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.Console;
using static System.Convert;
using static System.Math;

class Program
{
    static void Main(string[] args)
    {
        var q = ToInt32(ReadLine());
        const int NUM = 100001;
        var bo = new bool[NUM];
        for (var i = 2; i < NUM; i++)
            if (!bo[i])
                for (var j = 2 * i; j < NUM; j += i)
                    bo[j] = true;
        var sum = new int[NUM];
        for (var i = 3; i < NUM; i += 2)
            if (!bo[i] && !bo[(i + 1) / 2]) sum[i] = sum[i - 2] + 1;
            else sum[i] = sum[i - 2];
        var s = new int[q];
        for(var i = 0; i < q; i++)
        {
            var lr = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            s[i] = lr[0]!=1?sum[lr[1]] - sum[lr[0]-2]:sum[lr[1]];
        }
        WriteLine(string.Join("\n", s));
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}