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};

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

    let mut prime_flag = vec![true; 100_001];
    for i in 2..100_001 {
        if !prime_flag[i] { continue; }
        for j in 2..=100_000/i {
            prime_flag[j*i] = false;
        }
    }
    prime_flag[0] = false;
    prime_flag[1] = false;

    let primes: Vec<usize> = prime_flag.iter().enumerate()
        .filter_map(|(i, &v)| if v { Some(i) } else { None }).collect();
    let mut cnt: Vec<usize> = vec![0; 100_000];
    for &p in &primes {
        let idx = 2*p-1;
        if idx < 100_001 && prime_flag[idx] {
            for i in idx..100_000 { cnt[i] += 1; }
        }
    }
    for &(l, r) in &arr {
        let ans = cnt[r] - cnt[l-1];
        println!("{}", ans);
    }
}