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 reader = new Scanner(System.in);
		int N = reader.nextInt();
		int[][] arr = new int[N][2];
		for (int i = 0; i < N; i++) {
			arr[i][0] = reader.nextInt();
			arr[i][1]  = reader.nextInt();

		}
		int[] pr = new int[100000];
		for (int j = 3; j < 100000; j+=2) {
			pr[j] = pr[j-1];
			if (isPrime((j+1)/2)) {
				if (isPrime(j)) {
					pr[j]++;
				}
			}
			if (j < 99999) {
				pr[j+1] = pr[j];
			}
		}
		for (int i = 0; i < N; i++) {
			int ans = pr[arr[i][1]] - pr[Math.max(arr[i][0]-1, 0)];
			System.out.println(ans);
		}
		reader.close();
	}
	public static boolean isPrime(int num) {
		boolean result = true;
		if (num == 1) {
			return false;
		}
		if (num == 2) {
			return true;
		}
		for (int i = 2; i < num; i++) {
			if (num % i == 0) {
				result = false;
			}
		}
		return result;
	}
}