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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var Q = int.Parse(Console.ReadLine());
            var aggP = new int[(int)1e5 + 1];
            var prime = new Prime(2);
            for (var i = 2; i < aggP.Length; i++)
            {
                aggP[i] = aggP[i - 1];
                if (prime.IsPrime(i) && prime.IsPrime((i + 1) / 2)) aggP[i]++;
            }
            for (var i = 0; i < Q; i++)
            {
                var lr = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                var answer = aggP[lr[1]] - aggP[lr[0] - 1];
                Console.WriteLine(answer);
            }
        }


        public class Prime
        {
            public Dictionary<long, long> Factors => new Dictionary<long, long>(_factors);
            private Dictionary<long, long> _factors;
            private static HashSet<long> _primes;
            public Prime(long n)
            {
                if (_primes == null) _primes = new HashSet<long>();
                _factors = new Dictionary<long, long>();
                var tmp = n;
                var max = (long)Math.Sqrt(n);
                var p = 2;
                while (p <= max)
                {
                    if (tmp % p == 0)
                    {
                        _factors[p] = 0;
                        _primes.Add(p);
                        while (tmp % p == 0)
                        {
                            tmp /= p;
                            _factors[p]++;
                        }
                    }
                    p++;
                }
                if (tmp > 1)
                {
                    _factors[tmp] = 1;
                    _primes.Add(tmp);
                }
            }
            public bool IsPrime(long n)
            {
                if (_primes.Contains(n)) return true;
                var p = new Prime(n);
                return _primes.Contains(n);
            }
        }
    }
}