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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
input = sys.stdin.readline
Q = int(input())

LR = []
for _ in range(Q):
    l,r = map(int, input().split())
    LR.append((l,r))
    
def primes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return {i: True for i in range(n + 1) if is_prime[i]}

prime_dict = primes(10**5)
like_2017 = []
for n in prime_dict:
    if (n+1)//2 in prime_dict:
        like_2017.append(n)
#print(like_2017)
like_2017 = list(sorted(like_2017))


from bisect import bisect_left, bisect_right

def index(a, x):
    'Locate the leftmost value exactly equal to x'
    i = bisect_left(a, x)
    return i

for l, r in LR:
    if l == r:
        if l in like_2017:
            print(1)
        else:
            print(0)
    else:
        l_idx = index(like_2017, l)
        r_idx = index(like_2017, r)
        if r in like_2017:
            r_idx += 1
        print(r_idx-l_idx)