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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace Test
{
    class Program
    {
        static void Main(string[] args)
        {
            bool[] prime = new bool[100010];
            for (int i = 2; i < 100010; i++)
            {
                prime[i] = true;
            }
            for (long i = 0; i <= Math.Sqrt(100010); i++)
            {
                if (prime[i])
                {
                    for (long j = i * i; j < 100010; j += i)
                    {
                        prime[j] = false;
                    }
                }
            }
            int[] like2017 = new int[100010];
            for (int i = 1; i < 100010; i++)
            {
                like2017[i] = like2017[i - 1];
                if (i % 2 == 1 && prime[i] && prime[(i + 1) / 2]) like2017[i]++;
            }
            int n = int.Parse(Console.ReadLine());
            for (int i = 0; i < n; i++)
            {
                int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
                Console.WriteLine(like2017[x[1]] - like2017[x[0] - 1]);
            }
        }
    }
}