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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main
{
    static int gcd(int a , int b){return b == 0 ? a : gcd(b , a % b);}

    public static void main(String[] args) throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(br.readLine()) ;
        StringTokenizer st = new StringTokenizer(br.readLine()) ;
        int [] a = new int [n] ;
        for(int i = 0 ; i < n ; i ++)
            a[i] = Integer.parseInt(st.nextToken()) ;
        SparseTable sp = new SparseTable(a) ;
        HashMap<Integer , Long> count = new HashMap<>() ;
        int q = Integer.parseInt(br.readLine()) ;
        for(int i = 0 ; i < n ; i ++)
            for(int j = i ; j < n ; j++)
            {
                int val = sp.query(i , j) ;
                int next = j , start = j , end = n - 1 ;
                while (start <= end)
                {
                    int mid = start + end >> 1 ;
                    if(sp.query(i , mid) == val)
                    {
                        start = mid + 1 ;
                        next = mid ;
                    }
                    else
                        end = mid - 1;
                }
                count.put(val , count.getOrDefault(val , 0L) + next - j + 1);
                j = next ;
            }
        for(int i = 0 ; i < q ;i ++)
            out.println(count.getOrDefault(Integer.parseInt(br.readLine()) , 0L));

        out.flush();

    }
    static class SparseTable
    {
        int N , K;
        int [][] st ;

        SparseTable(int [] a)
        {
            N = a.length ;
            K = 32 - Integer.numberOfLeadingZeros(N - 1) ;
            st = new int [K + 1][N + 1] ;
            for(int i = 0 ; i < N ; i++)
                st[0][i] = a[i] ;

            for(int i = 1 ; (1 << i) <= N ;i++)
                for(int j = 0 ; j + (1 << i) - 1 < N ; j++)
                {
                    st[i][j] = gcd(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
                }
        }
        int query(int l , int r)
        {
            if(l > r)return 0;
            int log = 31 - Integer.numberOfLeadingZeros(r - l + 1) ;
            return gcd(st[log][l] , st[log][r - (1 << log) + 1]);
        }
    }
}