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: Accepted)

import java.util.BitSet;
import java.util.Scanner;

public class Main {
	static final int SIEVE = 10000000;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		BitSet prime = new BitSet(SIEVE);
		prime.flip(2, SIEVE);
		for (int i = 2;i < SIEVE;++ i) if (prime.get(i)) for (int j = i << 1;j < SIEVE;j += i) prime.set(j, false);
		int like[] = new int[100002];
		like[0] = 0;
		for (int i = 1;i <= 100000;++ i) like[i + 1] = like[i] + (prime.get(i) & prime.get(i + 1 >> 1) ? 1 : 0);
		int Q = sc.nextInt();
		while((Q--) != 0) {
			int l = sc.nextInt(), r = sc.nextInt()+1;
			System.out.println(like[r] - like[l]);
		}
		sc.close();
	}
}