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)

#!/usr/bin/env python3
import sys


def solve(Q: int, l: "List[int]", r: "List[int]"):
    # 10^5までの素数を予め計算しておく。
    INF = 100100
    is_prime = get_prime_numbers_array(INF)
    for i in range(Q):
        cnt = 0
        for j in range(l[i], r[i] + 1):
            if j % 2 == 0:
                continue
            if (is_prime[j] and is_prime[int((j+1)/2)]):
                cnt += 1
        print(cnt)
    return

def get_prime_numbers_array(n):
    """エラトステネスのふるいを用いてnまでの素数判定を行うための配列を返す

    Args:
        n ([int]): nまでの素数判定を行う
    """
    N = n + 1
    is_prime = [1] * N
    is_prime[0] = is_prime[1] = 0
    for i in range(2, N):
        if not is_prime[i]:
            continue
        for j in range(i * 2, N, i):
            is_prime[j] = 0
    return is_prime


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    Q = int(next(tokens))  # type: int
    l = [int()] * (Q)  # type: "List[int]"
    r = [int()] * (Q)  # type: "List[int]"
    for i in range(Q):
        l[i] = int(next(tokens))
        r[i] = int(next(tokens))
    solve(Q, l, r)

if __name__ == '__main__':
    main()