Description
Recently, the bear started studying data structures and faced the following problem.
You are given a sequence of integers x1, x2, ..., xn of length n and m queries, each of them is characterized by two integers li, ri. Let‘s introduce f(p) to represent the number of such indexes k, that xk is divisible by p. The answer to the query li, ri is the sum: , where S(li, ri) is a set of prime numbers from segment [li, ri] (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, ..., xn(2 ≤ xi ≤ 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, li andri(2 ≤ li ≤ ri ≤ 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
65 5 7 10 14 1532 113 124 4
Output
970
Input
72 3 5 7 11 4 828 102 123
Output
07
Hint
Consider the first sample. Overall, the first sample has 3 queries.
- 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.
- 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.
- 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;