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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
class Program{
	static void Main(){
		bool[] h=new bool[100001];
		h[1]=true;
		for(int i=2;i<100001;i++){
			for(int j=2;j<=i/2;j++){
				if(i%j==0){h[i]=true;break;}
			}
		}
		int n=int.Parse(Console.ReadLine());
		for(int i=0;i<n;i++){
			int[] q=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			int ans=0;
			for(int j=q[0];j<=q[1];j+=2){
				if(h[j]==false&&h[(j+1)/2]==false){ans++;}
			}
			Console.WriteLine("{0}",ans);
		}
	}

}