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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;

pub fn primes(n: usize) -> Vec<u64> {
  if n < 2 {
    return Vec::new();
  }
  let mut is_prime = vec![true; n + 1];
  is_prime[0] = false;
  is_prime[1] = false;
  let mut res = Vec::new();
  for i in 2..=n {
    if is_prime[i] {
      res.push(i as u64);
      let mut j = 2 * i;
      while j <= n {
        is_prime[j] = false;
        j += i;
      }
    }
  }
  res
}

fn main() {
  input! {
    q: usize,
    queries: [(usize, usize); q]
  };

  let n = 100_000;
  let primes = primes(n)
    .into_iter()
    .collect::<std::collections::HashSet<_>>();
  let mut cusum = vec![0; n + 1];
  for i in 2..=n {
    if i % 2 == 0 {
      cusum[i] = cusum[i - 1];
    } else {
      if primes.contains(&(i as u64)) && primes.contains(&(((i + 1) / 2) as u64)) {
        cusum[i] = cusum[i - 1] + 1;
      } else {
        cusum[i] = cusum[i - 1];
      };
    }
  }
  for (l, r) in queries {
    println!("{}", cusum[r] - cusum[l - 1]);
  }
}
*/

fn main() {
    let exe = "/tmp/bin24A2EAB2";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";