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 q = sc.nextInt();
    int[] s = new int[100001];
    for(int i = 1;i<=100000;i++){
      if(sosu(i)&&sosu((i+1)/2))s[i]=s[i-1]+1;
      else s[i]=s[i-1];
    }
    for(int i = 0;i < q;i++){
      int l = sc.nextInt();
      int r = sc.nextInt();
      System.out.println(s[r]-s[l-1]);
    }
  }
  public static boolean sosu(int n){
    if(n==1)return false;
    if(n==2)return true;
    if(n%2==0)return false;
    for(int i = 3;i <= Math.sqrt(n);i+=2)if(n%i==0)return false;
    return true;
  }
}