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 static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //var line = ReadLine().Split(' ').Select(value => int.Parse(value)).ToArray();
            var q = int.Parse(ReadLine());
            var answers = new List<int>();
            var isPrime = new bool[100001];
            for(var i = 3; i < isPrime.Length; i += 2)
            {
                isPrime[i] = true;
            }
            isPrime[2] = true;
            for(long i = 3; i < isPrime.Length; i += 2)
            {
                if(!isPrime[i])
                {
                    continue;
                }
                for(long j = i * i; j < isPrime.Length; j += i)
                {
                    isPrime[j] = false;
                }
            }

            var sumLike2017 = new int[100001];
            for(var i = 3; i < sumLike2017.Length; i += 2)
            {
                if(isPrime[i] && isPrime[(i + 1) / 2])
                {
                    sumLike2017[i] = 1;
                }
                sumLike2017[i] += sumLike2017[i - 2];
            }

            for(var i = 0; i < q; i++)
            {
                var line = ReadLine().Split(' ').Select(value => int.Parse(value)).ToArray();
                var l = line[0];
                var r = line[1];

                answers.Add(sumLike2017[r] - (l == 1 ? 0 : sumLike2017[l - 2]));
            }

            answers.ForEach(value => WriteLine(value));
        }
    }
}