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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use proconio::{
   fastout, input,
   marker::{Bytes, Isize1, Usize1},
};

#[fastout]
fn main() {
   input! {
      q: usize,
      lr: [(usize, usize); q]
   }
   let n = 200000;
   let mut prime = vec![true; n + 1];
   prime[0] = false;
   prime[1] = false;
   for i in 2..=n {
      if !prime[i] {
         continue;
      }
      let mut j = 2;
      while i * j <= n {
         prime[i * j] = false;
         j += 1;
      }
   }
   let mut bit = vec![0; n / 2 + 1];
   for i in 2..=n / 2 {
      if prime[i] && prime[(i + 1) / 2] {
         bit.add(i, 1);
      }
   }

   for &(l, r) in lr.iter() {
      println!("{}", bit.range(l, r + 1));
   }
}

use std::ops::{AddAssign, Sub};
trait BIT<T: Copy + Clone + Sub + AddAssign> {
   fn add(&mut self, idx: usize, w: T);
   fn sum(&self, idx: usize) -> T;
   fn range(&self, l: usize, r: usize) -> T;
}
impl<T: Copy + Clone + Sub<Output = T> + AddAssign> BIT<T> for [T] {
   /// let mut bit = vec![0; n+1];
   /// for (i, w) in 0..q {
   ///    bit.add(i, w);
   /// }
   fn add(&mut self, idx: usize, w: T) {
      let mut j = (idx + 1) as i64;
      while j < self.len() as i64 {
         self[j as usize] += w;
         j += j & -j;
      }
   }
   /// [0, r]
   fn sum(&self, idx: usize) -> T {
      let mut i = (idx + 1) as i64;
      let mut sum = self[0];
      while i != 0 {
         sum += self[i as usize];
         i -= i & -i;
      }
      sum
   }
   /// [l, r)
   fn range(&self, l: usize, r: usize) -> T {
      match (l, r) {
         (0, _) => self.sum(r - 1),
         _ => self.sum(r - 1) - self.sum(l - 1),
      }
   }
}