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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn get_primes() -> Vec<bool> {
    let n = 100000;
    let mut is_prime = vec![true; n];
    let mut primes = Vec::new();
    is_prime[0] = false;
    is_prime[1] = false;

    for i in 2..n {
        if is_prime[i] {
            primes.push(i);
            let mut j = 2 * i;
            while j < n {
                is_prime[j] = false;
                j += i;
            }
        }
    }
    is_prime
}

fn main() {
    let n: usize = read();
    let is_prime = get_primes();
    let mut accum_ans = vec![0; 100000];
    for i in 1..100000 {
        let mut temp = 0;
        if is_prime[i] && is_prime[(i + 1) / 2] {
            temp += 1;
        }
        accum_ans[i] = accum_ans[i - 1] + temp;
    }
    for _ in 0..n {
        let v: Vec<usize> = read_vec();
        let (l, r) = (v[0], v[1]);
        println!("{:?}", accum_ans[r] - accum_ans[l - 1]);
    }
}