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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
    public static bool f = false, t = true;
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        for (int i1 = 0; i1 < n; i1++)
        {
            int[] a = Read.ints();
            bool[] prime = new bool[100001];
            prime[1] = prime[0] = true;
            for (int i = 2; i < prime.Length; i++)
            {
                if (prime[i] == false)
                {
                    for (int j = i * 2; j < prime.Length; j += i)
                    {
                        prime[j] = true;
                    }
                }
            }
            int ans = 0;
            for (int i = a[0]; i <= a[1]; i += 2)
            {


                if (!prime[i] && prime[(i + 1) / 2] == false)
                {
                    ans++;
                }
            }
            Console.WriteLine(ans);
        }
        Console.ReadLine();
    }
    public static long gcd(long a, long b)
    {
        while (true)
        {
            if (a == 0) { return b; }
            if (b == 0) { return a; }
            if (a > b) { a -= b; }
            else { b -= a; }
        }
    }
    public static long lcm(long a, long b) { return a / gcd(a, b) * b; }
    public static bool IsPrime(int num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

        double sqrtNum = Math.Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                // 素数ではない
                return false;
            }
        }

        // 素数である
        return true;
    }
}
public static class Read
{
    public static void outl(string n = "") { Console.WriteLine(n); return; }
    public static long Long() { return long.Parse(Console.ReadLine()); }
    public static long[] longs() { return Console.ReadLine().Split().Select(long.Parse).ToArray(); }
    public static int Int() { return int.Parse(Console.ReadLine()); }
    public static int[] ints() { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
    public static string Str() { return Console.ReadLine(); }
    public static string[] Strs() { return Console.ReadLine().Split(); }
}