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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

q = int(input())
l_lst = []
r_lst = []
for i in range(q):
  l, r = map(int, input().split())
  l_lst.append(l)
  r_lst.append(r)
max_ = max(r_lst)

primes = [2]
for L in range(3, max_+1, 2):
    for L2 in primes:
        if L % L2 == 0:
            break
    else:
        primes.append(L)
        
for l, r in zip(l_lst, r_lst):
  cnt = 0
  for j in range(l, r+1):
    if j in primes and (j+1)//2 in primes:
      cnt += 1
  print(cnt)