Problem:
Score : 400 points

Problem Statement

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

1≤Q≤10^5

1≤l_i≤r_i≤10^5

l_i and r_i are odd.

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q
l_1 r_1
:
l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

6
1 53
13 91
37 55
19 51
73 91
13 49

Sample Output 3

4
4
1
1
1
2

Solution in PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

def prime_eratosthenes(n):
    prime_list = []
    num_list=[]
    for i in range(2, n+1):
        if i not in num_list:
            prime_list.append(i)
            for j in range(i*i, n+1, i):
                num_list.append(j)
    return prime_list

ls = prime_eratosthenes(100000)
ls2 = [i+1 for i in range(100000)]
Q = int(input())
for i in range(Q):
    l, r = map(int, input().split())
    ans = 0
    for j in range(l-1, r):
        if (ls2[j] in ls) and (ls2[j+1]//2 in ls):
            ans += 1
    print(ans)