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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            long Q = long.Parse(Console.ReadLine());

            int max = 100000;
            int[] is2017 = new int[max + 1];
            bool[] isPrime = new bool[max + 1];
            
            for (var i = 1; i <= max; i++)
            {
                is2017[i] = is2017[i - 1];
                isPrime[i] = IsPrime(i);
                if (isPrime[i] && isPrime[(i+1)/2])
                {
                    is2017[i]++;
                }
            }

            for (var i = 0; i < Q; i++)
            {
                var line = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

                Console.WriteLine(is2017[line[1]] - is2017[line[0]-1]);
            }
        }

        private 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;
                }
            }

            return true;
        }
    }
}