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.*;

class Main {
   public static void main(String[] args)
   {
      Scanner scan = new Scanner(System.in);
      int     n    = Integer.parseInt(scan.next());

      final int MAX = 100000 + 1;

      boolean[] primes = new boolean[MAX];

      primes[2] = true;

      for(int i = 3; i < MAX; i += 2){
          primes[i] = true;
          }

      for(int i = 3; i * i < MAX; i += 2){
          if(primes[i]){
             for(int j = i * 2; j < MAX; j += i){
                 primes[j] = false;
                 }
             }
          }

      for(int i = 0; i < n; i++){
          int a   = Integer.parseInt(scan.next());
          int b   = Integer.parseInt(scan.next());
          int cou = 0;
          for(int j = a; j < b + 1; j++){
              if(primes[j] == true){
                 if(primes[(j + 1) / 2] == true){
                    cou++;
                    }
                 }
              }
          System.out.println(cou);
          }
   }
}