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)

use proconio::{input, fastout};
use std::collections::HashSet;

#[fastout]
fn main() {
    input! {
        q: usize,
        arr: [(usize, usize); q],
    }

    let mut primes = vec![2, 3, 5, 7, 11, 13, 17, 19];
    'a: for i in 10..49_999 {
        let c = i*2 + 1;
        for p in &primes {
            if c % p == 0 { continue 'a; }
        }
        primes.push(c);
    }

    let mut primeset: HashSet<usize> = HashSet::with_capacity(100_000);
    for &p in &primes { primeset.insert(p); }
    let mut cnt: Vec<usize> = vec![0; 100_000];
    for &p in &primes {
        let idx = 2*p-1;
        if primeset.contains(&idx) {
            for i in idx..100_000 { cnt[i] += 1; }
        }
    }
    for &(l, r) in &arr {
        let ans = cnt[r] - cnt[l-1];
        println!("{}", ans);
    }
}