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 (1.15.1) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

use std::collections::HashSet;

fn divisors(N: i64) -> HashSet<i64> {
    let mut ds = vec![];
    let mut d = 1;
    while d * d <= N {
        if N % d == 0 {
            ds.push(d);
            ds.push(N / d);
        }
        d += 1;
    }
    let uniq: HashSet<i64> = ds.into_iter().collect();
    uniq
}

fn main() {
    let q: usize = read();
    let mut a: Vec<(usize, usize)> = vec![];
    for _ in 0..q {
        let l: usize = read();
        let r: usize = read();
        a.push((l, r));
    }

    let mut current = 0;
    let maxnum = 100_005;
    let mut memo = vec![0; maxnum];
    for i in 0..maxnum - 1 {
        let a = divisors(i as i64);
        let b = divisors(((i + 1) / 2) as i64);

        if a.len() == 2 && b.len() == 2 {
            current += 1;
        }

        memo[i] = current;
    }

    for i in 0..q {
        let ai = a[i];
        println!("{}", memo[ai.1] - memo[ai.0 - 1])
    }
}