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

        internal static void MakePrimeNumberList(uint UpLimit) {
            for(var iNumber = 2u; iNumber <= UpLimit;) {
                var isPrimeNumber=true;
                var maxPrime=0u;
                if(PrimeNumbers.Any()) {
                    foreach(var primeNumber in PrimeNumbers) {
                        if(primeNumber > maxPrime) maxPrime = primeNumber;
                        if(iNumber % primeNumber == 0u) {
                            isPrimeNumber = false;
                            break;
                        }
                    }
                    if(iNumber % maxPrime + 2 == 0u) {
                        isPrimeNumber = false;
                    }
                }
                if(isPrimeNumber) PrimeNumbers.Add(iNumber);
                iNumber += ( iNumber == 2u ? 1u : 2u );
            }
        }

        static bool IsPrimeNumber(uint n) {
            return PrimeNumbers.Contains(n);
        }

        static uint Find2017LikeNumbers(Tuple<uint, uint> boundary) {
            var n = 0u;
            for(var i = boundary.Item1; i <= boundary.Item2; ++i) {
                if(IsPrimeNumber(i) && IsPrimeNumber(( i + 1 ) / 2u)) ++n;
            }
            return n;
        }

        static void Main(string[] args) {
            var boundaries = GetBoundaries(Console.In);
            MakePrimeNumberList(boundaries.Select(x => x.Item2).Max());
            foreach(var tuple in boundaries) {
                Console.WriteLine(Find2017LikeNumbers(tuple));
            }
        }
    }
}