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D. CGCDSSQ
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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