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) {
		Scanner sc = new Scanner(System.in);
	
		int n = sc.nextInt();
		int[] l = new int[n];
		int[] r = new int[n];
		for(int i=0; i<n; i++) {
			l[i] = sc.nextInt();
			r[i] = sc.nextInt();
		}
		int[] res = new int[n];
		for(int i=0; i<n; i++) {
		
			if(l[i]<=r[i]) {
				int count = 0;
				for(int j=l[i]; j<=r[i]; j++) {
					if(isPrim(j)) {
						int tmp = (j+1)/2;
						if(isPrim(tmp)) {
							count ++;
						}
					}
				}
				res[i] = count;
			}
			
		}
		for(int i=0; i<n; i++) {
			System.out.println(res[i]);
		}
	
	}

	private static boolean isPrim(int j) {
		if(j<2) {
			return false;
		}
		if(j%2==0 && j>2) {
			return false;
		}
		for(int i=2; i<=Math.sqrt(j);i++) {
			if(j%i==0) {
				return false;
			}
		}
		return true;
	}
}