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 (3.8.2) (judge verdict: Time Limit Exceeded)

from bisect import bisect_left as bsl

def main():
    with open(0) as f:
        Q = int(f.readline())
        Query = [tuple(map(int, line.split())) for line in f.readlines()]
    
    p_table = makePtable(10**5)
    p_set = set(p_table)
    Like2017 = [p for p in p_table if (p+1)//2 in p_set]
    database = [bsl(Like2017, i) for i in range(1,10**5+1)]

    for l,r in Query:
        print(database[r] - database[l-1])

def makePtable(N):
    table = list(range(2,N+1))
    result = []
    while len(table) != 0:
        p = table[0]
        result.append(p)
        table = [x for x in table[1:] if x % p != 0]
    return result

main()