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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var n = 100000;

        var sosu = new int[n + 1];

        for (int i = 2; i <= Math.Sqrt(n);) {
            if (sosu[i] == 0) {
                var x = 2 * i;
                while (x <= n) {
                    sosu[x] = 1;
                    x += i;
                }
            }
            i += i == 2 ? 1 : 2;
        }

        var li = new List<int>();

        for (int i = 3; i <= n; i += 2) {
            if (sosu[i] == 0) {
                var x = (i + 1) / 2;
                if (sosu[x] == 0)
                    li.Add(i);
            }
        }

        var q = int.Parse(input.ReadLine());
        for (int i = 0; i < q; i++) {
            var spl = input.ReadLine().Split(' ');
            var l = int.Parse(spl[0]);
            var r = int.Parse(spl[1]);
            var c = li.Count(x => l <= x && x <= r);
            Console.WriteLine(c);
        }
        return null;
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }
}