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;
using System.Linq;
class Program
{
    static void Main()
    {
        //以下100000以下の素数の導出
        ArrayList ps = new ArrayList();
        bool[] nums = new bool[100001];
        nums[0] = true;
        nums[1] = true;
        for (int i = 0; i < 100001; i++)
        {
            if (!nums[i])
            {
                nums[i] = true;
                ps.Add(i);
                for (int j = 2; j <= 100000 / i; j++)
                    nums[i * j] = true;
            }
        }
        int[] primes = (int[])ps.ToArray(typeof(int));

        //素数を表示
        //for (int i = 0; i < 50; i++)
        //    Console.Write("{0} ", primes[i]);
        //Console.WriteLine();

        //以下2017liked奇数の個数の累積和を考える
        int[] sum = new int[50001];
        for (int i = 1; i < 50001; i++)
        {
            sum[i] = sum[i - 1];
            if (Array.IndexOf(primes, 2 * i - 1) >= 0 && Array.IndexOf(primes, i) >= 0)
                sum[i]++;
        }

        //累積和を表示
        //for (int i = 0; i < 50; i++)
        //    Console.Write("{0} ", sum[i]);
        //Console.WriteLine();

        //以下入力の受け取り(Qのみ)
        int q = int.Parse(Console.ReadLine());

        //以下各クエリの内容を受け取り解答を出力
        for (int i = 0; i < q; i++)
        {
            string[] lr = Console.ReadLine().Split(' ');
            Console.WriteLine(sum[(int.Parse(lr[1]) + 1) / 2] - sum[(int.Parse(lr[0]) + 1) / 2 - 1]);
        }
    }
}