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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

public class Prime
{
    int n;
    // Sieve of Eratosthenes
    BitArray sieve;

    public Prime(int _n)
    {
        n = _n;
        sieve = new BitArray(n + 1);
        var end = (int)(Math.Sqrt(n) + 0.1);
        for (int i = 2; i <= end; i++)
        {
            if (!sieve.Get(i))
            {
                for (int j = i * 2; j <= n; j += i)
                {
                    sieve.Set(j, true);
                }
            }
        }
    }

    public bool IsPrime(int i)
    {
        return !sieve.Get(i);
    }
}

class Solution
{
    static void Main()
    {
        var q = int.Parse(Console.ReadLine());
        var l = new int[q];
        var r = new int[q];

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

        var min = l.Min();
        var max = r.Max();
        var prime = new Prime(max);

        var accSum = new int[max + 1];

        for (int i = 1; i <= max; i++)
        {
            var isLike2017 = prime.IsPrime(i) && prime.IsPrime((i + 1) / 2);
            accSum[i] = accSum[i - 1];
            if (isLike2017)
            {
                accSum[i]++;
            }
        }

        for (int i = 0; i < q; i++)
        {
            var x = accSum[r[i]] - accSum[l[i] - 1];
            Console.WriteLine(x);
        }
    }
}