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:
import sys
from collections import defaultdict
from math import gcd, sqrt

MAX = pow(10, 5)
# stdin = open("testdata.txt", "r")
ip = sys.stdin

n = int(ip.readline())

a = list(map(int, ip.readline().split()))
gcd_count = defaultdict(int)

main_gcd = defaultdict(int)

main_gcd[a[0]] = 1
gcd_count[a[0]] = 1
for i in range(1, n):
	ele = a[i]
	temp_gcd = defaultdict(int)
	temp_gcd[ele] = 1
	gcd_count[ele] += 1
	for k, v in main_gcd.items():
		temp = gcd(ele, k)
		temp_gcd[temp] += v
		gcd_count[temp] += v
	main_gcd = temp_gcd

q = int(ip.readline())
for _ in range(q):
	k = int(ip.readline())
	print(gcd_count[k])