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_001;

#[fastout]
fn main() {
    input! {
        q: i32,
        ranges: [(usize, usize); q],
    }

    let mut primes = [i8::from(-1); MAX];
    primes[0] = 0;
    primes[1] = 0;
    primes[2] = 1;
    primes[3] = 1;
    let mut cal = [0; MAX];
    
    for i in (3..MAX).step_by(2) {
        let res1 = i;
        let res2 = (i+1) / 2;

        if primes[res1] == -1 {
            primes[res1] = is_prime(res1);
        }

        if primes[res2] == -1 {
            primes[res2] = is_prime(res2);
        }

        if primes[res1] == 1 && primes[res2] == 1 {
            cal[i] = cal[i-2] + 1;
        } else {
            cal[i] = cal[i-2];
        }
    }

    for (l, r) in ranges {
        println!("{}", cal[r] - cal[l.saturating_sub(2)]);
    }
}

fn is_prime(n: usize) -> i8 {
    let max = (n as f32).sqrt();
    for i in 2..=max as usize {
        if n % i == 0 {
            return 0;
        }
    }

    return 1;
}