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 => primes.Contains((x + 1) / 2));
                Console.WriteLine(count);
            }
        }

        IEnumerable<int> SieveOfEratosthenes(int max)
        {
            var isPrime = Enumerable.Repeat(true, max + 1).ToArray();
            //var nums = Enumerable.Range(0, max + 1).ToArray();

            isPrime[1] = false;
            for (int i = 2; i <= Math.Sqrt(max); i++)
            {
                if (!isPrime[i])
                    continue;
                for (int j = i*2; j <= max; j+=i)
                {
                    isPrime[j] = false;
                }
            }
            

            for(int i = 2; i <= max; i++)
            {
                if (isPrime[i])
                    yield return i;
            }

        }
    }
}