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: Runtime Error)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class Main {
    public void main(Scanner sc) {
        List<Integer> primeList = createPrime(100000);
        int like2017[] = new int[50000];
        for (int prime : primeList) {
            int tmp = (prime + 1) / 2;
            if (prime % 2 == 1 && primeList.contains(tmp)) {
                like2017[tmp] = 1;
            }
        }

        int sum = 0;
        for (int i = 0; i < 50000; i++) {
            sum += like2017[i];
            like2017[i] = sum;
        }

        int q = sc.nextInt();
        for (int i = 0; i < q; i++) {
            int l = sc.nextInt();
            int r = sc.nextInt();

            System.out.println(like2017[(r + 1) / 2] - like2017[(l - 1) / 2]);
        }
    }

    private List<Integer> createPrime(int n) {
        List<Integer> primeList = new ArrayList<>(Arrays.asList(2, 3, 5, 7));

        for (int i = 9; i <= n; i += 2) {
            boolean flag = true;
            for (long prime : primeList) {
                if (prime * prime > i) {
                    break;
                }
                if (i % prime == 0) {
                    flag = false;
                    break;
                }
            }
            if (flag) {
                primeList.add(i);
            }
        }

        return primeList;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        new Main().main(sc);
        sc.close();
    }
}