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)

#[allow(unused_macros)]
macro_rules! parse_line {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            iter.next().unwrap().parse::<$t>().unwrap()
        }
    );

    ( $( $t:ty), +) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ( $(iter.next().unwrap().parse::<$t>().unwrap()),* )
        }
    );
}

#[allow(unused_macros)]
macro_rules! read_line {
    () => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            line.pop();
            line
        }
    )
}

#[allow(unused_macros)]
macro_rules! parse_vec {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let iter = line.split_whitespace();
            iter.map(|v| v.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    )
}

fn solve (lqs: Vec<(u64, u64)>) -> Vec<u64> {
    let mut pmap = vec![true; 100001];
    pmap[0] = false;
    pmap[1] = false;

    for i in 0..100001 {
        if pmap[i] == false { continue; }

        for k in 2.. {
            if i*k > 100000 { break; }
            pmap[i*k] = false;
        }
    }

    let mut nmap = vec![0u64; 100001];
    let mut acc = 0;
    for i in 0..100001 {
        acc += if pmap[i] && pmap[(i+1)/2] {1} else {0};
        nmap[i] = acc;
    }

    lqs.iter().map(|&(l, q)| nmap[q as usize] - nmap[l as usize] + {if pmap[l as usize] && pmap[(l as usize +1)/2] {1} else {0}}).collect()
}

fn main() {
    let t = parse_line!(usize);


    let ans = (0..t).map(|_| parse_line!(u64, u64)).collect();

    for a in solve(ans) {
        println!("{}", a);
    }
}

#[test]
fn solve_test() {
    assert_eq!(solve(vec![(3,7)]), vec![2]);
    assert_eq!(solve(vec![(13,13), (7,11), (2017,2017)]), vec![1,0,1]);
}