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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		int q = cin.nextInt();
		int[] flag = new int[100009];
		int[] a = new int[100009];
		Arrays.fill(flag, 0);
		flag[1] = 1; 
		for(int i=2; i<=100000; i++) {
			for(int j=2*i; j<=100000; j+=i) {
				flag[j] = 1;
			}
		}
		for(int i=1; i<=100000; i++) {
			if(flag[i]==0 && flag[(i+1)/2]==0 && i!=2) {
				a[i] = a[i-1] + 1;
			}else
				a[i] = a[i-1];
		}
		while((q--)>0) {
			int l = cin.nextInt();
			int r = cin.nextInt();
			System.out.println(a[r]-a[l-1]);
		}
	}
}