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::io::{stdin, Read, StdinLock};
use std::str::FromStr;

#[allow(dead_code)]
struct Scanner<'a> {
    cin: StdinLock<'a>,
}
#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn input<T: FromStr>(&mut self) -> T {
        self.read().unwrap()
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let q: isize = sc.input();

    let max_n: isize = 1e5 as isize;
    let is_prime = get_primes(max_n);
    let mut cnt = vec![0; max_n as usize + 1];

    let mut i = 3;
    while i <= max_n as usize {
        if is_prime[i] && is_prime[(i + 1) / 2] { cnt[i] += 1; }
        i +=2;
    }
    for i in 0..max_n as usize {
        cnt[i + 1] += cnt[i];
    }
    for _ in 0..q {
        let (l, r): (usize, usize) = (sc.input(), sc.input());
        println!("{}", cnt[r] - cnt[l - 1]);
    }
}

fn get_primes(n: isize) -> Vec<bool> {
    let mut is_prime = vec![true; n as usize + 1];

    let mut i = 2;
    while i * i <= n {
        if is_prime[i as usize] {
            let mut j = i * i;
            while j <= n {
                is_prime[j as usize] = false;
                j += i;
            }
        }
        i += 1;
    }
    is_prime
}