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};

const MAX: usize = 100_000;

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

    let is_prime = sieve(MAX);

    let mut cumsum = vec![0; MAX+1];

    for i in 1..=MAX {
        cumsum[i] = cumsum[i-1];
        if is_prime[i] && is_prime[(i+1)/2] {
            cumsum[i] += 1;
        }
    }

    for &(l, r) in lr.iter() {
        let ans = cumsum[r] - cumsum[l-1];
        println!("{}", ans);
    }
}

fn sieve(n: usize) -> Vec<bool> {
    let mut is_prime = vec![true; n + 1];
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..=n {
        if !is_prime[i] {
            continue;
        }
        for j in 2..=n/i {
            is_prime[i * j] = false;
        }
    }
    is_prime
}