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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	static class Tuple {
		int l, r;

		Tuple(String line) {
			String[] tokens = line.split(" ");
			this.l = Integer.parseInt(tokens[0]);
			this.r = Integer.parseInt(tokens[1]);
		}
	}

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		int Q = Integer.parseInt(in.readLine());
		Tuple[] tuples = new Tuple[Q];
		for (int i = 0; i < Q; ++i) {
			tuples[i] = new Tuple(in.readLine());
		}
		// rの最大を求める
		int max = Integer.MIN_VALUE;
		for (Tuple tuple : tuples) {
			max = Math.max(max, tuple.r);
		}
		// ふるいでprimesを求める
		List<Integer> primes = getPrimes(max);
		Set<Integer> set = new HashSet<>();
		set.addAll(primes);
		for (int i = 0; i < tuples.length; ++i) {
			System.out.println(calc(tuples[i], primes, set));
		}

	}

	static int calc(Tuple tuple, List<Integer> primes, Set<Integer> primeSet) {
		int result = 0;
		for (int i = 0; i < primes.size(); ++i) {
			int prime = primes.get(i);
			if (prime < tuple.l || prime > tuple.r) {
				continue;
			}
			if (primeSet.contains((prime + 1) / 2)) {
				++result;
			}
		}
		return result;
	}

	static List<Integer> getPrimes(int max) {
		boolean[] conds = new boolean[max + 1];
		Arrays.fill(conds, true);
		conds[0] = false;
		conds[1] = false;
		List<Integer> primes = new ArrayList<>();
		for (int i = 2; i <= max; ++i) {
			if (!conds[i]) {
				continue;
			}
			primes.add(i);
			// ふるい
			for (int j = i + i; j <= max; j += i) {
				conds[j] = false;
			}
		}
		return primes;
	}
}