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.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.List;
import java.util.ArrayList;

public class Main {

    public static void main(String[] args) throws IOException{
        BufferedReader reader = null;
        PrintWriter writer = null;
        
        try {
            reader =new BufferedReader(new InputStreamReader(System.in));
            writer = new PrintWriter(System.out);
            
            int query = Integer.parseInt(reader.readLine());
            String readLine;
            
            List<Integer> sosu = new ArrayList<>();
            for(int i = 2; i <= 100000; i++){
                sosu.add(i);
            }
            for(int j = 0; j < sosu.size(); j++){
                for(int x = j + 1; x < sosu.size(); x++){
                    if(sosu.get(x) % sosu.get(j) == 0){ 
                        sosu.remove(x);
                    }
                }
            }
            
            while((readLine = reader.readLine()) != null){
                int ans = 0;
                String[] splitLine = readLine.split(" ");
                int start = Integer.parseInt(splitLine[0]), 
                    end = Integer.parseInt(splitLine[1]);
                
                
                for(int i = start; i <= end ; i += 2){
                    int likeNumber = (i + 1) / 2;
                    boolean IsItSosu = i > 2;
                    
                    if(sosu.indexOf(i) == -1){
                        IsItSosu = false;
                    }
                    if(sosu.indexOf(likeNumber) == -1){
                        IsItSosu = false;
                    }
                    
                    
                    if(IsItSosu){   ans ++; }

                }

                writer.println(ans);
                
            }
            
            
        }finally{
            if(reader != null){
                reader.close();
            }
            if(writer != null){
                writer.close();
            }
        }

    }
}