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.Scanner;

public class Main {
	public static void main(String args[]){

		boolean prime[]=new boolean[100000];
		prime[0]=true;
		for(int i=1;i<100000;i++) {
			if(!prime[i]) {
				for(int j=1;j<Math.ceil(100000/(i+1));j++) {
					prime[(i+1)*(j+1)-1]=true;
				}
			}
		}

		Scanner scan=new Scanner(System.in);

		int q=scan.nextInt();

		int l[]=new int[q];
		int r[]=new int[q];

		for(int i=0;i<q;i++) {
			l[i]=scan.nextInt();
			r[i]=scan.nextInt();
		}

		int count[]=new int[q];

		for(int i=0;i<q;i++) {
			for(int j=l[i];j<r[i]+1;j+=2) {
				if((!(prime[j-1]))&&(!(prime[(j+1)/2-1]))) {
					count[i]++;
				}
			}
			System.out.println(count[i]);
		}
	}
}