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.Generic;
using System.Linq;
using System.Text;

namespace algorithm
{
	class Program
	{
		static void Main(string[] args)
		{
			//N も ( N + 1 ) ÷ 2 も素数
			int n = int.Parse(Console.ReadLine());
			List<int[]> m = new List<int[]>();
			for (int i = 0; i < n; i++)
			{
				m.Add(Array.ConvertAll(Console.ReadLine().Split(), int.Parse));
			}
			int[] num = new int[100000];
			int cnt = 0;
			bool[] list = getPrimeList(100000);
			for (int i = 0; i < num.Length; i++)
			{
				if (list[i] && list[(i + 1) / 2])
				{
					cnt++;
				}
				num[i] = cnt;
			}
			foreach (int[] tmp in m)
					Console.WriteLine(num[tmp[1]] - num[tmp[0] - 1]);



		}

		static bool[] getPrimeList(int n)
		{
			n++;
			var isPrime = new bool[n];
			for (int i = 2; i < n; i++) isPrime[i] = true;
			var sqrt = (int)Math.Sqrt(n);
			for (int i = 2; i <= sqrt; i++)
			{
				if (isPrime[i])
				{
					var j = i + i;
					while (j < n)
					{
						isPrime[j] = false;
						j += i;
					}
				}
			}
			return isPrime;
		}
	}

}