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 math import gcd
from collections import defaultdict
from sys import stdin, stdout

##This method is better cause for all the same results we only calculate once
def main():
    GCD_count = defaultdict(int)
    GCD_map = defaultdict(int)
    arr_len = int(stdin.readline())
    arr = [int(x) for x in stdin.readline().split()]
    for start in range(arr_len):
        temp = defaultdict(int)
        GCD_count[arr[start]] += 1
        temp[arr[start]] += 1
        for gcd_now, occurence in GCD_map.items():
            res = gcd(gcd_now, arr[start])
            temp[res] += occurence
            GCD_count[res] += occurence
        GCD_map = temp
    num_queries = int(stdin.readline())
    for _ in range(num_queries):
        print(GCD_count[int(stdin.readline())])


main()