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;

    class Program
    {
        static void Main(string[] args)
        {
            var Q = int.Parse(Console.ReadLine());
            var primes = new bool[100001];
            primes[2] = true;
            for (var i = 3;i<primes.Length;i=i+2)
            {
                primes[i] = true;
            }
            for(var i = 3;i<primes.Length;)
            {
                for (var k = i; k < primes.Length; k = k + i)
                {
                    if (!primes[k]) continue;
                    if(k%i==0&&i!=k)
                    {
                        primes[k] = false;
                    }
                }
                for(i++; i<primes.Length; i++)
                {
                    if (primes[i]) break;
                }
            }

            var nearNum = new int[100002];
            for (var i = 3; i < primes.Length;i++)
            {
                nearNum[i] = primes[i]&& primes[(i+1)/2] ? nearNum[i - 1] + 1 : nearNum[i - 1];
            }

            for(var i =0;i<Q;i++)
            {
                var lr = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToList();
                var l = lr[0];
                var r = lr[1];
                Console.WriteLine(nearNum[r] - nearNum[l-1]);
            }
        }
    }