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

You are given a sequence of integers *x*<sub class="lower-index">1</sub>, *x*<sub class="lower-index">2</sub>, ..., *x*<sub class="lower-index">*n*</sub> of length *n* and *m* queries, each of them is characterized by two integers *l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub>. Let's introduce *f*(*p*) to represent the number of such indexes *k*, that *x*<sub class="lower-index">*k*</sub> is divisible by *p*. The answer to the query *l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub> is the sum: <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/5e448f6c1a0e40843cecdbbeb95970464626032f.png" style="max-width: 100.0%;max-height: 100.0%;"/>, where *S*(*l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub>) is a set of prime numbers from segment [*l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub>] (both borders are included in the segment).

Help the bear cope with the problem.
The first line contains integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">6</sup>). The second line contains *n* integers *x*<sub class="lower-index">1</sub>, *x*<sub class="lower-index">2</sub>, ..., *x*<sub class="lower-index">*n*</sub> (2 ≤ *x*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">7</sup>). 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*<sub class="lower-index">*i*</sub> and *r*<sub class="lower-index">*i*</sub> (2 ≤ *l*<sub class="lower-index">*i*</sub> ≤ *r*<sub class="lower-index">*i*</sub> ≤ 2·10<sup class="upper-index">9</sup>) — the numbers that characterize the current query.
import bisect

n = int(input())
a = [int(i) for i in input().split()]
primes = set()
count_primes = {}
for i in range(n):
    for j in range(2, int(a[i] ** 0.5) + 1):
        if a[i] % j == 0:
            if j in count_primes.keys():
                count_primes[j] += 1
            else:
                count_primes[j] = 1
            while a[i] % j == 0:
                a[i] = a[i] // j
            primes.add(j)
    if a[i] != 1:
        primes.add(a[i])
        if a[i] in count_primes.keys():
            count_primes[a[i]] += 1
        else:
            count_primes[a[i]] = 1

primes = list(primes)
primes.sort()
pref = [0] * (len(primes) + 1)
for i in range(1, len(primes) + 1):
    pref[i] = pref[i - 1] + count_primes[primes[i - 1]]
m = int(input())
for i in range(m):
    l, r = map(int, input().split())
    left_index = bisect.bisect_left(primes, l)
    right_index = bisect.bisect_left(primes, r)
    print(pref[right_index] - pref[left_index])
