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;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var Q = int.Parse(Console.ReadLine());
            var array = new int[Q][];

            for (var i = 0; i < Q; i++)
                array[i] = Console.ReadLine().Split().Select(int.Parse).ToArray();

            var min = array.Min(a => a[0]);
            var max = array.Max(a => a[1]);

            var all = new long[max + 1];
            all[1] = 0;
            for (var i = Math.Max(min, 2); i <= max; i++)
            {
                if (i % 2 == 1)
                {
                    if (IsPrime(i) && IsPrime((i + 1) / 2))
                        all[i] = all[i - 2] + 1;
                    else
                        all[i] = all[i - 2];
                }
                else
                    all[i] = all[i - 1];
            }

            for (var i = 0; i < Q; i++)
            {
                Console.WriteLine(all[array[i][1]] - all[array[i][0] - 1]);
            }
        }

        public static bool IsPrime(int num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {
                    // 素数ではない
                    return false;
                }
            }

            // 素数である
            return true;
        }
    }
}