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: Accepted)

def gen_is_prime(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, n + 1):
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    # return [i for i in range(n + 1) if is_prime[i]]
    return is_prime


if __name__ == "__main__":
    max_n = 10 ** 5
    is_prime = gen_is_prime(max_n)

    is_like_2017 = [False] * (max_n + 1)
    for i in range(max_n + 1):
        if is_prime[i] and is_prime[(i + 1) // 2]:
            is_like_2017[i] = True

    sum_is_like_2017 = [0] * (max_n + 2)
    for i in range(max_n + 1):
        sum_is_like_2017[i + 1] = sum_is_like_2017[i] + is_like_2017[i]

    q = int(input())
    lr = [map(int, input().split()) for _ in range(q)]
    for l, r in lr:
        print(sum_is_like_2017[r + 1] - sum_is_like_2017[l])