#D10470. CGCDSSQ
CGCDSSQ
CGCDSSQ
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
inputFormat
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).
outputFormat
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
样例
7
10 20 3 15 1000 60 16
10
1
2
3
4
5
6
10
20
60
1000
14
0
2
2
2
0
2
2
1
1