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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main{
	static Map<Long,Long> map= new TreeMap<>();
  public static void main(String[] args){
	  Scanner sc = new Scanner(System.in);
	   int n=sc.nextInt();
	   for(int i=0;i<n;i++) {
		   int l=sc.nextInt(),r=sc.nextInt(),count=0;
		   for(int j=l;j<=r;j+=2) {
			   if(prime(j)&&prime((j+1)/2))count++;
		   }
		   System.out.println(count);
	   }

	   /*primeEnum(n);
	   long sum=1;
	   for (long key : map.keySet()){

	   }*/
  }
	public static Map<Long,Long> primeEnum(long n) {
		for(long i=2;i<=Math.sqrt(n);i++) {
			if(n%i!=0)continue;
			long e=0;
			while(n%i==0) {
				e++;
				n/=i;
			}
			if(map.containsKey(i)) {
				map.put(i, e+map.get(i));
			}else {
				map.put(i, e);
			}
		}
		if(n!=1) {
			if(map.containsKey(n)) {
				map.put(n, 1+map.get(n));
			}else {
				map.put(n, 1L);
			}
		}
		return map;
	}
	public static long GCD(long min,long max) {
		if(max%min==0)return min;
		else return GCD(max%min,min);
	}

	public static boolean prime(long n) {
		if(n==1)return false;
		else if(n==2)return true;
		else if(n%2==0)return false;

		for(int i=2;i<=Math.sqrt(n);i++) {
			if(n%i==0)return false;
		}
		return true;
	}
}