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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Convert;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
          var q = cin.ReadInt;
			int[][] jaggedArray = new int[q][];

			int maxW = 0;
			for(int i = 0; i < q; i++)
			{
				var l = cin.ReadInt;
				var w = cin.ReadInt;
				if (maxW < w)
					maxW = w;
				jaggedArray[i] = new int[] { l, w};
			}
			//int sumArrCnt = (int)Math.Ceiling((decimal)maxW / 2) + 1;
			//int[] sumArr = new int[sumArrCnt];
			int cntLikenum = 0;
			Dictionary<int, int> dicLike2017 = new Dictionary<int, int>();
			int odd = 0;
			for (int i = 0; odd < maxW; i++)
			{
				//sumArr[i + 1] = sumArr[i];
				odd = 2 * i + 1;
				if (IsPrime(odd) && IsPrime((odd + 1) / 2))
					cntLikenum++;//sumArr[i+1]++;
				dicLike2017.Add(odd, cntLikenum);
			}
			for(int i = 0; i < q; i++)
			{
				int ans = 0;
				if(jaggedArray[i][1] == 1)
				{

				}
				else if (jaggedArray[i][0] == 1)
				{
					ans = dicLike2017[jaggedArray[i][1]];
				}
				else
				{
					ans = dicLike2017[jaggedArray[i][1]] - dicLike2017[jaggedArray[i][0] - 2];
				}
				WriteLine(ans);
			}
        }
      private static bool IsPrime(int num)
		{
			if (num < 2) return false;
			else if (num == 2) return true;
			else if (num % 2 == 0) return false;//偶数はあらかじめ除く

			double sqrtNum = Math.Sqrt(num);
			for (int i = 3; i <= sqrtNum; i += 2)
			{
				if (num % i == 0) return false;
			}
			//素数である
			return true;
		}
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); }}
        public int ReadInt { get { return int.Parse(Read); }}
        public long ReadLong { get { return long.Parse(Read); }}
        public double ReadDouble { get { return double.Parse(Read); }}
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret;}
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret;}
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret;}
    }
}