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.*;
 
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = 100001;
		boolean[] isPrime = new boolean[N];
                isPrime[2] = true;
		boolean useless = true;
		for(int i=3;i<N;++i){
			isPrime[i] = useless;
			useless = !useless;
		}
		for(int i=3;i<=(int)Math.sqrt((double)N);++i){
			if(isPrime[i]){
				for(int j=i*i;j<N;j+=2*i) isPrime[j] = false;
			}
		}		
		int[] ruiseki = new int[N];
		ruiseki[1] = 0;
		for(int i=3;i<N;i+=2){
			if(isPrime[i]&&isPrime[(i+1)/2]) ruiseki[i]++;
			ruiseki[i] += ruiseki[i-2];
		}
		
		int Q = sc.nextInt();
		for(int i=0;i<Q;++i){
			int l = sc.nextInt()-2;
			if(l<0) l=1;
			int r = sc.nextInt();
			System.out.println(ruiseki[r]-ruiseki[l]);
		}
		return;
	}
}