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 static System.Math;

namespace ConsoleApp1
{
    class Program
    {
        const int MaxQ = 100000 + 10;

        static void Main(string[] args)
        {
            int[] count = new int[MaxQ];
            bool[] isPrime = Enumerable.Repeat(true, MaxQ).ToArray();
            isPrime[0] = isPrime[1] = false;

            for (int i = 2; i * i < isPrime.Length; i++)
            {
                if (isPrime[i])
                {
                    int value = i + i;
                    while (value < isPrime.Length)
                    {
                        isPrime[value] = false;
                        value += i;
                    }
                }
            }

            for (int i = 1; i < count.Length; i++)
            {
                count[i] = count[i - 1];
                if (i % 2 == 1 && isPrime[i] && isPrime[(i + 1) / 2])
                {
                    count[i]++;
                }
            }

            int q = int.Parse(Console.ReadLine());
            for (int i = 0; i < q; i++)
            {
                var array = Console.ReadLine().Split().Select(int.Parse).ToArray();
                int l = array[0], r = array[1];
                int ans = count[r] - count[l - 1];
                Console.WriteLine(ans);
            }
        }
    }
}