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)

const MAX_N: usize = 100000;

fn main() {
    let mut sc = Scanner::new();

    let mut is_prime = vec![true; MAX_N + 1];
    is_prime[0] = false;
    is_prime[1] = false;
    for p in 2..(MAX_N + 1) {
        if !is_prime[p] {
            continue;
        }
        let mut cur = p * 2;
        while cur <= MAX_N {
            is_prime[cur] = false;
            cur += p;
        }
    }

    let mut is_liked = vec![false; MAX_N + 1];
    for n in 3..(MAX_N + 1) {
        if n % 2 == 1 && is_prime[n] && is_prime[(n + 1) / 2] {
            is_liked[n] = true;
        }
    }
    let mut sum = vec![0; is_liked.len() + 1];
    for i in 0..is_liked.len() {
        sum[i + 1] = sum[i] + if is_liked[i] { 1 } else { 0 };
    }

    let q: usize = sc.read();
    for _ in 0..q {
        let l: usize = sc.read();
        let r: usize = sc.read();
        println!("{}", sum[r + 1] - sum[l]);
    }
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner { ptr: 0, length: 0, buf: vec![0; 1024], small_cache: vec![0; 1024] }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool { b == b'\n' || b == b'\r' || b == b'\t' || b == b' ' }

    fn read<T>(&mut self) -> T where T: std::str::FromStr, T::Err: std::fmt::Debug, {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)]).parse().unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}