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: Accepted)

#!/usr/bin/env python3

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

Q = int(input())

L = []
R = []
for i in range(Q):
    l, r = map(int, input().split())
    L.append(l)
    R.append(r)


def primes(max_r):
    is_prime = [True] * (max_r + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(max_r**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, max_r + 1, i):
            is_prime[j] = False
    return [i for i in range(max_r + 1) if is_prime[i] and is_prime[(i+1)//2]]


max_r = max(R)
ps = primes(max_r)

S = [0]
for i in range(1, max_r+1):
    if i in ps:
        S.append(S[i-1]+1)
    else:
        S.append(S[i-1])


for i in range(Q):
    print(S[R[i]] - S[L[i]-1])