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;
using System.Collections.Generic;

namespace ABC084_D_2017_like_Number
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			int q = int.Parse(Console.ReadLine());
			int[] lArr = new int[q];
			int[] rArr = new int[q];
			
			string[] input;
			for (int i = 0; i < q; i++)
			{
				input = Console.ReadLine().Split(' ');
				lArr[i] = int.Parse(input[0]);
				rArr[i] = int.Parse(input[1]);
			}

			int count = 0;
			bool nIsPrime;
			bool nPlusOneIsPrime;
			for (int i = 0; i < q; i++) {
				for (int j = lArr[i]; j <= rArr[i]; j++)
				{
					nIsPrime = IsPrime(j);
					nPlusOneIsPrime = IsPrime((j + 1) / 2);
					/*for (int k = 2; k <= Math.Sqrt(j); k++)
						if (j % k == 0) nIsPrime = false;

					for (int k = 2; k <= Math.Sqrt((j + 1) / 2); k++)
						if ((j + 1) / 2 % k == 0) nPlusOneIsPrime = false;*/

					if (nIsPrime && nPlusOneIsPrime) count++;
				}
				
				Console.WriteLine(count);
				count = 0;
			}
			
		}
		
		static bool IsPrime(int num)
		{
			if (num < 2) return false;
			else if (num == 2) return true;
			else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

			double sqrtNum = Math.Sqrt(num);
			for (int i = 3; i <= sqrtNum; i += 2)
			{
				if (num % i == 0)
				{
					// 素数ではない
					return false;
				}
			}

			// 素数である
			return true;
		} 
	}
}