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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class Atk
{
	public int Type { get; private set; }  // 0:A, 1:B
	public long Damage { get; private set; }

	public Atk(int type, long damage)
	{
		Type = type;
		Damage = damage;
	}
}


public class D
{
	public static void Main()
	{
		int Q = Int32.Parse(Console.ReadLine());
		int[] l = new int[Q];
		int[] r = new int[Q];
		for(int i = 0; i < Q; i++)
		{
			string[] args = Console.ReadLine().Split(' ');
			l[i] = Int32.Parse(args[0]);
			r[i] = Int32.Parse(args[1]);
		}	

		int maxN = 100000;
		bool[] isPrime = new bool[maxN + 1];
		for(int i = 2; i <= maxN; i++)
			isPrime[i] = true;
		for(int i = 2; i <= maxN; i++)
			if(isPrime[i])
				for(int j = 2 * i; j <= maxN; j += i)
					isPrime[j] = false;

		int[] csum = new int[maxN + 1];
		for(int i = 2; i <= maxN; i++)
		{
			csum[i] = csum[i-1];
			if(isPrime[i] && isPrime[(i + 1)/2])
				csum[i]++;
		}

		for(int i = 0; i < Q; i++)
			Console.WriteLine(csum[r[i]] - csum[l[i]-1]);
	}
}