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)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

fn is_prime(n: usize) -> bool{

    for div in 2..(n as f64).sqrt().ceil() as usize + 1{
        if n%div == 0{
            return false;
        }
    }

    true
}

fn main(){
    let q = read_as_vec::<usize>()[0];
    let n = 100000;
    let mut v = vec![false;n];
    let mut primes = vec![false;n];
    primes[2] = true;
    for i in 1..n/2{
        primes[i*2+1] = is_prime(i*2+1);
        v[i*2+1] = primes[i*2+1] && primes[i+1];

    }
    let mut acc_v = vec![0;n+1];
    let mut acc = 0;
    for i in 1..n{
        if v[i]{
            acc += 1;
        }
        acc_v[i] = acc;
    }

    for _ in 0..q{
        let line = read_as_vec::<usize>();
        let (l, r) = (line[0], line[1]);

        println!("{}", acc_v[r] - acc_v[l-1]);
    }
}