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)

#![allow(non_snake_case,unused_imports,dead_code)]
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;
use std::collections::{HashMap,HashSet,VecDeque,BinaryHeap};
use std::cmp::Ordering;

use proconio::input;
use proconio::marker::{Chars,Usize1,Isize1};

fn comp_f64(a: &f64, b: &f64) -> Ordering {
    if a < b {
        return Ordering::Less;
    } else if a > b {
        return Ordering::Greater;
    }
    Ordering::Equal
}

fn main() {
    input!{
        Q:usize,
        LR:[(usize,usize);Q],
    }

    let INF = 100_010;
    let primes = get_primes(INF);
    let mut N = vec![0;INF];
    for &i in primes.iter(){
        let j = (i+1)/2;
        if primes.contains(&j){
            N[i] = 1;
        }
    }
    for i in 1..INF{
        N[i] += N[i-1];
    }
    for &(l,r) in &LR{
        println!("{}",N[r]-N[l-1]);
    }
}

fn get_primes(n:usize)->HashSet<usize>{
    let mut ret = HashSet::new();
    let mut checked = vec![false;n+1];
    for i in 2..=n{
        if checked[i] {continue;}
        ret.insert(i);
        for j in 1..=(n/i){
            checked[i*j] = true;
        }
    }
    ret
}