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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

class MainClass
{
    static void Main()
    {
        var A = new bool[100002].Select(_ => true).ToArray();
        A[0] = A[1] = false;
        for (int i = 0; i < 100002; i++)
        {
            if (A[i])
            {
                for (int j = i*2; j < 100002; j+=i)
                {
                    A[j] = false;
                }
            }
        }
        var B = new int[100001];
        for (int i = 1; i < 100001; i++)
        {
            B[i] = B[i - 1];
            if (A[i]&&A[(i+1)/2]) B[i]++;
        }
        var Q = int.Parse(ReadLine());
        for (int i = 0; i < Q; i++)
        {
            var lr = ReadLine().Split().Select(int.Parse).ToArray();
            var l = lr[0];
            var r = lr[1];
            WriteLine(B[r]-B[l-1]);
        }
    }
}