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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication6
{
    class Program
    {
        static List<int[]> list = new List<int[]>();
        static HashSet<int> primes = new HashSet<int>();
        static void Main(string[] args)
        {
            primes.Add(2);
            primes.Add(3);

            var q = int.Parse(Console.ReadLine());
            
            int i = 1;            
            while (i <= q)
            {
                var temp = Console.ReadLine().Split(' ').Select(x=>int.Parse(x)).ToArray();
                list.Add(temp);
                i++;
            }


            foreach(var item in list)
            {
                Console.WriteLine(Calc(item[0],item[1]));
            }
          
        }

        static int Calc(int a, int b)
        {
            int ans = 0;
            int i;
            for(i = a; i <= b; i = i+2)
            {
                int x = i;
                int x2 = (x + 1) / 2;

                if(Check(x) && Check(x2))
                {
                    ans++;
                }
                else
                {
                    
                }
            }

            return ans;
        }

        static bool Check(int p)
        {
            if(primes.Contains(p))
            {
                return true;
            }

            if (p % 2 == 0)
                return false;

            int i;
            for(i = 3; i <= Math.Sqrt(p);i = i+2)
            {
                if (p % i == 0)
                    return false;
            }

            primes.Add(p);
            return true;
        }

    }
}