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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC084D {
    class Program {
        static void Main(string[] args) {
            bool[] primes = Enumerable.Repeat(true, 100001).ToArray();
            primes[0] = false;
            primes[1] = false;
            for (int i = 2; i < 100001; i++) {
                if (primes[i]) {
                    int num = i * 2;
                    while (num < 100001) {
                        primes[num] = false;
                        num += i;
                    }
                }
            }
            int[] like2017Nums = new int[100001];
            int likeNum = 0;
            for (int i = 0; i < 100001; i++) {
                if (primes[i] && primes[(i + 1) / 2]) {
                    likeNum++; //2は外れるので大丈夫
                    like2017Nums[i] = likeNum;
                }
            }
            int Q = int.Parse(Console.ReadLine());
            for (int i = 0; i < Q; i++) {
                int[] input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                int l = input[0];
                int r = input[1];
                Console.WriteLine(like2017Nums[r] - like2017Nums[l - 1]);
            }
        }
    }
}