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 static Atcoder;
using System.Threading.Tasks;

public class Hello
{

    public static void Main()
    {
        int n = cin();
        bool[] box = new bool[100000];
        for (int i = 0; i < 100000; i++) box[i] = false;
        int[] b;
        for (int i = 0; i < n; i++)
        {
            int count = 0;
            b = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
            for (int j = b[0]; j <= b[1]; j += 2)
            {
                if (box[j]) {
                    count++;
                }
                else if (IsPrime(j) && IsPrime((j + 1) / 2)) {
                    box[j] = true;
                    count++;
                }
            }
            Console.WriteLine(count);
        }
    }

}



public class Atcoder
{
    static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
    public static int LCM(int a, int b)
    {
        int c = a * b;
        if (a < b) Swap(ref a, ref b);
        int d = a % b;
        while (d != 0)
        {
            a = b;
            b = d;
            d = a % b;
        }
        return c / b;
    }
    public static string strReverce(string s)
    {
        return new string(s.Reverse().ToArray());
    }
    public static int cin()
    {
        return int.Parse(Console.ReadLine());
    }
    public static bool IsPrime(int n)
    {
        if (n < 2) return false;
        if (n == 2) return true;
        if (n % 2 == 0) return false;

        for (int i = 3; i < n; i += 2)
        {
            if (n % i == 0) return false;
        }
        return true;
    }

    public static List<int> IndexOfPlural(string a, string b)
    {
        List<int> list = new List<int>();
        if (a.Length == 0 || b.Length == 0) { list.Add(-1); return list; }
        if (a.IndexOf(b) == -1) { list.Add(-1); return list; }
        int box = 0;
        int revision = 0;
        while (true)
        {
            if (a.Length == 0) break;
            box = a.IndexOf(b);
            if (box == -1) { break; }
            else
            {
                list.Add(box + revision);
                a = a.Remove(box, b.Length);
                revision += b.Length;
            }
        }
        return list;
    }
}