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 System.Threading.Tasks;

namespace ConsoleApp15
{
    class Class375
    {
        static void Main()
        {
            var Q = int.Parse(Console.ReadLine());
            var d = new int[100001];
            for (int i = 3; i < 100001; i++)
            {
                d[i] = d[i - 1];
                if (check(i)) d[i]++;
            }

            for (int i = 0; i < Q; i++)
            {
                var lr = Console.ReadLine().Split().Select(int.Parse).ToArray();
                if (lr[0] % 2 == 1) lr[0]--;
                if (lr[1] % 2 == 1) lr[1]++;
                Console.WriteLine(d[lr[1]]-d[lr[0]]);
            }
        }
        static bool check(int num)
        {
            if (num % 2 == 0) return false;
            for (int i = 2; i <= Math.Sqrt(num); i++)
            {
                if (num % i == 0) return false;
            }
            for (int i = 2; i <= Math.Sqrt((num+1)/2); i++)
            {
                if ((num+1) / 2 % i == 0) return false;
            }
            return true;
        }
    }
}