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 System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Solver
        {
            const int N = 100000;
            private int[] sums = new int[N + 1];
            public Solver()
            {
                var p1 = new HashSet<int>() { 2 };
                var p2 = new HashSet<int>();
                for (int i = 3; i <= N; ++i)
                {
                    if (p1.All(j => i % j != 0))
                    {
                        if (i * i <= N) { p1.Add(i); } else { p2.Add(i); }
                    }
                }
                Predicate<int> prime = n => (n * n <= N) ? p1.Contains(n) : p2.Contains(n);
                for (int i = 3; i < N; ++i)
                {
                    sums[i] = (i % 2 != 0 && prime(i) && prime((i + 1) / 2)) ? 1 + sums[i - 1] : sums[i - 1];
                    sums[i + 1] = sums[i];
                }
            }
            public int Solve(int l, int r)
            {
                return sums[r] - sums[l - 1];
            }
        }
        static void Main(string[] args)
        {
            int Q = ReadInt();
            var solver = new Solver();
            for (int i = 0; i < Q; ++i)
            {
                int[] v = ReadInts();
                Console.WriteLine(solver.Solve(v[0], v[1]));
            }
        }
    }
}