codeforces 385 c

Posted 2020-07-02 行尸走肉

Description

Recently, the bear started studying data structures and faced the following problem.

You are given a sequence of integers x₁, x₂, ..., x_n of length n and m queries, each of them is characterized by two integers l_i, r_i. Let‘s introduce f(p) to represent the number of such indexes k, that x_k is divisible by p. The answer to the query l_i, r_i is the sum: , where S(l_i, r_i) is a set of prime numbers from segment [l_i, r_i] (both borders are included in the segment).

Help the bear cope with the problem.

Input

The first line contains integer n(1 ≤ n ≤ 10⁶). The second line contains n integers x₁, x₂, ..., x_n(2 ≤ x_i ≤ 10⁷). The numbers are not necessarily distinct.

The third line contains integer m(1 ≤ m ≤ 50000). Each of the following m lines contains a pair of space-separated integers, l_i andr_i(2 ≤ l_i ≤ r_i ≤ 2·10⁹) — the numbers that characterize the current query.

Output

Print m integers — the answers to the queries on the order the queries appear in the input.

Sample Input

Input

6
5 5 7 10 14 15
3
2 11
3 12
4 4

Output

9
7
0

Input

7
2 3 5 7 11 4 8
2
8 10
2 123

Output

0
7

Hint

Consider the first sample. Overall, the first sample has 3 queries.

1. The first query l = 2, r = 11 comes. You need to count f(2) + f(3) + f(5) + f(7) + f(11) = 2 + 1 + 4 + 2 + 0 = 9.
2. The second query comes l = 3, r = 12. You need to count f(3) + f(5) + f(7) + f(11) = 1 + 4 + 2 + 0 = 7.
3. The third query comes l = 4, r = 4. As this interval has no prime numbers, then the sum equals 0.

 

 

 

查找一个区间内的，一系列数中，包含素数的个数。基本思路是：把这一系列数字中，到最大的数字Max之前是数字包含是素数的个数统计出来，然后用统计的个数区间的右端值减掉左端值减一，sum[right]-sum[left-1].因为求解的素数是包括最左端的这一个的，所以左端值应该减掉一。

比如说 对这样一个序列：5 6 7 ，则sum[1]=0;sum[2]=1;sum[3]=1;sum[4]=1;sum[5]=1;sum[6]=3;sum[7]=4; 若le=2，ri=7；ans=sum[7]-sum[1]=4;