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)

fn main() {
    proconio::input! {
        q: usize,
        lr: [(usize,usize);q],
    }
    let m=lr.iter().map(|lr|lr.1).max().unwrap()+1;
    let mut p=vec![true;m];
    p[0]=false;
    p[1]=false;
    for i in 2..m/2 {
        if p[i] {
            for p in p[i*2..].iter_mut().step_by(i) {
                *p=false;
            }
        }
    }
    let mut s=vec![0;m];
    for i in 2..m {
        s[i]=s[i-1]+if p[i]&&p[(i+1)/2] {1} else {0};
    }
    for (l,r) in lr {
        println!("{}",s[r]-s[l-1]);
    }
}