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;

namespace ABC084_D
{
    class Program
    {
        static void Main(string[] args)
        {
            var Q = int.Parse(Console.ReadLine());
            int n = 100000;
            bool[] p = new bool[n + 1];
            p[1] = true;
            for (int i = 2; i <= (int)Math.Sqrt(n); i++)
            {
                if (p[i]) continue;
                for (int j = 2; j * i <= n; j++)
                    p[i * j] = true;
            }

            int[] l = new int[n + 1];
            for (int i = 1; i <= n; i++)
                l[i] = l[i - 1] + (!p[i] && !p[(i + 1) / 2] ? 1 : 0);

            for (int i = 0; i < Q; i++)
            {
                var lr = Console.ReadLine().Split().Select(int.Parse).ToArray();
                Console.WriteLine(l[lr[1]] - l[lr[0]-1]);
            }
        }
    }
}