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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int Q = Integer.parseInt(scan.nextLine());
		for (int q = 0;q < Q ;q++ ) {
			String[] line = scan.nextLine().split(" ", 0);
			int l = Integer.parseInt(line[0]);
			int r = Integer.parseInt(line[1]);
			System.out.println(search(l,r));
		}
	}

	private static int search(int l,int r) {
		int ans = 0;
		for(int i = l; i <= r; i++) {
			if (i == 1) continue;
			if (i % 2 == 0) continue;
			if ((check(i)) && check((i + 1)/2)) ans++;
		}
		return ans;
	}
	private static boolean check(int i) {
		for (int j = 2;j < i ;j++ ) {
			if (i%j == 0) return false;
		}
		return true;
	}
}