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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.HashSet;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		HashSet<Integer> primes = new HashSet<Integer>();
		primes.add(2);
		primes.add(3);
		primes.add(5);
		primes.add(7);
		
		boolean isPrime;
		for (int i = 8; i < 100000;i++) {
			isPrime = true;
			for(Integer p:primes) {
				if(i%p == 0) {
					isPrime = false;
					break;
				}
			}
			if(isPrime) primes.add(i);
		}
		
		Scanner scan = new Scanner(System.in);
		int q = scan.nextInt();
		
		for (int i = 0; i < q; i++) {
			int a = scan.nextInt();
			int b = scan.nextInt();
			int counter = 0;
			
			for (int j = a; j <= b; j+=2) {
				if(primes.contains(j) && primes.contains((j+1)/2)) counter++;
			}
			
			System.out.println(counter);
		}
		scan.close();
		
	}

}