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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let 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)*}
    };
}

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

pub struct Sieve {
    primes: Vec<u64>,
    tbl: Vec<u64>,
}
impl Sieve {
    pub fn new(n: u64) -> Sieve {
        let sz: usize = (n + 1) as usize;
        let mut primes = Vec::new();
        let mut tbl = vec![0; sz];
        tbl[0] = 0;
        tbl[1] = 0;
        for i in 2..sz {
            if tbl[i] != 0 {
                continue;
            }
            primes.push(i as u64);
            tbl[i] = i as u64;
            let mut j = i * i;
            while j < sz {
                if tbl[j] == 0 {
                    tbl[j] = i as u64;
                }
                j += i;
            }
        }
        Sieve {
            primes: primes,
            tbl: tbl,
        }
    }
    pub fn primes(&self) -> &Vec<u64> {
        &self.primes
    }
    pub fn is_prime(&self, x: u64) -> bool {
        x > 1 && self.tbl[x as usize] == x
    }
    pub fn factorization(&self, x: u64) -> Vec<(u64, u64)> {
        let mut mx = x;
        let mut fl = Vec::new();
        while mx > 1 {
            let fx = self.tbl[mx as usize];
            fl.push(fx);
            mx /= fx;
        }
        if fl.is_empty() {
            return Vec::new();
        }
        let mut res = vec![(fl[0], 0)];
        for p in &fl {
            let l = res.len() - 1;
            let last = res[l];
            if last.0 == *p {
                res[l].1 += 1;
            } else {
                res.push((*p, 1));
            }
        }
        res
    }
}

fn main() {
    input! {
        q: usize,
        lrs: [(usize,usize);q]
    }
    let sieve = Sieve::new(100000);
    let s = (0..100000).scan(0, |acc, x| {
        *acc += if x % 2 != 0 &&
           sieve.is_prime(x) &&
           sieve.is_prime((x+1) / 2) {
            1
        } else { 0 };
        Some(*acc)
    }).collect::<Vec<_>>();
    for (l,r) in lrs {
        println!("{}", s[r] - s[l-1]);
    }
}