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

namespace Program
{
    public class ABC084D
    {
        static public void Main(string[] args)
        {
            var prime = new HashSet<int>(Prime(100000));
            var sumary = new int[100001];
            for (int i = 1; i <= 100000; ++i)
            {
                if (prime.Contains(i) && prime.Contains((i + 1) / 2))
                {
                    sumary[i] = 1;
                }
                sumary[i] += sumary[i - 1];
            }

            var Q = NextInt;
            for (int i = 0; i < Q; ++i)
            {
                var l = NextInt;
                var r = NextInt;
                Console.WriteLine(sumary[r] - sumary[l - 1]);
            }
        }

        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static int NextInt() => int.Parse(NextString());
            public static long NextLong() => long.Parse(NextString());
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => Console_.NextInt();
        static long NextLong => Console_.NextLong();
        static string NextString => Console_.NextString();

        static IEnumerable<int> Prime(int x)
        {
            if (x < 2) yield break;
            yield return 2;
            var table = new bool[x + 1];
            var max = (int)Math.Sqrt(x);
            for (int i = 3; i <= max; i += 2)
            {
                if (!table[i])
                {
                    yield return i;
                    for (int j = i * i; j <= x; j += i)
                    {
                        table[j] = true;
                    }
                }
            }
            for (int i = max + 1; i <= x; i += 2)
            {
                if (!table[i]) yield return i;
            }
        }
    }
}