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:
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;
public class Main {
	public static void main (String[] args) throws IOException{
		BufferedReader sc=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw=new PrintWriter(System.out);
	    int n=Integer.parseInt(sc.readLine().trim());
	    long a[]=new long[n];
	    String s[]=sc.readLine().trim().split(" ");
	    for(int i=0;i<n;i++)a[i]=Long.parseLong(s[i]);
	    HashMap<Long,Long> curr=new HashMap<Long,Long>();
	    HashMap<Long,Long> prev=new HashMap<Long,Long>();
	    HashMap<Long,Long> ans=new HashMap<Long,Long>();
	    
	    for(int i=0;i<n;i++){
	        curr.clear();
	        curr.put(a[i],curr.getOrDefault(a[i],0l)+1l);
	        ans.put(a[i],ans.getOrDefault(a[i],0l)+1l);
	        for(long k:prev.keySet()){
	            long gcd=gcd(a[i],k);
	            long prev_gcd_cnt=prev.get(k);
	            ans.put(gcd,ans.getOrDefault(gcd,0l)+prev_gcd_cnt);
	            curr.put(gcd,curr.getOrDefault(gcd,0l)+prev_gcd_cnt);
	        }
	        prev.clear();
	        prev.putAll(curr);
	    }
	    for(int q=Integer.parseInt(sc.readLine().trim());q>0;q--){
	        long x=Long.parseLong(sc.readLine().trim());
	        if(!ans.containsKey(x)){pw.println(0);pw.flush();}
	        else {pw.println(ans.get(x));pw.flush();}
	    }
	    sc.close();
	    pw.close();
	}
	public static long gcd(long a,long b){
	    if(b!=0)return gcd(b,a%b);
	    return a;
	}
}