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.Linq;
using System;

public class Hello
{
    public static void Main()
    {
        var p = new bool[100000];
        GeneratePrime(p);
        var q = int.Parse(Console.ReadLine().Trim());
        for (int i = 0; i < q; i++)
        {
            string[] line = Console.ReadLine().Trim().Split(' ');
            var L = int.Parse(line[0]);
            var r = int.Parse(line[1]);
            var count = 0;
            for (int j= L;j<= r; j+= 2)
                if (p[j] && p[(j + 1) / 2]) count++;
            Console.WriteLine(count);
        }
    }
    public static void GeneratePrime(bool[] p)
    {
        int prime;
        var m = p.Length;
        var sqrtMax = Math.Sqrt(m);
        var searchList = Enumerable.Range(2, m - 1).ToList();
        do
        {
            prime = searchList.First();
            p[prime] = true;
            searchList.RemoveAll(n => n % prime == 0);
        }
        while (prime < sqrtMax);
        foreach (var x in searchList)
            p[x] = true;
    }
}