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.IO;

namespace AtCoderTest
{
    class Program3
    {
        static List<int> intList = new List<int>();
        static int rowCount;
        static List<string> lineList = new List<string>();

        static void Main(string[] args)
        {
        //    Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            string line;
            while ((line = Console.ReadLine()) != null)
            {
                lineList.Add(line);
            }

            for (int i = 0; i <= 100000; i++)
            {
                if (IsPrime(i)) intList.Add(i);
            }

   //         for (int i = 0; (line = Console.ReadLine()) != null; i++)
            for (int i = 0; i < lineList.Count; i++)
            {
                line = lineList[i];
                if (i == 0)
                {
                    rowCount = int.Parse(line);
                }
                else
                {
                    Console.WriteLine(CountTarget(line));
                }
            }

       //     Console.ReadLine();
        }

        static int CountTarget(string str)
        {
            int startNum;
            int endNum;
            int cnt = 0;

            string[] words = str.Split(' ');
            startNum = int.Parse(words[0]);
            endNum = int.Parse(words[1]);

            for (int i = startNum; i <= endNum; i = i + 2)
            {
                if (IsLike2017(i))
                {
                    cnt++;
                }
            }
            return cnt;
        }

        static bool IsLike2017(int num1)
        {
            int num2 = (num1 + 1) / 2;
            bool flg1 = false;
            bool flg2 = false;

            foreach (int n in intList)
            {
                if (flg1 == false && n == num1) flg1 = true;
                if (flg2 == false && n == num2) flg2 = true;

                if (flg1 && flg2)
                {
                    return true;
                }

                if (num1 < n) return false;
            }
            return false;
        }

        static bool IsPrime(int num)
        {
            // 1 以下は素数ではない
            if (num <= 1)
            {
                return false;
            }

            // 2 は素数である
            if (num == 2)
            {
                return true;
            }

            // 2 以外の偶数は素数ではない
            if (num % 2 == 0)
            {
                return false;
            }

            //for (var i = 3; i < num; i += 2)
            //{
            //    if (num % i == 0)
            //    {
            //        return false;
            //    }
            //}

            foreach (int n in intList)
            {
                if (num % n == 0)
                {
                    return false;
                }
            }

            return true;
        }
    }
}