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;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var q = int.Parse(Console.ReadLine());
            var qList = new List<KeyValuePair<int, int>>(q);
            var minL = 100000;
            var maxR = 0;
            for (int i = 0; i < q; ++i)
            {
                var lr = Console.ReadLine().Split(' ');
                var l = int.Parse(lr[0]);
                var r = int.Parse(lr[1]);
                minL = l < minL ? l : minL;
                maxR = r > maxR ? r : maxR;
                qList.Add(new KeyValuePair<int, int>(l, r));
            }

            var likeList = CreateLike2017List(minL, maxR);
            var sumList = CreateSumList(likeList);

            foreach (var query in qList)
            {
                Console.WriteLine(sumList[query.Value - minL + 1] - sumList[query.Key - minL]);
            }
        }

        static List<int> CreateLike2017List(int min, int max)
        {
            var list = new List<int>(max - min + 1);
            for (var i = min; i <= max; ++i)
            {
                list.Add(Like2017(i));
            }
            return list;
        }

        static List<int> CreateSumList(List<int> src)
        {
            var total = 0;
            var sumList = new List<int>(src.Count + 1);
            sumList.Add(0);
            foreach (var value in src)
            {
                total += value;
                sumList.Add(total);
            }
            return sumList;
        }

        static int Like2017(int n)
        {
            return IsPrime(n) && IsPrime((n + 1) / 2) ? 1 : 0;
        }

        static bool IsPrime(int n)
        {
            if (n == 1)
            {
                return false;
            }
            if (n == 2)
            {
                return true;
            }
            if (n % 2 == 0)
            {
                return false;
            }
            int i = 3;
            while (i * i <= n)
            {
                if (n % i == 0)
                {
                    return false;
                }
                i = i + 2;
            }
            return true;
        }
    }
}