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 Rust (1.15.1) (judge verdict: Accepted)

const MAX: usize = 100000;

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let (_, is_prime) = sieve(MAX);
    let mut like_number = vec![false;MAX+1];
    for i in 0..MAX+1 {
        if i % 2 == 1 {
            like_number[i] = is_prime[i] && is_prime[(i+1)/2];
        }
    }
    let mut sum = vec![0;MAX+2];
    for i in 0..MAX {
        sum[i+1] = sum[i] + (if like_number[i] {1} else {0});
    }

    let q: usize = iter.next().unwrap().parse().unwrap();
    for _ in 0..q {
        let l: usize = iter.next().unwrap().parse().unwrap();
        let r: usize = iter.next().unwrap().parse().unwrap();
        println!("{}", sum[r+1] - sum[l]);
    }
}

#[doc = " return: (primes, is_prime)"]
#[allow(dead_code)]
fn sieve(n: usize) -> (Vec<usize>, Vec<bool>) {
    let mut primes = vec![];
    let mut is_prime = vec![true; n + 1];
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..n + 1 {
        if is_prime[i] {
            primes.push(i);
            for j in (2..).map(|j| j * i).take_while(|&j| j <= n) {
                is_prime[j] = false;
            }
        }
    }
    (primes, is_prime)
}