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) {

		int Q;

		Scanner sc = new Scanner(System.in);
		Q = sc.nextInt();
		int[] r = new int[Q];
		int[] l = new int[Q];
		for (int i = 0; i < Q; i++) {
			l[i] = sc.nextInt();
			r[i] = sc.nextInt();
		}

		for (int i = 0; i < Q; i++) {
			int ans = 0;
			for (int j = l[i]; j <= r[i]; j = j + 2) {
				ans += simiar2017Number(j);
			}
			System.out.println(ans);
		}
	}

	public static void main2(String[] args) {
		System.out.println(simiar2017Number(7));
		System.out.println(simiar2017Number(9));
		System.out.println(simiar2017Number(11));
	}

	private static int simiar2017Number(int N) {

		if (isPrime(N) && isPrime((N + 1) / 2)) {
			return 1;
		} else return 0;
	}

	private static boolean isPrime(int N) {

		if (N == 1)return false;
		if (N == 2)return true;
		if (N % 2 == 0)return false;
		for (int i = 3; i <= Math.floor(Math.sqrt(N)); i = i + 2) {
			if(N % i == 0) return false;
		}

		return true;
	}
}