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::cmp;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

fn make_memo(prime:[bool;100010]) -> [usize;100010] {
    let mut memo = [0; 100010];
    let size = 100010;
    for i in 2..size-5 {
        memo[i] = memo[i-1];
        if prime[i] && prime[(i+1)/2] {
            memo[i] += 1;
        }
    }
    memo
}



fn main() {
    let q = read_line().trim().parse::<usize>().expect("invalid");

    let mut prime = [true; 100010];
    let size = 100010;
    prime[0] = false;
    prime[1] = false;

    let mut i:u64 = 2;
    while i < size {
        if prime[i as usize] {
            let mut j:u64 = i;
            while i*j < size {
                let idx = (i*j) as usize;
                prime[idx] = false;
                j += 1;
            }
        }
        i += 1;
    }

    let memo = make_memo(prime);

    for _ in 0..q {
        let arr:Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let l = arr[0];
        let r = arr[1];


        println!("{}", memo[r]-memo[l-1]);
    }


}