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)

import sys

import numpy as np

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline


def searchPrimeNumber(N):
    N = N + 1
    is_prime = np.ones(N, dtype=bool)
    is_prime[:2] = 0
    N_max = int(np.sqrt(N))
    for j in range(2, N_max+1):
        if (is_prime[j]):
            is_prime[j*j::j] = False
    prime = np.arange(N)[is_prime]
    return prime


def main():
    Q = int(readline())
    m = map(int, read().split())
    LR = list(zip(m, m))
    A = searchPrimeNumber(10**5)
    B = np.zeros(10**5+3, dtype=np.int32)  # Bはゼロ始まり
    for a in A:
        if (a + 1) / 2 in A:
            B[a+1:] += 1  # like 2017の数より１つ大きい数から1増やす

    for l, r in LR:
        print(B[r+1] - B[l])


main()