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 (3.4.3) (judge verdict: Time Limit Exceeded)

import math

is_prime_list = {
    1: False
}

def is_prime(x):
    global primes

    if x in is_prime_list:
        return is_prime_list[x]

    for divisor in range(2, math.floor(math.sqrt(x))+1):
        if x % divisor == 0:
            is_prime_list[x] = False
            return is_prime_list[x]

    is_prime_list[x] = True
    return is_prime_list[x]

def main():
    global primes

    Q = int(input())

    query_list = []
    for i in range(Q):
        query_list.append([int(_) for _ in input().split()])

    for query in query_list:
        begin = query[0]
        end   = query[1] + 1

        like_2017 = 0
        for target in range(begin, end, 2):
            if is_prime(target) and is_prime((target + 1) // 2):
                like_2017 += 1

        print(like_2017)

main()