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 (2.4.0) (judge verdict: Accepted)

def p_prime(n): 
    prime = [2]
    for i in range(3,n+1):
        flag = 0
        for j in prime:
            if i%j == 0:
                flag = 1
                break
            if i**0.5 < j:
                break
        if flag == 0:
            prime.append(i)
    return prime

def main():
    import sys
    input = sys.stdin.readline
    
    Q = int(input())
    prime = p_prime(10**5)
    isprime = {}
    for i in prime:
        isprime[i] = 1
    A = [0]*(10**5+1)
    for i in range(1,10**5+1):
        if i in prime and (i+1)//2 in prime:
            A[i] = 1
    for i in range(1,10**5+1):
        A[i] += A[i-1]
    
    for i in range(Q):
        L,R = map(int,input().split())
        print(A[R]-A[L-1])
    
    
    
main()