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

namespace AtCoder
{
    class Program
    {
        public static void Main()
        {
            new Program().Solve();
        }

        void Solve()
        {
            var q = int.Parse(Console.ReadLine());
            var primes = SieveOfEratosthenes(100000);
            for (int i = 0; i < q; i++)
            {
                var tmp = Console.ReadLine().Split().Select(int.Parse).ToArray();
                int l = tmp[0];
                int r = tmp[1];
                var count = primes
                    .Where(x => x >= l && x <= r)
                    .Count(x => IsPrimeNumber((x + 1) / 2));
                //for(int j = l; j <= r; j += 2)
                //{
                //    if (IsPrimeNumber(j))
                //    {
                //        if(IsPrimeNumber((j+1)/2))
                //        {
                //            //Console.WriteLine("j" + j);
                //            count++;
                //        }
                //    }
                //}
                Console.WriteLine(count);
            }
        }

        bool IsPrimeNumber(int n)
        {
            if (n == 1)
                return false;
            if (n == 2 )
                return true;
            if (n % 2 == 0)
                return false;

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


        int[] SieveOfEratosthenes(int max)
        {
            if (max == 1)
                return new int[] { };
            var nums = Enumerable.Range(0, max + 1).ToArray();

            nums[1] = 0;
            for (int i = 2; i <= (int)Math.Sqrt(max); i++)
            {
                if (nums[i] <= 0)
                    continue;
                for (int j = i*2; j <= max; j+=i)
                {
                    nums[j] = 0;
                }
            }
            return nums.Where(x => x > 0).ToArray();

        }
    }
}