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.Linq;
class Clac
{
    public bool Check2017(int n)
    {
        if (n <= 2)
            return false;
        else
        {
            bool f = false;
            for (int i = 2; i < n; i++)
                f = f || (n % i == 0) || ((i < (n + 1) / 2) && (((n + 1) / 2) % i == 0));
            return !f;
        }
    }
}
class Program
{
    public static void Main()
    {
        int q = int.Parse(Console.ReadLine());
        int[] ans = new int[q];
        Clac c = new Clac();
        for (int i = 0; i < q; i++)
        {
            int[] lr = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            int count = 0;
            for (int n = lr[0]; n <= lr[1]; n++)
                if (c.Check2017(n))
                    count++;
            ans[i] = count;
        }
        for (int i = 0; i < q; i++)
            Console.WriteLine(ans[i]);
    }
}