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;
using System.Text;
using System.Threading.Tasks;


namespace D {
    class Program {
        static bool[] IsPrimeNumberTable;
        static List<int> NumbersLike2017 = new List<int>();

        static List<Tuple<int, int>> GetBoundaries(System.IO.TextReader reader) {
            var tuples=new List<Tuple<int,int>>();
            var N=int.Parse(reader.ReadLine());
            for(var i = 0u; i != N; ++i) {
                var nums=reader.ReadLine().Split().ToList().ConvertAll(int.Parse);
                tuples.Add(Tuple.Create(nums[ 0 ], nums[ 1 ]));
            }
            return tuples;
        }

        internal static void MakeIsPrimeNumberTable(int UpLimit) {
            IsPrimeNumberTable=new bool[UpLimit+1];
            for(var i = 2; i <= UpLimit; ++i) IsPrimeNumberTable[ i ] = true;
            for(var i = 2; i <= UpLimit; ++i) {
                for(var j = i + i; j <= UpLimit; j += i) 
                    IsPrimeNumberTable[ j ] = false;
            }
        }

        static int Count2017LikeNumbers(Tuple<int, int> boundary) {
            var n = 0;
            for(var i = boundary.Item1; i <= boundary.Item2; i += 2) {
                if(NumbersLike2017.Contains(i)
                    || ( IsPrimeNumberTable[i] && IsPrimeNumberTable[(( i + 1 ) / 2)] )) {
                    ++n;
                    NumbersLike2017.Add(i);
                }
            }
            return n;
        }

        internal static void SolveProblem(System.IO.TextReader reader, System.IO.TextWriter writer) {
            var boundaries = GetBoundaries(reader);
            MakeIsPrimeNumberTable(boundaries.Select(x => x.Item2).Max());
            foreach(var tuple in boundaries) {
                writer.WriteLine(Count2017LikeNumbers(tuple));
            }
        }

        static void Main(string[] args) {
            SolveProblem(Console.In, Console.Out);
        }
    }
}