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_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]



#[allow(unused_macros)]
macro_rules! invec {
    ( $ t : ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s
                .trim()
                .split_whitespace()
                .map(|s| s.parse::<$t>().unwrap())
                .collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }};
}

#[allow(unused_macros)]
macro_rules! get {
      ($t:ty) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.trim().parse::<$t>().unwrap()
          }
      };
      ($($t:ty),*) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              let mut iter = line.split_whitespace();
              (
                  $(iter.next().unwrap().parse::<$t>().unwrap(),)*
              )
          }
      };
      ($t:ty; $n:expr) => {
          (0..$n).map(|_|
              get!($t)
          ).collect::<Vec<_>>()
      };
      ($($t:ty),*; $n:expr) => {
          (0..$n).map(|_|
              get!($($t),*)
          ).collect::<Vec<_>>()
      };
      ($t:ty ;;) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.split_whitespace()
                  .map(|t| t.parse::<$t>().unwrap())
                  .collect::<Vec<_>>()
          }
      };
      ($t:ty ;; $n:expr) => {
          (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
      };
}

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}


#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    ($arg:expr) => (println!("{:?}",$arg));
}


#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}


use std::cmp;
use std::collections::HashMap;


#[allow(dead_code)]
static INF_I64 :i64 = 9223372036854775807;
#[allow(dead_code)]
static INF_I32 : i32 = 2147483647;
#[allow(dead_code)]
static INF_USIZE : usize = 18446744073709551615;



use std::ops::{ Add, Sub , Div , Mul };



// #[snippet = "ComplexNum"]
pub trait Monoid {
    type T: Clone;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
}



// #[snippet = "ComplexNum"]
pub struct SegTree<M:Monoid>{
    n :usize,
    data : Vec<M::T>,
}

impl<M:Monoid> SegTree<M>{
    pub fn new (n_ : usize) -> SegTree<M>{
        let mut n = 1 as usize;
        while(n< n_){
            n *=2;
        }
        SegTree{
            n:n,
            data:vec![M::id().clone();(2*n)],
        }

    }

    #[macro_use]
    pub fn update(&mut self , index : usize , v : M::T){
        let mut k = index + self.n-1;
        self.data[k] = v;
        while (k>0){
            k = (k-1)/2;
            self.data[k] = M::op(&self.data[2*k+1] , &self.data[2*k+2]);
        }

    }

    pub fn query(&mut self ,l:usize,r:usize)->M::T{
        
        let mut l = l+self.n-1;
        let mut r = r+self.n-1;
        if(l==r){
            return M::op(&M::id().clone() ,&self.data[l])
        }
        
        let mut ret = M::id().clone();
        while(l<r){
            if(l%2 == 0){
            //if((l&1_usize) == 0_usize){
                ret = M::op(&ret , &self.data[l]);
                
            }
            if(r%2 == 0){
            //if((r&1_usize) == 0_usize){
                ret = M::op(&ret , &self.data[r-1]);
                
            }

            l = l/2;
            r = (r-1)/2;

        }

        return ret;

    }

}


struct SUM;
impl Monoid for SUM {
    type T = u64;
    fn id() -> Self::T {
        0
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        *a + *b
    }
}


fn main() {

    input! { 
       n: usize,
       q : [(u32,u32);n],
    }

    let mut ans = 0;
    let len = 10_usize.pow(5);
    let mut primes = vec![false;len];
    primes[0] = true;
    primes[1] = true;

    for i in 2..len{
        if primes[i] == true {continue}
        else{
            let mut j = i+i;
            while j < len{
                primes[j] = true;
                j+=i;
            }
        }
    }

    let mut seg: SegTree<SUM> = SegTree::new(len);
    for i in 0..len{
        if(primes[i] == false){
            let j = (i+1)/2;
            //let tmp = if primes[j] == false { 1} else {0};
            if primes[j] == false{
                seg.update(i,1);
            }
            
        }
    }
    
    for item in &q{
        let ans = seg.query(item.0 as usize,(item.1 +1) as usize);
        println!("{}",ans);

    }


    


}