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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.Scanner;
public class Main{
 public static void main(String args[]){
  boolean flag=false;
  Scanner scan=new Scanner(System.in);
  String s;

  s=scan.next();
  int n=Integer.parseInt(s);

  int l[]=new int[n+10];
  int r[]=new int[n+10];
  int mx=0; 

  for(int i=0;i<n;i++){
   s=scan.next();
   l[i]=Integer.parseInt(s);
   s=scan.next();
   r[i]=Integer.parseInt(s);
   if(mx<r[i])mx=r[i];
  }

  boolean f1,f2;
  long a[]=new long[mx+10];
  for(int i=0;i<mx+1;i++){
   f1=prime(i);
   f2=prime((i+1)/2);
   if(i>0)a[i]=a[i-1];
   if(f1&&f2&&i%2==1)a[i]++;
  }

  for(int i=0;i<n;i++)System.out.println(a[r[i]]-a[l[i]-1]+" "+i);
 }
 public static boolean prime(long a){
  if(a<=1)return false;
  for(int i=2;i*i<=a;i++){
   if(a%i==0)return false;
  }
  return true;
 }
}