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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Int32;
using static System.Math;

class Program
{

    static void Main(string[] args)
    {
        label:
        var kusi = new bool[10001];
        for (int i = 2; i < 101; ++i)
        {
            if (kusi[i]) continue;
            for (int j = i * i; j < kusi.Length; j += i)
            {
                kusi[j] = true;
            }
        }
        var likeCounts = new int[kusi.Length];
        int c = 0;
        for (int i = 3; i < kusi.Length; ++i)
        {
            if (!kusi[i] && !kusi[(i + 1) / 2])
            {
                //WriteLine(i);
                likeCounts[i] = ++c;
            }
            else
            {
                likeCounts[i] = c;
            }
        }
        var results = new int[Parse(ReadLine())];
        for (int i = 0; i < results.Length; ++i)
        {
            var sp = ReadLine().Split();
            results[i] = likeCounts[Parse(sp[1])] - likeCounts[Parse(sp[0]) - 1];
        }
        foreach(int i in results)
        {
            WriteLine(i);
        }
    }
}