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).
给出一个长度为n(1<=n<=105)的序列和q(1<=q<=3*105)个询问,每个询问输出一行,询问gcd(al,al+1,...,ar)=x的 (l,r) 的对数.
Examples
Output
14
0
2
2
2
0
2
2
1
1