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)

#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::str::*;
#[allow(unused_imports)]
use std::collections::*;

#[allow(dead_code)]
fn read<T: FromStr>(s: &mut StdinLock) -> T {
    let s = s.by_ref().bytes().map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok().unwrap()
}

#[allow(unused_macros)]
macro_rules! p {
    ($x:expr) 
    => (println!("{}", $x));
    ($x:expr, $y:expr)
    => (println!("{} {}", $x, $y));
    ($x:expr, $y:expr, $z:expr) 
    => (println!("{} {} {}", $x, $y, $z));
}

#[allow(unused_macros)]
macro_rules! pl {
    ($x:expr) 
    => (println!("{}", $x));
    ($x:expr, $y:expr)
    => (println!("{}\n{}", $x, $y));
    ($x:expr, $y:expr, $z:expr) 
    => (println!("{}\n{}\n{}", $x, $y, $z));
}

fn main() {
    let s = stdin();
    let mut s = s.lock();
    let S = &mut s;

    for _ in 0..1 {
        let q: usize = read(S);
        let is_prime: Vec<_> = (0..100010u64).map(|i| {
            if i <= 1 {
                false
            } else {
                let mut p = true;
                for j in 2..i {
                    if j * j > i { break; }
                    if i % j == 0 {
                        p = false;
                        break;
                    }
                }
                p
            }
        }).collect();
        // println!("{:?}", &is_prime[0..10]);

        let mut cnt = vec![0u32; 100010];
        for i in 1..100005 {
            let ok = i % 2 != 0 && is_prime[i] && is_prime[(i+1)/2];
            cnt[i+1] = if ok {
                cnt[i] + 1
            } else {
                cnt[i]
            }
        }

        for _ in 0..q {
            let l: usize = read(S);
            let r: usize = read(S);
            p!(cnt[r+1] - cnt[l]);
        }
    }
}