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.Diagnostics;
using System.Linq;
using System.Text;

namespace AtCoder.D
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var Q = ReadLong();
            var L = new long[Q];
            var R = new long[Q];
            for (int i = 0; i < Q; i++)
            {
                (L[i], R[i]) = Read2Longs();
            }

            var es = new EratosthenesSieve(100000);
            var like2017 = new bool[100001];
            for (int i = 1; i <= 100000; i++)
            {
                var m = (long)(i + 1) / 2;
                if (es.IsPrime[i] && es.IsPrime[m])
                {
                    like2017[i] = true;
                }
            }
            var ruiseki = new long[100001];
            for (int i = 1; i <= 100000; i++)
            {
                ruiseki[i] = ruiseki[i - 1] + (like2017[i] ? 1 : 0);
            }

            var sb = new StringBuilder();
            for (int i = 0; i < Q; i++)
            {
                var count = ruiseki[R[i]] - ruiseki[L[i] - 1];
                sb.AppendLine(count.ToString());
            }

            return sb.ToString().Trim();
        }

        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
    public class EratosthenesSieve
    {
        public List<long> Primes { get; private set; }
        public Dictionary<long, bool> IsPrime { get; private set; }

        public EratosthenesSieve(long max)
        {
            Primes = new List<long>();
            IsPrime = new Dictionary<long, bool>();
            for (long i = 1; i <= max; i++)
            {
                IsPrime.Add(i, false);
            }

            for (long i = 2; i <= max; i++)
            {
                IsPrime[i] = true;
            }

            for (long i = 2; i <= max; i++)
            {
                if (IsPrime[i])
                {
                    Primes.Add(i);
                    for (long j = 2 * i; j <= max; j += i)
                    {
                        IsPrime[j] = false;
                    }
                }
            }
        }
    }
}