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;

#[allow(dead_code)]
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")
}

const PRIME_SIZE: usize = 1000000;
#[allow(dead_code)]
struct Eratosthnes {
    n: usize,
    bprime: Vec<bool>,
    prime: Vec<usize>,
}
#[allow(dead_code)]
impl Eratosthnes {
    fn new(n: usize) -> Eratosthnes {
        let mut bprime = vec![true; PRIME_SIZE + 1];
        let mut prime = vec![];
        bprime[0] = false;
        bprime[1] = false;
        for i in 2..n+1 {
            if !bprime[i] { continue; }
            prime.push(i);
            if i * i > n { continue; }
            let mut j = i * i;
            while j <= n {
                bprime[j] = false;
                j += i;
            }
        }
        Eratosthnes {
            n: n,
            bprime: bprime,
            prime: prime,
        }
    }
}

fn main() {
    let n = 1e+5 as usize + 10;
    let era = Eratosthnes::new(n as usize);
    let mut sums = vec![0; n];
    for i in 1..n {
        if era.bprime[i] && era.bprime[(i + 1) / 2] { sums[i] += 1; }
        sums[i] += sums[i - 1];
    }
    let q: usize = read();
    for _ in 0..q {
        let l: usize = read();
        let r: usize = read();
        println!("{}", sums[r] - sums[l - 1]);
    }
}