main() {
  int n = getint();
  for (int i = 1; i <= n; i++) {
    int x = getint();
    now[x]++;
    for (it = last.begin(); it != last.end(); it++) {
      int y = it->first;
      long long sum = it->second;
      now[gcd(x, y)] += sum;
    }
    for (it = now.begin(); it != now.end(); it++) ans[it->first] += it->second;
    swap(last, now);
    now.clear();
  }
  int t = getint();
  while (t--) {
    cout << ans[getint()] << endl;
  }
  return 0;
}