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 PYTHON3):

Solution:
from sys import stdin
n = int(stdin.readline())
a = [int(x) for x in stdin.readline().split()]

q = int(stdin.readline())

def gcd(a,b):
    while a != 0:
        a,b = b%a, a
    return b
    
totals = {}
new = {}

for x in a[::-1]:
    old = new
    new = {}
    for y in old:
        g = gcd(x,y)
        if g in new:
            new[g] += old[y]
        else:
            new[g] = old[y]
    if x in new:
        new[x] += 1
    else:
        new[x] = 1
    for y in new:
        if y in totals:
            totals[y] += new[y]
        else:
            totals[y] = new[y]
    
            


for x in range(q):
    c = int(stdin.readline())
    if c in totals:
        print(totals[c])
    else:
        print(0)