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.Linq;
using System.Collections.Generic;
class Program
{
	static void Main()
	{
  List<int> primeList = makePrimeList(100000);//100000以下の素数のリストを作成

    int q = int.Parse(Console.ReadLine());
    for(int i = 0; i < q; i++)//q個のクエリに答える
    {
      int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
      int answer = 0;
      for(int j = nums[0]; j <= nums[1]; j+=2)
      {
        int jj = (j+1)/2;
        if(primeList.BinarySearch(j) >= 0 && primeList.BinarySearch(jj) >= 0) answer++;  
      }
      Console.WriteLine(answer);
    }

	}

  static List<int> makePrimeList(int maxPrime)//引数max以下の素数のリストを作成。エラトステネスの篩を用いる。
  {
    List<int> searchList = Enumerable.Range(2,maxPrime).ToList();//探索リスト
    List<int> primeList = new List<int>();//素数リスト
    
    for(int i = 2; i < Math.Sqrt(maxPrime); i+=0)
    {
        searchList.Remove(i);
        primeList.Add(i);
        searchList.RemoveAll(n => n % i == 0);  
        if(searchList.Count() > 0) i = searchList[0];//次の素数
        else break;
    }

    primeList.AddRange(searchList);//探索リストに余った値も素数リストに追加
    return primeList;
  }
  
}