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: Accepted)

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException {
        System.setOut(new PrintStream(new BufferedOutputStream(System.out)));

        List<Integer> numberList = new ArrayList<>();
        for (int i = 1; i <= 100000; i += 2) {
            if (isPrime(i) && isPrime((i + 1) / 2)) {
                numberList.add(i);
            }
        }
        int[] numbers = numberList.stream().mapToInt(i -> i).toArray();
        // System.out.println(numbers.size());

        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int q = Integer.parseInt(reader.readLine());
        for (int i = 0; i < q; i++) {
            String[] words = reader.readLine().split(" ");
            int l = Integer.parseInt(words[0]);
            int r = Integer.parseInt(words[1]);
            int count = count(numbers, r) - count(numbers, l - 1);
            System.out.println(count);
        }
        System.out.flush();
    }

    private static int count(int[] xs, int x) {
        int returnValue = Arrays.binarySearch(xs, x);
        if (returnValue >= 0) {
            return returnValue + 1;
        } else {
            return -returnValue - 1;
        }
    }

    private static boolean isPrime(int x) {
        return BigInteger.valueOf(x).isProbablePrime(100);
    }
}