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 ABC084D
{
    class Program
    {
        static void Main(string[] args)
        {
            var Q = int.Parse(Console.ReadLine());
            var temp = new int[max];
            for (int i = 1; i < max; i++) temp[i] = i;
            P = temp.ToList();
            GetPrime(2);

            int[] like = new int[max];
            for(int i = 3; i < max - 1; i++)
            {
                if (i % 2 == 1 && P.Contains(i) && P.Contains((i + 1) / 2))
                {
                    like[i] = like[i - 1] + 1;
                }
                else
                {
                    like[i] = like[i - 1];
                }
            }

            int[] l = new int[max];
            int[] r = new int[max];
            for (int i = 0; i < Q; i++)
            {
                var line = Console.ReadLine().Split().Select(int.Parse).ToArray();
                l[i] = line[0];
                r[i] = line[1];
            }
            for(int i = 0; i < Q; i++)
            {
                int ans = like[r[i]] - like[l[i] - 1];
                Console.WriteLine(ans);
            }
            Console.ReadKey();
        }

        static int max = 100002;
        static List<int> P;
        static void GetPrime(int i)
        {
            if (i == P.Count - 1) return;
            int next = P[i];
            for (int j = 2 * next; j < max; j += next)
            {
                P.Remove(j);
            }
            GetPrime(i + 1);
        }
    }
}