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 int[] L, R;
        static int MaxR;

        static void LoadBoundaries(System.IO.TextReader reader) {
            var Q=int.Parse(reader.ReadLine());
            L = new int[Q]; R = new int[Q];
            for(var i = 0; i != Q; ++i) {
                var query=reader.ReadLine().Split().ToArray();
                L[i] = int.Parse(query[0]);
                R[i] = int.Parse(query[1]);
                if(MaxR < R[i]) MaxR = R[i];
            }
        }

        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(int LBound, int UBound) {
            int n = 0;
            for(var i = LBound; i <= UBound; ++i) {
                if(IsPrimeNumberTable[i] && IsPrimeNumberTable[( i + 1 ) / 2]) ++n;
            }
            return n;
        }

        internal static void SolveProblem(System.IO.TextReader reader, System.IO.TextWriter writer) {
            LoadBoundaries(reader);
            MakeIsPrimeNumberTable(MaxR);
            for(int i=0, cnt=L.Count(); i != cnt; ++i) {
                writer.WriteLine(Count2017LikeNumbers(L[i], R[i]));
            }
        }

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