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: Time Limit Exceeded)

use std::io;
//use std::collections::HashMap;
//use std::collections::BinaryHeap;
//use std::collections::HashSet;
//use std::mem; // mem::swap(&mut x,&mut y);
// use std::cmp; // cmp::max,cmp::min

// Rustメモ: https://hackmd.io/i0lQY1OKTDW1t66TECOmiw?both

#[allow(dead_code)]
fn read_line() -> String{
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

#[allow(dead_code)]
fn read_charvec() -> Vec<char>{
    read_line().chars().collect()
}

#[allow(dead_code)]
fn read_ints() -> Vec<i64>{
    let s = read_line();
    let split:Vec<&str> = s.split(" ").collect();
    split.iter().map(|&x| x.to_string().parse().unwrap()).collect()
}

#[allow(dead_code)]
fn read_int() -> i64{
    read_ints()[0]
}

#[allow(dead_code)]
fn reverse(s: &String) -> String{
    s.chars().rev().collect::<String>()
}

#[allow(dead_code)]
fn read_lines(n:i64) -> Vec<String>{
    let mut xs = Vec::new();

    for _i in 0..n{
        xs.push(read_line());
    }

    xs
}

#[allow(dead_code)]
fn read_ints2(n:i64) -> Vec<i64>{
    read_lines(n).iter().map(|x| x.parse().unwrap()).collect()
}

////////////////////////////////////////////////

fn prime_board(n:i64)->Vec<bool>{
    let mut ret = vec![true;(n+1) as usize];

    ret[0]=false;
    ret[1]=false;
    for i in 2..(n+1){
        if ret[i as usize] {
            for j in 2..(n/i){
                ret[(i*j) as usize]=false;
            }
        }
    }

    ret
}

fn main(){
    let n : usize = 100009;
    let board = prime_board(n as i64);
    let mut total = 0;
    let mut arr = vec![0 as i32;n/2];

    for i in 0..n/2{
        let m1 = i * 2 + 1;
        let m2 = (m1+1)/2;
        let flag = board[m1] && board[m2];

        arr[i] = total;

        if flag {
            total += 1;
        }
    }

    let q = read_int();

    for _ in 0..q{
        let input = read_ints();
        let (l,r) = (input[0],input[1]);

        let l_idx = (l-1)/2;
        let r_idx = (r-1)/2;

        let ans0 = arr[r_idx as usize+1]-arr[l_idx as usize];
        println!("{}",ans0);

        let mut ans = 0;
        for x in l..r+1{
            let m1 = x;
            let m2 = (x+1)/2;
            let flag = (x % 2 == 1) && board[m1 as usize] && board[m2 as usize];

            if flag{
                ans+=1;
            }
        }

        if ans0 != ans{
            panic!("");
            // println!("l={}",l);
            // println!("r={}",r);
            // println!("ans={}",ans);
        }
    }
}