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 get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn readln<T>() -> T
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().parse().unwrap()
}

fn main() {
    let q = readln();
    let mut lrs: Vec<(usize, usize)> = vec![];

    for _ in 0..q {
        let lr = reads();

        lrs.push((lr[0], lr[1]));
    }

    let m = 100000;
    let mut primes = vec![true; m + 1];
    primes[0] = false;
    primes[1] = false;

    sieve(&mut primes);

    let mut ps = vec![];
    count(&mut ps, &primes);

    for (l, r) in lrs {/*
        println!("l: {}, c: {}", l, ps[l / 2]);
        println!("r: {}, c: {}", r, ps[r / 2]);*/
        println!("{}", ps[r / 2] - ps[l / 2] +
        if 3 > l || ps[l / 2] == ps[l / 2 - 1] {
            0
        }
        else {
            1
        });
    }
}

fn sieve(primes: &mut Vec<bool>) {
    let n = (primes.len() as f64).sqrt().trunc() as usize;
    for i in 2..n {
        for j in (i + 1)..primes.len() {
            if primes[j] && j % i == 0 {
                primes[j] = false;
            }
        }
    }
}

fn count(ps: &mut Vec<u64>, primes: &Vec<bool>) {
    ps.push(0);
    let mut c = 0;
    for i in 3..primes.len() {
        if i % 2 == 0 {
            continue;
        }

        if primes[i] && primes[(i + 1) / 2] {
            c += 1;
        }
        ps.push(c);
    }
}