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 (7.3.0) (judge verdict: Accepted)

import math
from math import gcd
INF = float("inf")

import sys
input=sys.stdin.readline
import itertools
from collections import Counter

def main():
    def primes(n):
        is_prime = [True] * (n + 1)
        is_prime[0], is_prime[1] = False, 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 for i in range(n + 1) if is_prime[i]], is_prime

    q = int(input())
    primes_num, is_primes = primes(10**5+5)
    sums = []
    cnt = 0

    for i in range(0, 10**5+4):
        if i%2!=0:
            a = (i+1)//2
            if is_primes[i] and is_primes[a]:
                cnt += 1
        sums.append(cnt)

    for i in range(q):
        l,r = map(int, input().split())
        print(sums[r] - sums[l-1])

if __name__=="__main__":
    main()